An improved dune cat algorithm-based electric vehicle path planning method

Abstract

The application belongs to the field of path planning, and discloses an electric vehicle path planning method based on improved sand cat algorithm, which comprises the following steps: firstly, searching a high-dimensional solution space based on parallelism of the sand cat (SCSO) algorithm to quickly obtain an initial distribution scheme; secondly, adaptively screening an elite distribution route according to a target function, discretizing and coding the elite distribution route, sorting the elite distribution route, moving and mutating the elite distribution route, and then destroying and repairing the coding of the elite distribution route by using a large field search operator to improve the global search capability of the SCSO algorithm; finally, adopting an elite individual migration mechanism to share path information and give full play to the cooperation advantages among sand cat groups so as to improve the solution quality of the hybrid algorithm. The algorithm can effectively shorten the distribution time and reduce the invalid path time.

Description

Technical Field

[0001] This invention relates to the field of path planning technology, specifically a path planning method for electric vehicles based on an improved Sand Cat algorithm. Background Technology

[0002] Electric vehicles are the primary mode of transportation for urban logistics and distribution, and their rational route optimization and charging strategies are crucial for achieving urban carbon neutrality. The electric vehicle route optimization problem with time windows is a nondeterministic polynomial-hard problem, meaning it considers vehicle battery level, load capacity, and time window constraints in addition to the existing time window vehicle route optimization problem. This poses a significant challenge to traditional exact search optimization algorithms. For example, traditional tabu search, simulated annealing, and adaptive large neighborhood search iterate using a single candidate solution, achieving fast convergence but lacking global search capability.

[0003] Intelligent optimization algorithms based on population iterative search are methods that leverage computational intelligence to find optimal or satisfactory solutions to various complex optimization problems, and have been widely applied in many fields. However, the iterative optimization nature of these algorithms typically results in low efficiency, making them difficult to apply to large-scale, high-dimensional, or real-time-critical complex optimization problems. For example, genetic algorithms, sandcat swarm optimization, and ant colony optimization perform spatial searches on multiple candidate solutions, resulting in slower convergence speeds but effectively mitigating local optima.

[0004] With the rapid development of computer technology, many scholars at home and abroad have begun to focus on and study the cooperative mechanisms in various hybrid intelligent optimization algorithms. The aim is to improve algorithm performance by having multiple objects conduct cooperative searches through certain strategies, thereby leveraging the strengths of various algorithms to improve their performance and solve increasingly complex problems. Summary of the Invention

[0005] To address the shortcomings and deficiencies of existing technologies, this invention provides an accurate electric vehicle path planning method based on an improved Sand Cat algorithm, which effectively improves path planning efficiency.

[0006] To achieve the above objectives, the present invention is implemented through the following technical solution:

[0007] This invention is a path planning method for electric vehicles based on an improved Sand Cat algorithm, comprising the following steps:

[0008] Step 1: Establish an optimization function for the electric vehicle route planning problem model under the condition of uncertain delivery vehicle quantity, and set corresponding time windows, power constraints and other restrictions;

[0009] Step 2: Initialize the various parameters in the Sand Cat algorithm, the move mutation algorithm, and the large neighborhood search algorithm, and discretize the Sand Cat population;

[0010] Step 3: Calculate the sand cat sensitivity based on the initial parameters, obtain the stage decision variables, divide the sand cat group activity into two stages: attack and search, and thus generate a preliminary solution;

[0011] Step 4: Decode the preliminary solution. The optimal solution is used as the elite cat and proceeds to Step 5. The others are used as ordinary cats and proceed to Step 6.

[0012] Step 5: Use moving mutation as the individual mutation method for sand cats. Remove customers with low relevance weights based on location and path factors, and insert the removed customers into the position with the minimum global cost using the farthest insertion heuristic.

[0013] Step 6: Update the individual search using the particle swarm optimization algorithm, and make the optimization solution of the ordinary cat approach that of the elite cat based on the individual migration mechanism;

[0014] Step 7: Repeat steps 3-6 until the maximum number of iterations is reached; calculate and compare the optimal solutions for elite cats and ordinary cats to obtain the global optimal solution.

