Intelligent vehicle multi-target global path planning method and system, storage medium and program product

Abstract

The invention relates to the technical field of intelligent vehicle path planning, in particular to an intelligent vehicle multi-target global path planning method and system, a storage medium and a program product. According to the method, the planning environment, obstacles, multi-target requirements and constraint conditions are comprehensively considered, the multi-target dynamic path planning model of the system is constructed, and a theoretical basis is provided for a subsequent path planning strategy. An improved IMNSGA-II algorithm is provided, and the solving quality and adaptability of the algorithm in multi-target path planning are improved by fusing RRT-A * hybrid initialization, improving dynamic congestion distance measurement, optimizing path crossover and mutation operation, binary population selection and other special operators. According to the method, the path length, the smoothness and the safety are balanced and optimized, indexes such as the hyper-volume and the set coverage are remarkably improved, the Pareto solution set and the recommended path which are high in coverage degree and high in performability can be output, and the method is suitable for logistics, industry and intelligent traffic scenes.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of intelligent vehicle path planning, and in particular to an intelligent vehicle multi-target global path planning method and system, a storage medium and a program product. BACKGROUND

[0002] With the continuous development of artificial intelligence, computer vision, the Internet of Things, perception technology and automatic driving technology, intelligent vehicles, as intelligent mobile carriers integrating autonomous perception, intelligent decision-making and autonomous control, have shown wide application value in many fields. Intelligent vehicles mainly include mobile robots with autonomous navigation functions and intelligent cars with partial automatic driving functions, and their application in fields such as logistics distribution, industrial automation and intelligent transportation is deepening, and they gradually become an important technical direction for promoting the construction of intelligent transportation systems and the development of automation systems. At present, the core problem in this field is to simultaneously optimize path length, smoothness and driving safety and other conflicting targets in an environment containing static / dynamic obstacles, generate an executable path that meets kinematic and geometric safety constraints, and maintain adaptability to environmental changes.

[0003] There are mainly three representative routes in the prior art. The first is graph search / lattice-based planning. The A-based method performs global search on a predefined lattice graph through heuristic cost, which can quickly give an approximate shortest path, but is prone to sticking to obstacles, has many turning points, and has discontinuous curvature, and needs post-processing smoothing. The existing patent "Intelligent vehicle global path planning method based on improved A algorithm" (Chinese patent CN114281084B) performs smoothing on the initial path on the basis of key point extraction and target point guidance, but its essence still belongs to the weighted single-target paradigm, and the uniformity and diversity maintenance capability of the Pareto solution set is limited.

[0004] The second is sampling-based geometric planning, such as RRT / RRT* and its improved versions. This type of method does not rely on complete graph structures and is suitable for high-dimensional scenes and complex obstacles, but the original RRT path has strong randomness, poor smoothness and optimality. Existing patents such as "Intelligent vehicle path planning system and method based on control sampling" (Chinese patent CN107063280A / B) obtain a continuous path through state expansion and B-spline interpolation with tangent constraints, improving the executability; and "Mobile robot path planning method and system based on improved RRT algorithm" (Chinese patent CN111752281A) and "Improved RRT path planning method based on explorer algorithm" (Chinese patent CN114593744A) improve search efficiency and obstacle avoidance ability by introducing convergence factors, dynamic step lengths or guided paths, but still lack support for multi-target optimization and solution set diversity maintenance.

[0005] Thirdly, the planning based on multi-objective evolutionary algorithm. NSGA-II relies on non-dominated sorting, crowding distance and elite preservation, and is applied in path / trajectory multi-objective optimization. For example, the "trajectory planning method based on non-dominated sorting genetic algorithm II" (Chinese patent CN104729509A) obtains a multi-objective Pareto solution set through non-dominated sorting, which is used for trajectory planning in complex environment. However, the traditional scheme mostly uses random initialization and static crowding distance, which is prone to premature convergence and uneven distribution of the front in the multi-peak target or complex scene, and it is difficult to guarantee coverage and diversity.

[0006] In addition, the industry side also appears multi-objective collaborative path and scheduling ideas for autonomous driving, such as "multi-objective collaborative path planning and scheduling system and method for autonomous vehicle" (Chinese patent CN119354224A, application disclosure) tries to combine deep reinforcement learning and graph model for multi-objective trade-off, but still belongs to the data-driven paradigm, and does not solve the global-local integrated Pareto optimization and feasibility repair problem based on explicit objectives and constraints.

[0007] In summary, the main shortcomings of the existing technology are: ①the quality and diversity of the initial solution are insufficient, which limits the global search ability (typical like random initialization of NSGA-II). ②The crowding degree measurement is mostly static, and the individual reduction in the layer is not adaptive, which is prone to cause "overcrowding / overcrowding" of the Pareto front. ③The crossover and mutation are mostly undirectional disturbance, which is difficult to realize accelerated convergence and feasibility repair under the constraints of minimum turning radius, maximum heading increment and minimum safety distance. ④Single algorithm initialization (only A or only RRT) has weak adaptability to complex environment, and it is difficult to balance the advantages of "high-quality skeleton" and "random exploration". Therefore, it is necessary to propose an improved IMNSGA-II multi-objective global path planning method: to generate high-quality and diverse initial values by RRT-A hybrid, to maintain uniform front by combining dynamic crowding degree, to cooperate with constraint-aware crossover and target-oriented gradual mutation, and to control convergence by elite preservation and coverage index, so as to obtain high-quality and fully-covered Pareto solution set and recommended path in complex dynamic environment, and to make up for the shortcomings of the above existing technologies. SUMMARY

[0008] The technical purpose of the present application is to solve the problems of insufficient initialization quality and diversity, premature convergence caused by static congestion degree measurement, difficulty in balancing path length, smoothness, safety and vehicle kinematic constraints in existing path planning in complex environments containing static / dynamic obstacles, and propose a multi-objective global path planning method for intelligent vehicles based on improved IMNSGA-II. The method improves global search ability and convergence efficiency through RRT-A* hybrid initialization, dynamic congestion degree maintenance, constraint-aware crossover and target-oriented progressive mutation mechanisms, generates collision-free feasible paths that meet the minimum turning radius and minimum safety distance, and outputs a high-coverage and uniformly distributed Pareto solution set and recommended path, achieving adaptive and multi-objective balanced optimization in complex dynamic environments.

[0009] In order to achieve the above-mentioned purpose, the present application adopts the following technical solutions:

[0010] A multi-objective global path planning method for intelligent vehicles based on improved IMNSGA-II, characterized in that the method comprises the following steps:

[0011] S1, environment modeling and feasible region construction, load the map, mark the obstacle set and obtain the feasible region, set the starting point and the ending point in the unified coordinate system, represent the path as a sequence of connected waypoints, and require all waypoints to be located in the feasible region;

[0012] S2, establish a multi-objective optimization model considering path length, path smoothness and driving safety, and introduce mechanical and geometric safety constraints to make the path segment meet the minimum turning radius, maximum heading increment and minimum safety distance from obstacles;

[0013] S3, adopt RRT-A* hybrid initialization strategy: obtain several shortest skeleton in multi-resolution grid, uniformly resample as initial tree of fast random tree, combine dynamic step and random sampling expansion to improve the quality and diversity of initial solution;

[0014] S4, evaluate the multi-objective fitness of the population individuals and perform fast non-dominated sorting to obtain multiple Pareto layers;

[0015] S5, calculate the improved dynamic congestion degree in each layer, the congestion degree combines the traditional congestion distance, the statistics of the difference between the same layer targets and the proportion of current feasible solutions, when the individuals in the layer are excessive, delete them in order of dynamic congestion degree from small to large, and update the congestion degree immediately after each deletion;

[0016] S6, constraint-aware crossover and goal-directed progressive mutation are performed under the premise of feasibility, crossover is only performed between sub-segments that can be spliced and do not cross obstacles, mutation is pushed in the direction of the terminal point and the step size decays with iteration, and local repair or rollback is performed on individuals that violate constraints;

[0017] S7, the elite preservation strategy is adopted to combine the parents and offspring and cut off the next generation according to the non-dominated level and dynamic congestion degree;

[0018] S8, termination is performed when the coverage index improves below the threshold value within a preset number of generations or reaches the maximum number of generations, the Pareto solution set is output, and a recommended path is given according to the knee point or preference criteria.

[0019] As a preferred, the multi-objective optimization is expressed as:

[0020] minF(x)={f1(x),f2(x),…,f m (x)∣x∈X},

[0021] and satisfies the constraint set:

[0022] X={x∣h j (x)≥0,j=1,…,J;g k (x)=0,k=1,…,K};

[0023] wherein: x is the decision variable (path encoding); x is the feasible solution set; m is the number of objectives; h j (·) is the jth inequality constraint; g k (·) is the kth equality constraint.

[0024] As a preferred, the working space and feasible region satisfy:

[0025]

[0026] Z f =Z-Z o ,

[0027] The waypoint and endpoint satisfy:

[0028] x i =(x i ,y i )∈Z、p1=p s ,p m =p D ;

[0029] wherein: Z is the working space; Z o is the obstacle set; Z f is the feasible region; p s , p D are the starting point and the terminal point, respectively.

[0030] As a preferred option, the target path length is:

[0031]

[0032] Where: L is the total length; L i is the Euclidean distance between adjacent waypoints; m is the number of waypoints.

[0033] As a preferred option, the path smoothness target is:

[0034]

[0035] θ i =atan2(y i -y i-1 ,x i -x i-1 ),

[0036] Δθ i =|θ i+1 -θ i |;

[0037] Where: Θ represents the cumulative heading change; θ i Let Δθ be the heading angle of the i-th segment. i This represents the difference in heading between adjacent segments.

[0038] As a preferred option, a piecewise risk function is used for driving safety:

[0039]

[0040] Wherein: H i For the risk at point i; h CiO h is the distance from the vehicle's center of gravity to the nearest obstacle's center of gravity. min ,h max To achieve the minimum safety and maximum impact radius.

[0041] As a preferred option, the formula for calculating the radius of the risk circle for intelligent vehicles and obstacles is:

[0042]

[0043] Safety constraints in intelligent vehicle path planning:

[0044]

[0045] Where: h cl ,h cw h represents the vehicle's length and width. ol ,h ow The length and width of the obstacle; The center of mass of the obstacle.

[0046] As a preferred option, intelligent vehicle path planning is in p i Formulas for calculating the curvature and turning radius of a point:

[0047]

[0048] The minimum turning radius limit for the kinematic constraints of intelligent vehicles is as follows:

[0049] R i ≥R min ;

[0050] Wherein: κ i Let ΔL be the curvature of the i-th segment; i R is the length of this segment. i R is the turning radius; min This is the minimum turning radius threshold;

[0051] As a preferred option, the dynamic obstacle model is as follows:

[0052] x d+1 =x d (t)+v d cosθ d ,

[0053] y d+1 =y d (t)+v d sinθ d ;

[0054] Where: (x d ,y d ) represents the current position of the obstacle; v d θ is a velocity scalar; d The direction angle of motion; the subscript d+1 indicates the next moment.

