Urban traffic path planning method based on multi-modal multi-target differential evolution

Abstract

The invention discloses an urban traffic path planning method based on multi-modal multi-target differential evolution. The urban traffic path planning method is specifically implemented according to the following steps: step 1, preprocessing address data and simulating according to the address data to obtain an urban map; 2, determining an optimization target according to a map; and step 3, obtaining an optimal path by using a multi-modal multi-target differential evolution algorithm with the purpose of minimizing an optimization target. According to the method, the problem that a plurality of optimal paths cannot be found in urban traffic path planning through a multi-objective evolutionary algorithm in the prior art is solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of urban traffic path planning methods, and relates to an urban traffic path planning method based on multi-modal multi-objective differential evolution. Background Art

[0002] The urban traffic path planning problem is a common multi-objective optimization problem. When facing different problems, different needs of different decision makers need to be considered. For example, there may be three different paths from the starting point to the end point. At present, most urban traffic path planning methods can only find one of the paths. However, if more than one shortest path cannot be identified, it may affect the decision maker's choice. In real life, traffic congestion and the number of intersections passed are important factors affecting traffic flow. For example, a traveler wants to pass through a certain intersection. However, if only one or two paths are provided, the best path will be missed. In fact, different decision makers have different preferences, so it is necessary to provide multiple excellent solutions.

[0003] In the past few decades, multi-objective evolutionary algorithms have achieved good performance, such as NSGA-II (a fast elite multi-objective genetic algorithm), MOEA / D (a decomposition-based multi-objective evolutionary algorithm), etc. However, the existing multi-objective evolutionary algorithms cannot find multiple equivalent Pareto optimal solution sets in the decision space. For general multi-objective optimization algorithms, finding a Pareto optimal solution set in the decision space means that the problem has been solved. At the same time, the convergence priority strategy will lead to the loss of solution diversity in the decision space, thereby weakening the exploration ability of the multi-objective evolutionary algorithm. Traditional multi-objective evolutionary algorithms face severe challenges in solving urban traffic path planning problems, so the development of new methods is crucial to this field.

[0004] In the past few decades, many researchers have begun to pay attention to the diversity of decision spaces, and many researchers have proposed many different optimization algorithms. Deb and Tiwari proposed an Omni-optimizer (omni-optimizer: single-objective and multi-objective optimization program) algorithm to solve multiple optimization problems, including single-modal and multi-modal, single-objective and multi-objective optimization problems. In the global optimizer, in order to maintain the diversity of solutions, the crowding distance is considered in the decision space. Liu Yiping et al. proposed TriMOEA-TA&R (a multimodal multi-objective evolutionary algorithm based on dual archiving and reorganization strategy, published date: 2018-11-06), using the overall framework of two archives, fusion archive and diversity archive, to collaboratively solve these problems. Subsequently, Yue Caitong et al. used an index-based ring topology structure in MO_Ring_PSO_SCD (particle swarm algorithm based on ring topology and special crowding distance, published date: 2017-09) to generate niches without introducing parameters, thereby identifying more Pareto optimal solutions, and used special crowding distance as a measure of crowding distance in decision and objective space. Although many multimodal multi-objective evolutionary algorithms have been designed to solve multimodal multi-objective optimization problems, there are still some challenges in dealing with urban traffic path planning problems. First, although the search capabilities of multimodal multi-objective evolutionary algorithms in decision space and target space are constantly improving, the number of paths in the decision space is still insufficient. Second, some multimodal multi-objective evolutionary algorithms tend to select individuals with good convergence rather than individuals with good diversity. Individuals with slightly better distribution in the decision space may be replaced by individuals with better distribution in the target space. Third, balancing the exploration ability and maintaining the main distribution of multiple equivalent Pareto optimal paths is still a huge challenge. Summary of the invention

[0005] The purpose of the present invention is to provide an urban traffic path planning method based on multi-modal multi-objective differential evolution, which solves the problem that the multi-objective evolutionary algorithm in the prior art cannot find multiple optimal paths in urban traffic path planning.

[0006] The technical solution adopted by the present invention is an urban traffic path planning method based on multi-modal multi-objective differential evolution, which is specifically implemented in the following steps:

[0007] Step 1, preprocessing address data and simulating a city map based on the address data;

[0008] Step 2, determine the optimization target according to the map;

[0009] Step 3: Use a multi-modal multi-objective differential evolution algorithm to obtain the optimal path with the goal of minimizing the optimization objective.

[0010] The present invention is also characterized in that:

[0011] In step 1, the city map is simulated as a matrix consisting of 0 or 1. The area represented by 0 is a passable area, and the area represented by 1 is an impassable area. In the map, only up, down, left, and right walking are allowed. Repeated walking is not allowed, and it is forbidden to go beyond the boundary of the map. The coordinate value of each step in the walking sequence is used to represent the corresponding path;

[0012] White areas are set up in the city map to simulate traffic jams; T-junctions and intersections are regarded as intersections.

