A vehicle path planning method, system and terminal based on a circle search algorithm

Abstract

The application belongs to the technical field of intelligent computing, and discloses a vehicle path planning method, system and terminal based on a circle search algorithm. First, a population is divided into a main group and an assisting group at a certain ratio. The main group adopts a multi-scale control factor strategy, divides the whole evolution process into multiple stages, adopts different control factors, and realizes the alternative search of the global and local. The assisting group learns from the group optimal solution and the global optimal solution, and sets an adaptive learning step length. In the early stage, the convergence speed is accelerated, and in the later stage, the algorithm can stably converge when approaching the optimal solution, realizing the cooperative evolution of the main group and the assisting group. A destruction operator and a repair operator are used to perform local search on the solution, and a better solution is obtained. Until the iteration is completed, the optimal path is generated. Through the method, the solving effect of the vehicle path planning problem with capacity constraints can be effectively improved.

Description

Technical Field

[0001] This invention belongs to the field of intelligent computing technology, and in particular relates to a vehicle path planning method, system and terminal based on a circle search algorithm. Background Technology

[0002] The Vehicle Routing Problem (VRP) is a classic NP-hard problem. It involves scheduling a fixed number of vehicles between different origins and destinations, ensuring that each customer point is visited at least once, and minimizing the vehicle's travel distance or cost. The VRP has wide applications in logistics, transportation, and distribution. Solving this problem can effectively save transportation costs and improve transportation efficiency, thus attracting widespread attention from academia and industry.

[0003] Methods for solving the VRP problem mainly include two types: exact algorithms and heuristic algorithms. Exact algorithms, typically based on integer programming or branch and bound methods, guarantee finding the optimal solution, but their long computation time limits their application to large-scale problems. Heuristic algorithms, on the other hand, emphasize a balance between solution speed and solution quality, including genetic algorithms, simulated annealing, and tabu search. They often obtain a relatively good solution by optimizing a local part of the problem.

[0004] It is generally believed that NP-hard problems are difficult to solve using exact algorithms. Therefore, heuristic and metaheuristic algorithms are employed. Heuristic algorithms search using heuristic information based on experience and intuition, quickly finding approximate optimal solutions. Unlike exact algorithms, heuristic algorithms do not guarantee finding the global optimum, but they can usually find a good solution in a relatively short time. Heuristic algorithms are not well-suited for high-dimensional problems, while the high-dimensional complexity of real-world problems has led to increased attention on metaheuristic algorithms in optimization research. Metaheuristic algorithms are commonly used to solve NP-hard problems and large-scale combinatorial optimization problems. They possess good adaptability and robustness, enabling them to effectively solve problems in practical applications. Metaheuristic algorithms are algorithms inspired by nature or biology. The most popular metaheuristic algorithms include genetic algorithms, particle swarm optimization, artificial bee colony optimization, ant colony optimization, and Harris Eagle algorithm.

[0005] The Circle Search Algorithm (CSA) is a novel metaheuristic algorithm proposed by Mohammed H. Qais et al. in 2022. It can be categorized as a geometry-based metaheuristic method. CSA searches for the optimal solution within a random circle to expand the search range. With the center of the circle as the target point, the angle between the contact point of the tangent and the circumference gradually decreases until it approaches the center, at which point the angle of contact between the tangent and the contact point changes randomly. The contact point X... tConsider it as the search population of CSA, and assume the center point X c This is the optimal position in the algorithm. CSA updates the search population in response to contact point X. t The movement proceeds towards the center. However, to prevent CSA from getting stuck in local solutions, the contact point is updated randomly by changing the angle. A circle is the most commonly used geometry because of its unique properties, such as diameter, circumference, center point, and tangent. The radius passing through the tangent point is perpendicular to the tangent, and the orthogonal function is the ratio of the radius to the perpendicular tangent. The orthogonal function changes significantly with small changes in angle, which can speed up the CSA probing phase.

[0006] Existing vehicle routing methods have the following drawbacks in industrial applications:

[0007] High computational complexity: The vehicle routing problem is an NP-hard problem, and exact algorithms typically need to traverse the entire solution space, causing computation time to increase exponentially with problem size. This limits the application of exact algorithms to large-scale problems, especially in real-time or near-real-time scenarios.

[0008] Low computational efficiency: While heuristic algorithms can find good solutions in a short time, they cannot guarantee finding the global optimum. In some cases, heuristic algorithms may get stuck in local optima, failing to find the optimal path or a suboptimal solution.

[0009] Not suitable for high-dimensional problems: Heuristic algorithms typically perform poorly on high-dimensional problems. The dimensionality of the vehicle routing problem stems from factors such as the number of vehicles, customer points, and time windows, causing the problem's complexity to increase with dimensionality. Existing heuristic algorithms may not find satisfactory solutions for high-dimensional problems.

[0010] Lack of robustness: Some heuristic algorithms are sensitive to the choice of input parameters and initial solutions. Small changes can cause the algorithm to produce unstable results. This can be problematic in practical applications because input parameters can be affected by uncertainty and change.

[0011] To address the above problems, existing technologies need to solve the following technical issues:

[0012] Developing efficient solution algorithms: Efficient algorithms need to be designed and developed to solve large-scale vehicle routing problems. These algorithms should be able to find near-optimal solutions within a reasonable timeframe to meet the needs of practical applications.