[0055] As a preferred option, let there be a total of M objective functions, namely f1, f2, ..., f M Then each individual X i The fitness value is expressed as:

[0056] F i =(f1(X) i ),…,f M (X i )),

[0057] f j (X i Individual X i The fitness of the j-th objective function.

[0058] As a preferred method, the non-dominated sorting process is as follows: First, for each individual X in the population... iCalculate the number of times n it is dominated by other individuals. i and the set of individuals S it governs i Secondly, all n i Individuals with a value of 0 are assigned to the first Pareto front, F1. Then, after removing individuals from F1, the above process is repeated for the remaining individuals to obtain F2, F3, ..., until all individuals are assigned to the corresponding front.

[0059]

[0060] As a preferred option, for each Pareto front F k The steps for calculating the crowding distance are as follows: For F k The individuals in the dataset are sorted according to each objective function value; for each individual X i In F k In this process, the distances between adjacent individuals on each objective function are calculated, and the crowding distance is obtained by summing them:

[0061]

[0062] Where: S represents the current population; M represents the target number; This represents the maximum / minimum value of the target at the same level.

[0063] As a preferred approach, the RRT-A* hybrid initialization population strategy includes the following steps:

[0064] 1) First, use the A* algorithm to generate three initial solutions POPs of the shortest distance from the specified starting point to the target point at three different grid resolutions. Ai Then, the paths at all resolutions are resampled onto a grid of the same resolution to ensure that the paths have a consistent location representation in the same environment;

[0065] 2) Use the path generated by A* as the initial tree for RRT, expand the path using dynamically adjusted step size and random sampling sequence, and select nodes R from the initial path. i As the starting point for RRT path planning, P is generated. init - 3 mutation paths Backtracking R i Previous paths and new variant paths Store it in POP Ri middle;

[0066] 3) Merge POPs Ai With POP Ri This forms the final initial population POP. init .

[0067] As a preferred option, the improved dynamic congestion level satisfies:

[0068]

[0069] Among them: ADCD i V represents the adaptive dynamic crowding distance for the lower i individuals. rni It is the variance of the crowding distance to the i-th neighboring individuals, representing the ADCD of the i-th individual. i The dispersion of crowding distance indicates the degree of difference in crowding distance across different target dimensions; N o For adjacent items on the same level; N obj The number of target dimensions.

[0070] As a preferred option, the optimized fitness path crossover operation process is as follows:

[0071] Input: A set of paths to be intersected. p =[P S ,P1,…,P n ,P D ],path q =[P S ,P′1,…,P′ m ,P D ], An environment raster map containing obstacles: map; Output: A set of intersecting paths: path' p ,path q ;

[0072] 1) Find the path with fewer nodes and set it as the path. pc The other one is set as path qc ;

[0073] 2) In path pc Choose an intermediate point P i , in path qc Find the distance P i The nearest point P j ;

[0074] 3) P i With P j Set as a pair of corresponding points (P) i_pair ,P′ j_pair );

[0075] 4) If CollisionFree((P i-1 ,P′ j_pair ),(P′ j_pair ,P i+1 ),(P′ j-1 ,P i_pair ),(P i_pair ,P′ j+1 If )) is true, then:

[0076]

[0077] if but:

[0078]

[0079] Otherwise if but:

[0080]

[0081] As a preferred approach, the goal-oriented incremental path mutation operation model is as follows:

[0082] For a certain mutation point P in the path i Its mutation direction is from the target point P t Determining the new path point P′ i Compared to the original path point P i Closer to the target area:

[0083]

[0084] Where: p i / p′ i p represents the waypoints before and after the mutation. t Let α be the target point; α be the variable asynchronous length; α max ,α min This represents the initial step size and the final step size, t is the current iteration number, and T is the maximum iteration number.

[0085] Preferably, the performance evaluation method of the method includes one or more of the following:

[0086] 1) Hypervolume metric

[0087] In the D-dimensional solution space, suppose S = {s1, s2, ..., s} n As a set of non-dominated solutions, ref={r1,r2,,r n} As a reference point for the corresponding scene map, the value of Hv is obtained by the following formula:

[0088]

[0089] Where L refers to the Lebesgue measure used to calculate volume, h(a i ) indicates that by a i The hypercube is composed of a reference point and a reference point. The reference point refers to the combination of worst-case scenarios corresponding to different objectives, that is, the worst-case values ​​of path length, path safety, and path smoothness obtained in the simulation experiment.

[0090] 2) SC Collection Coverage Indicators

[0091] Let A = {a1, a2, ..., a} n} and B = {b1,b2,…,b m Let} be two approximate sets close to the Pareto front. SC(A,B) is the proportion of non-dominated solutions in B dominated by non-dominated solutions in A, i.e.:

[0092]

[0093] Where |B| represents the total number of solutions in the solution set B; if SC(A,B)=1, it means that all non-dominated solution sets in B are dominated by the non-dominated solution sets in solution set A, indicating that each solution in the solution set B is completely covered by solution set A; if SC(A,B)=0, it means that none of the non-dominated solution sets in B are dominated by the non-dominated solution sets in A.

[0094] 3) The number of non-dominated solutions in the NNS neighborhood and the proportion of non-dominated solutions in the RNS neighborhood

[0095] Assume S i ={S1,S2,…,S n The non-dominated solution set is obtained by calculating different algorithms. This represents the combined solution set of the Pareto front solutions obtained by the above five algorithms, for S I By performing non-dominated sorting, we obtain the comprehensive Pareto front for multi-objective path planning in different scenarios, NNS(S i ) represents S i The number of solutions in the solution set that are not dominated by other solutions in the synthesized Pareto solution set S, i.e.:

[0096]

[0097] in, It means that solution y dominates solution x, NNS(S) i The larger the value of S, the greater the value of S. i The solution set generated by the corresponding algorithm is in the solution set S of all algorithms. I It occupies more non-dominant positions in the Pareto front solution set S, and has higher coverage quality;

[0098] The RNS index represents S i The proportion of non-dominated solutions in the overall Pareto solution set S; the calculation formula is as follows:

[0099]

[0100] RNS(S i The larger the value of ), the stronger the solution set S. iThe higher the proportion of undominated solutions in the integrated Pareto front solution set, the higher the nondomination and diversity of the solution set generated by the algorithm.

[0101] Furthermore, this invention also provides a multi-objective path planning system for implementing the method, comprising: a map and feasible region construction module, an objective and constraint evaluation module, an RRT-A* hybrid initialization module, a fitness calculation and non-dominated sorting module, a dynamic congestion maintenance module, a constraint-aware crossover module, an objective-oriented progressive mutation module, a parent-child merging and elite retention module, and a quality assessment and termination determination module; its processor executes the modules, and its memory stores the set {m,J,K,R} therein. min ,h min ,h max ,α max ,α min ,N,T} and output the Pareto solution set and recommended path.

[0102] Furthermore, the present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method.

[0103] Furthermore, the present invention also provides a computer program product, including a computer program or instructions that, when executed by a processor, implement the method.

[0104] This invention, by employing the aforementioned technical solution and through a collaborative design of "RRT-A* hybrid initialization, dynamic congestion maintenance, constraint-aware crossover, and goal-oriented progressive mutation," delivers quantifiable and perceptible comprehensive technical effects: First, the initial solution simultaneously possesses skeleton quality and diverse coverage, significantly reducing the risk of premature convergence caused by random initialization; Second, the improved dynamic congestion updates the frontier density in real time during in-layer pruning, maintaining a uniform Pareto solution set distribution and broad coverage, resulting in stable improvements in metrics such as hypervolume (HV) and set coverage (SC); Third, the crossover and mutation processes embed geometric and kinematic feasibility checks (minimum turning radius, maximum range)... The system employs several mechanisms: First, it optimizes the flow of data to increase the speed of convergence and reduce the risk of failure. Second, it minimizes the risk of failure by using incremental and minimum safety margins to reduce the cost of infeasible individuals and subsequent repairs, resulting in a smoother and safer executable path. Third, it enables a goal-oriented step-by-step approach, facilitating a "global first, local later" approach to improve convergence speed and reduce solution jitter. Fourth, in scenarios with dynamic obstacles, it combines temporal prediction and risk segmentation costs to maintain a high collision-free pass rate and adaptability to environmental changes. Fifth, the early stopping and optimization mechanism linked to the overall framework and evaluation (HV / SC / NNS / RNS) ensures a more robust balance between length, smoothness, and safety in the recommended path, while also providing better transferability and engineering feasibility. Attached Figure Description

[0105] Figure 1 This is a schematic diagram of the Pareto front.

[0106] Figure 2 This is a schematic diagram illustrating the dominance relationships for solving the problem.

[0107] Figure 3 This is a schematic diagram of the geometric features of the path segment.

[0108] Figure 4 This is a schematic diagram of the geometric model of a circular intelligent vehicle and its obstacles.

[0109] Figure 5 This is a diagram illustrating the maximum and minimum safe distances between nodes.

[0110] Figure 6 This is a diagram illustrating node risk.

[0111] Figure 7 This is a cross operation.

[0112] Figure 8 This is a mutation operation.

[0113] Figure 9 This is a flowchart of the IMNSGA-II algorithm.

[0114] Figure 10 This is a schematic diagram of path encoding.

[0115] Figure 11 A diagram illustrating two-dimensional dynamic congestion.

[0116] Figure 12 This provides a simulation environment for path planning.

[0117] Figure 13 This is a comparison chart of the Hv values ​​for the five algorithms.

[0118] Figure 14 A comparison of the SC values ​​of the five algorithms.

[0119] Figure 15 This is a Pareto front distribution diagram for each algorithm in the Map1 scenario.

[0120] Figure 16 This is a Pareto front distribution diagram for each algorithm in the Map2 scenario.

[0121] Figure 17 This is a Pareto front distribution map for each algorithm in the Map3 scenario.

[0122] Figure 18 This is a Pareto front distribution map for each algorithm in the Map4 scenario. Detailed Implementation

[0123] The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the protection scope of the present invention.

