Robot optimal path planning method based on improved Hemma optimization algorithm

Abstract

The invention discloses a robot optimal path planning method based on an improved Hemma optimization algorithm. A plurality of improvement measures are provided for problems possibly existing in path planning of a Hemma optimization algorithm. Firstly, a Circle chaotic mapping strategy is adopted to replace random initialization, so that the quality and distribution uniformity of an initial population are improved, and the global exploration capability is enhanced. Secondly, mathematical models of three core behavior stages of a standard HO algorithm are deeply optimized, and adaptive dynamic weight, a dynamic weighting strategy based on a current optimal solution and individual fitness and guided Levy flight direction adjustment are introduced; and finally, introducing a dynamic stage conversion and adaptive exploration intensity mechanism DPTAEI, and dynamically adjusting the participation proportion of the individual in different behavior stages and the intensity of the exploration behavior according to the real-time search progress of the algorithm. Through the improvements, the optimization precision, the convergence speed and the global search capability of the IHO algorithm in the aspect of robot path planning are remarkably improved.

Description

Technical Field

[0001] The invention belongs to the field of path planning design and is a robot optimal path planning method based on an improved Hippo optimization algorithm. Background Art

[0002] Path planning, a core technology in modern industry and robotics, is of great importance. Its purpose is to help a robot plan a collision-free, feasible path from a specified starting point to a destination within a specific working environment, based on certain optimization criteria (such as shortest path, optimal time, and lowest energy consumption).

[0003] Traditional path planning algorithms, such as the A* algorithm, Dijkstra's algorithm, and rapidly expanding random trees (RRT) and their variants, have been applied in specific scenarios. However, when faced with increasingly complex operating environments, such as high-dimensional search spaces, a large number of irregular obstacles, and dynamically changing environmental information, these traditional methods often expose limitations such as high computational complexity, low search efficiency, susceptibility to local optimal solutions, strong dependence on the accuracy of environmental models, and insufficient adaptability in dynamic environments. Therefore, developing more efficient path planning algorithms that can adapt to complex environments has become a research hotspot and urgent need in the fields of robotics and artificial intelligence.

[0004] In recent years, metaheuristic optimization algorithms inspired by biological swarm behavior or physical phenomena (such as particle swarm optimization (PSO), grey wolf optimization (GWO), and genetic algorithms (GA)) have shown significant potential for solving complex optimization problems (such as path planning) due to their strong global search capabilities, low dependency on mathematical models, and inherent parallel adaptability. However, practical applications still face challenges such as complex parameter tuning, slow convergence, and susceptibility to local optima.

[0005] The Hippopotamus Optimization (HO) algorithm is a recently proposed metaheuristic algorithm that simulates the behavior of hippopotamus groups in natural environments. Preliminary studies have shown that the HO algorithm exhibits good optimization performance and the ability to balance exploration and exploitation on some standard optimization test functions.

[0006] However, when the standard HO algorithm is directly applied to the specific and complex optimization domain of robot path planning, its performance and adaptability still have room for improvement. For example, in complex environments with dense obstacles and a large number of local minima in the path solution space, the standard HO algorithm may, similar to other emerging metaheuristic algorithms, face problems such as the initial population quality having a significant impact on subsequent search, a less refined exploration mechanism leading to slow convergence, or, in certain situations, premature loss of population diversity leading to being trapped in a local optimal path. Therefore, based on the characteristics of the robot path planning problem, an in-depth analysis of the standard HO algorithm to further improve its convergence speed, path quality, and robustness of global search and obstacle avoidance has important research value and practical application prospects.

[0007] Based on the above background, the present invention proposes an improved Hippo optimization algorithm, which aims to provide a more efficient and reliable path planning solution for the autonomous navigation of robots in complex environments. Summary of the Invention

[0008] Purpose of the invention: In view of the deficiencies of the existing technology, in order to overcome the shortcomings of the existing technology and the limitations of the standard Hippo optimization algorithm in the application of robot path planning, the present invention proposes a robot optimal path planning method based on the improved Hippo optimization algorithm.

[0009] Technical solution: The present invention discloses a robot optimal path planning method based on an improved Hippo optimization algorithm, comprising the following steps:

[0010] Step 1: Use the Circle chaos mapping strategy to generate the initial hippo population, where each hippo represents an independent candidate solution, i.e., a possible robot path;

[0011] Step 2: Based on the individual fitness values ​​obtained during the search process, the behavior of the hippo population is iteratively updated. The three stages of the standard HO algorithm are improved, and an adaptive dynamic weight ω is added in the first stage. A In the second stage, the Levy flight strategy is improved by introducing dynamic weight ω B As a scale adjustment and optimized direction guidance, the third stage adds an adaptive coefficient σ3(t) to adjust the search step size or range to perform local search;

[0012] Step 3: In robot path planning, the objective function is set to minimize the path length from the starting point to the end point, while satisfying the following constraints: the path must not intersect with obstacles in the environment; the minimum distance between each node on the path and all obstacles must be greater than a safety threshold; the above constraints are handled by introducing a penalty term in the fitness function;

[0013] Step 4: When the preset maximum number of iterations is reached or other termination conditions are met, the iteration stops. The coding sequence represented by the currently recorded global optimal hippopotamus individual with the minimum fitness value is the node sequence of the planned optimal path. The coding of the optimal hippopotamus is converted into actual two-dimensional coordinate points, and these path nodes are connected using linear interpolation or other smoothing techniques to generate a continuous smooth path that can be executed by the robot.