[0013] The optimization objectives in step 2 are as follows:

[0014]

[0015] Step 3 is as follows:

[0016] Step 3.1, generate a population according to step 1, each individual in the population represents a solution to path planning, that is, each individual in the population represents a path from the starting point to the end point in the city map of step 1;

[0017] Step 3.2, randomly initialize the population in the decision space. When initializing the population, map each path through a function to form the solution's passable path length, the number of white areas passed, and the number of intersections passed by the phenotype f(x), f(x) = {f 1 (x),f 2 (x),f 3 (x)};

[0018] Where: f 1 (x) represents the value of the path length, f 2 (x) represents the number of passes through the white area, f 3 (x) represents the number of intersections passed;

[0019] Step 3.3, perform non-dominated sorting based on fine-grained special crowding distance on the initialized population, and output the sorted new population;

[0020] Step 3.4, adaptively select excellent individuals and randomly select two solutions x from the new population obtained in step 3 r1 and x r2 , applying DE / current-to-exemplar / 1 mutation strategy to produce offspring to generate the daughter population;

[0021] Step 3.5, merge the offspring population obtained in step 3.4 with the parent population, perform non-dominated sorting based on fine-grained special crowding distance on the merged population, and calculate the DC of the individuals in the last non-dominated frontier i Value, according to DCi The value is to select the next generation population, that is, the individual with the smallest target, that is, the optimal individual;

[0022] Step 3.6, determine whether the evolutionary generation of the next generation population obtained in step 3.5 reaches the set maximum evolutionary generation. If it does not reach the maximum evolutionary generation, it means that the termination condition is not met, and jump to step 3.3. Otherwise, output the next generation population obtained in step 3.5 as the optimal solution set.

[0023] Step 3.3 is as follows:

[0024] Step 3.3.1, perform non-dominated sorting on the initialized population and divide the population into multiple non-dominated frontiers (F 1 ,F 2 ,…F num ), num is the number of non-dominated frontiers;

[0025] Step 3.3.2, after non-dominated sorting, each non-dominated front is divided into N clusters by the k-means clustering algorithm. In each cluster, the fine-grained special crowding distance value of each individual is calculated, that is, the ISCD value;

[0026] Step 3.3.3, sort all the solutions in the population according to the non-dominated order, and divide the population into multiple non-dominated frontiers (F 1 ,F 2 ,…F num ), num is the number of non-dominated frontiers, the solutions in the same non-dominated front are sorted according to the ISCD value, and finally the sorted new population is output.

[0027] For each class of n individuals, the i-th individual x i , which is based on the fine-grained special crowding distance value ISCD i Calculate according to the following formula:

[0028]

[0029] Among them, CD i,x For each class of n individuals, the i-th individual x i The decision space crowding distance, CD i,f For each class of n individuals, the i-th individual x i The target space crowding distance;

[0030] Among them, ICD i,x =CD i,x -(CD avg,f -CD i,f ), ICD i,f =CD i,f -(CD avg,x-CD i,x );

[0031] CD i,x =(|x i-1,1 -x i+1,1 | / |x 1,1 -x n,1 |)+(|x i-1,2 -x i+1,2 | / |x 1,2 -x n,2 |)

[0032] CD i,f =(|x i-1,1 -x i+1,1 | / |x 1,1 -x n,1 |)+(|x i-1,2 -x i+1,2 | / |x 1,2 -x n,2 |)

[0033] Among them, x i-1 Indicates the clustering x i The left neighbor of an individual, x i+1 Indicates the clustering x i The right neighbor of an individual, x 1 represents the first individual of the cluster, x n represents the last individual in the cluster, x i,1 Represents individual x i The value of the first dimension in the decision space, x i,2 Represents individual x i The value of the second dimension in the decision space, x n,2 Represents individual x n The value of the second dimension in the decision space, x n,1 Represents individual x n The value of the first dimension in the decision space.

[0034] The specific steps of non-dominated sorting in step 3.3.1 are as follows: Initialize each solution in the population into two sets: the dominated solution set S i and dominate count n i , where the dominated solution set S i is the set of all solutions dominated by solution i, with domination count n i That is, how many solutions dominate solution i;

[0035] Traverse each pair of solutions in the initialized population solution, for any pair of solutions x i Reconciliation j , according to the definition of dominance relation, check the solution x i Whether it dominates the solution x j, specifically:

[0036] If the solution i is in f(x) = {f 1 (x),f 2 (x),f 3 (x)} is not worse than solution j, and is better in any preferred goal, then solution i is judged to dominate solution j, and solution j is added to the dominating set S of solution i i , and the dominance count n of solution j j Add 1;

[0037] According to the above judgment method, the dominant solution set and domination count of each solution are obtained. Among all solutions, if the domination count of the corresponding solution is 0, then the solution is the first layer of non-dominated frontier; for each solution belonging to the first frontier, check the solutions it dominates, and reduce the domination count of the solutions it dominates by 1. If the domination count of a solution drops to 0, it will be placed in the next layer of frontier, and so on. All solutions have been assigned to different frontiers. At this time, the non-dominated sorting process is completed, and the population is divided into multiple non-dominated frontiers (F 1 ,F 2 ,…F num ).

[0038] Step 3.4 is as follows:

[0039] Step 3.4.1, define a parameter p 1 , Among them, G c refers to the current generation, while maxgen refers to the maximum generation;

[0040] Step 3.4.2, generate a random number between 0 and 1. If the random number is less than p 1 , it is considered that the evolution process is in the early stage, then the five candidate individuals with the largest ISCD value are selected from the new population obtained in step 3.3, and an individual is randomly selected from all the candidate individuals as an excellent individual; otherwise, it is considered that the evolution process has entered the middle and late stages, then the convergence of each individual in the new population obtained in step 3.3 is calculated, and the five individuals with the best convergence are selected as candidate individuals, and the individual with the largest ISCD value is selected from the candidate individuals as an excellent individual; where the individual convergence is calculated as the sum of each dimension of the individual in the target space, and the convergence con of any individual i is i The calculation formula is: Where M is the dimension of the target space; f k (x i ) represents individual x i The value of the kth dimension in the target space;