[0124] This invention addresses the multi-objective global path planning problem for intelligent vehicles in static environments. It comprehensively considers practical factors such as the planning environment, the influence of dynamic / static obstacles, multiple objectives of path planning, and constraints. A systematic model of multi-objective path planning for intelligent vehicles is constructed, providing a theoretical foundation for subsequent path planning strategies. Secondly, a solution algorithm is designed for the constructed model. Based on the traditional NSGA-II algorithm, an improved IMNSGA-II algorithm is proposed. This algorithm improves the solution quality and adaptability of the IMNSGA-II algorithm by incorporating special improved operators such as the RRT-A* hybrid initialization population strategy and the dynamic congestion distance metric method. Finally, path planning is performed and compared with four other multi-objective planning algorithms in different environments. Simulation results show that the IMNSGA-II algorithm can provide higher quality Pareto solutions with higher solution coverage in different environments, exhibiting stronger global search capabilities and solution diversity.

[0125] I. Overview of Multi-Objective Optimization Problems

[0126] Multi-objective optimization (MOO), also known as multi-criteria or multi-attribute optimization, refers to the process of simultaneously optimizing two or more conflicting objectives under certain constraints. The optimization process typically involves weighing the pros and cons of different objectives to find a set of Pareto optimal solutions that achieve a balance between the multiple objectives.

[88] Multi-objective optimization has wide applications in engineering, economics, logistics, and other fields, where optimal decisions among multiple objectives are often required. For example, in logistics, multi-objective programming can comprehensively consider multiple indicators such as cost, delivery time, and inventory levels to find the optimal logistics solution to maximize efficiency and minimize cost. In flexible workshop scheduling problems, optimization objectives include minimizing completion time, maximizing equipment utilization, and minimizing cost. Multi-objective optimization can be used to weigh the advantages and disadvantages of different solutions among multiple objectives, providing support for decision-making.

[0127] The multi-objective optimization problem can be formalized as:

[0128] minF(x)={f1(x),f2(x),L,f m (x)|x∈X} (0-1)

[0129] St.h j (x)≥0,j=1,2,…,J (0-2)

[0130] h j (x)≥0,j=1,2,…,J (0-3)

[0131] g k (x)=0,k=1,2,…,K (0-4)

[0132] X={x|h j (x)≥0,j=1,2,…,J;g k (x)=0,k=1,2,…,K} (0-5)

[0133] Among them, f i (x) represents the objective function, the total number of objectives is m, and X represents the feasible solution set. Equation (0-2)h j (x) indicates that there are a total of J inequality constraints, and equation (0-4)g k (x) indicates that there are K equality constraints.

[0134] In single-objective optimization problems, the quality of a solution can be determined by directly comparing the objective function values. For example, in a minimization problem, if the objective function value of solution X is less than that of solution Y, then solution X is superior to solution Y. However, in multi-objective optimization problems, due to the often contradictory relationships between different objective indicators, traditional single-objective function value comparison methods cannot be directly applied to evaluating the quality of multi-objective solutions. The Pareto dominance relation provides a systematic comparison framework for multi-objective optimization problems. Its core idea is: if solution X is not inferior to solution Y on all objective functions, and is strictly superior to Y on at least one objective, then X is said to dominate Y. The key difference between multi-objective optimization and single-objective optimization lies in the non-uniqueness of its solution set. Each objective may have different optimization directions, thus requiring trade-offs among objectives to find a set of optimal solutions that balance all objectives, resulting in the Pareto Front (PF) of the multi-objective problem. In multi-objective optimization, the Pareto dominance relation is used to screen out non-dominated solutions. All non-dominated solutions together constitute the Pareto Front, providing decision-makers with a set of optimal solutions that achieve the best balance among multiple objectives. For minimization problems, the Pareto dominance relation is mathematically defined as follows:

[0135]

[0136] There are two sets of solutions, X = (x1, x2, ..., x...). m Y = (y1, y2, ..., y) mLet i ∈ {1,2,…,m} and j ∈ {1,2,…,m}. When equation (0-6) holds, solution X is said to dominate solution Y. The solution to a multi-objective problem is not unique; it is composed of multiple solutions. The Pareto dominance method provides the mutual dominance relationships between different solutions. A solution set X is called a Pareto optimal solution if and only if the solution set X belongs to the global solution set S, and no other solution Y in the global solution set S dominates X. The mathematical definition of a Pareto optimal solution P is as follows:

[0137]

[0138] The boundary or curve formed by all Pareto optimal solutions is called the Pareto optimal front. The Pareto optimal front means that each solution in the front cannot improve any other objective without making at least one objective worse. The mathematical definition of the Pareto optimal solution set PF is as follows:

[0139] PF={F(X)|X∈P} (0-8)

[0140] Figure 1 The Pareto optimal solution and dominance relations of the biobjective problem are defined. The solutions ABCDEFGHIJ constitute the Pareto front of the biobjective problem; there are no dominance relations between solutions on the Pareto front. The solution LKMNO constitutes the second dominance layer; there exist non-dominated solutions on the first Pareto front that can dominate solutions in the second layer. Figure 2 It can be seen that after mapping the solution sets representing different independent variables to the objective function space, the dominance relations are as follows: A, B, C, D, E, F, G, H, I, J do not dominate each other, L, K, M, N, O do not dominate each other, F dominates K, M, N, O, L, O, P, and M dominates L, O, P.

[0141] In multi-objective programming and optimization research, non-dominance relationships are key to problem-solving. The desired outcome is typically a set of Pareto optimal solutions, an equilibrium of satisfaction levels across multiple objectives, or a single solution that satisfies the decision-maker's subjective preferences. Early path planning problems focused on minimizing the total length of a single path. However, with ongoing research, scholars have incorporated practical factors such as safety, energy consumption, and smoothness into their considerations based on varying real-world scenarios. Multi-objective optimization problems aim to search for the optimal set of solutions within the feasible region that meets both objectives and constraints, thus the intelligent vehicle path planning problem proposed in this application is essentially a multi-objective optimization problem.

[0142] II. Problem Modeling

[0143] This invention systematically constructs a multi-objective dynamic path planning model for intelligent vehicles by analyzing the constraints and different objective functions of multi-objective path planning, laying the foundation for subsequent algorithm design and experimental verification.

[0144] 2.1 Constraints of Multi-Objective Path Planning

[0145] (1) Motion space constraints

[0146] First, define the environmental space for intelligent vehicles to perform path planning as Z. This application requires obtaining an efficient and safe path from the initial node to the target node in an environment with both dynamic and static obstacles, where P represents the set of paths. i (x i ,y i ) represents the i-th node, i = 1, 2, 3, ..., m, where m is the total number of nodes; p s (x s ,y s ) represents the starting node; p D (x D ,y D ) represents the target node; O j Represents obstacles in the map, j = 1, 2, 3, ..., k, where there are k obstacles in the environment; v i Indicates that intelligent vehicles are in p i The speed of the vehicle at point Z; o Z represents an infeasible region with obstacles. o ={O1,O2,…,O k}; Define Z f If Z is the feasible movement area without obstacles, then f :

[0147] Z f =ZZ o (0-9)

[0148] To ensure the feasibility and safety of the planned path, the planned path must be located within an obstacle-free area; therefore:

[0149] P∈Z f (0-10)

[0150] (2) Kinematic constraints

[0151] The kinematics of intelligent vehicles are more complex than those of robots. Most intelligent vehicles cannot achieve the zero-turning-radius steering characteristic of robots. Therefore, the kinematic constraints of intelligent vehicles must be considered as one of the reference bases when planning paths. To plan accurate, efficient, and feasible desired paths, this application considers two constraints related to the nonholonomic characteristics of intelligent vehicles: increasing the continuity of the path and curvature constraints, to ensure that the intelligent vehicle can reliably follow the path. Continuity requires that the directional changes of the intelligent vehicle on the path be continuous, avoiding sudden jumps, and ensuring that the heading angle changes smoothly and without interruption. The curvature of the path can quantify the degree of curvature of the path, and curvature directly affects the rate of change of the heading angle. Therefore, the curvature of the path needs to be limited within a dynamic range and the changes should be kept as gradual as possible.

[0152] To address the aforementioned continuity requirement, θ is defined. i Indicates that intelligent vehicles are in p i The heading angle θ at the previous moment before the position i =atan2[(y i -y i-1 ) / (x i -x i-1 )], θ i+1 Indicates that intelligent vehicles are in p i The heading angle θ at the next moment after the position i+1 =atan2[(y i+1 -y i ) / (x i+1 -x i )],△θ i Smart cars in p i Changes in position and heading angle, Δθ i =|θ i+1 -θ i |, thus obtaining △θ i It should be as small as possible; regarding the above curvature constraints, define κ. i Planning routes for intelligent vehicles in p i The curvature of a point, κ i =△θ i / △L i ; △θ max R is the maximum change in heading angle. i For smart cars in p i The turning radius of the point, R i =1 / κ i ;R min The geometric features of the path segment in the planning model are illustrated as follows, representing the minimum turning radius for the intelligent vehicle. Figure 3 As shown. When the intelligent car is at node p i The maximum change in heading angle Δθ is reached max When the rate of change of heading angle is greater than Δθ max / △t, i.e., curvature κ i Maximum turning radius R i It will reach the minimum value R min To satisfy the kinematic constraints of the intelligent vehicle, the turning radius of the intelligent vehicle should be greater than the minimum allowable value. Therefore:

[0153] R i ≥R min (0-11)

[0154] (3) Security constraints

[0155] In dynamic path planning, avoiding collisions between the intelligent vehicle and other static and dynamic obstacles is a crucial component. To plan more efficient and feasible paths, the intelligent vehicle cannot be simply treated as a point mass during conflict determination; its inherent geometric dimensions and the computational complexity of risk detection must be considered. This application comprehensively considers the characteristics of the intelligent vehicle's geometric model and the computational complexity of risk detection, employing a circular model to construct the geometric model of the intelligent vehicle and obstacles in the path planning research. Define Q. C (x C ,y C Q represents the center of gravity of the intelligent vehicle; j (x j ,y j ) represents the location of the obstacle's center of gravity, j = 1, 2, 3, ..., k; h Cl h is the total length of the intelligent vehicle. Cw h represents the total width of the intelligent vehicle. Ojl h is the length of the obstacle. Ojw h is the width of the obstacle. CR The radius of the intelligent vehicle's geometric model. h OR The radius of the obstacle's geometric model. h CiO For intelligent vehicles, the core of quality is at node p i The total distance from the point of origin to the nearest obstacle object. Circular intelligent vehicle and obstacle geometric model, such as Figure 4 As shown.