[0014] Furthermore, in step 1, the Circle chaos mapping strategy is used to generate the initial hippo population, specifically:

[0015] The Circle chaotic map is iteratively generated as shown in formula (1):

[0016]

[0017] Among them, mod is the remainder function, x k represents the chaotic variable value of the kth iteration, and its value range is [0,1]; a and b are control parameters;

[0018] Map the chaotic sequence generated by formula (1) to the feasible solution space where the individuals of the population are located. For the position X of the kth hippopotamus in the i-th dimension, k,i , that is, the row coordinates of the path in a certain column, which is generated as shown in formula (2):

[0019] X k,i =lb i +c k,i ·(ub i -lb i ) (2)

[0020] Among them, c k,i It is X through formula (1) k,i Generated chaos value; ub i Indicates the current upper bound of the i-th dimension, lb i Represents the current lower bound of the i-th dimension, and replaces the original random population initialization function with a population initialized using the Circle chaos mapping strategy.

[0021] Furthermore, the specific improvements in step 2 are as follows:

[0022] According to the fitness value sorting information obtained from the search, the path with the lowest fitness value is selected as the current optimal candidate path X best , according to the behavior of hippo populations at different stages, part or all of the hippo populations are updated through adaptive dynamic weights and improved search strategies:

[0023] (1) Adding adaptive dynamic weight ω to the first stage of the Hippo optimization algorithm, i.e., updating the position of the hippo in the river / pond A , the update formula is shown in formula (3):

[0024] X k (t+1)=X k (t)+ω A ·rand1·(X best (t)-I1·X k (t)) (3)

[0025] Among them, X k (t) is the position of hippopotamus k in generation t; X best (t) is the global optimal solution of the tth generation; rand1 is a random number uniformly distributed in the interval (0,1); I1 is an integer randomly selected from {1,2};

[0026] Adaptive dynamic weight ω A The calculation method of consists of two parts. One part is adjusted with the number of iterations, and the other part considers the fitness difference between the current individual and the optimal individual. The calculation formula is shown in formula (4):

[0027]

[0028] Among them, t represents the current number of iterations, Max i ter represents the maximum number of iterations, ω A,max and ω A,min The weights ω are A The upper and lower limits of the basic range, p A1 is the exponent that controls the decay rate of the first part, f best (t) and f k (t) are the current global optimal fitness and the fitness of individual k, ε is a very small positive number to prevent division by zero, α A and β A is the balance coefficient of the two parts;

[0029] (2) The second stage of the Hippo optimization algorithm, i.e., the Levy flight strategy in the Hippo defense against predators, is improved by introducing the dynamic weight ω B As a scale adjustment and optimized direction guidance, Hippo X k The position update at this stage is shown in formula (5):

[0030]

[0031] Where Levy(β) is a random vector generated by the standard Levy distribution with parameter β, Represents the element-wise product of vectors, Dirk (t) is the direction guidance item, dynamic weight ω B (t) is the adaptive scaling factor of the Levy flight, and is calculated as shown in formula (6):

[0032]

[0033] Among them, Scale B,start is the initial maximum value of the Levy flight scale, Scale B,end is the minimum scale value in the later stage of iteration, P B1 is an exponent that controls the rate of scale decay;

[0034] (3) The third stage of the hippopotamus optimization algorithm, i.e., the hippopotamus escapes from the predator, is improved by adding the adaptive coefficient σ3(t). The update formula of this stage is shown in formula (7):

[0035] X k (t+1)=X k (t)+σ3(t)·(2·rand3-1)·LocalSearchRadius(t) (7)

[0036] Where rand3 is a random number in (0,1), (2 rand3-1) generates a random direction and size in the range [-1,1], and LocalSearchRadius(t) is the local search radius that is dynamically adjusted with iterations and is set to (ub-lb) ratio local , where ratio local is a small proportion that decreases with t;

[0037] The adaptive coefficient σ3(t) is shown in formula (8):

[0038]

[0039] Among them, σ 3,max Usually 1.0, p C1 is an exponent that controls the rate of deceleration.