[0013] Improving the performance of heuristic algorithms: Existing heuristic algorithms need to be improved to enhance their performance and solution quality for high-dimensional problems. This may involve research on algorithm improvements, parameter tuning, and improvements to initial solutions.

[0014] Developing new algorithms applicable to high-dimensional problems: It is necessary to explore novel metaheuristic algorithms to address high-dimensional vehicle pathing problems. These algorithms should possess good adaptability and robustness, enabling them to effectively solve problems in practical applications.

[0015] Considering practical constraints and variations: Vehicle routing problems typically involve many practical constraints, such as vehicle capacity, time windows, and road congestion. Existing technologies need to better consider these practical constraints and adapt to real-time changes in order to provide feasible and optimized route planning solutions.

[0016] In summary, existing technologies for solving the vehicle routing problem suffer from drawbacks such as long computation time, low computational efficiency, inapplicability to high-dimensional problems, and lack of robustness. To address these issues, it is necessary to develop efficient solution algorithms, improve the performance of heuristic algorithms, develop new algorithms suitable for high-dimensional problems, and consider practical constraints and variations. This will promote the further application and development of the vehicle routing problem in industrial applications. Summary of the Invention

[0017] To address the problems existing in the prior art, this invention provides a vehicle path planning method, system, and terminal based on a circle search algorithm.

[0018] This invention is implemented as follows: a vehicle path planning method based on a circle search algorithm, comprising:

[0019] S1: Set the population size SearchAgents_no, maximum number of iterations MaxIter, number of dimensions dim, initial number of vehicles v_num, maximum vehicle load cap, and penalty factor β;

[0020] S2: Real number encoding is used, with each real number limited to [1, v_num]. The integer part of the real number represents the service vehicle, and the fractional part represents the path order of the vehicle service. Random real numbers within the initial generation range are used as the initial population. A dual-population strategy is adopted, dividing the population into two parts, population S = S_num. m ∪S s S m Main group, S s To assist the group;

[0021] S3: Calculate the fitness function value for each individual in the initial population based on the fitness function formula. The fitness value represents the total distance traveled by the vehicle along the path. Based on the fitness function value of each individual in the initial population, calculate S... m and S s The individual with the best fitness is assigned a value to S. m The optimal individual in the group, main_Group and Ss The optimal individual in the group, assistant_Group, has fitness denoted as main_fit and assistant_fit, respectively. The fitness function formula is:

[0022]

[0023] Where K represents the number of vehicles, N represents the number of customers, and d ij This represents the distance from vertex i to vertex j. This indicates whether there exists a path between vertex i and vertex j for vehicle k. If so, The value is 1 if it does not exist. q is 0; β represents the penalty factor, which is used to add a positive penalty value to the fitness value of a path when the path violates the capacity constraint. i This represents the demand of customer i. This indicates whether the customer is in vehicle k. It is 1 if it is true, otherwise it is 0.

[0024] S4: Calculate the main group S m The next generation position of the individual:

[0025] X t+1 =X c +(X c -X t )×tan(θ);

[0026] Among them, X t X is the current solution. c It is the globally optimal solution;

[0027] S5: Computational assistance group S s The next generation position of the individual:

[0028]

[0029] Among them, X t X is the current solution. c It is the global optimal solution, step is the learning step size, main_Group is the best individual in the main group, and assistant_Group is the best individual in the assistant group;

[0030] S6: Use a local search heuristic algorithm to search X. t Update the solution to further improve its quality;

[0031] S7: Based on the fitness function formula in S3, calculate the fitness function value of each individual in the current population, and determine the global optimal solution and global optimal fitness value of each individual in the current population based on the fitness function value of each individual in the current population.

[0032] S8: Determine if the maximum number of iterations has been reached. If it has, proceed to step S9; otherwise, proceed to the next iteration and execute steps S3-S8.

[0033] S9: Output the solution with the minimum fitness value as the result of the vehicle path problem with capacity constraints.

[0034] Furthermore, in step S4, when calculating the next-generation position, different calculation methods are needed depending on the current iteration number. The formula for the specific update mechanism of the next-generation position is as follows:

[0035]

[0036]

[0037]

[0038] w = a × rand - a;

[0039]

[0040] The total number of iterations is MaxIter. The entire evolutionary process is divided into four segments, with each segment having T1 iterations. Different control factors are used in each segment: when Iter < T1, the control factor a decreases from λ1 + β1 to β1; when T1 < Iter < 2T1, the control factor a decreases from λ2 + β2 to β2; when 2T1 < Iter < 3T1, the control factor a decreases from λ3 + β3 to β3; and when 3T1 < Iter < MaxIter, the control factor a decreases from λ4 to 0. t It is the current individual, X c It is the global optimal solution, a is the control factor, Iter is the current iteration number, MaxIter is the maximum iteration number, and rand is a random number between 0 and 1. As the iteration number increases, the variable w changes from -π to 0, the variable a changes from π to 0, the variable p changes from 1 to 0, and the angle θ changes from -π to 0.

[0041] Furthermore, during iteration, as the number of iterations increases, the search focus gradually shifts from the global to the local. The constant c, used to control the balance between the local and global search, has three states:

[0042] State 1: c = 0, which causes the angle θ = w × rand. The angle at which the tangent contacts the point will change randomly, which makes the algorithm pay more attention to the global search process.