[0041] Step 3.4.3, randomly select two individuals x from the new population generated in step 3.3 r1 and xr2 , apply the DE / current-to-exemplar / 1 operator to generate offspring, where the DE / current-to-exemplar / 1 formula is as follows:

[0042] v i =x i +RR i ·(x exemplar -x i )+RR i ·(x r1 -x r2 )

[0043] Among them, v i represents the newly generated mutant individual, x i represents the current individual, x exemplar represents the excellent individuals selected in step 3.4.2, RR i is the scale factor;

[0044] Step 3.4.4, determine whether all individuals in the new population generated in step 3.3 have produced offspring. If an individual has not produced offspring, it means that the termination condition is not met, and jump to step 3.4.3, otherwise the loop ends.

[0045] The specific process of selecting the next generation population in step 3.5 is:

[0046] Step 3.5.1, when the new population generated in step 3.3 and the offspring of each individual obtained in step 3.4 are combined to form a combined population;

[0047] Step 3.5.2, according to the method in step 3.3.1, the combined population is classified into different frontiers (F1, F2, ...) through non-dominated sorting based on fine-grained special crowding distance, and then the frontiers are selected in turn to construct the population P. P is initialized as an empty set. Starting from F1, the individuals in the frontier are added to the population P in turn until the frontier Fj-1, where |F1∪F2∪...∪Fj-1|<|F1∪F2∪...∪Fj-1∪Fj|≥NP, and NP is the size of the parent population or the child population;

[0048] Step 3.5.2, initialize an archive set Ar as an empty set, find a solution with the largest special crowding distance value based on fine-grainedness in the jth frontier, and put it into an archive Ar;

[0049] Step 3.5.3: exclude the individuals put into the file Ar in step 3.5.2 from the population P. The remaining individuals in the population P form the set Fj\Ar. Calculate each solution x in the set Fj\Ar. i The decision space distance D to the archive Ar i,x , where Di,x Represents the solution x in the decision space i The minimum distance to each individual in the archive Ar, D i,x Calculate according to the following formula:

[0050]

[0051] Among them, d dec (x i ,x j ) represents the decision space x i and x j The distance between

[0052] In the target space, calculate the target space distance D from each solution i in the solution set Fj\Ar to the file Ar i,f , where D i,f Represents the solution x in the target space i The minimum distance to each individual in the archive Ar, therefore, D i,f Calculate according to the following formula:

[0053]

[0054] Among them, d obj (x i ,x j ) represents x in the target space i and x j The distance between

[0055] Step 3.5.4, calculate the mean value D of the distance from all solutions to the archive Ar in the target space and decision space respectively avg,f and D avg,x , x i The final distance D of the individual i Calculate according to the following formula:

[0056]

[0057] Step 3.5.5, calculate the DC of each individual i :

[0058] DC i =ISCD i +D i

[0059] Among them, ISCD i Represents individual x i Based on the fine-grained special crowding distance value, select the indicator DC in the solution set Fj\Ar iThe largest solution is put into the set Ar, and the above process is repeated until the number of solutions in the file Ar plus the number of solutions in the solution set P equals NP;

[0060] Step 3.5.6, the individuals in the solution set P are considered to be the optimal individuals, that is, the optimal path. The individuals in the final solution set P include all the individuals in the first j-1 frontiers and some individuals in the jth frontier, that is, the optimal individuals.

[0061] The beneficial effects of the present invention are:

[0062] The present invention proposes a strategy based on fine-grained special crowding distance that comprehensively considers the crowding distance of decision space and target space, which can effectively measure the crowding distance of individual target space and decision space and optimize the individual selection process; when selecting excellent individuals, the present invention defines the parameter p 1 , If the random value is less than p 1 , it is believed that the evolutionary process is in the early stage, and more emphasis should be placed on exploration ability, and individuals with good diversity should be selected as excellent individuals to improve the exploration ability of the algorithm. On the contrary, it is believed that the evolutionary process has entered the middle and late stages, and more emphasis should be placed on development ability, and individuals with good convergence and diversity should be selected as excellent individuals to improve the development ability of the algorithm. Adjust the balance between exploration and development according to the early, middle and late stages of evolution to ensure that the algorithm has an adaptive selection strategy at different stages; in environmental selection, in order to find more optimal solutions, a subset selection method based on the dual-space distance of the target space and the decision space is proposed, which comprehensively considers the distance from the individuals in the solution set in the target space and the decision space, and finally uses a new indicator DC i Comprehensively consider each solution based on fine-grained crowding distance ISCD i and distance D i , compared with the traditional environmental selection process based on crowding distance, the algorithm we proposed retains more different non-dominated solutions to a large extent. These methods can solve the problem that traditional multi-objective evolutionary algorithms cannot find multiple optimal paths in urban traffic path planning. Through this method, the algorithm can find more widely distributed non-dominated solutions, thereby generating multiple optimal paths more efficiently in practical applications. Ultimately, the present invention provides a more comprehensive solution set for urban traffic path planning problems, helping decision makers obtain more alternative high-quality path choices, and significantly improving the optimization effect of traffic path planning. This improvement enables us to achieve the ultimate goal of multi-modal multi-objective optimization, that is, to find multiple optimal paths that meet different needs in a complex urban traffic environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1It is a flow chart of the urban traffic path planning method based on multi-modal multi-objective differential evolution of the present invention;

[0064] Figure 2 is a map of a real city in Embodiment 6 of the present invention;

[0065] Figure 3 It is the map of the simulated city in Embodiment 6 of the present invention;

[0066] Figure 4 It is the first optimal path found in the map of the simulated city in Example 6 of the present invention.