[0040] Furthermore, the direction guide item Dir k (t) Combined with the simulated "predator" position X predator The reaction and the current global optimal solution X best The approach is as shown in formula (9):

[0041] Dir k (t) = δ1·F interact ·(X target (t)-X k (t))+δ2·rand b·(X best (t)-X k (t)) (9)

[0042] Among them, X target (t) is a simulated exploration target point, F interact Represents individual and X predator (t) interaction strength or direction, based on fitness comparison: if fit(X k )>fit(X predator ), then X target (t) = X predator (t), that is, it is attracted at this time; otherwise, X target (t) = X k (t)+(X k (t)-X predator (t)), that is, to exclude or stay away from; rand b is a random number or random vector in (0,1), δ1 and δ2 are weight coefficients.

[0043] Furthermore, the dynamic phase transition and adaptive exploration intensity mechanism DPTAEI is introduced into the HO algorithm in step 2:

[0044] 1) Adjustment of dynamic exploration rate ER:

[0045] Define the global exploration rate ER(t), which increases from a higher initial value ER with the number of iterations t. start Nonlinearly decreasing to a lower final value ER end , the calculation formula of ER(t) is shown in formula (10):

[0046]

[0047] Among them, k ER Control the deceleration rate and the total number of hippos N participating in the first and second stages of exploration explore Dynamically determined according to ER(t): N explore =round(ER(t)-SearchAgents n o), N explore Individuals are then allocated to the corresponding exploration phase according to a preset ratio or dynamic strategy, while the remaining individuals focus more on executing the exploitation behavior in the third phase;

[0048] 2) Adaptive exploration intensity enhancement based on stagnation detection:

[0049] Set the stagnation counter stagnation_count, if continuous Iter stag The global optimal solution f best The improvement is less than a preset minimum threshold ∈s , it is judged to be stagnant. When stagnation is detected, the following exploration enhancement strategy is executed, including the following three aspects:

[0050] Temporarily increase the exploration rate: the current ER(t) is calculated according to the formula ER new =min(ER start ,ER old (1 + boost_factorER)) for boosting, where boost_factorER is a small boost factor;

[0051] Enhance the strength of the core exploration operator: temporarily increase the weight ω of the first stage A The upper limit of (t)ω A，max Or slow down its decay rate, that is, reduce p A1 Increase the dynamic weight ω of the Levy flight scale in the second stage B (t) current value or its initial value Scale B,start ; At the same time, increase the random component in the second stage direction guidance item or towards X best The weight of δ2;

[0052] Selective population disturbance: N with the lowest fitness ranking in the population perturb Individuals are reinitialized using Circle chaos mapping, or a random strong perturbation based on Cauchy distribution or Gaussian distribution with large standard deviation is imposed on their current positions;

[0053] After executing the above enhancement strategy, stagnation_count is reset to 0 to avoid continuous over-enhancement.

[0054] Beneficial effects:

[0055] The present invention discloses a robot optimal path planning method based on an improved Hippo optimization algorithm. First, the Circle chaos mapping strategy is used to replace the traditional random node initialization distribution, so that the distribution of the Hippo population in the search space is more uniform, the quality and diversity of the initial population are improved, the global exploration capability is enhanced, and the risk of the algorithm falling into the local optimum too early is reduced. Secondly, by introducing the adaptive dynamic weight ω A and ω B(Lévy scale) and improve the search direction guidance mechanism in stages 1 and 2, allowing the algorithm to automatically adjust its exploration intensity and direction at different iteration stages, optimizing optimization efficiency and accuracy and better balancing global exploration and local exploitation. Furthermore, the added adaptive coefficient σ3(t) enables the algorithm to better control the search step size during local exploitation in stage 3, allowing for more refined fine-tuning in the later stages of the iteration, which helps improve the quality of the final solution. Finally, the innovative introduction of the Dynamic Phase Transition and Adaptive Exploration Intensity (DPTAEI) mechanism monitors the algorithm's stagnation state in real time, dynamically adjusts the exploration rate and the intensity of operators in each stage, and, supplemented by a population diversity injection strategy, significantly enhances the algorithm's ability to escape local optima and its robustness to complex environments. In summary, through the above-mentioned multiple improvements, the present invention significantly improves the convergence speed, optimization accuracy, and global search capability of the Hippo optimization algorithm for robot optimal path planning in complex environments, providing a more efficient and reliable technical solution for robot autonomous navigation. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 Flowchart of the improved Hippo optimization algorithm;

[0057] Figure 2 Initialize the population for Circle Chaos Map and the scatter plot of the randomly initialized population;

[0058] Figure 3 The two-dimensional path diagram of the improved Hippo optimization algorithm and the original algorithm in the environment of 20*20 grid map;

[0059] Figure 4 Partial iteration graphs for solving 23 classic functions using the improved Hippo optimization algorithm, the original algorithm, and SSA. DETAILED DESCRIPTION

[0060] The present invention will be described in detail below with reference to the embodiments shown in the accompanying drawings.