[0043] State 2: c = 1, which leads to angle θ = w × p, making the algorithm focus more on the local search process;

[0044] State 3: 0<c<1, which balances global search and local search;

[0045] During iteration, as the number of iterations increases, the search focus should gradually shift from global to local. At this time, the value of a should be appropriately reduced, so that the θ angle of the circular search algorithm is appropriately reduced.

[0046] Further, the assisting group in step S5 focuses on utilizing and learning from the existing optimal solution, simultaneously learning the global optimal individual and the historical optimal individuals, and converges to their arithmetic mean point. The expression of the learning step size step is:

[0047]

[0048] Wherein, ξ is used to control the random part, and the range of the random part is [0,ξ]; ζ is used to control the fixed step size, so that the entire learning step size is within [ζ,ξ+ζ]; the size of the learning step size is automatically adjusted according to the current number of iterations in the optimization process, so that the step size gradually decreases, which accelerates the convergence speed of the algorithm in the early stage and ensures stable convergence of the algorithm when approaching the optimal solution in the later stage.

[0049] Further, the local search operation in step S6 includes a remove operator and an insert operator, and the strategy of the remove operator is as follows:

[0050] Randomly select a customer from the original customer set, calculate the correlation between the selected customer and other customers, and then remove the customers in descending order of correlation according to the number of customers to be removed. Wherein the expression for the correlation between customer i and customer j is:

[0051]

[0052]

[0053] Wherein, Relateness(i,j) is the correlation between customer i and customer j, c ij represents the Euclidean distance from customer i to customer j, c ij * represents the standardized value of c ij , when customer i and customer j are not on the same route, V ij = 1; if they are on the same route, V ij = 0;

[0054] Further, a random element is added during the removal process, and the expression is:

[0055] index = (Random([0,1])) D ×Remain_cusnum;

[0056] D is adjustable. When D=1, the customers removed are selected completely randomly. The larger D is, the more favorable it is to customers with high relevance. Remain_cusnum is the number of customers remaining in the current solution.

[0057] The Insert operator strategy is as follows:

[0058] The removed customer is reinserted into the new solution. Using the farthest insertion heuristic, all insertion points that satisfy the capacity constraint are first found. Then, the distance increment of all the above insertion points is calculated. The point with the smallest distance increment among the above insertion points is found. If it exists, the point with the smallest distance increment is found as the optimal insertion point. Otherwise, a new car is added.

[0059] Another objective of this invention is to provide a vehicle routing system based on the circle search algorithm, which applies the aforementioned vehicle routing method. The vehicle routing system based on the circle search algorithm includes:

[0060] The parameter setting module is used to set the required parameters;

[0061] The population classification module is used to divide a population into two parts using a two-population strategy, where population S = S0 m ∪S s S m Main group, S s To assist the group;

[0062] The fitness calculation module is used to calculate the fitness function value of each individual in the initial population according to the fitness function formula.

[0063] The main group position calculation module is used to calculate the main group S. m The next generation position of an individual;

[0064] The assist group position calculation module is used to calculate the assist group S. s The next generation position of an individual;

[0065] The update module is used to update X using a local search heuristic algorithm. t Update the solution to further improve its quality;

[0066] The global optimal solution determination module is used to calculate the fitness function value of each individual in the current population, and determine the global optimal solution and global optimal fitness value of each individual in the current population based on the fitness function value of each individual in the current population.

[0067] The output module is used to output the solution with the minimum fitness value as the result of the vehicle path problem with capacity constraints.

[0068] Another object of the present invention is to provide a computer device, the computer device including a memory and a processor, the memory storing a computer program, which, when executed by the processor, causes the processor to perform the steps of the vehicle path planning method based on the circle search algorithm.

[0069] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the vehicle path planning method based on the circle search algorithm.

[0070] Another objective of this invention is to provide an information data processing terminal for implementing the vehicle path planning system based on the circle search algorithm.

[0071] Based on the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solution to be protected by this invention are as follows:

[0072] First, this invention proposes an improved circle search algorithm and applies it to the vehicle path planning problem with capacity constraints. This algorithm combines a multi-scale control factor strategy, a dual-population co-evolution strategy, and an adaptive learning step size strategy. Comparison with other algorithms on 23 standard benchmark functions shows that the improved circle search algorithm outperforms other algorithms in some test functions, exhibiting a smaller fitness value, significantly improving performance, and balancing convergence speed and accuracy. This verifies the superiority of the improved circle search algorithm.

[0073] This invention employs a novel metaheuristic algorithm to more effectively solve the vehicle routing optimization problem. Furthermore, the algorithm's parameters can be adjusted as needed to determine whether it favors global or local search to achieve the desired results. The improved circular search algorithm, to a certain extent, better balances exploration and development during the evolutionary process, resulting in shorter travel distances and fewer vehicles when solving the vehicle routing optimization problem.

[0074] Second, when calculating the next generation position, this invention divides the population into a main group and a helper group. The main group utilizes a multi-scale control factor strategy to achieve alternating global and local searches during the evolutionary process, enabling exploration and utilization at each stage and preventing the population from stagnation. The helper group learns from existing optimal solutions and can directly learn from the best individuals in the main group or the helper group. It has an adaptive learning step size, which can be adaptively adjusted according to the number of iterations to gradually decrease the step size. This accelerates the convergence speed of the algorithm in the early stages and ensures that the algorithm can converge stably when it is close to the optimal solution in the later stages. Furthermore, a local search method is used to further improve the quality of the solution.