[0156] To ensure a safe planned path without collisions with obstacles, the position of the intelligent vehicle between the i-th node and the obstacle must satisfy the following:

[0157] h CiO ≥h CR +h OR (0-12)

[0158] (4) Dynamic obstacle model

[0159] Modeling dynamic obstacles is a crucial issue in path planning and motion control because it involves avoiding moving obstacles during movement. The motion of dynamic obstacles can be represented by a motion model. In this application, it is assumed that the motion of the dynamic obstacle varies with time and at a constant velocity v. d If a particle moves linearly and unidirectionally along a straight line in a constant direction, then its position is related to time as follows:

[0160] x d (t+1)=x d (t)+v d ·cosθ d (0-13)

[0161] y d (t+1)=y d (t)+v d ·sinθ d (0-14)

[0162] Where, p d (x d ,y d ) represents the real-time coordinates of the dynamic obstacle, and t represents the time step of a single iteration.

[0163] 2.2 Objective Function of Multi-Objective Path Planning

[0164] To efficiently obtain a collision-free safe path for an intelligent vehicle from the starting point to the destination, this application establishes an objective function for a multi-objective path planning model, with the shortest path length, the highest path smoothness, and the highest path safety as sub-objectives.

[0165] (1) Path length

[0166] From the starting point p s (x s ,y s ) to target point p D (x D ,y D The total path P is determined by partially selecting adjacent nodes p. i =(x i ,y i Let i = 1, 2, 3, ..., m and the paths between them form a node p. i and p i+1 The distance between them is L i , Let L be the total path length, then To obtain the shortest path, the objective function is set as follows:

[0167]

[0168] (2) Path smoothness

[0169] Path smoothing is a crucial aspect of autonomous navigation technology, directly impacting the stability, safety, and yaw costs of intelligent vehicles. Unsmooth paths reduce the vehicle's stability and safety during tracking, significantly increasing yaw costs, including fuel / electricity consumption and path tracking complexity. Path smoothness is related to the rate of change of heading angle and curvature; when the change in heading angle Δθ per unit time... i As the heading angle increases, the rate of change Δθ i As / Δt increases, the path curvature increases. i =△θ i / △L i Turning radius R i The smaller the value, the lower the path smoothness. Therefore, in order to improve driving efficiency and safety and reduce the aforementioned yaw costs, this application uses minimizing path smoothness as one of the objective functions, and uses the change in heading angle as the objective function to measure path smoothness.

[0170] As defined above, θ i Is it a smart car in p i The heading angle θ at the previous moment before the position i+1 Smart cars in p i The heading angle Δθ at the next moment after the position i Smart cars in p i The change in heading angle is defined as Θ, which is the total change in heading angle along the path.

[0171] and, Set the smoothness objective function as follows:

[0172]

[0173] (3) Path risk value

[0174] The safety of the intelligent vehicle's driving path is one of the important foundations for ensuring the feasibility of the planned path. The safety index is directly related to the total risk index; the higher the safety, the lower the risk value. Therefore, this application uses the total risk value of the path as the objective function to measure the path safety. This application constructs a set of invisible double-circular risk assessment regions for each path node, and uses the intelligent vehicle's centroid at node p... i The total distance h between the object and the obstacle's center at time of travel CiO Quantify the risk value of the path.

[0175] Define H i For intelligent vehicles, the core of quality is at node p i The risk value at the time of travel, where H is the total risk value of the intelligent vehicle's path. The center of gravity of intelligent vehicles is at node p iThe total distance from the point to the nearest obstacle object center is h. CiO Assume that at each node p i Surrounded by a radius of h min and h max The non-circular region is defined as h. max h is the maximum radius of influence that the obstacle can produce. min h is the minimum safe distance between an intelligent vehicle and an obstacle. min =h CR +h OR Therefore, the planned path nodes must satisfy h CiO ≥h min Constraints are defined, and the risk values ​​for each path node are:

[0176]

[0177] To ensure the path is as safe as possible from the starting point to the destination, the risk value of the planned path should be reduced. Therefore, the objective function for the path risk value is set as follows:

[0178]

[0179] Figure 5 This is a diagram illustrating the maximum and minimum safe distances between nodes. Figure 6 This is a diagram illustrating node risk.

[0180] 2.3 Modeling of Multi-Objective Path Planning System

[0181] Multi-objective programming refers to the simultaneous consideration of multiple objectives when solving a problem, attempting to find an optimal set of solutions that optimizes or balances the objectives across different dimensions. It has wide applications in engineering, economics, logistics, and other fields. Multi-objective programming and optimization typically require optimal decision-making among multiple objectives. This application applies it to intelligent vehicle path planning and optimization, aiming to find a path from the starting point p... s (x s ,y s ) to target point p D (x D ,y D The desired multi-objective equilibrium path P, which has the shortest path length, highest smoothness, and highest safety, is obtained by comprehensively considering and integrating the above constraints and objective functions. The resulting multi-objective path planning model is as follows:

[0182]

[0183] x i =(x i ,y i )∈Z (0-23)

[0184] Z f =Z-Z o (0-24) P∈Z f (0-25)

[0185] p1(x1,y1)=p s (x s ,y s ) (0-26)

[0186] p m (x m ,y m )=p D (x D ,y D ) (0-27)

[0187]

[0188] θ i =atan2[(y i -y i-1 ) / (x i -x i-1 )],i=2,3,4,…,m (0-29)

[0189] △θ i =|θ i+1 -θ i |,i=2,2,3,…,m (0-30)

[0190] κ i =△θ i / △L i ,i=2,3,4,…,m (0-31)

[0191] R i =1 / κ i (0-32)

[0192] R i ≥R min ,i=1,2,3,…,m (0-33)

[0193]

[0194] h CiO ≥h CR +h OR ,i=1,2,3,…,m (0-37)

[0195] x d+1 =x d (t)+v d ·cosθd (0-38)

[0196] y d+1 =y d (t)+v d ·sinθ d (0-39)

[0197]

[0198] The above is the system model for global multi-objective path planning in this application. Equations (0-19) to (0-21) represent the sub-objectives of the multi-objective path planning problem, respectively representing the objectives of shortest path length, highest path smoothness, and highest path safety; Equations (0-22) to (0-25) represent environmental modeling and constraints, representing the path within the feasible area without obstacles; Equations (0-26) and (0-27) represent the starting and ending point configuration information of the path planning problem; Equation (0-28) is the formula for calculating the path length, which is calculated using Euclidean distance in this application; Equations (0-29) and (0-30) are the specific formulas for calculating the path planning smoothness, which is measured by the change in heading angle in this application; Equations (0-31) and (0-32) represent the path planning of the intelligent vehicle in p i Formulas for calculating the curvature and turning radius of a point: Equation (0-33) is the minimum turning radius limit for the kinematic constraints of the intelligent vehicle; Equation (0-34) is the Euclidean distance from the center of mass of the intelligent vehicle to the center of mass of the obstacle; Equations (0-35) and (0-36) are the formulas for calculating the risk circle radius of the intelligent vehicle and the obstacle; Equation (0-37) is the safety constraint in the path planning of the intelligent vehicle; Equations (0-38) and (0-39) are the models of dynamic obstacles; Equation (0-40) is the formula for calculating the risk value of the path planned by the intelligent vehicle.

[0199] III. Basic Principles Analysis of the NSGA-II Algorithm

[0200] Multi-objective optimization problems, due to their complexity and NP-hard nature, place high demands on the computational efficiency and optimization capabilities of solution algorithms, requiring efficient algorithms to ensure the feasibility and quality of solutions. Non-dominated sorting genetic algorithms, as an outstanding evolutionary algorithm with robust optimization capabilities, offer advantages due to their relatively low computational complexity (O(MN)). 2 The NSGA-II algorithm, with its high efficiency in large-scale problems, is widely used in engineering optimization, scheduling problems, and neural network training. Its core advantage lies in balancing the quality, diversity, and convergence of solutions. Therefore, this application selects the NSGA-II algorithm as the fundamental algorithm for solving the main problem to conduct in-depth research on the multi-objective path planning problem of intelligent vehicles.

[0201] 3.1 Introduction to Algorithm Principles

[0202] The core idea of ​​the NSGA-II algorithm is to abstract the optimization problem into an evolutionary process of individuals and populations by simulating natural selection and genetic mechanisms. Using genetic operations such as selection, crossover, and mutation, it gradually evolves a solution set in the solution space that satisfies the requirements of multi-objective optimization. Based on the genetic algorithm framework, this algorithm introduces core mechanisms such as fast non-dominated sorting, crowding calculation, and elitist strategies to improve the quality and diversity of solutions, obtaining a uniformly distributed and comprehensively covered Pareto optimal solution set.

[0203] By employing a fast non-dominated sorting mechanism, the NSGA-II algorithm can divide the population into dominance levels, classifying individuals into different grades according to their non-dominated relationships, ensuring that the optimization process prioritizes individuals on the non-dominated front. By adding a crowding calculation mechanism, the algorithm has the ability to measure the distribution density of individuals in the population, ensuring that the selected solutions are evenly distributed on the Pareto front, improving solution diversity and global exploration capabilities. By introducing an elitist strategy mechanism, excellent individuals are retained to the next generation, avoiding the loss of high-quality solutions due to random selection, and accelerating the algorithm's convergence speed.

[0204] 3.2 Basic Algorithm Flow

[0205] The main steps of the traditional NSGA-II algorithm are as follows: initialize the population, evaluate fitness, select, crossover, mutate, generate a new population, merge the offspring population and the parent population, sort non-dominated solutions and calculate crowding distance, select individuals with better fitness to generate a new population, and end the evolution when the exit condition is reached.

[0206] (1) Initialize the population

[0207] Initializing the population is the starting step of the NSGA-II algorithm. Its purpose is to generate a randomly distributed initial population to provide diverse solutions for the subsequent evolutionary process, ensuring breadth of coverage of the search space. Each individual in the population represents a solution, consisting of a set of decision variables. Let the population size be N and the dimension of the decision variables be D, then the initial population can be represented as:

[0208] P0 = {X1, X2, ..., X} N} (0-41)

[0209] Among them, X i =(x i1 ,x i2 ,…,x iD Let x represent the decision variable vector for the i-th individual. ij ∈[h j ,l j ], h j and l j These are the upper and lower bounds of the j-th variable, respectively.

[0210] (2) Fitness evaluation

[0211] Fitness evaluation assesses the performance of each individual in a population on an objective function. For multi-objective optimization problems, each individual typically has multiple objective function values. Let there be M objective functions, denoted as f1, f2, ..., f... M Then each individual X i The fitness value can be expressed as:

[0212] F i =(f1(X) i ),f2(X i ),…,f M (X i )) (0-42)f j (X i Individual X i The fitness on the j-th objective function provides the basis for subsequent non-dominated sorting and selection operations.

[0213] (3) Quick Nondominated Sort

[0214] Fast non-dominated sorting divides individuals in a population into different Pareto fronts based on their dominance relationships. The non-dominated sorting process is as follows: First, for each individual X in the population... i Calculate the number of times n it is dominated by other individuals. i and the set of individuals S it governs i Secondly, all n i Individuals with a value of 0 are assigned to the first Pareto front, F1. Then, after removing individuals from F1, the above process is repeated for the remaining individuals, resulting in F2, F3, and so on, until all individuals are assigned to the corresponding front.