[0061] refer to Figure 1 , a robot optimal path planning method based on an improved Hippo optimization algorithm disclosed in the present invention is described in detail, comprising the following steps:

[0062] Step 1: To improve the quality and diversity of the initial population of the standard HO in the path planning problem, the present invention adopts the Circle Chaos Map strategy to replace the Hippo population with random node initialization distribution. Each Hippo represents an independent candidate solution, and each candidate solution represents a possible path. These Hippopotamuses continuously update the fitness value through iteration, and determine the better solution by the size of the fitness value. The present invention is based on the improved Hippopotamus optimization algorithm to solve the single-objective (shortest path) optimization problem under the constraint conditions, thereby optimizing the planned path.

[0063] The Circle chaotic map is iteratively generated as shown in formula (1):

[0064]

[0065] Among them, mod is the remainder function, x k represents the chaotic variable value of the kth iteration, and its value range is [0,1]; a and b are control parameters, and a=0.5 and b=0.2 can be set to produce good chaotic characteristics and ergodicity. The chaotic sequence generated by formula (1) is mapped to the feasible solution space where the individuals of the population are located. For the position X of the kth hippopotamus in the i-th dimension, k,i (row coordinates of the path in a certain column), which is generated as shown in formula (2):

[0066] X k,i =lb i +c k,i ·(ub i -lb i ) (2)

[0067] Among them, c k,i is X through formula 1 k,i Generated chaotic value (usually several iterations are performed before generation to eliminate the influence of the initial value); ub i Indicates the current upper bound of the i-th dimension, lb i Represents the current lower bound of the i-th dimension. Replace the original random population initialization function with a population initialized using the Circle chaos map strategy.

[0068] The population generated by initialization of Circle chaotic map is more evenly distributed than random nodes, which makes the algorithm have better traversability and covers a wider search space, improves the quality and diversity of the initial population, and helps the algorithm to obtain better global optimization effect. When applied to robot path planning, the X representing the grid row coordinate generated by formula (2) is k,i The calculated initial position is rounded and must be checked to see if it falls on an obstacle. If the calculated initial position is on an obstacle, a new position should be randomly selected in the obstacle-free grid corresponding to that dimension (column).

[0069] Step 2: According to the fitness value sorting information obtained by the search, select the path with the lowest fitness value as the current optimal candidate path (X best According to the behavior of hippopotamus population at different stages, part (or all) of the hippopotamus population is updated through adaptive dynamic weights and improved search strategies.

[0070] (1) Adding adaptive dynamic weight ω to the first stage of the Hippo optimization algorithm (updating the position of the hippo in the river / pond)A : This stage simulates the individual hippopotamus to the current optimal hippopotamus (Dominant_hippopotamus, denoted as X best ) or the mean position of a randomly selected subset within a group (MeanGroup) and the behavior of approaching is one of the main exploration mechanisms. In order to improve the effectiveness of learning at this stage and adjust the exploration intensity with the iterative process, the adaptive dynamic weight ω is introduced A .

[0071] Take individual X in standard HO k Towards the optimal individual X best Taking the core part of the update as an example, the improved update formula is shown in formula (3):

[0072] X k (t+1)=X k (t)+ω A ·rand1·(X best (t)-I1·X k (t)) (3)

[0073] Among them, X k (t) is the position of hippopotamus k in generation t; X best (t) is the global optimal solution of the tth generation; rand1 is a random number uniformly distributed in the interval (0,1); I1 is an integer randomly selected from {1,2}.

[0074] Adaptive dynamic weight ω A The calculation method of consists of two parts. One part is adjusted with the number of iterations, and the other part considers the fitness difference between the current individual and the optimal individual. The overall calculation formula is shown in formula (4):

[0075]

[0076] Among them, t represents the current number of iterations, Max i ter represents the maximum number of iterations. A,max and ω A,min The weights ω are A The upper and lower limits of the basic range are generally taken as ω A,max =1.0,ω A,min =0.1. p A1 is an exponent that controls the decay rate of the first part. best (t) and f k (t) are the current global optimal fitness and the fitness of individual k, respectively. ε is a very small positive number to prevent division by zero. A and β A is the balance coefficient of the two parts (e.g. α A =0.7,βA =0.3, and α A +β A =1).

[0077] The first part ensures that the weight transitions smoothly from a larger initial value to a smaller final value, so that the algorithm has a larger search step size in the early iteration to promote global exploration, and a smaller step size in the later iteration to facilitate local fine search and convergence.