[0067] Figure 5 It is the second optimal path found in the map of the simulated city in Example 6 of the present invention.

[0068] Figure 6 It is the third optimal path found in the map of the simulated city in Example 6 of the present invention. DETAILED DESCRIPTION

[0069] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0070] Example 1

[0071] The present invention is based on a multi-modal multi-objective differential evolution urban traffic path planning method, the process of which is as follows: Figure 1 As shown, the specific steps are as follows:

[0072] Step 1, preprocessing address data and simulating a city map based on the address data;

[0073] Step 2, determine the optimization target according to the map;

[0074] Step 3: Use a multi-modal multi-objective differential evolution algorithm to obtain the optimal path with the goal of minimizing the optimization objective.

[0075] Example 2

[0076] On the basis of Example 1, in step 1, the city map is simulated as a matrix consisting of 0 or 1, the area represented by 0 is a passable area, and the area represented by 1 is an impassable area, and only up, down, left, and right walking are allowed in the map, repeated walking is not allowed, and it is forbidden to go beyond the boundary of the map, and the coordinate value of each step in the walking sequence is used to represent the corresponding path;

[0077] Number each intersection on the map and record the number of the intersection that can be directly reached from the top, bottom, left, and right of each intersection;

[0078] White areas are set up in the city map to simulate traffic jams; T-junctions and intersections are regarded as intersections.

[0079] Example 3

[0080] Based on Example 2, the optimization target in step 2 is specifically:

[0081]

[0082] Example 4

[0083] Based on Example 3, step 3 is specifically as follows:

[0084] Step 3.1, generate a population according to step 1, each individual in the population represents a solution to path planning, that is, each individual in the population represents a path from the starting point to the end point in the city map of step 1;

[0085] Step 3.2, randomly initialize the population in the decision space. When initializing the population, map each path through a function to form the solution's passable path length, the number of white areas passed, and the number of intersections passed by the phenotype f(x), f(x) = {f 1 (x),f 2 (x),f 3 (x)};

[0086] Where: f 1 (x) represents the value of the path length, f 2 (x) represents the number of passes through the white area, f 3 (x) represents the number of intersections passed;

[0087] Step 3.3, perform non-dominated sorting based on fine-grained special crowding distance on the initialized population, and output the sorted new population;

[0088] Step 3.4, adaptively select excellent individuals and randomly select two solutions x from the new population obtained in step 3 r1 and x r2 , applying DE / current-to-exemplar / 1 mutation strategy to produce offspring to generate the daughter population;

[0089] Step 3.5, merge the offspring population obtained in step 3.4 with the parent population, perform non-dominated sorting based on fine-grained special crowding distance on the merged population, and calculate the DC of the individuals in the last non-dominated frontier i Value, according to DC i The value is to select the next generation population, that is, the individual with the smallest target, that is, the optimal individual;

[0090] Step 3.6, determine whether the evolutionary generation of the next generation population obtained in step 3.5 reaches the set maximum evolutionary generation. If it does not reach the maximum evolutionary generation, it means that the termination condition is not met, and jump to step 3.3. Otherwise, output the next generation population obtained in step 3.5 as the optimal solution set.

[0091] Example 5

[0092] Based on Example 4, clustering-based special crowding distance (CSCD) is a method widely used in MMOPs. The clustering algorithm is combined with SCD to form a CSCD method. Assume that the 9 solutions in the decision space are divided into three categories, the first category (6, 7, 8, 9), the second category (1, 2, 3, 4), and the third category (5). The calculation formula of the CSCD of individual 8 is as follows:

[0093] CD 8,x =(|x 7,1 -x 9,1 | / |x 6,1 -x 9,1 |)+(|x 7,2 -x 9,2 | / |x 6,2 -x 9,2 |)

[0094] CD 8,f =(|x 7,1 -x 9,1 | / |x 1,1 -x 9,1 |)+(|x 7,2 -x 9,2 | / |x 1,2 -x 9,2 |)

[0095]

[0096] We improved the above formula by subdividing it into four cases and proposed a fine-grained special crowding distance (ISCD):

[0097]

[0098] By improving CSCD, we proposed a fine-grained special crowding distance (ISCD) to measure the crowding distance of the solution more accurately. The new algorithm process including non-dominated sorting and ISCD method is called non-dominated sorting based on fine-grained special crowding distance. First, the population is non-dominated sorted and divided into multiple non-dominated frontiers (F 1 ,F 2 ,…F num), num is the number of non-dominated frontiers. After non-dominated sorting, each non-dominated frontier is divided into multiple classes by the k-means algorithm. In each class, the ISCD value of each individual is calculated, that is, the fine-grained special crowding distance value of each individual is calculated. Step 3.3 is specifically as follows:

[0099] Step 3.3.1, perform non-dominated sorting on the initialized population and divide the population into multiple non-dominated frontiers (F 1 ,F 2 ,…F num ), num is the number of non-dominated frontiers;

[0100] Step 3.3.2, after non-dominated sorting, each non-dominated front is divided into N clusters by the k-means clustering algorithm. In each cluster, the fine-grained special crowding distance value of each individual is calculated, that is, the ISCD value;

[0101] Step 3.3.3, sort all the solutions in the population according to the non-dominated order, and divide the population into multiple non-dominated frontiers (F 1 ,F 2 ,…F num ), num is the number of non-dominated frontiers, the solutions in the same non-dominated front are sorted according to the ISCD value, and finally the sorted new population is output.