[0215]

[0216] (4) Crowding distance calculation

[0217] Crowding distance calculation is used to measure the distribution density of individuals in a target space to maintain population diversity. For each Pareto front F... k The steps for calculating the crowding distance are as follows: For F k The individuals in the dataset are sorted according to each objective function value; for each individual X i In F k In this process, the distances between adjacent individuals on each objective function are calculated, and the crowding distance is obtained by summing them:

[0218]

[0219] In the formula: These are the maximum and minimum values ​​of the m-th objective function, respectively.

[0220] (5) Select parent individuals

[0221] The selection operation is used to choose individuals from the current population as parents to generate new offspring. NSGA-II employs a binary tournament selection method. The selection process is as follows: two individuals A and B are randomly selected, their non-dominated ranks are compared, and the individual with the lower non-dominated rank is selected. If the ranks are the same, the individual with the larger crowding distance is selected. Selection is performed on the population based on non-dominated ranking and crowding value, improving the quality of the iteratively evolved population by selecting individuals with better fitness to enter the next generation.

[0222] (6) Cross

[0223] like Figure 7 As shown, the principle of crossover is that individuals produce offspring by pairing up and exchanging their genetic information. Common crossover operations include single-point crossover, multi-point crossover, and simulated binary crossover. The new individuals produced by crossover are generated from the genetic information of the crossover parents.

[0224] (7) Variation

[0225] like Figure 8 As shown, mutation operations are used to introduce gene mutations into new individuals, increasing population diversity and preventing premature convergence. Mutation operations are often performed using methods such as polynomial mutation.

[0226] (8) Merge the offspring population and the parent population

[0227] The new offspring population P generated through crossover and mutation t Will be in conjunction with the current parent population Q t The populations merge to form an intermediate population R of size 2N. t :

[0228] R t =P t ∪Q t (0-45)

[0229] (9) Non-dominated solution sorting and crowding distance calculation

[0230] For the merged population R t Fast nondominated sorting and crowding distance calculation are performed to obtain multiple Pareto fronts F1, F2, F3, ... etc.

[0231] (10) Retaining individuals with better fitness to generate a new population.

[0232] From the merged population R tIn the process, individuals with the best fitness are selected based on the results of the non-dominated ordination and the crowding value, and these individuals are formed into a new population. The principle for selecting individuals in the new population is as follows: prioritize all individuals of the first level F1 in the non-dominated hierarchy. If the number of individuals in the first level exceeds N, then individuals are selected based on the crowding value. If the number of individuals in the first level is less than N, then individuals of the second level are selected, and so on, until N individuals are selected.

[0233] Through the above steps, the NSGA-II algorithm iteratively generates a new population and eventually converges to the Pareto optimal solution set.

[0234] IV. Design of Multi-Objective Global Path Planning Algorithm for Improved IMNSGA-II Algorithm

[0235] This application applies the NSGA-II algorithm to the field of intelligent vehicle path planning. However, the traditional NSGA-II algorithm is prone to limitations such as loss of population diversity, premature convergence, getting trapped in local optima, and slow convergence speed when dealing with highly complex or multimodal objective functions. In order to improve the convergence speed of the NSGA-II algorithm, maintain population diversity, and enhance global search capabilities, this application proposes an improved IMNSGA-II algorithm based on the traditional NSGA-II algorithm.

[0236] The IMNSGA-II algorithm improves the overall quality and diversity of the initial population by introducing an A*-RRT hybrid initialization strategy. It incorporates the concept of dynamic adaptive crowding distance into the NSGA-II algorithm to overcome the unevenness of traditional crowding distance calculations, ensuring the diversity and uniform distribution of individuals within the population. Parents are selected based on non-dominated hierarchical sorting and dynamic crowding distance, and optimized fitness crossover and goal-oriented progressive mutation operations are performed to generate offspring populations, enhancing fitness, accelerating convergence, and avoiding getting trapped in local optima. The specific process of the IMNSGA-II algorithm is as follows: Figure 9 As shown.

[0237] 4.1 Path Encoding Method

[0238] This application employs a decimal encoding method to simulate the complexity of global path planning for intelligent vehicles. The specific encoding method is as follows: Figure 10 As shown, the variable is the feasible region Z in the planned environment. f Grid numbering within

[69] .

[0239] Figure 10 The content shown represents one chromosome. This application treats the chromosome as a complete solution, i.e., a path in a path planning problem. It is a sequence of points starting from a given origin and ending at a destination. In this path on a two-dimensional plane, each gene segment φ... i Store a point pi =(x i ,y i ).

[0240] 4.2 RRT-A* Hybrid Population Initialization Strategy

[0241] Traditional NSGA-II typically uses random methods to generate the initial population, but this carries risks such as getting trapped in local optima and losing population diversity. This application combines the highly efficient A* algorithm for finding the shortest path with the widely randomized RRT algorithm to generate paths, forming a hybrid initialization strategy that improves the diversity and quality of the initial population. The specific process design is shown below:

[0242] (1) First, the A* algorithm is used to generate three initial solutions POP of the shortest distance from the specified starting point to the target point at three different grid resolutions. Ai Then, the paths at all resolutions are resampled onto a grid of the same resolution to ensure that the paths have a consistent location representation in the same environment;

[0243] (2) Use the path generated by A* as the initial tree of RRT, expand the path using dynamically adjusted step size and random sampling sequence, and select nodes R from the initial path. i As the starting point for RRT path planning, P is generated. init - 3 mutation paths Backtracking R i Previous paths and new variant paths Store it in POP Ri middle;

[0244] (3) Merge POPs Ai With POP Ri This forms the final initial population POP. init .

[0245] Table 1. Pseudocode illustration of the mixed initial strategy

[0246]

[0247] 4.3 Improved Dynamic Congestion Distance Measurement Method

[0248] In the NSGA-II algorithm, crowding distance (CD) serves as a metric for measuring the distribution of individuals within the population, primarily used to maintain population diversity. NSGA-II employs a crowding distance-based strategy for population maintenance, where a smaller crowding distance indicates that the individual is closer to other solutions in the solution space. When eliminating individuals, individuals with smaller crowding distances are typically removed first to ensure a uniform distribution of the population in the target space. Traditional crowding distance measurement methods rely on static calculations based on Euclidean distance, which have the following limitations:

[0249] (1) Traditional crowding distance calculation methods may lead to some regions of the Pareto front being overly dense, while other regions are relatively sparse. The non-dominated solution set is unevenly distributed in the target space, affecting the overall diversity of the population.

[0250] (2) Traditional crowding distance calculation methods may lead to unreasonable elimination of individuals in some cases. Take a two-dimensional objective optimization problem as an example, such as... Figure 11 As shown, in traditional crowding distance calculation methods, the crowding degree of an intermediate individual is usually calculated by summing the distances between its (i+1)th and (i-1)th adjacent individuals across each target dimension, and then normalized to the range of the corresponding target values. For example, if the difference in value of a solution B across target dimension f2 is much greater than the difference across target dimension f1, and the sum of the differences between adjacent individuals across target dimensions f1 and f2 is lower than the sum of the differences between adjacent individuals across target dimensions of solution F, the traditional method would prioritize eliminating solution B. However, from the perspective of maintaining a horizontally uniform distribution of the population, solution B should not be removed.

[0251] (3) During each population maintenance process, the crowding distance is usually calculated only once and remains unchanged after individuals are removed in turn, failing to dynamically adjust according to the current population distribution. Therefore, this method is insufficient in terms of adaptive adjustment, which may lead to insufficient local diversity and reduced optimization ability.

[0252] To address the aforementioned issues, this application employs an Adaptive Dynamic Crowding Distance (ADCD) metric strategy to enhance the population diversity maintenance capability of the NSGA-II algorithm during the optimization process. The ADCD strategy introduces a dynamic adjustment mechanism when calculating the individual crowding distance, more reasonably preserving solutions that contribute to maintaining a uniform distribution of the Pareto front, and updating the crowding distance in real-time during individual elimination within the same number of iterations, thereby improving the global search capability and local optimization capability of NSGA-II. i The calculation formula is as follows:

[0253]

[0254] Among them, ADCD i V represents the adaptive dynamic crowding distance for the lower i individuals. rni It is the variance of the crowding distance to the i-th neighboring individuals, representing the ADCD of the i-th individual. i The dispersion of crowding distance indicates the degree of difference in crowding distance across different target dimensions. If an individual's V... rni Larger, then ADCD i A larger value indicates a higher degree of individual dispersion and a greater probability of being retained. Figure 11 G should be retained while F should be removed. The pseudocode for dynamic congestion in this application is shown in Table 2.

[0255] Table 2 Pseudocode for Dynamic Congestion

[0256]

[0257] 4.4 Optimize fitness path crossover operation

[0258] In the field of multi-objective optimization, crossover is a key step in genetic algorithms, used to generate offspring that inherit the superior traits of their parents. The path crossover operation proposed in this application generates new feasible paths by exchanging some nodes between two selected paths, checks the feasibility of the new paths, and evaluates their fitness. If the overall fitness of the crossover path is better than that of the original path, the crossover operation is confirmed; otherwise, the original path is retained.

[0259] The crossover operation is performed in descending order, grouping individuals in pairs. Specific details are explained in the pseudocode in Table 3. To ensure the feasibility of path crossover, the following constraints must be met: the line connecting the crossed point to the previous and next points in the original path must not pass through obstacles; the newly formed path segment should be within a feasible region without obstacles. This optimized fitness path crossover operation not only allows newly generated offspring to inherit the superior characteristics of their parents but also ensures the feasibility and effectiveness of the newly generated paths.

[0260] Table 3. Pseudocode for Optimized Fitness Path Crossover Operation

[0261]

[0262] 4.5 Goal-Oriented Incremental Path Variation Operation

[0263] Path mutation aims to optimize path planning by adjusting path nodes, making it more aligned with the problem's optimization objective. Unlike the random mutation method used in the traditional NSGA-II algorithm, the goal-oriented dynamic progressive path mutation strategy introduces directionality and adaptive adjustment mechanisms during path adjustment to improve search efficiency and optimization capability. The core objective of this strategy is to gradually guide the path towards the target region while ensuring the feasibility and quality of the path. This path mutation operation has the following four main characteristics:

[0264] (1) Goal-Oriented Path Mutation Strategy. Traditional random mutation methods may lead to the disordered expansion of path points in the search space, resulting in a large number of invalid mutations and reducing search efficiency. To improve the effectiveness of path optimization, the improved path mutation strategy adopts a goal-oriented mutation approach, adjusting the path points to move closer to the goal point during each mutation. This method can reduce unnecessary deviations and make the mutated path more directional globally, thereby improving search efficiency and accelerating optimization convergence. Specifically, for a mutation point P in the path... i Its mutation direction is from the target point P t Determining the new path point P′ i Compared to the original path point P i Closer to the target area:

[0265] P′ i =P i +α·[(P t -P i ) / ||P t -P i ||] (0-50)

[0266] Here, α is the variable asynchronous length, which determines the rate at which the path point advances towards the target point.