[0078] The second part introduces a dynamic adjustment term based on the fitness difference between the current individual and the optimal solution, and multiplies it by a cosine factor that changes periodically with the iteration. k (t) is far worse than the optimal fitness f best (t) (i.e. the denominator is large), this term has an effect on ω A The contribution of (t) decreases relatively; when the two are close, the contribution increases relatively (but is modulated by the cos factor). This makes the contribution of this part the smallest in the middle of the iteration (when t is close to Max_iter / 2), and the contribution larger in the early and late stages. This periodic modulation is intended to prevent the algorithm from converging prematurely in the early stages of the iteration due to the large difference between the optimal solution and the worst solution, or completely losing the motivation to explore in the later stages due to the small difference.

[0079] This design makes it possible to adaptively adjust the weight ω A The first half of (t) plays a major role in regulating the number of iterations, while the second half plays a regulatory role when the population falls into a local optimum or the difference between an individual and the optimal solution changes, and has strong adaptability.

[0080] (2) Modify the Levy flight strategy in stage 2 (Hippopotamus defense against predators) of the Hippopotamus optimization algorithm and introduce the dynamic weight ω B As scale adjustment and optimization direction guidance: This stage simulates the defensive jumping behavior of the hippopotamus (based on Levy flight) to conduct global exploration, which is crucial for the algorithm to jump out of the local optimum. The present invention improves the application of Levy flight in the standard HO algorithm. The contribution term of Levy flight in the original HO algorithm is modified, and the hippopotamus X k The position update at this stage is shown in formula (5):

[0081]

[0082] where Levy(β) is a random vector generated by a standard Levy distribution with parameter β (typically 1.5). Represents the element-wise product of vectors, Dir k (t) is the direction guidance term. Dynamic weight ω B(t) (as the adaptive scaling factor of the Levy flight) is calculated as shown in formula (6):

[0083]

[0084] Among them, Scale B,start is the initial maximum value of the Levy flight scale, Scale B,end is the minimum scale value in the later stage of iteration, P B1 is an exponent that controls the rate of scale decay. This formula allows the exploration range of the Levy flight to smoothly transition from large-scale jumps in the early stages to small-scale precise perturbations in the late stages.

[0085] Direction guide item Dir k (t) is an improvement to make Levy flights more purposeful. It combines the simulation of the Predator's position X predator The reaction and the current global optimal solution X best The approach is as shown in formula (7):

[0086] Dir k (t) = δ1·F interact ·(X target (t)-X k (t))+δ2·rand b ·(X best (t)-X k (t)) (7)

[0087] Among them, X target (t) is a simulated exploration target point, which can be randomly generated, or based on the worst individual position, or a point with a certain distance from the current optimal solution. interact Represents individual and X predator The interaction strength or direction of (t) can be compared based on fitness: if fit(X k )>fit(X predator ), then X target (t) = X predator (t), that is, it is attracted at this time; otherwise, X target (t) = X k (t)+(X k (t)-X predator (t)), that is, to repel or stay away. rand bis a random number or vector in the range (0,1). δ1 and δ2 are weight coefficients that can be fixed (e.g., δ1 = 0.7, δ2 = 0.3) or adaptively adjusted with iteration. For example, increasing δ1 in early iterations favors exploring unknown or threatening areas, while increasing δ2 in later iterations favors utilizing known optimal information. Through formulas (6) and (7), the intensity and direction of Lévy flight are dynamically and purposefully adjusted, improving exploration efficiency.

[0088] (3) Modify Phase 3 of the Hippopotamus optimization algorithm (the hippopotamus escaping from predators and exploiting the environment) by adding an adaptive coefficient σ3(t). This phase primarily performs a local search, simulating the hippopotamus's escape behavior to a safe area. To optimize the precision of the local search and avoid oscillation or premature stagnation near the optimal solution due to inappropriate step size, the adaptive coefficient σ3(t) is introduced to adjust the search step size or range.

[0089] The update formula of this stage in the original HO algorithm is shown in formula (8):

[0090] X k (t+1)=X k (t)+LocalPerturbationTerm (8)

[0091] The present invention modifies it as shown in formula (9):

[0092] X k (t+1)=X k (t)+σ3(t)·(2·rand3-1)·LocalSearchRadius(t) (9)

[0093] Among them, rand3 is a random number in (0,1) (or k Random vectors of the same dimension), (2·rand3-1) generates a random direction and size in the range [-1,1]. LocalSearchRadius(t) is the local search radius that is dynamically adjusted with iterations and can be set to (ub-lb)·ratio local , where ratio local It is a small ratio that decreases with t (such as from 0.05 to 0.001).

[0094] The adaptive coefficient σ3(t) is designed so that it gradually decreases from a larger initial value (such as 1.0) to a smaller value (such as 0.1 or less) with the number of iterations t, as shown in formula (10):

[0095]

[0096] Among them, σ3,max Usually 1.0, p C1 is the exponent that controls the rate of deceleration (p C1 2 or 3). The value of σ3(t) decreases with each iteration of the algorithm, gradually reducing the amplitude of the random perturbation. In the early stages of the iteration, σ3(t) is large, allowing for a larger local search step size. In the later stages of the iteration, σ3(t) gradually decreases, making the local search more refined, helping to improve the accuracy of the solution. It also gradually reduces the need for significant modifications to the current solution, avoiding the destruction of the excellent structure found, thereby better enabling fine-tuning near the optimal solution.