[0102] For each class of n individuals, the i-th individual x i , which is based on the fine-grained special crowding distance value ISCD i Calculate according to the following formula:

[0103]

[0104] Among them, CD i,x For each class of n individuals, the i-th individual x i The decision space crowding distance, CD i,f For each class of n individuals, the i-th individual x i The target space crowding distance;

[0105] Among them, ICD i,x =CD i,x -(CD avg,f -CD i,f ), ICD i,f =CD i,f -(CD avg,x -CD i,x );

[0106] CD i,x =(|x i-1,1 -x i+1,1 | / |x1,1 -x n,1 |)+(|x i-1,2 -x i+1,2 | / |x 1,2 -x n,2 |)

[0107] CD i,f =(|x i-1,1 -x i+1,1 | / |x 1,1 -x n,1 |)+(|x i-1,2 -x i+1,2 | / |x 1,2 -x n,2 |)

[0108] Among them, x i-1 Indicates the clustering x i The left neighbor of an individual, x i+1 Indicates the clustering x i The right neighbor of an individual, x 1 represents the first individual of the cluster, x n represents the last individual in the cluster, x i,1 Represents individual x i The value of the first dimension in the decision space, x i,2 Represents individual x i The value of the second dimension in the decision space, x n,2 Represents individual x n The value of the second dimension in the decision space, x n,1 Represents individual x n The value of the first dimension in the decision space.

[0109] The specific steps of non-dominated sorting in step 3.3.1 are as follows: Initialize each solution in the population into two sets: the dominated solution set S i and dominate count n i , where the dominated solution set S i is the set of all solutions dominated by solution i, with domination count n i That is, how many solutions dominate solution i;

[0110] Traverse each pair of solutions in the initialized population solution, for any pair of solutions x i Reconciliation j , according to the definition of dominance relation, check the solution x i Whether it dominates the solution x j , specifically:

[0111] If the solution i is in f(x) = {f 1 (x),f 2 (x),f 3(x)} is not worse than solution j, and is better in any preferred goal, then solution i is judged to dominate solution j, and solution j is added to the dominating set S of solution i i , and the dominance count n of solution j j Add 1;

[0112] According to the above judgment method, the dominant solution set and domination count of each solution are obtained. Among all solutions, if the domination count of the corresponding solution is 0, then the solution is the first layer of non-dominated frontier; for each solution belonging to the first frontier, check the solutions it dominates, and reduce the domination count of the solutions it dominates by 1. If the domination count of a solution drops to 0, it will be placed in the next layer of frontier, and so on. All solutions have been assigned to different frontiers. At this time, the non-dominated sorting process is completed, and the population is divided into multiple non-dominated frontiers (F 1 ,F 2 ,…F num ).

[0113] The strategy of adaptively selecting exemplar (demonstration) individuals, DE / current-to-pbest / 1 strategy has been proven to have good effects in single-objective optimization. However, in multi-objective optimization, it is impossible to determine a unique pbest (historical best) individual. This embodiment forms a new mutation strategy DE / current-to-exemplar / 1 by modifying the mutation strategy DE / current-to-pbest / 1. The key to the DE / current-to-exemplar / 1 mutation strategy is to find exemplar individuals. Exemplar individuals represent excellent individuals. The evolutionary process hopes to produce more excellent individuals around this individual. Due to different requirements for convergence and diversity at different stages of the algorithm, the selection criteria for excellent individuals are also different. Therefore, we use the strategy of adaptively selecting exemplar individuals. Therefore, the process of adaptively selecting excellent individuals in this embodiment is as follows:

[0114] Step 3.4.1, define a parameter p 1 , Among them, G c refers to the current generation, while maxgen refers to the maximum generation;

[0115] Step 3.4.2, generate a random number between 0 and 1. If the random number is less than p 1, it is believed that the evolution process is in the early stage and more emphasis should be placed on exploration ability. Then, the five candidate individuals with the largest ISCD value are selected from the new population obtained in step 3.3, and an individual is randomly selected from all the candidate individuals as an excellent individual; otherwise, it is believed that the evolution process has entered the middle and late stages and more emphasis should be placed on development ability. Then, the convergence of each individual in the new population obtained in step 3.3 is calculated, and the five individuals with the best convergence are selected as candidate individuals. The individual with the largest ISCD value is selected from the candidate individuals as an excellent individual; among them, the individual convergence is calculated as the sum of each dimension of the individual in the target space, and the convergence con of any individual i is i The calculation formula is: Where M is the dimension of the target space; f k (x i ) represents individual x i The value of the kth dimension in the target space;

[0116] Step 3.4.3, randomly select two individuals x from the new population generated in step 3.3 r1 and x r2 , apply the DE / current-to-exemplar / 1 operator to generate offspring, where the DE / current-to-exemplar / 1 formula is as follows:

[0117] v i =x i +RR i ·(x exemplar -x i )+RR i ·(x r1 -x r2 )

[0118] Among them, v i represents the newly generated mutant individual, x i represents the current individual, x exemplar represents the excellent individuals selected in step 3.4.2, RR i is the scale factor;

[0119] Step 3.4.4, determine whether all individuals in the new population generated in step 3.3 have produced offspring. If an individual has not produced offspring, it means that the termination condition is not met, and jump to step 3.4.3, otherwise the loop ends.