[0015] A further improvement of this invention is that the model optimization function established in step 1 is as follows:

[0016]

[0017] Where η represents the weight of the number of vehicles used, and d ij V represents the distance between vertices, V represents the set of vertices containing charging stations and all customers, and V0 represents the set of vertices containing distribution centers and all customers. N+1 Let x represent the set of vertices containing charging stations, distribution centers, and all customers. ij These are binary decision variables.

[0018] The constraint condition is:

[0019] (1) There is only one distribution center. All electric logistics vehicles depart after being fully charged at the distribution center, complete the delivery task, and return to the distribution center.

[0020] (2) Electric logistics vehicles are homogeneous vehicles, and all vehicles have the same load capacity, charging rate, power consumption rate and battery capacity.

[0021] (3) Each customer can only visit once and can only use one vehicle.

[0022] (4) The time window remains unchanged for each customer.

[0023] (5) The distribution center has sufficient vehicle reserves.

[0024] (6) The load on each vehicle shall not exceed the vehicle’s maximum load capacity.

[0025] A further improvement of the present invention is that the specific process of step 2 is as follows:

[0026] For the electric vehicle routing problem under d-dimensional multi-constraints, the initialization steps of the improved Sand Cat algorithm are as follows: (1) Each Sand Cat represents a delivery scheme for electric vehicle routing under multi-constraints, so the dimension of the Sand Cat is set to d; (2) The position of each Sand Cat is defined as vector X. i =(x i1 ,x i2 ,...,x id (3) The location of the sand cat is converted into a discretized code, and its chromosome length d = N + M + 1, where N is the number of customers and M is the maximum number of vehicles used. The sand cat location is discretized by sorting to generate the sand cat chromosome Y. i =(y i1 ,y i2 ,...,y id (4) Set the probability of movement mutation P m And the number of transferred customers C.

[0027] A further improvement of the present invention lies in the specific process of step 3:

[0028] The attack and search phases of the sand cat are distinguished based on the stage decision variable R. When S M / 2≤|R|≤S M At that time, the sand cat is in the search phase; when |R|≤S M At / 2, the Sand Cat is in its attack phase, where S M This is the initial sensitivity value.

[0029] (1) Search phase: During the search phase, the sand cats determine their best historical position based on F. ib (k), Current position F c (k) and sensitivity range r update position F c (k+1), the specific formula is as follows:

[0030] F c (k+1)=r·(F ib (k)-rand(0,1)·F c (k))

[0031] Where k is the number of iterations. The sensitivity range r allows for relatively random location selection, effectively preventing the generation of local optima.

[0032] (2) Attack Phase: During the attack phase, the Sand Cat uses its optimal global position F b (k)Pos b (i) Current position F c (k), random direction θ, and sensitivity range r update position F c (k+1), where each individual can choose a search direction from any angle of its original position, ensuring the randomness of the algorithm. The specific formula is as follows:

[0033] F s (k+1)=|rand(0,1)·F b (k)-F c (k)|

[0034] F c (k+1)=F b (k)-r·F s (k+1)cosθ

[0035] A further improvement of this invention is that: in step 5, the positions of all sand cats in all attack phases are calculated, and all positions are discretized and used as sand cat chromosome numbers. Elite cats are then selected based on the objective function. Elite cats require removal and insertion operations involving movement mutation and large-domain search. After movement mutation, clients with low C-position relevance are removed from the elite cats based on their weights; and the removed clients are inserted into the position with the lowest global cost using the furthest insertion heuristic.

[0036] Specifically, the steps include the following:

[0037] Step 5.1: Use movement mutation as the mutation method. Randomly select a gene from the chromosome and move it a few positions to the left or right.

[0038] Step 5.2: After disrupting and reconstructing the chromosome, a new feasible solution is sought. This process provides a better mechanism to reduce local optima caused by genetic algorithms.

[0039] 1) Removal: This refers to selecting customers to be removed using a certain weight ω(i,j). The two factors affecting the weight are: distance factor R. ij ', Path Factor N ij '. The distance d between vertices i and j. ij To define the distance correlation R between two points ij ', R ij The smaller the value, the greater the distance correlation between the two points. Similarly, the path correlation N between two points on the same transportation route... ij The path correlation is greater than that of different paths. The weight ω(i,j) can be defined as:

[0040]

[0041]

[0042] Among them, R ij The value range is [0,1]. N is calculated when customers i and j are on the same path. ij 'Take a value of 1 otherwise. Calculate the relevance weight ω(i,j) between each customer and other customers in turn, and remove the T customers with the lowest relevance weights.