[0097] (4) Introducing the Dynamic Phase Transition and Adaptive Exploration Intensity (DPTAEI) mechanism: To enable the algorithm to dynamically adjust the balance between its exploration and exploitation strategies, as well as the intensity of search behavior at each stage, based on the actual search situation, the DPTAEI mechanism is introduced. This mechanism macro-controls the search behavior of the entire algorithm, rather than modifying a specific formula, but rather serves as an overarching strategy.

[0098] Dynamic Exploration Rate (ER) Adjustment:

[0099] Define a global exploration rate ER(t), which increases from a higher initial value ER with the number of iterations t. start (0.7-0.8) nonlinearly decreasing to a lower final value ER end (0.2-0.3), the calculation formula of ER(t) is shown in formula (11):

[0100]

[0101] Among them, k ER Control the deceleration rate (k ER = 1.5 or 2). The total number of hippos N participating in the exploration-based phases 1 and 2 explore Dynamically determined according to ER(t): N explore =round(ER(t)-SearchAgents n o). These N explore Individuals are then assigned to the corresponding exploration phase according to a preset ratio or dynamic strategy. The remaining individuals focus more on executing the exploitation behavior in phase 3.

[0102] Adaptive exploration intensity enhancement based on stagnation detection:

[0103] Set the stagnation counter stagnation_count. If continuous Iter stag Iterations (e.g., Iter stag =round(0.05·Max i ter), the minimum is 5-10 times) the global optimal solution fbest The improvement is less than a preset minimum threshold ∈ s (e.g. 10 -6 ), the algorithm may be stagnant. When stagnation is detected, the following exploration enhancement strategy is executed, including the following three aspects:

[0104] Temporarily increase the exploration rate: the current ER(t) is calculated according to the formula ER new =min(ER start ,ER old (1 + boost_factorER)) for boosting, where boost_factorER is a small boost factor (0.1 to 0.25).

[0105] Strengthen the core exploration operator: temporarily increase the weight ω of stage 1 A The upper limit of (t)ω A，max Or slow down its decay rate; increase the Levy flight scale ω in stage 2 B (t) current value or its initial value Scale B,start ; At the same time, you can increase the random component of the direction guidance item in stage 2 or towards X best The weight δ2.

[0106] Selective population disturbance: N with the lowest fitness ranking in the population perturb Individuals (e.g., 10%-20% of the total) are reinitialized using the Circle Chaos Map, or a random strong perturbation based on a Cauchy distribution or a large standard deviation Gaussian distribution is applied to their current positions (the perturbation amplitude can be larger than the normal perturbation in stage 3) to force the population diversity to increase and help the algorithm escape the current local optimum. After executing the above enhancement strategy, the state_count is reset to 0 to avoid continuous over-enhancement.

[0107] This DPTAEI mechanism enables the IHO algorithm to dynamically and specifically adjust the focus and intensity of its search strategy based on its own optimization status. When the algorithm is progressing smoothly, it smoothly transitions from exploration to exploitation; when the algorithm stagnates, it automatically enhances its exploration capabilities, thereby improving the algorithm's global optimization performance and robustness.

[0108] Step 3: In robot path planning, the objective function is typically set to minimize the path length from the starting point to the end point. At the same time, the following constraints must be met: the path must not intersect with obstacles in the environment; and the minimum distance between each node on the path and all obstacles must be greater than a safety threshold (i.e., greater than zero). These constraints are typically addressed by introducing a penalty term into the fitness function. If a candidate path violates a constraint (e.g., collides with an obstacle), its fitness value is assigned a large penalty, placing it at a disadvantage in the selection process.

[0109] Step 4: When the algorithm reaches the preset maximum number of iterations or meets other termination conditions, the iterations cease. The encoded sequence represented by the currently recorded global optimal hippopotamus individual with the minimum fitness value is the node sequence of the planned optimal path. The encoding of the optimal hippopotamus is converted into actual two-dimensional coordinate points. These path nodes can then be connected using linear interpolation or other smoothing techniques to generate the final, continuous, smooth path that the robot can execute.

[0110] Figure 2 This experiment is a comparison experiment of population initialization strategies. To verify the effectiveness of the initialization strategy, this experiment compares the distribution effects of Circle chaotic mapping and traditional random initialization in generating 200 initial points in a two-dimensional unit space. Figure 2 As shown in the figure, the random initialization on the right has obvious clustering and blank areas, and the distribution is uneven; while the Circle chaotic map on the left shows excellent ergodicity, its point set distribution is more uniform, and the coverage is wider, which can provide a more diverse and higher quality initial population for the global search of the algorithm.