[0120] The specific process of selecting the next generation population in step 3.5 is:

[0121] Step 3.5.1, when the new population generated in step 3.3 and the offspring of each individual obtained in step 3.4 are combined to form a combined population;

[0122] Step 3.5.2, according to the method in step 3.3.1, the combined population is classified into different frontiers (F1, F2, ...) through non-dominated sorting based on fine-grained special crowding distance, and then the frontiers are selected in turn to construct the population P. P is initialized as an empty set. Starting from F1, the individuals in the frontier are added to the population P in turn until the frontier Fj-1, where |F1∪F2∪...∪Fj-1|<|F1∪F2∪...∪Fj-1∪Fj|≥NP, and NP is the size of the parent population or the child population;

[0123] Step 3.5.2, unlike the traditional method of deleting solutions with high crowding, this method selects only one solution from the j-th front each time during the environmental selection process, specifically: initialize an archive set Ar as an empty set, find a solution with the largest special crowding distance value based on fine-grainedness in the j-th front, and put it into an archive Ar;

[0124] Step 3.5.3: exclude the individuals put into the file Ar in step 3.5.2 from the population P. The remaining individuals in the population P form the set Fj\Ar. Calculate each solution x in the set Fj\Ar. i The decision space distance D to the archive Ar i,x , where D i,x Represents the solution x in the decision space i The minimum distance to each individual in the archive Ar, D i,x Calculate according to the following formula:

[0125]

[0126] Among them, d dec (x i ,x j ) represents the decision space x i and x j The distance between

[0127] In the target space, calculate the target space distance D from each solution i in the solution set Fj\Ar to the file Ar i,f , where D i,f Represents the solution x in the target space i The minimum distance to each individual in the archive Ar, therefore, D i,f Calculate according to the following formula:

[0128]

[0129] Among them, d obj (x i ,x j ) represents x in the target space i and x j The distance between

[0130] Step 3.5.4, calculate the mean value D of the distance from all solutions to the archive Ar in the target space and decision space respectively avg,f and D avg,x , x i The final distance D of the individual i Calculate according to the following formula:

[0131]

[0132] Step 3.5.5, if only D is used i This may lead to a reduction in solution diversity. Therefore, we also need to consider the crowding distance of each solution when selecting the environment. The fine-grained special crowding distance can effectively measure the crowding distance between the individual target space and the decision space. Finally, a new indicator DC is used i Comprehensively consider each decongestion distance ISCD i and distance D i , calculate the DC of each individual i :

[0133] DC i =ISCD i +D i

[0134] Among them, ISCD i Represents individual x i Based on the fine-grained special crowding distance value, select the indicator DC in the solution set Fj\Ar i The largest solution is put into the set Ar, and the above process is repeated until the number of solutions in the file Ar plus the number of solutions in the solution set P equals NP;

[0135] Step 3.5.6, the individuals in the solution set P are considered to be the optimal individuals, that is, the optimal path. The individuals in the final solution set P include all the individuals in the first j-1 frontiers and some individuals in the jth frontier, that is, the optimal individuals.

[0136] Example 6

[0137] Based on Example 5, this example adopts the CEC2021 multi-modal multi-objective path planning (MMOPP) test problem. As we all know, the main roads in China's large cities have distinct characteristics, such as roundabouts, long straight roads, and complex alleys. The mapping of this test problem is created by simulating these characteristics. In addition, a fair and reasonable evaluation standard is given to evaluate the performance of different algorithms. The actual map of this example is as follows Figure 2 As shown, the simulated map is Figure 3As shown, the details are as follows: The map is simulated by a matrix composed of 0 or 1, where 0 represents a passable area and 1 represents an impassable area. In this problem, only up, down, left, and right walking are allowed, repeated walking is not allowed, and it is forbidden to go beyond the boundaries of the map. Each step is passable, and the coordinate value of each step in the walking sequence is used to represent this path. In real life, traffic jams and the number of intersections passed are important factors affecting traffic flow. In order to simulate this situation, some white areas are set in the map to simulate traffic jams.

[0138] There are three optimization objectives for the multimodal multi-objective path planning problem. A three-objective optimization model is established, which includes minimizing the length of the traversable path, the number of congested sections, and the number of intersections passed. The details are as follows:

[0139] f 1 : The length of the path that can be passed;

[0140] f 2 : The number of passing through the white area (traffic jam);

[0141] f 3 : The number of intersections passed.

[0142] The simulation results are shown in Figure 4-Figure 6 , recording the three different solutions found in this embodiment to solve the multi-modal multi-objective path planning problem. The following conclusions can be drawn:

[0143] The optimal path found in this embodiment is a path that has the best path length, the number of congested sections passed, and the number of intersections passed. In order to more intuitively display the different optimal paths found, Figure 4-Figure 6 These are three different optimal paths found by the multi-modal and multi-objective differential evolution algorithm.

[0144] Figure 4 The corresponding path is:

[0145] 127→119→95→68→43→44→26→27→28→29→37→38;

[0146] The path information represented by the solution is obtained through decoding as follows:

[0147] The length of the traversable path is 105; the number of congested sections is 3; the number of intersections passed is 10;

[0148] Figure 5 The corresponding path is:

[0149] 127→119→95→68→43→44→45→46→34→35→36→37→38;

[0150] The path information represented by the solution is obtained through decoding as follows:

[0151] The length of the traversable path is 97; the number of congested sections is 4; the number of intersections passed is 10;

[0152] Figure 6 The corresponding path is:

[0153] 127→119→95→96→97→70→69→44→45→46→34→35→36→37→38;

[0154] The path information represented by the solution is obtained through decoding as follows:

[0155] The length of the traversable path is 103; the number of congested sections passed is 3; and the number of intersections passed is 12.

