CN112132312B - Path planning method based on evolutionary multi-objective multi-task optimization - Google Patents
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Abstract
The invention provides a vehicle path planning method based on evolution multi-objective multi-task optimization, which takes each objective function of vehicle path planning as an independent task and solves a plurality of tasks simultaneously by utilizing operations of population structure, information migration, generation of filial generation, population updating and the like in the multi-task optimization; adopting a two-stage strategy of alternately performing multi-task optimization and multi-target optimization, switching the multi-task optimization process to the multi-target optimization process when a set switching condition is met, and optimizing a non-dominant solution set through operations of multi-target optimization such as population structure, generation of filial generation, population updating and external archive updating; and (3) adopting a population reconstruction strategy based on elite retention, retaining only part of elite solutions when set reconstruction conditions are met, and regenerating and adding the rest planning schemes into the population in a Gaussian walking-based mode. The method provided by the invention solves the problem that the optimization information of the similar problem can not be effectively exchanged and cooperated in the solving process, realizes the information sharing of the similar problem and improves the solving performance of the VRP.
Description
Technical Field
The invention relates to the field of path planning, in particular to a path planning method based on evolution multi-objective multi-task optimization.
Background
The Vehicle Routing Problem (VRP) is a key link for optimization in modern logistics service, is also a link with the most service cost consumption in the logistics service, and is an indispensable support part for developing modern electronic commerce activities. On the other hand, postal delivery problems, airplane flight scheduling, railway vehicle marshalling, wharf dispatching, water transportation ship dispatching, bus dispatching, power dispatching, medical resource dispatching in home care and the like in the real world can be abstracted as VRP. At present, most of research on vehicle path problems focuses on abstracting the vehicle path problems into a single-target or multi-target model, and then solving the vehicle path problems by using a single-target or multi-target optimization method.
In the research of the vehicle path problem, the target is generally solved independently, and the optimization information of similar problems cannot be effectively exchanged and cooperated in the solving process, so that the solving efficiency of the algorithm is limited.
Disclosure of Invention
The invention mainly aims to overcome the defects in the prior art, and provides a path planning method based on evolution multi-objective multi-task optimization, which adopts a solving paradigm of evolution multi-task optimization, solves the problem that optimization information of similar problems cannot be effectively exchanged and cooperated in the solving process, realizes information sharing of the similar problems, and improves the solving performance of VRP.
The invention adopts the following technical scheme:
a path planning method based on evolution multi-objective multi-task optimization specifically comprises the following steps:
s1: population initialization: generating an initial sequence set by adopting a random arrangement-based coding mode, then generating a planning scheme for each sequence in the set by adopting a construction method, evaluating according to an objective function, adding all the planning schemes into an initial population for updating an external archive, wherein the objective function is as follows:
f 2 (s)＝max k＝1，..，M c(r k )
wherein M represents the number of vehicle paths contained in the planning plan s, r k Indicates the kth vehicle path, c (r) k ) Represents the distance traveled by the k-th vehicle route, f 1 (s) and f 2 (s) respectively represent the total distance traveled by the vehicle and the longest vehicle path length for the path planning scenario s.
S2: evolution multitask optimization: sequentially carrying out multitask population construction, multitask information migration, multitask offspring generation, multitask population updating and external archiving updating;
s3: two-stage switching: if the external archive is updated, the step S4 is executed to execute the multi-objective optimization phase; otherwise, returning to step S2, the multitask optimization phase continues to be executed.
S4: carrying out multi-target population structure, multi-target offspring generation, multi-target population updating and external archiving updating in sequence;
s5: judging whether to execute reconstruction: if the algebra of the external archive which is not changed is larger than the set threshold value, the step S6 is entered, and the population reconstruction operation is executed; otherwise, the process proceeds to step S7.
S6: and (3) population reconstruction: and obtaining an optimal population according to a non-dominant sorting method and a crowding distance method, and forming a new population by adopting a Gaussian walking-based mode.
S7: judging whether the algorithm is finished: if the iteration times reach the set maximum iteration times, outputting all planning schemes in the external archive, and ending the algorithm; otherwise, return to step S2.