[0111] Figure 3 For robot path planning example comparison, this experiment aims to verify the actual path planning performance of the IHO algorithm in a 20*20 grid map and compare it with the standard HO algorithm. Figure 3 As shown in the figure, under the same parameter settings, the path length planned by IHO is 29.01, significantly better than HO's 32.50. The shorter and smoother path found by IHO proves that the improved strategy of this invention effectively enhances the algorithm's optimization ability, enabling it to find lower-cost solutions in complex constrained environments.

[0112] Figure 4 In order to compare the performance of the algorithm on the standard test function and to comprehensively evaluate the optimization performance and robustness of IHO, this experiment selected F2 (simple single peak, Figure 4 (a)) and F8 (complex multimodal, Figure 4(b) Two standard test functions are used to compare IHO with HO and SSA. In comparison, the IHO algorithm of the present invention, with its powerful global exploration and dynamic adjustment capabilities, successfully avoids the pitfalls of HO and continuously optimizes, ultimately converging to a significantly better solution.

[0113] The above embodiments are intended only to illustrate the technical concepts and features of the present invention. Their purpose is to enable those skilled in the art to understand the contents of the present invention and implement them accordingly. They are not intended to limit the scope of protection of the present invention. Any equivalent changes or modifications made in accordance with the spirit of the present invention are intended to be covered by the scope of protection of the present invention.

Claims

1. A robot optimal path planning method based on an improved Hippo optimization algorithm, characterized in that: The following steps are involved: Step 1: Use the Circle chaos mapping strategy to generate the initial hippo population, where each hippo represents an independent candidate solution, i.e., a possible robot path; Step 2: Based on the individual fitness values ​​obtained during the search process, the behavior of the hippo population is iteratively updated. The three stages of the standard HO algorithm are improved, and an adaptive dynamic weight ω is added in the first stage. A In the second stage, the Levy flight strategy is improved by introducing dynamic weight ω B As a scale adjustment and optimized direction guidance, the third stage adds an adaptive coefficient σ3(t) to adjust the search step size or range to perform local search; Step 3: In robot path planning, the objective function is set to minimize the path length from the starting point to the end point, while satisfying the following constraints: the path must not intersect with obstacles in the environment; the minimum distance between each node on the path and all obstacles must be greater than a safety threshold; the above constraints are handled by introducing a penalty term in the fitness function; Step 4: When the preset maximum number of iterations is reached or other termination conditions are met, the iteration stops. The coding sequence represented by the currently recorded global optimal hippopotamus individual with the minimum fitness value is the node sequence of the planned optimal path. The coding of the optimal hippopotamus is converted into actual two-dimensional coordinate points, and these path nodes are connected using linear interpolation or other smoothing techniques to generate a continuous smooth path that can be executed by the robot.

2. The robot optimal path planning method based on the improved Hippo optimization algorithm according to claim 1 is characterized in that: In step 1, the Circle chaos mapping strategy is used to generate the initial hippo population, specifically: The Circle chaotic map is iteratively generated as shown in formula (1): Among them, mod is the remainder function, x k represents the chaotic variable value of the kth iteration, and its value range is [0,1]; a and b are control parameters; Map the chaotic sequence generated by formula (1) to the feasible solution space where the individuals of the population are located. For the position X of the kth hippopotamus in the i-th dimension, k,i , that is, the row coordinates of the path in a certain column, which is generated as shown in formula (2): X k,i =lb i +c k,i ·(ub i -lb i ) (2) Among them, c k,i It is X through formula (1) k,i Generated chaos value; ub i Indicates the current upper bound of the i-th dimension, lb i Represents the current lower bound of the i-th dimension, and replaces the original random population initialization function with a population initialized using the Circle chaos mapping strategy.