[0075] Third, the expected benefits and commercial value of the technical solution of this invention after transformation are as follows: cost savings and efficiency improvement: By optimizing vehicle routes, this invention can reduce the total travel distance and time, thereby saving fuel costs, vehicle maintenance costs, and labor costs. Furthermore, reducing travel time can improve transportation efficiency and provide faster service, achieving more efficient operation management and reducing unnecessary travel distance and time consumption. This will make the logistics process smoother, reduce unnecessary waiting and stoppages, and improve overall transportation efficiency.

[0076] Improved resource utilization: This invention allows for better planning of vehicle routes, ensuring that each vehicle's transportation tasks are fully utilized. This will reduce empty runs and redundant trips, improving the utilization rate of vehicles and human resources.

[0077] Reducing carbon emissions and environmental impact: Optimizing routes can help reduce travel distance and time, thus reducing carbon emissions from vehicles. This aligns with environmental protection and sustainable development requirements and has a positive impact on corporate image and social responsibility.

[0078] Enhancing customer satisfaction and loyalty: Optimized route planning improves on-time and accuracy delivery, better meeting customer needs. Providing reliable and efficient service increases customer satisfaction, fosters loyalty, and can lead to repeat business and positive word-of-mouth.

[0079] Fourth, the significant technological advancements in each step of the vehicle path planning method based on the circle search algorithm are as follows:

[0080] 1) S1 (Parameter Settings):

[0081] Parameterizing the algorithm allows it to adapt to problems of different scales and characteristics, enhancing the method's versatility and flexibility.

[0082] 2) S2 (Population Initialization and Segmentation):

[0083] Employing real-number encoding, combined with the order of vehicles and service paths, makes the solution representation more compact and efficient. The dual-population strategy further enhances the diversity of the search and reduces the risk of getting trapped in local optima.

[0084] 3) S3 (Calculate initial fitness):

[0085] The fitness function introduces capacity constraints and a penalty mechanism, which effectively takes into account the capacity limitations of vehicles and prevents the generation of illegal solutions through the penalty strategy, thereby improving the stability of the algorithm.

[0086] 4) S4 (Calculate the next generation position of the main group):

[0087] By considering the global optimal solution, the main group is always optimized towards the global optimal direction during the search process, which accelerates the convergence speed of the algorithm.

[0088] 5) S5 (Calculate the next generation position of the cooperative group):

[0089] By combining the learning step size and two optimal individuals, the assisting group helps to explore a wider solution space, enhancing the algorithm's global search capability.

[0090] 6) S6 (Local Search Heuristic Algorithm):

[0091] The local search strategy further optimizes the quality of the solution and improves the accuracy of the final solution.

[0092] 7) S7 (Update Global Optimal Solution):

[0093] By updating the global optimal solution in real time, the algorithm is always searching in the most promising region, which enhances its optimization performance.

[0094] 8) S8 (Check termination condition):

[0095] Setting clear termination conditions ensures that the algorithm terminates in a timely manner after achieving the expected results or meeting specific conditions, thus improving the algorithm's efficiency.

[0096] 9) S9 (Output Result):

[0097] The optimal solution to the vehicle routing problem with capacity constraints is obtained, providing executable path planning results for practical applications and realizing the transformation from theory to practice.

[0098] This vehicle routing method based on the circle search algorithm has achieved significant technological advancements in several aspects, including algorithm strategy, solution representation, search efficiency, and fitness evaluation, giving it strong advantages and application value in solving practical vehicle routing problems.

[0099] Fifth, this vehicle path planning method based on the circle search algorithm has the following significant technological advancements:

[0100] Real-number encoding and dual-population strategy: The real-number encoding method transforms the vehicle routing problem into a real-number optimization problem, improving the solution efficiency. Simultaneously, a dual-population strategy is introduced, increasing the diversity of the search and global search capabilities through the cooperation of the main group and the assisting group.

[0101] Fitness function design: A fitness function was designed by comprehensively considering factors such as vehicle travel distance, path constraints, and capacity constraints. This function can accurately evaluate the path planning quality of each individual and penalize paths that violate constraints according to the penalty factor, thereby obtaining a better path planning scheme.

[0102] Cooperative optimization of the main group and the assistant group: When calculating the next generation position of individuals in the main group and the assistant group, the influence of the global optimal solution and the learning step size is considered. Through the interaction between the main group and the assistant group, the individual position is optimized and updated, which improves the convergence speed and solution quality of the algorithm.

[0103] Local search heuristic: Introducing a local search heuristic allows for local optimization of individual solutions, further improving solution quality. Local search enables in-depth searching within local regions of the solution space, helping the algorithm escape local optima and find better solutions.

[0104] Thanks to these technological advancements, vehicle routing methods based on the circle search algorithm can efficiently solve large-scale vehicle routing problems in industrial applications and yield high-quality routing solutions. These advancements improve the efficiency, accuracy, and robustness of routing planning, which is of great significance for optimizing logistics transportation, reducing costs, and improving service quality. Attached Figure Description

[0105] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments of the present invention will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0106] Figure 1 This is a flowchart of the vehicle path planning method based on the circle search algorithm provided in an embodiment of the present invention;

[0107] Figure 2 This is a schematic diagram of the real number encoding and decoding method provided in an embodiment of the present invention;

[0108] Figure 3 These are fitness value variation curves of different methods provided in the embodiments of the present invention on the test function; where (a) F1, (b) F13. Detailed Implementation

[0109] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0110] To address the problems existing in the prior art, this invention provides a vehicle path planning method, system, and terminal based on a circle search algorithm. The invention will be described in detail below with reference to the accompanying drawings.