[0267] (2) Dynamic Incremental Step Size Strategy. Traditional fixed-step mutation methods struggle to balance global search and local optimization, potentially leading to insufficient search in the early stages or premature convergence in the later stages. The improved mutation strategy introduces a dynamic incremental step size, employing a larger step size in the early stages to promote global exploration; while gradually reducing the step size in the later stages of optimization to achieve a more refined local search. The step size adjustment mechanism can be represented as follows:

[0268] α=α max ·(1-t / T)+α min ·t / T (0-51)

[0269] Where, α max and α min This represents the initial step size and the final step size, t is the current iteration number, and T is the maximum iteration number.

[0270] (3) Feasibility Detection and Obstacle Avoidance Mechanism. In path planning problems, path feasibility is one of the key constraints. If the mutated path point is located in an obstacle region, or if the line connecting the mutated point to its preceding and following adjacent points crosses an obstacle, the path cannot be executed. To solve this problem, the improved mutation strategy incorporates a feasibility detection and obstacle avoidance mechanism during the mutation process to ensure that the mutated path point is always located in a feasible region. The specific method is as follows: First, obstacle detection is performed, and then a new mutated node P′ is generated. i Next, it checks whether the path falls into an obstacle area. If a conflict occurs, the mutation direction is readjusted or the step size is reduced. Then, connectivity is checked to ensure the new path point P′ is within the obstacle area. i With the preceding and following path points P i-1 and P i+1 The connecting lines must not intersect with obstacles; otherwise, path re-variation or local adjustment will be performed.

[0271] (4) Target value-driven path optimization mechanism. After each path mutation, the algorithm evaluates the mutated path and the original path at the non-dominated level in three target dimensions: path length, path smoothness, and path safety, and retains the path with the smaller non-dominated level.

[0272] By introducing goal-oriented optimization, dynamic step size adjustment, feasibility detection and obstacle avoidance, and goal-value-driven optimization mechanisms, the algorithm can reduce invalid searches, improve path quality, and ensure the feasibility of the mutated path. Detailed implementation information is provided in the pseudocode shown in Table 4.

[0273] Table 4. Pseudocode for goal-oriented incremental path mutation operation.

[0274]

[0275] 4.6 Population Selection Operation Improved Based on Hierarchical Ranking and Dynamic Crowding Distance

[0276] In the NSGA-II algorithm, the selection strategy directly affects the optimization performance and population diversity. Commonly used selection methods in NSGA-II include traditional selection methods, binary competition selection, and static non-dominated sorting methods. Among these, traditional roulette wheel selection tends to lead to the dominance of high-fitness individuals, reducing population diversity; while binary competition selection is computationally simple, it only compares two individuals at a time, lacking global information; static non-dominated sorting methods and crowding distance calculations, due to their fixed calculation methods, are difficult to adapt to dynamic changes in the population, potentially leading to uneven solution distribution. Therefore, this application proposes a population selection method based on hierarchical sorting and dynamic crowding distance optimization to improve search quality and optimize population diversity.

[0277] The core idea of ​​the population selection operation based on hierarchical sorting and dynamic crowding distance improvement is to combine hierarchical sorting of dominance relationships with dynamic crowding distance calculation for population selection, taking into account both individual quality and population diversity. First, a non-dominant sorting method is used, prioritizing individuals with lower rankings in the Pareto dominance hierarchy to ensure the overall superiority of the selected population. Second, for the number of individuals at different levels, a filling strategy and a pruning strategy are employed. If the number of individuals at the current level is less than the required number, all individuals at the current level are retained for the next generation of the population, and this process is repeated for each subsequent level, re-evaluating whether the required number is met until the requirement is met. If the number of individuals at the current level exceeds the required number, the population is sorted in descending order according to the dynamic crowding distance, and individuals with the smallest ADCD are deleted sequentially. Crowding is recalculated after each deletion to ensure that the deletion process considers the global distribution information of the population. Compared with traditional crowding distance calculation methods, this method can more accurately measure the population distribution, thereby effectively maintaining population diversity and preventing individuals from being over-concentrated in certain areas. Specific details are explained in the pseudocode shown in Table 5.

[0278] Table 5. Population selection algorithm improved based on hierarchical sorting and dynamic crowding distance.

[0279]

[0280] V. Simulation Experiments and Result Analysis

[0281] To verify the effectiveness of the proposed IMNSGA-II, this application designed a combined simulation experiment to validate the algorithm's effectiveness. First, the algorithm's performance was quantitatively analyzed based on multiple evaluation metrics to measure its optimization capability and convergence characteristics. Second, the adaptability of IMNSGA-II in multi-objective path planning tasks was tested under different simulation scenarios and parameter configurations. Finally, IMNSGA-II was compared and analyzed globally with four other multi-objective optimization algorithms to evaluate its advantages in search efficiency, solution quality, and population diversity maintenance.

[0282] 5.1 Evaluation Indicators

[0283] In multi-objective global path planning research, evaluating algorithm performance is a crucial step in measuring its effectiveness. Pareto's Hv hypervolume calculation, SC, NNS, and RNS are representative and scientifically sound evaluation metrics, each providing insights into the algorithm's capabilities and limitations from different perspectives.

[0284] (1) Hypervolume index

[0285] Hypervolume represents the volume of the hypercube bounded by the reference point in the target space and the Pareto front. It is an important metric for measuring the distribution and diversity of feasible solutions in multi-objective spaces. In the D-dimensional solution space, assume S = {s1, s2, ..., s...} n As a set of non-dominated solutions, ref={r1,r2,…,r n As a reference point for the corresponding scene map, the value of Hv can be obtained by the following formula:

[0286]

[0287] Where L refers to the Lebesgue measure used to calculate the volume.

[89] ,h(a i ) indicates that by a i The hypercube is composed of a reference point and a worst-case combination of different objectives, which is the worst-case values ​​of path length, path safety, and path smoothness obtained in the simulation experiment.

[0288] (2) SC Collection Coverage Indicator

[0289] The SC index measures the proportion of non-dominated solutions overlapping and dominating each other between different solution sets, and is used to compare the quality of two solution sets. Let A = {a1, a2, ..., a...} n} and B = {b1,b2,…,b m Let} be two approximate sets close to the Pareto front. SC(A,B) is the proportion of non-dominated solutions in B dominated by non-dominated solutions in A, i.e.:

[0290]

[0291] Here, |B| represents the total number of solutions in the solution set B. If SC(A,B)=1, it means that all non-dominated solution sets in B are dominated by the non-dominated solution sets in A, indicating that all solutions in B are completely covered by solution set A. If SC(A,B)=0, it means that none of the non-dominated solution sets in B are dominated by the non-dominated solution sets in A. Note that the dominance relation between two approximate sets is asymmetric; SC is a binary metric, and SC(B,A) is not necessarily equal to 1-SC(A,B).

[90] Therefore, it is necessary to calculate both SC(B,A) and SC(A,B).

[0292] (3) The number of non-dominated solutions in the NNS neighborhood and the proportion of non-dominated solutions in the RNS neighborhood

[0293] The NNS metric is used to compare the dominance of different algorithms in the global Pareto front. Assume S... i ={S1,S2,…,S nThe non-dominated solution set is obtained by calculating different algorithms. This represents the combined solution set of the Pareto front solutions obtained by the above five algorithms, for S I By performing non-dominated sorting, we obtain the comprehensive Pareto front for multi-objective path planning in different scenarios, NNS(S i ) represents S i The number of solutions in the solution set that are not dominated by other solutions in the synthesized Pareto solution set S, i.e.:

[0294]

[0295] in, It means that solution y dominates solution x, NNS(S) i The larger the value of S, the greater the value of S. i The solution set generated by the corresponding algorithm is in the solution set S of all algorithms. I It occupies a more non-dominant position in the Pareto front solution set S, and has a higher coverage quality.

[0296] The RNS index represents S i The proportion of non-dominated solutions in the overall Pareto solution set S. The calculation formula is as follows:

[0297]

[0298] RNS(S i The larger the value of ), the stronger the solution set S. i The higher the proportion of undominated solutions in the integrated Pareto front solution set, the higher the nondomination and diversity of the solution set generated by the algorithm.

[0299] 5.2 Scenarios and Parameter Configuration

[0300] To evaluate the performance of the proposed algorithm IMNSGA-II, this application employs... Figure 12 The four representative environment maps shown are used to verify the effectiveness of IMNSGA-II. Map 1 is a high-density obstacle cluster with a large feasible area, typically used to simulate outdoor environments such as industrial parks and mining areas. Map 2 represents a structured environment with high-density regular obstacles, typically used to simulate indoor and outdoor scenarios with regular facility and equipment layouts, such as factories, workshops, and warehouses. Map 3 is an asymmetric real-world environment map simulating the urban layout of different cities, derived from Nathan Sturtevant's mobile AI experiment. Map 4 presents an indoor real-world environment with obstacles featuring door structures. (Source: References)

[67] Each of the above maps has been standardized to 100×100 pixels.

[0301] To ensure the comprehensiveness and reliability of the simulation, as well as the effectiveness of the proposed IMNSGA-II algorithm, this application independently tested five effective multi-objective global path planning algorithms on the four maps mentioned above. The five algorithms are IMNSGA-II, IACO-A*, MOFA, MOPSO, and NSGA-II proposed in this application. Table 6 provides the coordinates of the starting point and the target point in the four environment maps.

[0302] Table 6 Configuration information in different map environments

[0303]

[0304] Adjusting the optimal parameters of a multi-objective optimization algorithm can be divided into automatic adjustment.

[78] and manual adjustment

[79] Two methods. To adjust the parameter configuration of the multi-objective optimization algorithm IMNSGA-II, this application references...

[80] The algorithm employs extensive manual adjustments through numerous experiments to optimize parameters. First, the key parameters of the algorithm design are categorized. Based on the fundamental NSGA-II algorithm, the key parameters of the proposed algorithm are defined as population size Pn, crossover probability Pc, mutation probability Pm, and the maximum number of consecutive iterations for each solution Gn. Second, the possible value ranges of different parameters are defined based on their properties, and five possible uniformly distributed values ​​are established. Third, the values ​​of each parameter are permuted and combined, and the algorithm is run 30 times for each set, with the average Hv value calculated. Finally, the optimal parameter combination is obtained based on the results. The uniformly distributed parameter values ​​and the optimal parameter combination are shown in Table 7.