3. The robot optimal path planning method based on the improved Hippo optimization algorithm according to claim 1 is characterized in that: The specific improvements in step 2 are as follows: According to the fitness value sorting information obtained from the search, the path with the lowest fitness value is selected as the current optimal candidate path X best , according to the behavior of hippo populations at different stages, part or all of the hippo populations are updated through adaptive dynamic weights and improved search strategies: (1) Adding adaptive dynamic weight ω to the first stage of the Hippo optimization algorithm, i.e., updating the position of the hippo in the river / pond A , the update formula is shown in formula (3): X k (t+1)=X k (t)+ω A ·rand1·(X best (t)-I1·X k (t)) (3) Among them, X k (t) is the position of hippopotamus k in generation t; X best (t) is the global optimal solution of the tth generation; rand1 is a random number uniformly distributed in the interval (0,1); I1 is an integer randomly selected from {1,2}; Adaptive dynamic weight ω A The calculation method of consists of two parts. One part is adjusted with the number of iterations, and the other part considers the fitness difference between the current individual and the optimal individual. The calculation formula is shown in formula (4): Among them, t represents the current number of iterations, Max i ter represents the maximum number of iterations, ω A,max and ω A,min The weights ω are A The upper and lower limits of the basic range, p A1 is the exponent that controls the decay rate of the first part, f best (t) and f k (t) are the current global optimal fitness and the fitness of individual k, ε is a very small positive number to prevent division by zero, α A and β A is the balance coefficient of the two parts; (2) The second stage of the Hippo optimization algorithm, i.e., the Levy flight strategy in the Hippo defense against predators, is improved by introducing the dynamic weight ω B As a scale adjustment and optimized direction guidance, Hippo X k The position update at this stage is shown in formula (5): Where Levy(β) is a random vector generated by the standard Levy distribution with parameter β, Represents the element-wise product of vectors, Dir k (t) is the direction guidance item, dynamic weight ω B (t) is the adaptive scaling factor of the Levy flight, and is calculated as shown in formula (6): Among them, Scale B,start is the initial maximum value of the Levy flight scale, Scale B,end is the minimum scale value in the later stage of iteration, P B1 is an exponent that controls the rate of scale decay; (3) The third stage of the hippopotamus optimization algorithm, i.e., the hippopotamus escapes from the predator, is improved by adding the adaptive coefficient σ3(t). The update formula of this stage is shown in formula (7): X k (t+1)=X k (t)+ σ3(t)·(2·rand3-1)·LocalSearchRadius(t) (7) Where rand3 is a random number in (0,1), (2 rand3-1) generates a random direction and size in the range [-1,1], and LocalSearchRadius(t) is the local search radius that is dynamically adjusted with iterations and is set to (ub-lb) ratio local , where ratio local is a small proportion that decreases with t; The adaptive coefficient σ3(t) is shown in formula (8): Among them, σ 3,max Usually 1.0, p C1 is an exponent that controls the rate of deceleration.

4. The robot optimal path planning method based on the improved Hippo optimization algorithm according to claim 3 is characterized in that: Direction guide item Dir k (t) Combined with the simulated "predator" position X predator The reaction and the current global optimal solution X best The approach is as shown in formula (9): Dir k (t)=δ1·F interact ·(X target (t)-X k (t))+δ2·rand b ·(X best (t)-X k (t)) (9) Among them, X target (t) is a simulated exploration target point, F interact Represents individual and x predator (t) interaction strength or direction, based on fitness comparison: if fit(X k )>fit(X ptedator ), then x target (t) = x predator (T), that is, it is attracted at this time; otherwise, x target (T) = x k (T)+(X k (t)-X predator (t)), that is, to exclude or stay away from; rand b is a random number or random vector in (0,1), δ1 and δ2 are weight coefficients.

5. The robot optimal path planning method based on the improved Hippo optimization algorithm according to claim 1, characterized in that: The HO algorithm in step 2 also introduces the dynamic phase transition and adaptive exploration intensity mechanism DPTAEI: 1) Adjustment of dynamic exploration rate ER: Define the global exploration rate ER(t), which increases from a higher initial value ER with the number of iterations t. start Nonlinearly decreasing to a lower final value ER end , the calculation formula of ER(t) is shown in formula (10): Among them, k ER Control the deceleration rate and the total number of hippos N participating in the first and second stages of exploration explore Dynamically determined according to ER(T): N explore =round(ER(t)-SearchAgents n o), N explore Individuals are then allocated to the corresponding exploration phase according to a preset ratio or dynamic strategy, while the remaining individuals focus more on executing the exploitation behavior in the third phase; 2) Adaptive exploration intensity enhancement based on stagnation detection: Set the stagnation counter stagnation_count, if continuous Iter stag The global optimal solution f best The improvement is less than a preset minimum threshold ∈ s , it is judged to be stagnant. When stagnation is detected, the following exploration enhancement strategy is executed, including the following three aspects: Temporarily increase the exploration rate: the current ER(t) is calculated according to the formula ER new =min(ER start ,ER old (1 + boost_factorER)) for boosting, where boost_factorER is a small boost factor; Enhance the strength of the core exploration operator: temporarily increase the weight ω of the first stage A The upper limit of (t)ω A，max Or slow down its decay rate, that is, reduce p A1 Increase the dynamic weight ω of the Levy flight scale in the second stage B (t) current value or its initial value Scale B,start ; At the same time, increase the random component in the second stage direction guidance item or towards X best The weight of δ2; Selective population disturbance: N with the lowest fitness ranking in the population perturb Individuals are reinitialized using Circle chaos mapping, or a random strong perturbation based on Cauchy distribution or Gaussian distribution with large standard deviation is imposed on their current positions; After executing the above enhancement strategy, stagnation_count is reset to 0 to avoid continuous over-enhancement.

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