[0111] like Figure 1As shown, this embodiment of the invention provides a vehicle path planning method based on a circle search algorithm, including:

[0112] S1: Set the population size SearchAgents_no, maximum number of iterations MaxIter, number of dimensions dim, initial number of vehicles v_num, maximum vehicle load cap, and penalty factor β;

[0113] S2: Real number encoding is used, with each real number limited to [1, v_num]. The integer part of the real number represents the service vehicle, and the fractional part represents the path order of the vehicle service. Random real numbers within the initial generation range are used as the initial population. A dual-population strategy is adopted, dividing the population into two parts, population S = S_num. m ∪S s S m Main group, S s To assist the group;

[0114] S3: Calculate the fitness function value for each individual in the initial population according to the fitness function formula. Based on the fitness function value of each individual in the initial population, assign S... m and S s The individual with the best fitness is assigned a value to S. m The optimal individual in the group, main_Group and S s The optimal individual in the group, assistant_Group, has fitness denoted as main_fit and assistant_fit, respectively. The fitness function formula is:

[0115]

[0116] Where K represents the number of vehicles, N represents the number of customers, and d ij This represents the distance from vertex i to vertex j. This indicates whether there exists a path between vertex i and vertex j for vehicle k. If so, The value is 1 if it does not exist. The value is 0. β represents the penalty factor, which is used to add a positive penalty value to the fitness value of a path when it violates the capacity constraint. i This represents the demand of customer i. This indicates whether the customer is in vehicle k. It is 1 if it is true, otherwise it is 0.

[0117] S4: Calculate the principal group S using the following formula. m The next generation position of the individual:

[0118] X t+1 =X c +(X c -Xt )×tan(θ)

[0119] Among them, X t X is the current solution. c It is the globally optimal solution.

[0120] S5: Calculate the cooperative group S using the following formula. s The next generation position of the individual:

[0121]

[0122] Among them, X t X is the current solution. c It is the global optimal solution, step is the learning step size, main_Group is the best individual in the main group, and assistant_Group is the best individual in the assistant group.

[0123] S6: Use a local search heuristic algorithm to search X. t Update the solution to further improve its quality;

[0124] S7: Based on the fitness function formula in S3, calculate the fitness function value of each individual in the current population, and determine the global optimal solution and global optimal fitness value of each individual in the current population based on the fitness function value of each individual in the current population.

[0125] S8: Determine if the maximum number of iterations has been reached. If it has, proceed to step S9; otherwise, proceed to the next iteration and execute steps S3-S8.

[0126] S9: Output the solution with the minimum fitness value found by the algorithm as the result of the vehicle path problem with capacity constraints.

[0127] Several conditions must be considered when solving this problem:

[0128] (1) The vehicle departs from the warehouse and returns to the warehouse;

[0129] (2) The vehicle visits only one customer on a single trip, then returns to the starting point (i.e., the warehouse), and then proceeds to another customer;

[0130] (3) Customers may not request delivery from multiple vehicles.

[0131] (4) The cargo capacity of each vehicle shall not exceed its maximum cargo capacity.

[0132] In one implementation, when calculating the next-generation position in step S4, different calculation methods are needed depending on the current iteration number. The specific update mechanism for calculating the next-generation position is shown in the following formula:

[0133]

[0134]

[0135]

[0136] w=a×rand-a

[0137]

[0138] Wherein, the total number of iterations is MaxIter, the entire evolution process is divided into 4 stages, and the number of iterations of each stage is set as T1. The population adopts different control factors in each stage. When Iter<T1, the control factor a decreases from λ1+β1 to β1; when T1<Iter<2T1, the control factor a decreases from λ2+β2 to β2; when 2T1<Iter<3T1, the control factor a decreases from λ3+β3 to β3; when 3T1<Iter<MaxIter, the control factor a decreases from λ4 to 0; X t is the current individual, X c is the global optimal solution, a is a control factor, Iter is the current number of iterations, MaxIter is the maximum number of iterations, and rand is a random number between 0 and 1; as the number of iterations increases, the variable w changes from -π to 0, the variable a changes from π to 0, the variable p changes from 1 to 0, and the angle θ changes from -π to 0.

[0139] During iteration, as the number of iterations increases, the search focus gradually shifts from global search to local search. There are three following states for the constant c that controls and balances local search and global search:

[0140] State 1: c=0, which results in the angle θ=w×rand, the tangent contact angle at the point will change randomly, so that the algorithm pays more attention to the global search process;

[0141] State 2: c=1, which results in the angle θ=w×p, so that the algorithm pays more attention to the local search process;

[0142] State 3: 0<c<1, which balances global search and local search;

[0143] During iteration, as the number of iterations increases, the search focus needs to be gradually shifted from global search to local search. At this time, the value of a should be appropriately reduced, so that the θ angle of the circular search algorithm is appropriately reduced, and thus the algorithm tends to perform local exploitation.

[0144] In one embodiment, the assistance group in step S5 focuses on utilizing and learning the existing optimal solution, simultaneously learns the global optimal individual and the historical optimal individual of the population, and converges to the arithmetic average point thereof. The expression of the learning step step is:

[0145]

[0146] Here, ξ controls the random component, which ranges from [0, ξ], and ζ controls the fixed step size, ensuring the entire learning step size is within [ζ, ξ + ζ]. The learning step size is automatically adjusted based on the current iteration count in the optimization process, gradually decreasing to accelerate convergence in the early stages and ensure stable convergence near the optimal solution in the later stages.