Claims

1. An urban traffic path planning method based on multi-modal multi-objective differential evolution, characterized in that: The specific steps are as follows: Step 1, preprocessing address data and simulating a city map based on the address data; Step 2, determine the optimization target according to the map; Step 3: Use a multi-modal multi-objective differential evolution algorithm to obtain the optimal path with the goal of minimizing the optimization objective.

2. The urban traffic path planning method based on multi-modal multi-objective differential evolution according to claim 1 is characterized in that: The city map in step 1 is a matrix simulation composed of 0 or 1, where the area represented by 0 is a passable area, and the area represented by 1 is an impassable area. In the map, only up, down, left, and right walking are allowed, and repeated walking is not allowed. It is forbidden to go beyond the boundaries of the map, and the coordinate value of each step in the walking sequence is used to represent the corresponding path; Number each intersection on the map and record the number of the intersection that can be directly reached from the top, bottom, left, and right of each intersection; A white area is provided in the city map to simulate traffic jam; T-junctions and intersections are both regarded as intersections.

3. The urban traffic path planning method based on multi-modal multi-objective differential evolution according to claim 2 is characterized in that: The optimization goal in step 2 is specifically:

4. The urban traffic path planning method based on multi-modal multi-objective differential evolution according to claim 3 is characterized in that: The step 3 is specifically as follows: Step 3.1, generate a population according to step 1, each individual in the population represents a solution to path planning, that is, each individual in the population represents a path from the starting point to the end point in the city map of step 1; Step 3.2, randomly initialize the population in the decision space. When initializing the population, map each path through a function to form the solution's passable path length, the number of white areas passed, and the number of intersections passed, phenotype f(x), f(x) = {f1(x), f2(x), f3(x)}; Among them: f1(x) represents the value of the path length, f2(x) represents the number of white areas passed, and f3(x) represents the number of intersections passed; Step 3.3, perform non-dominated sorting based on fine-grained special crowding distance on the initialized population, and output the sorted new population; Step 3.4, adaptively select excellent individuals and randomly select two solutions x from the new population obtained in step 3 r1 and x r2 , applying DE / current-to-exemplar / 1 mutation strategy to produce offspring to generate the daughter population; Step 3.5, merge the offspring population obtained in step 3.4 with the parent population, perform non-dominated sorting based on fine-grained special crowding distance on the merged population, and calculate the DC of the individuals in the last non-dominated frontier i Value, according to DC i The value is to select the next generation population, that is, the individual with the smallest target, that is, the optimal individual; Step 3.6, determine whether the evolutionary generation of the next generation population obtained in step 3.5 reaches the set maximum evolutionary generation. If it does not reach the maximum evolutionary generation, it means that the termination condition is not met, and jump to step 3.

3. Otherwise, output the next generation population obtained in step 3.5 as the optimal solution set.

5. The urban traffic path planning method based on multi-modal multi-objective differential evolution according to claim 4 is characterized in that: The step 3.3 is specifically as follows: Step 3.3.1, perform non-dominated sorting on the initialized population and divide the population into multiple non-dominated frontiers (F1, F2, ... F num ), num is the number of non-dominated frontiers; Step 3.3.2, after non-dominated sorting, each non-dominated front is divided into N clusters by the k-means clustering algorithm. In each cluster, the fine-grained special crowding distance value of each individual is calculated, that is, the ISCD value; Step 3.3.3, sort all the solutions in the population according to the non-dominated sorting method and divide the population into multiple non-dominated frontiers (F1, F2, ... F num ), num is the number of non-dominated frontiers, the solutions in the same non-dominated front are sorted according to the ISCD value, and finally the sorted new population is output.

6. The urban traffic path planning method based on multi-modal multi-objective differential evolution according to claim 5 is characterized in that: For each class of n individuals, the i-th individual x i , which is based on the fine-grained special crowding distance value ISCD i Calculate according to the following formula: Among them, CD i,x For each class of n individuals, the i-th individual x i The decision space crowding distance, CD i,f For each class of n individuals, the i-th individual x i The target space crowding distance; Among them, ICD i,x = CD i,x -(CD avg,f -CD i,f ), ICD i,f = CD i,f -(CD avg,x -CD i,x ) ; CD i,x =(|x i-1,1 -x i+1,1 | / |x 1,1 -x n,1 |)+(|x i-1,2 -x i+1,2 | / |x 1,2 -x n,2 |) CD i,f =(|x i-1,1 -x i+1,1 | / |x 1,1 -x n,1 |)+(|x i-1,2 -x i+1,2 | / |x 1,2 -x n,2 |) Among them, x i-1 Indicates the clustering x i The left neighbor of an individual, x i+1 Indicates the clustering x i The right neighbor of an individual, x1 represents the first individual in the cluster, x n represents the last individual in the cluster, x i,1 Represents individual x i The value of the first dimension in the decision space, x i,2 Represents individual x i The value of the second dimension in the decision space, x n,2 Represents individual x n The value of the second dimension in the decision space, x n,1 Represents individual x n The value of the first dimension in the decision space.