Specifically, the evolution multitask optimization in step S2: sequentially carrying out multitask population construction, multitask information migration, multitask offspring generation, multitask population updating and external archiving updating, and specifically comprising the following steps:
s21: multitask population construction: and calculating scalar adaptation values of all planning schemes of the initial population, then selecting the planning scheme with the largest scalar adaptation value, and constructing the population of the corresponding task.
S22: and (3) multi-task information migration: initializing a temporary population of the corresponding tasks, adding the planning scheme with the maximum scalar adaptation value in the population of the corresponding tasks constructed in the step 2 into the temporary population, and selecting the planning scheme with the maximum adaptation value from another task to add into the temporary population.
S23: and (3) generating multitask filial generation: and performing variation and cross operation of a differential evolution algorithm on a sequence corresponding to each planning scheme in the temporary population corresponding to the task, generating a filial generation sequence by using a maximum sequence value rule, obtaining the corresponding planning scheme and a target function value of the corresponding planning scheme on the corresponding task by using a construction method, performing local search operation on each planning scheme, and replacing the original planning scheme in the temporary population with the obtained new planning scheme.
S24: multitask population updating and external archiving updating: and (3) calculating scalar adaptation values of all planning schemes in the population obtained in the step (2) and the temporary population obtained in the step (3) according to the objective function values, selecting the planning scheme with the largest scalar adaptation value to form a new population, and updating external archives of each planning scheme in the new population according to a non-dominated sorting and crowding distance method.
Specifically, the evolutionary multi-objective optimization in step S4, which is to sequentially perform multi-objective population structure, multi-objective offspring generation, multi-objective population update, and external archive update, specifically includes:
s41: multi-target population structure: and constructing a new multi-target population by using a non-dominated sorting and crowding distance selection method.
S42: generating multi-target filial generation: and performing sequential crossing operation and exchange variation operation on the multi-target population to generate new sequences, respectively constructing new planning schemes for the sequences by using a construction method, evaluating the new planning schemes, adding the non-dominated planning schemes into the corresponding multi-target temporary population, and performing local search operation.
S43: multi-target population updating and external archiving updating: and selecting a planning scheme from the multi-target population and the corresponding multi-target temporary population by adopting a non-dominated sorting and crowding distance method to form a new multi-target population, and simultaneously using the multi-target temporary population for updating external archives.
As can be seen from the above description of the present invention, compared with the prior art, the present invention has the following advantages:
1. the invention takes each objective function of VRPRB as an independent task, solves a plurality of tasks simultaneously by utilizing operations of population structure, information migration, generation of filial generation, population updating and the like in multi-task optimization, adopts a two-stage strategy of alternately performing multi-task optimization and multi-objective optimization, switches the multi-task optimization process to the multi-objective optimization process when set switching conditions are met, accelerates the simultaneous solution of a plurality of vehicle path planning tasks by migrating similar information among different vehicle path planning tasks, solves the problem that the optimization information of the similar problem cannot effectively exchange and cooperate in the solving process, realizes the information sharing of the similar problem, and improves the solving performance of VRP.
2. Optimizing a non-dominant solution set by using an evolutionary multi-objective optimization strategy, namely, multi-objective optimized population structure, generation of filial generations, population updating, external archive updating and other operations; and guiding the generation process of a new planning scheme by a non-dominated sorting and crowding distance selection mode, and improving the diversity of the optimal planning scheme set.
3. And a population reconstruction strategy based on elite reservation is adopted, when a set reconstruction condition is met, only part of elite solutions are reserved, and other planning schemes are regenerated and added into the population in a Gaussian walking-based mode, so that the optimality of the planning schemes is further improved.
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FIG. 1 is a schematic flow chart of an embodiment of the present invention.
The invention is described in further detail below with reference to the figures and specific examples.
Detailed Description
The invention is further described below by means of specific embodiments.