[0147] In one implementation, the local search operation in step S6 includes a remove operator and an insert operator, and the remove operator strategy is as follows:

[0148] A customer is randomly selected from the existing customer set. The correlation between this customer and other customers is calculated. Then, based on the required number of customers to be removed, customers with the highest correlation are removed in descending order. The expression for the correlation between customer i and customer j is:

[0149]

[0150]

[0151] Where Relateness(i,j) is the correlation between customer i and customer j, c ij c represents the Euclidean distance from customer i to customer j. ij * This means c ij The standardized value, V, is used when customer i and customer j are not on the same path. ij =1; if on the same path, V ij =0;

[0152] In practice, customers who are closer in Euclidean distance are more correlated than those who are farther apart; customers on the same path are more correlated than those on different paths. If customers are selected solely based on correlation, the same customers might be repeatedly selected. To avoid this, a random element is added during the removal process, expressed as:

[0153] index = (Random([0,1])) D ×Remain_cusnum

[0154] D is adjustable. When D=1, the customers removed are selected completely randomly. The larger D is, the more favorable it is to customers with high relevance. Remain_cusnum is the number of customers remaining in the current solution.

[0155] The Insert operator strategy is as follows:

[0156] The removed customer is reinserted into the new solution. Using the farthest insertion heuristic, all insertion points that satisfy the capacity constraint are first found. Then, the distance increment of all the above insertion points is calculated. The point with the smallest distance increment among the above insertion points is found. If it exists, the point with the smallest distance increment is found as the optimal insertion point. Otherwise, a new car is added.

[0157] Calculate the fitness value for the new solution after using local search. If the fitness value is smaller than the original solution, update the current position and the fitness value of the current position.

[0158] In the specific implementation process, benchmark test function parameters were set, and 23 benchmark test functions were used to verify the improved algorithm. The population size and maximum number of iterations for all algorithms were set to 30 and 500, respectively. The parameters of the control algorithms were all set to default values. The numerical efficiency of the ICSA algorithm was verified by solving the classic benchmark functions used in the 23 optimization literature. The benchmark test functions were divided into unimodal functions, multimodal functions, and fixed-dimensional multimodal functions. During testing, the optimization algorithm was used to find the global minimum fitness, making the test results as close as possible to the theoretical minimum fitness. The algorithm was run 50 times on each benchmark function.

[0159] II. Application Examples. To demonstrate the inventiveness and technical value of the technical solution of this invention, this section provides application examples of the technical solution of the claims on specific products or related technologies.

[0160] An application embodiment of the present invention provides a computer device, which includes a memory and a processor. The memory stores a computer program, and when the computer program is executed by the processor, the processor performs the steps of a vehicle path planning method based on a circle search algorithm.

[0161] An application embodiment of the present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of a vehicle path planning method based on a circle search algorithm.

[0162] An application embodiment of the present invention provides an information data processing terminal, which is used to implement a vehicle path planning system based on a circle search algorithm.

[0163] III. Evidence of the Relevant Effects of the Embodiments. The embodiments of the present invention have achieved some positive effects during research and development or use, and indeed possess significant advantages compared to existing technologies. The following description, in conjunction with data, charts, and other materials from the experimental process, illustrates these advantages.

[0164] To verify the effectiveness of this invention, the method proposed in this embodiment is compared with different algorithms on Set_A instances of the ABEFMP dataset to evaluate the processing capabilities for solving CVRP problems of different scales. The Set_A benchmark is an important standard benchmark, containing 27 instances with 32 to 80 customers, which can test the ability of each algorithm to solve discrete combinatorial problems. These datasets can be found at https: / / neo.lcc.uma.es / vrp / vrp-instances / capacitated-vrp-instances / . The population size and maximum number of iterations in all algorithms are 30 and 500, respectively. Set_A contains the given 27 CVRP instances. The title of these instances is a substring (An) concatenated with the number of customers, followed by a substring (-k) concatenated with the number of vehicles. The main parts of these instances are the number of customers, the number of vehicles, the demand requested by each customer, a constant vehicle capacity (all models and all vehicles are set to 100), customer coordinates (x and y), and finally warehouse coordinates (x and y). The models started vary in dimension, with the number of customers ranging from 32 to 80. The number of vehicles is between 5 and 10.

[0165] Table 1 shows the comparison results of the selected algorithm on the Set_A dataset. The meanings of the abbreviations in Table 1 are as follows:

[0166] DE stands for Differential Evolution Algorithm, SSA for Sparrow Search Algorithm, PSO for Particle Swarm Optimization, APPE for Advanced Phasmatodea Population Evolution Algorithm (proposed in the paper "Advanced Phasmatodea Population Evolution Algorithm for Capacitated Vehicle Routing Problem"), and ICSA for Improved Circle Search Algorithm (proposed in this invention). The BKV term represents the most well-known value among the instances. Other terms represent the optimal fitness values ​​of each method on different instances.

[0167] Table 1. Performance comparison of the algorithm of this invention with other algorithms on dataset Set_A

[0168]

[0169]

[0170] As shown in Table 1, the vehicle path planning method based on the circle search algorithm of the present invention found a better solution than other algorithms in 24 out of 27 instances for the dataset Set_A.