[0043] 2) Insertion: Let Δi be the delivery cost of removing customer i and inserting it into a position on the removed chromosome, where this position minimizes the cost increase. The process continues until all removed customers are reinserted onto the removed chromosome. During each insertion, the furthest insertion heuristic selects the removed customer i with the lowest global cost and inserts it into the position that minimizes the global cost. This continues until all removed customers are reinserted onto the removed chromosome.

[0044] A further improvement of the present invention is that: the specific process of step 6 is that ordinary cats learn from elite cats by speed update and position update to optimize their own position, so that the generated solution is closer to the solution of elite cats; the ordinary group adopts an elite learning strategy to share the position information of elite cats.

[0045] A further improvement of the present invention is that the model comprehensively considers actual factors such as vehicle cargo capacity, battery range, charging time and customer time window, and the method uses a multi-population hybrid collaborative intelligent evolution mechanism to enhance the local search capability of the algorithm while improving the evolutionary capability of the sand cat population.

[0046] The beneficial effects of this invention are as follows: First, the improved Sand Cat algorithm of this invention introduces the idea of ​​movement mutation in genetic algorithms and large-area search to improve the local search capability of the Sand Cat algorithm; second, it adopts an elite individual migration mechanism to share information and achieve the co-evolution of the population; finally, it designs an adaptive method to increase the number of calls to the local search module as the number of iterations increases, so that the algorithm can improve the convergence speed while ensuring convergence accuracy.

[0047] This invention enables electric logistics vehicles to more accurately plan delivery times and power consumption, and the optimized method is highly efficient and low-carbon. Attached Figure Description

[0048] Figure 1 The improved Sand Cat algorithm described in this invention optimizes the path diagram for electric vehicles.

[0049] Figure 2 This refers to the Elite Cat Movement Mutation Method described in this invention.

[0050] Figure 3 This is the farthest insertion heuristic method described in this invention.

[0051] Figure 4 The figure shows the optimal cost iteration curve in the later stage of the RC101 search using the method of this invention in the simulation. Detailed Implementation

[0052] The embodiments of the present invention will be disclosed below with reference to the drawings. For clarity, many practical details will be described in the following description. However, it should be understood that these practical details are not intended to limit the invention. That is, in some embodiments of the invention, these practical details are not essential.

[0053] like Figure 1 As shown, this invention is a path planning method for electric vehicles based on an improved Sand Cat algorithm. The planning method includes the following steps:

[0054] Step 1: Establish the optimization function for the electric logistics vehicle route planning problem under the condition of uncertain delivery vehicle quantity, expressed as:

[0055]

[0056] Where η represents the weight of the number of vehicles used, and d ij V represents the distance between vertices, V represents the set of vertices containing charging stations and all customers, and V0 represents the set of vertices containing distribution centers and all customers. N+1 Let x represent the set of vertices containing charging stations, distribution centers, and all customers. ij These are binary decision variables.

[0057] The constraints for determining the delivery route are as follows:

[0058] (1) There is only one distribution center. All electric logistics vehicles depart after being fully charged at the distribution center, complete the delivery task, and return to the distribution center.

[0059] (2) Electric logistics vehicles are homogeneous vehicles, and all electric logistics vehicles have the same load capacity, charging rate, power consumption rate and battery capacity.

[0060] (3) Each customer can only visit once and can only use one electric logistics vehicle;

[0061] (4) The time window remains unchanged for each customer;

[0062] (5) The distribution center has a sufficient reserve of electric logistics vehicles;

[0063] (6) The load of each electric logistics vehicle shall not exceed the vehicle’s maximum load capacity.

[0064] Step 2: Initialize the parameters in the Sand Cat algorithm, the move mutation algorithm, and the large neighborhood search algorithm, and discretize the Sand Cat population.