7. The urban traffic path planning method based on multi-modal multi-objective differential evolution according to claim 6 is characterized in that: The non-dominated sorting in step 3.3.1 is specifically as follows: each solution in the population is initialized into two sets: the dominated solution set S i and dominate count n i , where the dominated solution set S i is the set of all solutions dominated by solution i, with domination count n i That is, how many solutions dominate solution i; Traverse each pair of solutions in the initialized population solution, for any pair of solutions x i Reconciliation j , according to the definition of dominance relation, check the solution x i Whether it dominates the solution x j , specifically: If solution i is not worse than solution j on f(x) = {f1(x), f2(x), f3(x)} and is better on any preferred target, then solution i is judged to dominate solution j and solution j is added to the dominating set S of solution i i , and the dominance count n of solution j j Add 1; According to the above judgment method, the dominant solution set and domination count of each solution are obtained. Among all the solutions, if the domination count of the corresponding solution is 0, then the solution is the first layer of non-dominated frontier; for each solution belonging to the first frontier, check the solutions it dominates, and reduce the domination count of the solutions it dominates by 1. If the domination count of a solution drops to 0, it will be placed in the next layer of frontier, and so on. All solutions have been assigned to different frontiers. At this time, the non-dominated sorting process is completed, and the population is divided into multiple non-dominated frontiers (F1, F2, ... F num ).

8. The urban traffic path planning method based on multi-modal multi-objective differential evolution according to claim 6 is characterized in that: The step 3.4 is specifically as follows: Step 3.4.1, define a parameter p1, Among them, G c refers to the current generation, while maxgen refers to the maximum generation; Step 3.4.2, generate a random number between 0 and 1. If the random number is less than p1, it is considered that the evolution process is in the early stage, and the five candidate individuals with the largest ISCD value are selected from the new population obtained in step 3.3, and an individual is randomly selected from all the candidate individuals as an excellent individual; otherwise, it is considered that the evolution process has entered the middle and late stages, and the convergence of each individual in the new population obtained in step 3.3 is calculated, and the five individuals with the best convergence are selected as candidate individuals, and the individual with the largest ISCD value is selected from the candidate individuals as an excellent individual; where the individual convergence is calculated as the sum of each dimension of the individual in the target space, and the convergence con of any individual i is i The calculation formula is: Where M is the dimension of the target space; f k (x i ) represents individual x i The value of the kth dimension in the target space; Step 3.4.3, randomly select two individuals x from the new population generated in step 3.3 r1 and x r2 , apply the DE / current-to-exemplar / 1 operator to generate offspring, where the DE / current-to-exemplar / 1 formula is as follows: v i =x i +RR i ·(x exemplar -x i )+RR i ·(x r1 -x r2 ) Among them, v i represents the newly generated mutant individual, x i represents the current individual, x exemplar represents the excellent individual selected in step 3.4.2, RR i is the scale factor; Step 3.4.4, determine whether all individuals in the new population generated in step 3.3 have produced offspring. If an individual has not produced offspring, it means that the termination condition is not met, and jump to step 3.4.3, otherwise the loop ends.

9. The urban traffic path planning method based on multi-modal multi-objective differential evolution according to claim 8 is characterized in that: The specific process of selecting the next generation population in step 3.5 is as follows: Step 3.5.1, when the new population generated in step 3.3 and the offspring of each individual obtained in step 3.4 are combined to form a combined population; Step 3.5.2, according to the method in step 3.3.1, the combined population is classified into different frontiers (F1, F2, ...) through non-dominated sorting based on fine-grained special crowding distance, and then the frontiers are selected in turn to construct the population P. P is initialized as an empty set. Starting from F1, the individuals in the frontier are added to the population P in turn until the frontier Fj-1, where |F1∪F2∪...∪Fj-1|<|F1∪F2∪...∪Fj-1∪Fj|≥NP, and NP is the size of the parent population or the child population; Step 3.5.2, initialize an archive set Ar as an empty set, find a solution with the largest special crowding distance value based on fine-grainedness in the jth frontier, and put it into an archive Ar; Step 3.5.3: exclude the individuals put into the file Ar in step 3.5.2 from the population P. The remaining individuals in the population P form the set Fj\Ar. Calculate each solution x in the set Fj\Ar. i The decision space distance D to the archive Ar i,x , where D i,x Represents the solution x in the decision space i The minimum distance to each individual in the archive Ar, D i,x Calculate according to the following formula: Among them, d dec (x i ,x j ) represents the decision space x i and x j The distance between In the target space, calculate the target space distance D of each solution i in the solution set Fj\Ar to the file Ar i,f , where D i,f Represents the solution x in the target space i The minimum distance to each individual in the archive Ar, therefore, D i,f Calculate according to the following formula: Among them, d obj (x i ,x j ) represents x in the target space i and x j The distance between Step 3.5.4, calculate the mean value D of the distance from all solutions to the archive Ar in the target space and decision space respectively avg,f and D avg,x , x i The final distance D of the individual i Calculate according to the following formula: Step 3.5.5, calculate the DC of each individual i : DC i =ISCD i +D i Among them, ISCD i Represents individual x i Based on the fine-grained special crowding distance value, select the indicator DC in the solution set Fj\Ar i The largest solution is put into the set Ar, and the above process is repeated until the number of solutions in the file Ar plus the number of solutions in the solution set P equals NP; Step 3.5.6, the individuals in the solution set P are considered to be the optimal individuals, that is, the optimal path. The individuals in the final solution set P include all the individuals in the first j-1 frontiers and some individuals in the jth frontier, that is, the optimal individuals.

Images