[0171] Figure 3 The graphs show the fitness values ​​of the proposed method compared to Sparrow Search Algorithm (SSA), Whale Optimization Algorithm (WOA), Particle Swarm Optimization (PSO), and Chaotic Game Search Algorithm (CGO) on test functions F1 and F13. The graphs demonstrate that the proposed method exhibits superior fitness compared to the other four methods.

[0172] The vehicle routing method based on the circle search algorithm of this invention achieves state-of-the-art results in almost all small, medium, and large-scale instances compared to other metaheuristic algorithms. The method proposed in this invention can improve the time efficiency and accuracy of solving vehicle routing problems. The improved circle search algorithm of this invention has a smaller fitness value compared to other common optimization algorithms.

[0173] Example 1: Route planning for express delivery company vehicles

[0174] 1) Problem background and parameter settings: A courier company needs to plan delivery routes from a distribution center to 100 customer locations for its 10 courier vehicles (each with a capacity of 200kg).

[0175] 2) Initial population settings: Set the population size to 100, the maximum number of iterations to 500, the number of dimensions to 100, the initial number of vehicles to 10, the maximum vehicle load capacity to 200kg, and select an appropriate penalty factor according to S1.

[0176] 3) Population initialization and grouping: Based on the guidance of S2, an initial population is randomly generated and divided into a main population and a supporting population.

[0177] 4) Calculate the initial fitness: Calculate the initial fitness function value for each individual according to S3, and select the best individuals in the main group and the helper group.

[0178] 5) Iterative optimization: Calculate the next generation positions of the main group and the helper group using S4 and S5, and then update the population using the local search heuristic algorithm in S6.

[0179] 6) Update the global optimum: Update the global optimum in the population according to S7.

[0180] 7) Check the termination condition: Determine whether the maximum number of iterations has been reached based on S8.

[0181] 8) Output the result: According to S9, output the solution with the minimum fitness value, that is, the optimal delivery route for each delivery vehicle.

[0182] Example 2: Urban Public Transport Route Planning

[0183] 1) Problem background and parameter settings: A city bus system needs to plan transportation routes from the bus center to 150 bus stops for its 50 buses (each with a capacity of 50 people).

[0184] 2) Initial population settings: Set the population size to 150, the maximum number of iterations to 1000, the number of dimensions to 150, the number of vehicles to a fixed number of 50, the maximum vehicle capacity to 50 people, and select an appropriate penalty factor according to S1.

[0185] 3) Population initialization and grouping: Based on the guidance of S2, an initial population is randomly generated and divided into a main population and a supporting population.

[0186] 4) Calculate the initial fitness: Calculate the initial fitness function value for each individual according to S3, and select the best individuals in the main group and the helper group.

[0187] 5) Iterative optimization: Calculate the next generation positions of the main group and the helper group using S4 and S5, and then update the population using the local search heuristic algorithm in S6.

[0188] 6) Update the global optimum: Update the global optimum in the population according to S7.

[0189] 7) Check the termination condition: Determine whether the maximum number of iterations has been reached based on S8.

[0190] 8) Output the result: According to S9, output the solution with the minimum fitness value, that is, the optimal transportation route for each bus.

[0191] Both of these embodiments are specific applications of the original technical solution, applying the principles to actual transportation or delivery scenarios to obtain practical and effective vehicle routing solutions.

[0192] It should be noted that embodiments of the present invention can be implemented in hardware, software, or a combination of both. The hardware portion can be implemented using dedicated logic; the software portion can be stored in memory and executed by a suitable instruction execution system, such as a microprocessor or dedicated-design hardware. Those skilled in the art will understand that the above-described devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuitry such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field-programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of the above-described hardware circuitry and software, such as firmware.