[0065] For the electric vehicle routing problem under d-dimensional multi-constraints, the initialization steps of the improved Sand Cat algorithm are as follows: (1) Each Sand Cat represents a delivery scheme for electric vehicle routing under multi-constraints, so the dimension of the Sand Cat is set to d; (2) The position of each Sand Cat is defined as vector X. i =(x i1 ,x i2 ,...,x id (3) The location of the sand cat is converted into a discretized code, and its chromosome length d = N + M + 1, where N is the number of customers and M is the maximum number of vehicles used. The sand cat location is discretized by sorting to generate the sand cat chromosome Y. i =(y i1 ,y i2 ,...,y id (4) Set the probability of movement mutation P m And the number of transferred customers C.

[0066] Step 3: Calculate the sand cat sensitivity based on the initial parameters from Step 2, obtain the stage decision variables, and divide the sand cat group activity into two stages: attack and search, thereby generating a preliminary solution, specifically:

[0067] The attack and search phases of the sand cat are distinguished based on the stage decision variable R. When S M / 2≤|R|≤S M At that time, the sand cat is in the search phase, when |R|≤S M At / 2, the Sand Cat is in its attack phase, where S M This is the initial value for sensitivity, specifically...

[0068] (1) Search phase: During the search phase, the sand cats determine their best historical position based on F. ib (k), Current position F c (k) and sensitivity range r update position F c (k+1), the specific formula is as follows:

[0069] F c (k+1)=r·(F ib (k)-rand(0,1)·F c (k))

[0070] Where k is the number of iterations, and the sensitivity range r makes the location selection relatively random, effectively preventing the generation of local optima.

[0071] (2) Attack Phase: During the attack phase, the Sand Cat uses its optimal global position F b (k)Pos b (i) Current position Fc (k), random direction θ, and sensitivity range r update position F c (k+1), each individual can choose a search direction from any angle of its original position, ensuring the randomness of the algorithm. The specific formula is as follows:

[0072] F s (k+1) = |rand(0,1).F b (k)-F c (k)|

[0073] F c (k+1)=F b (k)-r·F s (k+1)cosθ

[0074] Step 4: Decode the preliminary solution generated in Step 3. The optimal solution is used as the elite cat and the operation in Step 5 is performed. The other solutions are used as ordinary cats and the operation in Step 6 is performed.

[0075] Step 5: Calculate the positions of the sand cats in all attack phases, and discretize all positions as sand cat chromosome numbers. Based on the objective function, select elite cats. Elite cats require removal and insertion operations involving movement mutation and large-domain search. After movement mutation, remove customers with low C-position relevance based on their weights, and insert the removed customers into the position with the minimum global cost using the furthest insertion heuristic. Specifically, this includes the following steps:

[0076] Step 5.1, as follows Figure 2 As shown, a moving mutation is used as the mutation method. A gene is randomly selected from the chromosome and moved a few positions to the left or right. When the sand cat's position k is the optimal position, the moving mutation is used to finely optimize the sand cat's position. After the elite cats are subjected to the moving mutation, customers with low C-position relevance are removed. Then, the removed customers are inserted into the delivery route using the farthest insertion heuristic.

[0077] Step 5.2: After destroying the chromosome, rebuild it and look for new feasible solutions. This process provides a better mechanism to reduce local optima caused by genetic algorithms.

[0078] (1) Removal: This refers to selecting customers to be removed using a certain weight ω(i,j). The two factors affecting the weight are: distance factor R. ij ', Path Factor N ij ', using the distance d between vertices i and j ij To define the distance correlation R between two points ij ', R ij The smaller the value of N, the greater the distance correlation between the two points. Similarly, the greater the path correlation N between two points on the same transportation route.ij For path correlations greater than different paths, the weight ω(i,j) can be defined as:

[0079]

[0080]

[0081] Among them, R ij The value range is [0,1], and N is the value when customers i and j are on the same path. ij 'Take a value of 1, otherwise take a value of 0. Calculate the relevance weight ω(i,j) between each customer and other customers in turn, and remove the T customers with lower relevance weights.'

[0082] (2) Let Δi be the delivery cost after removing customer i and inserting it into a certain position on the removed chromosome, where this position minimizes the increase in cost, such as... Figure 3 As shown, the process continues until all removed clients are re-inserted into the removed chromosome. When inserting a client, the farthest insertion heuristic selects the removed client i with the lowest global cost and inserts it into the position with the lowest global cost. This continues until all removed clients are re-inserted into the removed chromosome.