The VRP according to the present invention is a Vehicle Route Problem (VRPRB) with Route Balancing. The core of the vehicle path problem with path balancing, compared to other vehicle path problems, is to balance the workload of the various paths as much as possible while minimizing the total distance traveled. Therefore, the optimization goals of VRPRB are: total distance traveled and balance metrics. The first optimization objective of the vehicle path problem with path balancing is derived from the classical vehicle path problem and the second optimization objective is related to the balancing of the workload. For the second goal, there are currently several measurement methods: calculate the difference between the longest and shortest path lengths, minimize the longest path, and lexicographically minimum and maximum. According to the existing research results, the three different measurement methods have respective advantages and disadvantages in terms of balancing the workload. In the present invention, minimizing the longest path serves as a second optimization goal for the VRPRB model.
There may be some adjustments to the order of the steps in order to fully illustrate the content of this embodiment.
S101, problem model definition and solution representation
VRPRB can be defined as an optimization problem that includes two objectives, i.e. it is required to find an optimal set of vehicle path planning schemes to minimize the total driving distance while balancing the workload of each vehicle path as much as possible, and specifically, VRPRB is defined by a completely undirected graph G ═ N, E, where N ═ {0, 1.. N } is the node set and E { (i, j) | i, j ∈ N } is the edge set. The point set N consists of a yard 0 and N customers, and each node i belongs to N and has two attributes.
The solution for VRPRB (i.e. vehicle planning scheme) is defined as a set of paths consisting of M paths, s ═ r 1 ,...,r M Each path can be represented as
I.e. path r k Is composed of client points accessed in a back-and-forth order,
denotes the parking lot, n k Is the number of client points visited in the k-th path. To ensure the effectiveness of the planning scenario s, it is required that each customer can only be included in one route and that the required capacity of the route cannot exceed the maximum capacity of the vehicle. Is provided with
Is the distance traveled by the k-th route,
indicating vehicle departure from customer location
To the customer site
The distance of travel of (a) is,
representing the jth customer to be served on the kth path, the model of VRPRB can be expressed as:
min f＝{f 1 ，f 2 }
wherein:
f 2 ＝max k＝1，..，M c(r k )
constraint conditions are as follows:
first objective function f 1 Representing the total distance travelled by the planning scheme, a second objective function f 2 Represents the maximum path length of the planning scenario, and C is the maximum capacity of the vehicle.
S102: construction of initial population
In this embodiment, an initial sequence is generated using a random permutation-based encoding scheme, each sequence representing a route from the yard (represented by the serial number "0"), sequentially visiting all customer site serial numbers, and returning to the yard. For each sequence, it is necessary to convert it into a feasible path planning scheme, depending on the number of vehicles. Here, two different target (or task) based construction methods will be used to segment a sequence into two different planning schemes. Generation of the sequence S ═ 0, π 1 ，π 2 ，...，π n ) In which pi j The number of vehicles corresponding to the serial number of the jth visiting client is M. The first construction method (CM1) is based on the goal of total path length minimization. Specifically, L [ k ]][i]Indicating the use of m vehicles to visit a sequence of customer points (pi) 1 ，π 2 ，...，π n ) The minimum driving distance of (a) is divided according to the following dynamic programming recursion formula:
L[k][i]＝min 0≤j≤i&&cap(j+1，i)≤C {L[m-1][j]+cost[j+1，i]}
wherein cos t (j, i) and cap (j, i) represent the sequence (0, π j ，...，π i 0) distance traveled and required capacity.
The second construction method (CM2) is designed based on the goal of minimizing the longest path length. F [ k ]][i]Representing m vehicles visiting a sequence of customer points (pi) 1 ，π 2 ，...，π n ) The recursive formula of dynamic programming is as follows:
F[k][i]＝min 0≤j≤i&&cap(j+1，i)≤C {max{F[k-1][j]，cost[j+1，i]}}
the above-mentioned | OP | sequences are generated by a random arrangement-based manner, and for eachSequence adoption construction method CM 1 And method of construction CM 2 Two planning schemes are generated respectively. By this procedure, a total of 2. multidot. OP. planning plans are generated as the initial population OP g . For each planning scenario, the evaluation is performed according to two objective functions f1 and f 2.
S103, evolution multitask optimization strategy
In the evolutionary multitask optimization strategy, 4 components are mainly included: population construction, information migration, child generation and population updating. These 4 components will be described in detail below.