[0305] Table 7 IMNSGA-II Configuration Variables

[0306]

[0307] 5.3 Global Simulation Comparison and Analysis of Five Multi-Objective Programming Algorithms

[0308] In this application, we present and analyze the results obtained by IMNSGA-II in four different scenarios. The simulation environment and dimensions of each map are detailed in Section 5.2. We conducted independent simulation experiments on five algorithms for the four scenarios (Map1-Map4), resulting in 20 simulation experiment combinations. For each combination, we performed 30 simulation tests to ensure the statistical significance of the evaluation results. Based on the simulation results, we recorded the average hypervolume Hv value, SC value, NNS value, and RNS value for each experimental combination, as shown in Tables 8 to 10.

[0309] (1) Results and comparative analysis of Hv values ​​of five algorithms

[0310] Table 8 Comparison of Hv values ​​for five algorithms

[0311]

[0312] The Hv value is a key indicator used to measure the coverage and diversity of the solution set in a multi-objective optimization problem space. A higher Hv value means that the solution set can better cover the objective space and has better diversity. Table 8 and Figure 13 The comparison results of Hv values ​​are shown in Table 8. The first column refers to the scenarios used for simulation testing, and columns 2 to 6 show the Pareto front Hv values ​​obtained by five algorithms (INMSGA-II, NSGA-II, MOFA, MOPSO, and IACO-A*) under different scenarios. (From Table 8 and...) Figure 13 It can be seen from this:

[0313] I. The five algorithms showed different performance in Hv values ​​on different maps Map1, Map2, Map3, and Map4. Since the reference point is fixed and covers the worst area of ​​the entire target space, the Hv values ​​obtained in different environments are generally above 0.5. This indicates that the solution sets found by different algorithms in different environments perform well on multiple objectives at the same time, covering more than 50% of the theoretical optimal trade-off space, and can balance the multi-objective problem in path planning to a certain extent.

[0314] II. As shown in the last column of Table 8, the IMNSGA-II algorithm has the highest average Hv value across different environments, with an average Hv value of 0.6329. It exhibits strong solution set coverage (close to 0.65) particularly on Map2 and Map4. The MOFA algorithm performs second best. While it performs well on some maps, such as Map4 where the Hv value is 0.6206, its overall average Hv value is still lower than that of IMNSGA-II. Furthermore, the stability of the solution quality obtained by the algorithm is not high for different maps. The traditional NSGA-II, MOPSO, and IACO-A* algorithms perform slightly weaker, with an overall average Hv value of around 0.5500. Their Hv values ​​are lower on Map3 and Map4, indicating limited optimization effectiveness in complex path planning problems.

[0315] (2) SC value index results and comparative analysis of five algorithms

[0316] Table 9 Comparison of SC values ​​for five algorithms

[0317]

[0318] The SC value measures the proportion of solutions in one solution set X that are dominated by another solution set Y. To calculate the SC value of each algorithm, this application sets the worst-performing point in different target dimensions for each scenario as the reference point for calculating the SC value, and performs SC value calculations for five algorithms. Table 9 and Figure 14 The comparison results of five algorithms in terms of SC values ​​are given. Algo1, Algo2, Algo3, Algo4, and Algo5 represent the IMNSGA-II, NSGA-II, MOFA, MOPSO, and IACO-A* algorithms, respectively. (See Table 9 and...) Figure 14 It can be known that:

[0319] The set coverage value obtained by the I.IMNSGA-II algorithm on the Pareto front surface is close to 1.000, and it is better than the other four algorithms in many aspects, especially in terms of the comprehensive coverage of the solution set of the NSGA-II, MOPSO and IACO-A* algorithms.

[0320] II. As can be seen from the last row of Table 9, in the worst case, more than 87% of the solutions obtained by the IMNSGA-II algorithm are better than the solutions obtained by the other four algorithms, while in the best case, only 13.9% of the solutions obtained by the other comparison algorithms are better than the solutions obtained by the IMNSGA-II algorithm.

[0321] (3) Results and comparative analysis of NNS and RNS metrics for the five algorithms

[0322] The NNS index is used to compare the dominance of different algorithms in the global Pareto front. Table 10 shows the comprehensive comparison results of the NNS and RNS values ​​of five algorithms under different environments. Columns 2, 4, 6, 8, and 10 in the table are the NNS values ​​of the five algorithms, and columns 3, 5, 7, 9, and 11 are the RNS values ​​of the five algorithms.

[0323] Table 10 Comparison of NNS / RNS values ​​for five algorithms

[0324]

[0325] I. Based on the calculated NNS and RNS values ​​of the five algorithms, it can be seen that the IMNSGA-II algorithm performs best on all maps, and the NNS and RNS values ​​of the solution set obtained by the IMNSGA-II algorithm are better than those obtained by other comparison algorithms in each map environment.

[0326] II. According to the last column of Table 10, under different map environments, the IMNSGA-II algorithm has the highest average NNS and RNS values ​​among all algorithms, with average NNS and RNS values ​​of 33.354 and 0.685 respectively, which is significantly better than the second-ranked MOFA algorithm.

[0327] III. The NNS and RNS values ​​of NSGA-II, MOPSO, and IACO-A* are generally not high, and they perform poorly on complex maps Map3 and Map4, indicating certain limitations in the performance of global search and optimization in complex environments.

[0328] Figure 15 This paper presents the Pareto front 3D plots and their projections onto three different target combinations obtained using five algorithms (IMNSGA-II, NSGA-II, MOFA, MOPSO, and IACO-A*) in a simple Map1 environment. Figure 15 It can be seen that the non-dominated solutions obtained by the IMNSGA-II algorithm are in three dimensions. Figure 15 (a) and its two-dimensional projections 2-15 (b~d) on different combinations of the three objectives are most close to the minimum point (theoretical ideal solution) of each objective, and it has an advantage over other comparative algorithms in the number of non-dominated solutions.

[0329] pass Figure 16 As shown in the three-dimensional Pareto front plot in (a), the non-dominated solution set obtained by the IMNSGA-II algorithm in the simple Map2 environment is closest to the ideal solution, significantly outperforming the second-ranked MOFA algorithm, followed by NSGA-II, MOPSO, and IACO-A* algorithms; through Figure 16 As can be seen from the two-dimensional projection diagrams (b-d) in the middle, the IMNSGA-II algorithm achieves an effective balance between path length and risk value. Although it is slightly lacking in the balance between path length and smoothness, its overall performance is still better than other algorithms.

[0330] according to Figure 17 As shown in the three-dimensional plot of the Pareto front in the complex Map3 environment (a), the non-dominated solution set obtained by the IMNSGA-II algorithm is generally closest to the minimum point of each objective, and the multi-objective optimization performance is strong. In terms of the optimal value of path length, the solutions of the IMNSGA-II algorithm and the MOFA algorithm are close to each other, but the MOFA algorithm is slightly inferior in terms of risk value and smoothness. The IMNSGA-II algorithm can generate solutions close to the coordinate axis, indicating that the algorithm can effectively take into account the extreme optimization of each objective and generate corresponding solutions, and the solution set has a wide coverage.

[0331] Figure 18The Pareto front results and their projections obtained by five multi-objective algorithms in the complex map Map4 environment are presented by... Figure 18 As shown in (a), IMNSGA-II achieves a good balance between path length and path risk value, as well as path risk value and smoothness, but its balance in the path length and smoothness aspect is slightly insufficient, and the solution set distribution is relatively concentrated; from Figure 18 (a) and each combination of two dimensions Figure 18 As can be seen from (b~d), the overall value of MOFA is second only to IMNSGA-II, especially in the minimum value of risk, the difference between the two is small; other algorithms have different advantages in balancing, such as NSGA-II performing well in balancing path length-smoothness and path length-risk value, and IACO-A* having a stronger balancing effect in balancing path smoothness-risk value.

[0332] In summary, by analyzing the evaluation metrics (Tables 2-7 to 2-10) and Pareto front distribution of five multi-objective path optimization algorithms under four environments (Map1-Map4), this study demonstrates the effectiveness of these algorithms. Figures 15 to 18 It can be known that:

[0333] (1) In map environments with different complexity, the IMNSGA-II algorithm generates competitive Pareto optimal solution sets. Its Pareto front can reflect the trade-off between different objectives well, which verifies the effectiveness of the algorithm in multi-objective path planning under different complexity environments. This shows that the algorithm has good adaptability, reliability and multi-objective optimization capabilities.

[0334] (2) Compared with algorithms such as MOFA, MOPSO, IACO-A* and traditional NSGA-II, IMNSGA-II is superior in terms of the number of Pareto solutions and the diversity of solution sets. It generates richer and more evenly distributed solution sets and performs better in terms of convergence and scalability.

[0335] (3) IMNSGA-II excels in the distribution range of solutions and optimization of extreme cases. Its solution set is distributed in a uniform and wide area, which can effectively cover the solution space and take into account extreme optimization cases with conflicting objectives. It provides an efficient, flexible and reliable solution for multi-objective path planning of intelligent vehicles.

[0336] (4) Different algorithms differ in their performance in balancing objective dimensions. For example, IMNSGA-II and MOFA perform better in balancing path length and risk; NSGA-II is more advantageous in balancing path length and smoothness; and IACO-A is more prominent in balancing smoothness and risk, indicating that different algorithms have their own advantages in multi-objective optimization.

[0337] This invention addresses the multi-objective global path planning problem for intelligent vehicles in static environments. This application comprehensively considers the planning environment, obstacles, multi-objective requirements, and constraints to construct a multi-objective dynamic path planning model for the system, providing a theoretical foundation for subsequent path planning strategies. An improved IMNSGA-II algorithm is proposed, which enhances the solution quality and adaptability in multi-objective path planning by incorporating special operators such as RRT-A* hybrid initialization, improved dynamic congestion distance metric, optimized path crossing mutation operation, and binary population selection. Based on this, a multi-objective algorithm evaluation index is proposed, and four simulation environments with different complexities are designed to compare the IMNSGA-II algorithm with four other multi-objective path planning algorithms. Simulation results show that the IMNSGA-II algorithm can generate higher quality and broader coverage Pareto solution sets in different environments, possessing stronger global search capabilities and diversity, making it an effective solution for solving multi-objective path planning problems.