[0193] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A vehicle path planning method based on a circle search algorithm, characterized in that, Combining the dual-population strategy and real coding, initial random real numbers represent vehicles and the order of their service paths, and then the fitness of each individual is calculated; the two strategies of the main population and the assisting population make the search more efficient, wherein individuals in the main population consider the global optimal solution, while the assisting population combines the learning step size and the optimal individuals of the two populations to determine the next position; a local search heuristic algorithm is combined to further optimize the quality of the solution, and the global optimal solution is continuously updated through the fitness function until the preset maximum number of iterations is reached; S1: Set the population size SearchAgents_no, maximum number of iterations MaxIter, number of dimensions dim, initial number of vehicles v_num, maximum vehicle capacity cap, and penalty factor. ; S2: Real number encoding is used, and the value of each real number is restricted to 1. The integer part of the real number represents the service vehicle, and the fractional part represents the path order of the vehicle service. An initial population of random real numbers within the generated range is used. A dual-population strategy is employed, dividing the population into two parts: the first part represents the service vehicle, and the second part represents the service path order. ,in Main group, To assist the group; S3: Calculate the fitness function value of each individual in the initial population according to the fitness function formula. Based on the fitness function value of each individual in the initial population, respectively... and The individual with the best fitness is assigned a value. The optimal individual in the group, main_Group, and The optimal individual in the group, assistant_Group, has fitness denoted as main_fit and assistant_fit, respectively. The fitness function formula is: ； Where K represents the number of vehicles and N represents the number of customers. This represents the distance from vertex i to vertex j. This indicates whether there exists a path between vertex i and vertex j for vehicle k. If so, The value is 1 if it does not exist. =0; This represents the penalty factor, which is used to add a positive penalty value to the fitness value of a path when the path violates the capacity constraint. This represents the demand of customer i. This indicates whether the customer is in vehicle k. It is 1 if it is true, otherwise it is 0. S4: Compute the main group The next generation position of the individual: ； in, This is the current solution. It is the globally optimal solution; S5: Computational Assistant Group The next generation position of the individual: ； in, This is the current solution. It is the global optimal solution, step is the learning step size, main_Group is the best individual in the main group, and assistant_Group is the best individual in the assistant group; S6: Use a local search heuristic algorithm to... Update the solution to further improve its quality; S7: According to the fitness function formula in S3, calculate the fitness function value of each individual in the current population, and determine the global optimal solution and the global optimal fitness value of the current population individuals according to the fitness function value of each individual in the current population; S8: Determine whether the maximum number of iterations is reached. If reached, perform step S9; otherwise, perform the next iteration and execute steps S3 to S8; S9: Output the solution with the minimum fitness value found as the result of the capacitated vehicle routing problem; When calculating the next-generation position in step S4, different calculation methods shall be adopted according to the current number of iterations, and the specific update mechanism formula for calculating the next-generation position is: ； ； ； ； ； The total number of iterations is MaxIter, and the entire evolutionary process is divided into 4 segments, with each segment having an iteration count of 100. In each phase, the group uses different control factors. At that time, control factor from Decrease to ;when At that time, control factor from Decrease to ;when At that time, control factor from Decrease to ;when At that time, control factor from Decrease to 0; It is the current individual. It is the globally optimal solution. The variable w is a control factor, where Iter is the current iteration number, MaxIter is the maximum iteration number, and rand is a random number between 0 and 1. As the iteration number increases, the variable w changes from... When variable a becomes 0, variable a changes from When the variable p changes from 1 to 0, the angle θ changes from 0 to 0. It becomes 0; The local search operation in step S6 includes a remove operator and an insert operator, and the strategy of the remove operator is as follows: Randomly select a customer from the original customer set, calculate the correlation between the selected customer and other customers, then remove customers in descending order of correlation according to the number of customers to be removed, wherein the expression of the correlation between customer i and customer j is: ； ； Where Relateness(i,j) is the correlation between customer i and customer j, c ij c represents the Euclidean distance from customer i to customer j. ij * This means c ij The standardized value, when customer i and customer j are not on the same path, If on the same path, .

2. The vehicle path planning method based on the circle search algorithm as described in claim 1, characterized in that, During iteration, as the number of iterations increases, the search focus gradually shifts from global search to local search, and there are three states of the constant c used to control and balance local search and global search: State 1: c=0, resulting in angle θ changes randomly, which makes the algorithm focus more on the global search process; State 2: c=1, resulting in angle This makes the algorithm focus more on the local search process; State 3: 0<c<1, which balances global search and local search; During iteration, as the number of iterations increases, the search focus should gradually shift from the global to the local. At this point, the search level should be appropriately reduced. The size of this makes the circle search algorithm... The angle should be appropriately reduced.

3. The vehicle path planning method based on the circle search algorithm as described in claim 1, characterized in that, The assisting population in step S5 focuses on learning and utilizing the existing optimal solution, learns both the population optimal individual and the historical optimal individual, and converges to their arithmetic average point. The expression of the learning step size step is: ； in, Used to control the random component, the range of which is... , Used to control a fixed step size, ensuring the entire learning step size is within a certain range. Based on the number of iterations in the current optimization process, the learning step size is automatically adjusted to gradually decrease, which speeds up the algorithm's convergence in the early stages and ensures that the algorithm can converge stably when it is close to the optimal solution in the later stages.

4. The vehicle path planning method based on the circle search algorithm as described in claim 1, characterized in that, Random elements are added during the removal process, and the expression is: ； D is adjustable. At that time, the customers removed are selected completely randomly; the larger D is, the more beneficial it is to customers with high relevance. It represents the number of customers remaining in the current solution; The strategy of the insert operator is as follows: Reinsert the removed customers back into the obtained new solution, adopt the farthest insertion heuristic: first find all insertion points that satisfy the capacity constraint, then calculate the distance increment of all the above insertion points, find the point with the minimum distance increment among the above insertion points, if such a point exists, take this point with the minimum distance increment as the optimal insertion point, otherwise add a new vehicle.

5. A vehicle routing system based on a circle search algorithm, applying the vehicle routing method based on the circle search algorithm as described in any one of claims 1 to 4, characterized in that, The vehicle routing planning system based on the circular search algorithm includes: a parameter setting module, configured to set required parameters; The population classification module is used to divide a population into two parts using a dual-population strategy. ,in Main group, To assist the group; a fitness calculation module, configured to calculate the fitness function value of each individual in the initial population according to the fitness function formula; The main group location calculation module is used to calculate the main group. The next generation position of an individual; The assistance group location calculation module is used to calculate the assistance group's location. The next generation position of an individual; The update module is used to perform local search heuristics on... Update the solution to further improve its quality; a global optimal solution determination module, configured to calculate the fitness function value of each individual in the current population, and determine the global optimal solution and the global optimal fitness value of the current population individuals according to the fitness function value of each individual in the current population; an output module, configured to output the solution with the minimum fitness value found as the result of the capacitated vehicle routing problem.

6. A computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the vehicle path planning method based on the circle search algorithm as described in any one of claims 1 to 4.

7. An information data processing terminal, which is used to implement the vehicle path planning system based on the circle search algorithm as described in claim 5.

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