1) Multitask population structure
In VRPRB, each objective function is treated as an independent task. Therefore, in a multitask optimization environment, VRPRB can be defined as an optimization problem that includes two tasks w1 and w 1. The population construction process for task w1 is as follows:
first, OP is put into g According to which all planning plans i (s y ) The values are sorted in a long sequence to obtain each planning scheme s y Factor ranking r for task w1 ij . Then, a scalar fitness value for the planning plan is calculated based on the factor rankings
Finally, h1 planning schemes with the largest scalar fitness value are selected as the group Pw1 of the task w 1.
2) Multitasking information migration
Information migration between different tasks is mainly achieved by migrating the best planning scheme of other tasks to the population of the task. In particular, the amount of the solvent to be used,
for task w1(w2), first, a temporary population is initialized for it
Then, the h1 planning schemes with the maximum adaptive quantity value in the task group Pw1 are reserved and copied to
In (1). Then, h2 planning schemes with the largest scalar fitness value are selected from tasks w2(w1), and are copied into TPw1(TPw 2).
3) Multitask child generation
For the sequences corresponding to each of the plans TPw1 and TPw2, new progeny sequences are generated by the mutation and crossover operations of the differential evolution algorithm. For the s th y The planning scheme adopts the mutation operation and the cross operation which are respectively as follows:
v y ＝s best +rand(0，1)*(s r1 -s r2 )
wherein v is y Indicates the variant solution generated, u j,l Represents the resulting experimental solution u j The l-dimension variable, s best Represents the best solution in the population, s r1 ,s r2 Representing two different solutions randomly selected in the population, Cr representing the crossover rate. Since the resulting trial solution is not a sequence of integers, it needs to be converted to a sequence related to the customer site. For this purpose, the conversion is carried out using the maximum order value rule: arranging each dimension of the test solution according to the numerical value from large to small; then, the dimension is set to the client point number corresponding to its rank.
Through this process, the sequence corresponding to each experimental solution can be obtained. Next, using the construction method CM 1 (CM 2 ) The corresponding planning scheme and its objective function value at task w1(w2) are obtained.
To further improve the quality of the new planning scenario, for each planning scenario, sp is used k To perform a local search operation (section 5 will be described in detail).
Finally, the resulting new planning scheme is completely substituted TPw1(TPw2) for all planning schemes originally in it.
4) Multitask population update
In a multitasking environment, the population for each task is updated individually. For task w1, first, all planning solutions in Pw1(Pw2) and TPw1(TPw2) are sorted according to their objective function values on tasks w1 and w2, scalar fitness values thereof are calculated, and h1(h2) planning solutions with the largest scalar fitness values are selected to constitute a new Pw1(Pw 2). Meanwhile, each planning scenario in TPw1(TPw2) is used to update the external archive (section 7, described in detail).
S104 evolution multi-objective optimization strategy
The objective of the evolutionary multi-objective optimization strategy is to increase the diversity of the population through a non-dominated sorting and crowding distance selection method. The process of evolving a multi-objective optimization strategy mainly comprises 3 main components: population construction, child generation and population update. The method comprises the following specific steps:
1) multi-target population structure
In the evolutionary multi-objective optimization process, an algorithm sets an independent population for the evolutionary multi-objective optimization process. The construction method of the population is as follows: will OP g ，Pw 1 And Pw 2 Combining a temporary population, selecting 2 × NP planning schemes from the temporary population by using a non-dominated sorting and crowding distance selection method in NSGA-II, and constructing a new multi-target population AP g 。
In the initial stage of the algorithm, i.e. when g is 1, let AP 0 ＝AP 1 As an initial population for a multi-objective optimization process.