Claims

1. A multi-objective global path planning method for intelligent vehicles based on an improved IMNSGA-II, characterized in that, The method includes the following steps: S1. Perform environmental modeling and feasible domain construction, load the map, mark the obstacle set and obtain the feasible area, set the start and end points in a unified coordinate system, and represent the path as a sequence of waypoints connected in sequence, requiring all waypoints to be located in the feasible area; S2. Establish a multi-objective optimization model that simultaneously considers path length, path smoothness, and driving safety, and introduce mechanical and geometric safety constraints to ensure that the path segment meets the minimum turning radius, maximum heading increment, and minimum safe distance from obstacles. S3. Adopt the RRT-A* hybrid initialization strategy: obtain several shortest path skeletons under multi-resolution grid, and use them as the initial tree of the fast random tree after unified resampling. Combine dynamic step size and random sampling expansion to improve the quality and diversity of the initial solution at the same time. S4. Perform multi-objective fitness evaluation on individuals in the population and execute fast non-dominated sorting to obtain multiple Pareto layers; S5. Calculate the improved dynamic congestion degree in each layer. The congestion degree is determined by combining the traditional congestion distance, the statistical measure of the difference between the targets in the same layer and the proportion of contemporary feasible solutions. When the number of individuals in the layer exceeds the limit, the congestion degree is reduced in order from small to large. The congestion degree is updated immediately after each reduction. S6. Under the premise of ensuring feasibility, perform constraint-aware crossover and goal-oriented progressive mutation. Crossover is only performed between segments that can be spliced ​​and do not cross obstacles. Mutation is advanced in the direction pointing to the endpoint and the step size decreases with iteration. Individuals that violate the constraints are locally repaired or rolled back. S7. Employ an elite retention strategy to merge the parent and offspring generations and truncate the next generation based on the non-dominated hierarchy and dynamic crowding. S8. When the coverage index improves below the threshold or reaches the maximum number of generations within the preset number of generations, the process terminates, outputs the Pareto solution set, and provides a recommended path based on the knee point or preference criterion.

2. The method according to claim 1, characterized in that, Multi-objective optimization is expressed as: minF(x)={f1(x),f2(x),…,f m (x)∣x∈X}, And satisfy the constraint set: X={x∣h j (x)≥0,j=1,…,J;g k (x)=0,k=1,…,K}; Where: x is the decision variable (path encoding); X is the feasible solution set; m is the number of objectives; h j (.) represents the j-th inequality constraint; g k (.) represents the k-th equality constraint; And / or, the workspace and feasible area satisfy: WITH f =ZZ o , Waypoints and endpoints satisfy: x i =(x i ,y i )∈Z、p1=p s ,p m =p D ; Where: Z represents the workspace; Z o For the set of obstacles; Z f This is a feasible region; p s ,p D These are the starting point and the ending point, respectively.

3. The method according to claim 1, characterized in that, The target path length is: Where: L is the total length; L i m is the Euclidean distance between adjacent waypoints; m is the number of waypoints. And / or, the path smoothness objective is: θ i =atan2(y i ―y i―1 ,x i ―x i―1 ), Dth i =|θ i+1 ―θ i |; Where: Θ represents the cumulative heading change; θ i Let Δθ be the heading angle of the i-th segment. i The difference in heading between adjacent segments; And / or, driving safety is achieved using a piecewise risk function: Wherein: H i For the risk at point i; h CiO h is the distance from the vehicle's center of gravity to the nearest obstacle's center of gravity. min ,h max To achieve the minimum safety and maximum radius of influence; And / or, the formula for calculating the radius of the risk circle for intelligent vehicles and obstacles is: Safety constraints in intelligent vehicle path planning: Where: h cl ,h cw h represents the vehicle's length and width. ol ,h ow The length and width of the obstacle; The center of mass of the obstacle; And / or, intelligent vehicle path planning in p i Formulas for calculating the curvature and turning radius of a point: The minimum turning radius limit for the kinematic constraints of intelligent vehicles is as follows: R i ≥R min ; Wherein: κ i Let ΔL be the curvature of the i-th segment; i R is the length of this segment. i R is the turning radius; min This is the minimum turning radius threshold; And / or, the model for dynamic obstacles is as follows: x d+1 =x d (t)+v d cosθ d , and d+1 / and d (t)+v d sinθ d ; Where: (x d ,y d ) represents the current position of the obstacle; v d θ is a velocity scalar; d The direction angle of motion; the subscript d+1 indicates the next moment.

4. The method according to claim 1, characterized in that, wherein... There are a total of M objective functions, namely f1, f2, ..., f M Then each individual X i The fitness value is expressed as: F i =(f1(X i ),…,f M (X i )), f j (X i Individual X i Fitness on the j-th objective function; And / or, the non-dominated sorting process is as follows: First, for each individual X in the population... i Calculate the number of times n it is dominated by other individuals. i and the set of individuals S it governs i Secondly, all n i Individuals with a value of 0 are assigned to the first Pareto front F. i Next, after removing individuals from F1, repeat the above process for the remaining individuals to obtain F2, F3L in sequence, until all individuals are assigned to the corresponding frontier. And / or, for each Pareto front F k The steps for calculating the crowding distance are as follows: For F k The individuals in the dataset are sorted according to each objective function value; for each individual X i In F k In this process, the distances between adjacent individuals on each objective function are calculated, and the crowding distance is obtained by summing them: Where: S is the current population; M is the target number; f m max ,f m min This represents the maximum / minimum value of the target at the same level.

5. The method according to claim 1, characterized in that, The RRT-A* hybrid initialization population strategy includes the following steps: 1) First, use the A* algorithm to generate three initial solutions POPs of the shortest distance from the specified starting point to the target point at three different grid resolutions. Ai Then, the paths at all resolutions are resampled onto a grid of the same resolution to ensure that the paths have a consistent location representation in the same environment; 2) Use the path generated by A* as the initial tree for RRT, expand the path using dynamically adjusted step size and random sampling sequence, and select nodes R from the initial path. i As the starting point for RRT path planning, generate p init - 3 mutation paths Backtracking R i Previous paths and new variant paths Store it in POP Ri middle; 3) Merge POPs Ai With POP Ri This forms the final initial population POP. init .

6. The method according to claim 1, characterized in that, The improved dynamic congestion satisfies: or Among them: ADCD i V represents the adaptive dynamic crowding distance for the lower i individuals. rni It is the variance of the crowding distance to the i-th neighboring individuals, representing the ADCD of the i-th individual. i The dispersion of crowding distance indicates the degree of difference in crowding distance across different target dimensions; N o For adjacent items on the same level; N obj The number of target dimensions; And / or, the optimization of fitness path crossover operation process is as follows: Input: A set of paths to be intersected. p =[P S ,P1,L,P n ,P D ],path q =[P S ,P1',L,P m ',P D ], An environment raster map containing obstacles: map; Output: A set of intersecting paths: path p ',path q '; 1) Find the path with fewer nodes and set it as the path. pc The other one is set as path qc ; 2) In path pc Choose an intermediate point P i , in path qc Find the distance P i The nearest point P j ; 3) P i With P j Set as a pair of corresponding points (P) i_pair ,P' j_pair ); 4) If CollisionFree((P i-1 ,P' j_pair ),(P' j_pair ,P i+1 ),(P' j-1 ,P i_pair ),(P i_pair ,P' j+1 If )) is true, then: if but: Otherwise if but: And / or, the goal-oriented incremental path mutation operation model is as follows: For a certain mutation point P in the path i Its mutation direction is from the target point P t Determining that the new path point P is determined i Compared to the original path point P i Closer to the target area: Where: p i / p i 'Represents waypoints before and after the mutation; p t Let α be the target point; α be the variable asynchronous length; α max ,α min This represents the initial step size and the final step size, t is the current iteration number, and T is the maximum iteration number.

7. The method according to claim 1, characterized in that, The performance evaluation methods of the method include one or more of the following: 1) Hypervolume metric In the D-dimensional solution space, suppose S = {s1, s2, ..., s} n As a set of non-dominated solutions, ref={r1,r2,L,r n } As a reference point for the corresponding scene map, the value of Hv is obtained by the following formula: Where L refers to the Lebesgue measure used to calculate the volume[89], h(a i ) indicates that by a i The hypercube is composed of a reference point and a reference point. The reference point refers to the combination of worst-case scenarios corresponding to different objectives, that is, the worst-case values ​​of path length, path safety, and path smoothness obtained in the simulation experiment. 2) SC Collection Coverage Indicators Let A = {a1, a2, ..., a} n } and B={b1,b2,L,b m Let} be two approximate sets close to the Pareto front. SC(A,B) is the proportion of non-dominated solutions in B dominated by non-dominated solutions in A, i.e.: Where |B| represents the total number of solutions in the solution set B; if SC(A,B)=1, it means that all non-dominated solution sets in B are dominated by the non-dominated solution sets in solution set A, indicating that each solution in the solution set B is completely covered by solution set A; if SC(A,B)=0, it means that none of the non-dominated solution sets in B are dominated by the non-dominated solution sets in A. 3) The number of non-dominated solutions in the NNS neighborhood and the proportion of non-dominated solutions in the RNS neighborhood Assume S i ={S1,S2,L,S n The non-dominated solution set is obtained by calculating different algorithms. This represents the combined solution set of the Pareto front solutions obtained by the above five algorithms, for S I By performing non-dominated sorting, we obtain the comprehensive Pareto front for multi-objective path planning in different scenarios, NNS(S i ) represents S i The number of solutions in the solution set that are not dominated by other solutions in the synthesized Pareto solution set S, i.e.: Where yf x represents the solution y governing the solution x, NNS(S i The larger the value of S, the greater the value of S. i The solution set generated by the corresponding algorithm is in the solution set S of all algorithms. I It occupies more non-dominant positions in the Pareto front solution set S, and has higher coverage quality; The RNS index represents S i The proportion of non-dominated solutions in the overall Pareto solution set S; the calculation formula is as follows: RNS(S i The larger the value of ), the stronger the solution set S. i The higher the proportion of undominated solutions in the integrated Pareto front solution set, the higher the nondomination and diversity of the solution set generated by the algorithm.

8. A multi-objective path planning system for implementing the method of any one of claims 1–7, comprising: The module includes: map and feasible region construction module, goal and constraint evaluation module, RRT-A* hybrid initialization module, fitness calculation and non-dominated sorting module, dynamic congestion maintenance module, constraint-aware crossover module, goal-oriented progressive mutation module, parent-child merging and elite retention module, and quality assessment and termination determination module. Its processor executes the module, and the memory stores the set {m,J,K,R} therein. min ,h min ,h max ,α max ,α min ,N,T} and output the Pareto solution set and recommended path.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by a processor, it implements the method of any one of claims 1–7.

10. A computer program product, comprising a computer program or instructions, characterized in that, When the computer program or instructions are executed by a processor, they implement the method of any one of claims 1–7.

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