[0083] Step 6: Update the individual search using the particle swarm optimization algorithm. Based on the individual migration mechanism, the optimal solution for ordinary cats is made closer to that of elite cats.

[0084] The specific process is as follows: Ordinary cats learn from elite cats by updating their speed and position, optimizing their own positions to make the generated solutions closer to those of the elite cats. The ordinary group adopts an elite learning strategy to share the location information of the elite cats.

[0085] Step 7: In the baseline VRPTW optimization example, 21 charging stations were added to form a baseline EVRPTW optimization instance to verify the performance of the proposed algorithm. The parameters of SCSO-GA were set as follows: sand cat population size N0 = 500, maximum number of iterations M. g =400, S M =2, learning factors c1=c2=1.5, inertia weight w=0.8, mutation probability P m =0.05, the penalty function coefficient for violating the capacity constraint is 100, and the penalty function coefficient for violating the time window constraint is 100. The improved Sand Cat Algorithm (SCSO-GA) and the Genetic Large Neighbor Search Algorithm (GA-LNS) described in this invention are used to plan multi-constraint electric vehicle paths.

[0086] Table 1 compares the path planning results of the method of this invention and the genetic big-field search algorithm in the simulation.

[0087] Table 1

[0088]

[0089] Table 1 shows that the SCSO-GA algorithm is significantly better than the GA-LNS algorithm, with a shorter running time. This indicates that the improved Sand Cat algorithm utilizes a genetic algorithm to enhance its overall running speed. The SCSO-GA algorithm iterated 400 times, calling the genetic algorithm part 4223 times, while the GA-LNS algorithm required 10000 calls. Therefore, the introduction of the Sand Cat swarm optimization algorithm greatly accelerated the algorithm's running speed, and the addition of the genetic algorithm strengthened the algorithm's local search capability. Figure 4 As shown, with the increase of the number of iterations, the improved algorithm makes the change of its cost curve in the later stage significantly greater than the stagnation stage caused by local optima in the middle stage.

[0090] The algorithm proposed in this invention can effectively shorten delivery time and reduce invalid route time.

[0091] The above description is merely an embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principle of the present invention should be included within the scope of the claims of the present invention.

Claims

1. A path planning method for electric vehicles based on an improved Sand Cat algorithm, characterized in that: The electric vehicle route planning method includes the following steps: Step 1: Establish an optimization function for the route planning problem of electric logistics vehicles under uncertain delivery vehicle volume, and set corresponding time windows and power constraints. Step 2: Initialize the parameters in the Sand Cat algorithm, the move mutation algorithm, and the large neighborhood search algorithm, and discretize and encode the Sand Cat population; Step 3: Calculate the sand cat sensitivity based on the initial parameters in Step 2, obtain the stage decision variables, divide the sand cat group activity into two stages: attack and search, and thus generate a preliminary solution; Step 4: Decode the preliminary solution generated in Step 3. The optimal solution is used as the elite cat and the operation in Step 5 is performed. The other solutions are used as ordinary cats and the operation in Step 6 is performed. Step 5: Use moving mutation as the individual mutation method for sand cats. Remove customers with low relevance weights based on location and path factors, and insert the removed customers into the position with the minimum global cost using the farthest insertion heuristic. Step 6: Update the individual search using the particle swarm optimization algorithm, and make the optimization solution of the ordinary cat close to that of the elite cat based on the individual migration mechanism; Step 7: Repeat steps 3-6 until the maximum number of iterations is reached. Calculate and compare the optimal solutions for elite cats and ordinary cats to obtain the global optimal solution, where: In step 5, the positions of all sand cats in all attack phases are calculated, and all positions are discretized and used as sand cat chromosome numbers. Elite cats are selected according to the objective function. Elite cats need to undergo removal and insertion operations through movement mutation and large-domain search. After the elite cats undergo movement mutation, customers with low C-position relevance are removed from them according to their weight. The removed customers are then inserted into the position with the minimum global cost using the farthest insertion heuristic. The specific steps include the following: Step 5.1: Use movement mutation as the mutation method. Randomly select a gene from the chromosome and move it a few positions to the left or right. Step 5.2: Destroy and reconstruct the chromosome to find new feasible solutions.