2) Multi-target child generation
In embodiments of the present invention, sequential crossover operations and crossover mutation operations are employed to generate new progeny sequences. The specific operation is as follows:
and (3) sequential crossing operation: from the parent population (OP) g ) Wherein the solution is selected for sequential interleaving. Firstly, randomly selecting a solution from a population; second, a second solution is selected, either randomly or based on path similarity. (the probability of using the path similarity selection method is set to 0.01). The path similarity of the two solutions is calculated based on the Jacccards similarity coefficient, i.e., the ratio of the number of shared arcs between the two solutions to the total number of arcs in the two solutions is calculated. In the population, each solution is associated with a similarityAnd the vector is used for storing the path similarity of the solution and the rest solutions in the population. In the process of selecting the solutions for the crossover operation, after the first solution is selected, the solution which has the smallest path similarity value and is not selected yet is selected as the second solution. Then, a sequential interleaving operation is performed on each set of solutions, resulting in two new solutions. The sequential interleaving operation is performed as follows: firstly, randomly selecting two segmentation points from one solution; secondly, copying the segment between the two segmentation points into the solution of the child thereof; then, deleting the elements appearing in the fragment in another solution; finally, the remaining elements in the other solution are inserted in order into the free positions of the first child solution. The other child solution is generated in a manner consistent with the first child solution. By sequential interleaving operations, | OP can be generated g L new sequences.
Exchange mutation operation: for each newly generated child solution, crossover mutation operations are performed with a probability of 0.1. Specifically, two elements are randomly selected from the solution and their positions are exchanged, resulting in a new solution.
When the sequence crossing operation and the exchange mutation operation are completed, the newly generated | AP is processed g L sequences, respectively using CM 1 And CM 2 Construction 2. about. | AP g And | planning schemes and evaluating. Then, adding the non-dominant planning scheme to the temporary population AP g ' of (1). Finally, the method of tournament selection is used to select from the AP g ∪AP g ' y planning plans are selected for local search operations (section 5, described in detail).
3) Multi-target population updates
AP is processed by adopting non-dominated sorting method and congestion distance calculation method g ∪AP g ' the combined population is sorted, and | AP is selected from the sorted combined population g And l planning schemes form a new multi-target population. At the same time, the AP g ' is used to update the external archive.
Local search operation S105
In this embodiment, for the planning scheme, the following four common local search operations are adopted: such as:
exchange (j', j): path r 1 Client j's routing path r 2 Client j instead, path r in (1) 2 Client j in (1) is represented by path r 1 Client j' of (1).
relocate (j', j): will route r 1 Client j' of (a) is removed and inserted into path r 2 Client j in the list.
2-opt (j', j): will route r 1 All customer points after customer j' are removed and inserted into path r 2 After customer j in (1), then path r 2 All clients behind client j in (1) remove and insert path r 1 Of customer j'.
reverse (j', j): for a certain path in the scenario, the customer point between location j ' to location j is inverted so that this partial path changes from (j ', j ' +1 …, j-1, j) to (j, j-1 …, j ' +1, j ').
In the local searching process, firstly, a path with a longer driving distance is selected according to a roulette method; then, one of the above four partial search operations is selected by probability to be performed. For each planning scheme, the above local search process Iter is repeatedly performed, Iter is the set number of local searches, and Iter in this embodiment is 30.
Selection probabilities sp for these four local search operations k (k is 1,2,3, 4). Initially, the selection probabilities are all set to 1/4. At the end of each iteration, namely when the number of iterations reaches the set maximum value of the iteration number, updating the probability value of each local search operation in the following mode:
firstly, counting the times of each local search operation being selected and the times of improving the quality of the original planning scheme, and respectively recording the times as nt k And ns k (k is 1,2,3, 4). The selection probability for each local search operation is then updated according to the following formula:
sp k ＝(1-θ)*sp k +θns k /nt k
s106, population reconstruction mechanism
If Stagnation ≧ GrsIn order to solve this problem and further improve the search performance of the algorithm, a population reconstruction mechanism is introduced g Sorting is carried out, RS ═ α ×. 2 ×. NP are reserved for the best-ranked planning schemes, and α takes a value of 0-1. Other planning schemes will reinitialize by means of gaussian walk based approach, namely:
s′ e RS ＝Gausslan(μ，σ)+(rand(0，1)*s RS +rand(0，1))
wherein s is RS Is a random one of RS planning schemes reserved, s' e RS For the e-th reinitialized planning scheme, Gaussian (μ, σ) represents a Gaussian function with μ set to the selected s RS σ is set to
Reinitialized s' e RS Instead of a sequence of integers, it needs to be converted into a sequence for the client point. For this purpose, the conversion is carried out using the maximum order value rule: s' e RS Each dimension of (a) is arranged from large to small according to the value of the dimension; then, setting the dimension as the serial number of the client point corresponding to the ranking; then, using the construction method CM respectively 1 And CM 2 To two new planning scenarios.
The above reinitialization process (1- α) × 2 × NP is repeated. And finally, sequencing the newly obtained 2 x (1-alpha) 2 x NP new planning schemes according to a non-dominant sequencing method and a crowding distance method, and selecting the best (1-alpha) 2 x NP planning schemes to be added into the population.
S107 external archive update mechanism
The epsilon dominance mechanism is employed when updating the external archive. Specifically, in an archive with a dominance of ε, each non-dominated solution in the archive corresponds to one relevance vector B ═ B 1 ,B 2 Therein of，
B i ＝log(f i +1)/log(1+ε)，
One non-dominated solution is stored in each hypercube. Thus, an archive based on epsilon dominance not only evenly distributes the non-dominant solution, but effectively limits the size of the external archive during the search.
The following specific test examples and experimental results are verified and explained;
to verify the effectiveness of the proposed method, the present invention uses seven CVRP reference examples proposed by Christofides and Eilon et al. In this example, the number of customers ranges from 50 to 199 people, and the number of vehicles is the minimum number of vehicles required to service these customers. The naming mode of the examples used in the invention refers to the mode used by Zhang et al, and the name of each example is as follows: ei-jk, where E indicates that the distance in the example is the Euclidean distance; i is the number of vertices (including the yard). j is the number of available vehicles. k is a symbol indicating that the calculation is from Christofides or Eilon, if k ═ e, the calculation is as proposed by Christofides and Eilon et al, otherwise, Christofides et al. To obtain a fair result, each example was run 10 times in the experiment.
Based on the above test calculation set, the present invention selects the M-NSGA-II algorithm proposed by Zhang et al as the comparison (Zhang Z, Sun Y, Xie H, et al GMMA: GPU-based multi-objective metric algorithms for improving the resolution with the route balancing [ J ]. Applied Intelligence,2019,49(1): 63-78). The termination condition of the algorithm proposed by the present invention is set to maxGen 1000. To compare the two algorithms under the same conditions, the termination condition of the M-NSGA-II algorithm was also set to 1000. Statistics and analysis were performed by running 10 times each of the examples independently. In the case of minimizing the total travel distance, the proposed algorithm can obtain a smaller total travel distance than that of M-NSGA-II over 5 examples, respectively: E76-10E, E101-08E, E121-07c, E151-12c, and E200-17 c; the two algorithms perform equivalently on the examples E51-05E and E101-08E. In case of the minimized maximum path length, the proposed algorithm can obtain a smaller maximum path length than that of M-NSGA-II over 3 examples, respectively: E51-05E, E121-07c and E200-17 c; the algorithms proposed on examples E76-10E, E101-08E and E151-12c performed slightly worse. In general, the proposed algorithm is slightly better than M-NSGA-II, especially when optimizing total distance traveled.
In order to compare the performance of the proposed algorithm with that of the M-NSGA-II algorithm on seven reference examples, three indexes widely used by a multi-objective optimization algorithm are adopted, namely: IGD, HV and C-Metric. They are used to show the convergence and diversity of the algorithm from different perspectives, where IGD and HV are unitary indicators, and C-metric binary indicators. Aiming at the IGD index, the proposed algorithm is obviously superior to M-NSGA-II in 1 calculation example, the performance of the algorithm is equal to that of M-NSGA-II in 6 calculation examples, and no calculation example which is obviously inferior to that of M-NSGA-II exists; aiming at HV indexes, the proposed algorithm is obviously superior to M-NSGA-II in 1 calculation example, has the same performance with M-NSGA-II in 6 calculation examples, and does not have calculation examples which are obviously inferior to M-NSGA-II; aiming at the C-Metric index, the proposed algorithm is remarkably superior to M-NSGA-II in 1 arithmetic example, has the same performance with M-NSGA-II in 5 arithmetic examples, and is remarkably inferior to M-NSGA-II in 1 arithmetic example. In general, the path planning method based on the evolutionary multi-objective multi-task optimization can provide a more effective solution frame for the vehicle path problem.