2. The electric vehicle path planning method based on the improved Sand Cat algorithm according to claim 1, characterized in that: The optimization function of the electric logistics vehicle route planning problem model established in step 1 under the condition of uncertain delivery vehicle quantity is expressed as: in, The weight of the number of vehicles used is represented by d. ij V represents the distance between vertices, V represents the set of vertices containing charging stations and all customers, and V0 represents the set of vertices containing distribution centers and all customers. N+1 Let x represent the set of vertices containing charging stations, distribution centers, and all customers. ij These are binary decision variables.

3. A method for electric vehicle path planning based on an improved Sand Cat algorithm according to claim 1 or 2, characterized in that: The power constraint set in step 1 is as follows: (1) There is only one distribution center. All electric logistics vehicles depart after being fully charged at the distribution center, complete the delivery task, and return to the distribution center. (2) Electric logistics vehicles are homogeneous vehicles, and all electric logistics vehicles have the same load capacity, charging rate, power consumption rate and battery capacity. (3) Each customer may only visit once and may only use one electric logistics vehicle; (4) The time window remains unchanged for each customer; (5) The distribution center has a sufficient reserve of electric logistics vehicles; (6) The load of each electric logistics vehicle shall not exceed the maximum load capacity of the vehicle.

4. The electric vehicle path planning method based on the improved Sand Cat algorithm according to claim 1, characterized in that: The specific process of initializing the parameters in the Sand Cat algorithm, the move mutation algorithm, and the large neighborhood search algorithm in step 2, and discretizing the Sand Cat population, includes the following steps: Step 2.1: Each Sand Cat represents a delivery scheme for electric vehicle path planning under multiple constraints, so the dimension of the Sand Cat is set to d; Step 2.2: Generate the position of each sand cat, defined as vector X. i =(x i1 ,x i2 ,...,x id The total number of individuals is set to n; Step 2.3: The location of the sand cat is transformed into a discretized code, with a chromosome length d = N + M + 1, where N is the number of customers and M is the maximum number of vehicles. The sand cat location is discretized using a sorting method to generate the sand cat chromosome Y. i =(y i1 ,y i2 ,...,y id ); Step 2.4: Set the migration mutation probability P m And the number of transferred customers C.

5. The electric vehicle path planning method based on the improved Sand Cat algorithm according to claim 1, characterized in that: In step 3, the sand cat sensitivity is calculated based on the initial parameters from step 2 to obtain the stage decision variables. The sand cat group activity is divided into two stages: attack and search, thereby generating a preliminary solution, specifically: The attack and search phases of the sand cat can be distinguished based on the stage decision variable R: (1) Search phase: During the search phase, the sand cats determine their best historical position F based on their individual history. ib (k), Current position F c (k) and sensitivity range r update position F c (k+1), the specific formula is as follows: Where k is the number of iterations; (2) Attack Phase: During the attack phase, the Sand Cat uses its global optimal position F b (k), Current position F c (k), random direction θ, and sensitivity range r update position F c (k+1), the specific formula is as follows: 。 6. The electric vehicle path planning method based on the improved Sand Cat algorithm according to claim 1, characterized in that: Step 5.2 specifically includes: Step 5.2.1, Removal: refers to removing items by applying a certain weight. When selecting customers to be removed, two factors influence the weighting: distance. Path factors The distance between vertices i and j To define the distance correlation between two points , The smaller the distance, the greater the correlation between the two points. Similarly, the greater the path correlation between two points on the same transportation route. Path correlation greater than different paths, weight Defined as: in, The value range is [0,1], when customers i and j are on the same path. The value is 1 if the value is 1, otherwise it is 0, and so on. Relevance weights between each customer and other customers Remove customers in position T with low relevance weight; Step 5.2.1, set To minimize the delivery cost of removing customer i by inserting it into a certain position on the removed chromosome, the process continues until all removed customers are reinserted into the removed chromosome. During each insertion, the farthest insertion heuristic selects the removed customer i with the lowest global cost and inserts it into the position that minimizes the global cost. This process continues until all removed customers are reinserted into the removed chromosome.

7. The electric vehicle path planning method based on the improved Sand Cat algorithm according to claim 1, characterized in that: The specific process of step 6 is as follows: ordinary cats learn from elite cats by updating speed and position to optimize their own position, so that the generated solution is closer to the solution of elite cats. The ordinary group adopts the elite learning strategy to share the position information of elite cats.

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