The above description is only an embodiment of the present invention, but the design concept of the present invention is not limited thereto, and any insubstantial modifications made by using the design concept should fall within the scope of infringing the present invention.
Claims (1)
1. A path planning method based on evolution multi-objective multi-task optimization specifically comprises the following steps:
s1: population initialization: generating an initial sequence set by adopting a random arrangement-based coding mode, then generating a planning scheme for each sequence in the set by adopting a construction method, evaluating according to an objective function, adding all the planning schemes into an initial population for updating an external archive, wherein the objective function is as follows:
f 2 (s)＝max k＝1,..,M c(r k )
wherein M represents the number of vehicle paths contained in the planning plan s, r k Denotes the kth vehicle path, c (r) k ) Represents the distance traveled by the k-th vehicle route, f 1 (s) and f 2 (s) respectively representing the total vehicle driving distance and the longest vehicle path length of the path planning scheme s;
s2: evolution multitask optimization: sequentially carrying out multitask population construction, multitask information migration, multitask offspring generation, multitask population updating and external archiving updating;
sequentially carrying out multitask population construction, multitask information migration, multitask offspring generation, multitask population updating and external archiving updating, and specifically comprising the following steps of:
s21: multitask population construction: calculating scalar adaptation values of all planning schemes of the initial population, then selecting the planning scheme with the largest scalar adaptation value, and constructing a population corresponding to the tasks;
s22: multi-task information migration: initializing a temporary population corresponding to the tasks, adding the planning scheme with the maximum scalar adaptation value in the population corresponding to the tasks constructed in the step (2) into the temporary population, and selecting the planning scheme with the maximum adaptation value from another task to add into the temporary population;
s23: and (3) generating a multitask filial generation: executing variation and cross operation of a differential evolution algorithm on a sequence corresponding to each planning scheme in the temporary population corresponding to the task, generating a filial generation sequence by using a maximum sequence value rule, obtaining a corresponding planning scheme and a target function value of the corresponding planning scheme on the corresponding task by using a construction method, performing local search operation on each planning scheme, and replacing the original planning scheme in the temporary population with the obtained new planning scheme;
s24: multitask population updating and external archiving updating: calculating scalar adaptation values of all planning schemes in the population obtained in the step 2 and the temporary population obtained in the step 3 according to the objective function values, selecting the planning scheme with the largest scalar adaptation value to form a new population, updating each planning scheme in the new population according to a non-dominated sorting and crowding distance method, and updating an external archive S3: two-stage switching: if the external archive is updated, the step S4 is executed to execute the multi-objective optimization phase; otherwise, returning to the step S2 to continue executing the multi-task optimization stage;
s4: the evolution multi-objective optimization comprises the steps of sequentially carrying out multi-objective population structure, multi-objective offspring generation, multi-objective population update and external archive update;
sequentially carrying out multi-target population structure, multi-target offspring generation, multi-target population updating and external archiving updating, and specifically comprising the following steps:
s41: multi-target population structure: constructing a new multi-target population by using a non-dominated sorting and crowding distance selection method;
s42: generating multi-target filial generation: performing sequential crossing operation and exchange variation operation on the multi-target population to generate new sequences, respectively constructing new planning schemes for the sequences by using a construction method, evaluating the new planning schemes, adding the non-dominated planning schemes into the corresponding multi-target temporary population, and performing local search operation;
s43: multi-target population updating and external archiving updating: selecting a planning scheme from the multi-target population and the corresponding multi-target temporary population by adopting a non-dominated sorting and crowding distance method to form a new multi-target population, and simultaneously using the multi-target temporary population for updating an external archive;
s5: judging whether to execute reconstruction: if the algebra of the external archive which is not changed is larger than the set threshold, the step S6 is entered, and the population reconstruction operation is executed; otherwise, go to step S7;
s6: and (3) population reconstruction: obtaining an optimal population according to a non-dominated sorting method and a crowding distance method, and forming a new population by adopting a Gaussian walking-based mode;
s7: judging whether the algorithm is finished: the iteration times reach the set maximum iteration times, all planning schemes in an external archive are output, and the algorithm is ended; otherwise, return to step S2.
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