CN114819249A - Community material vehicle path optimization method based on improved lion group algorithm under epidemic situation - Google Patents

Community material vehicle path optimization method based on improved lion group algorithm under epidemic situation Download PDF

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CN114819249A
CN114819249A CN202210137321.0A CN202210137321A CN114819249A CN 114819249 A CN114819249 A CN 114819249A CN 202210137321 A CN202210137321 A CN 202210137321A CN 114819249 A CN114819249 A CN 114819249A
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宫婧
祝子豪
孙知信
孙哲
赵学健
胡冰
汪胡青
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Nanjing University of Posts and Telecommunications
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Abstract

The invention provides a community material vehicle path optimization method under epidemic situation based on improved lion group algorithm, firstly establishing a path planning mathematical model and initializing algorithm parameters; a sequential encoding, ordering the individuals using a pareto non-dominant ordering mechanism and individual crowding distance; detecting whether an external enemy invades; using a lion group passage operator and the trial times to update the position of the lion group; optimizing a workload balancing goal by using a balancing operator; updating the best position, and re-determining the identity of the lion group individuals; and repeating until the iteration times are reached, and recording the historical optimal individual of the lion group. According to the method, a position updating strategy of an original lion group algorithm is improved, lion group position updating is achieved by using lion group passage operators and trial times, a balancing operator is used for optimizing a work load balancing target, and the problem that the existing vehicle path optimization method cannot meet the requirement of optimizing vehicle paths in community material transportation under epidemic conditions, so that the fairness of work load is guaranteed, and the high efficiency is guaranteed.

Description

Community material vehicle path optimization method based on improved lion group algorithm under epidemic situation
Technical Field
The invention relates to a community material vehicle path optimization method under epidemic situation based on an improved lion group algorithm, and belongs to the field of path prediction.
Background
In conventional vehicle route optimization problem research, goals of reducing total transportation cost, carbon emission amount and transportation time cost and improving customer satisfaction are always established, and the goals are related to business problems. However, in disaster relief, emergency and humanitarian logistics, there are many non-profit organizations, citizens and government agencies voluntarily sending disaster relief materials to where needed. In recent two years, the method is influenced by new crown epidemic situations, and many communities in China adopt closed management, so that the spread range of the epidemic situations and the infection risk of residents can be reduced to the maximum extent. The demands of daily necessities of residents in the community become a problem, and for convenience of management and reduction of capital pressure as far as possible, many communities recruit volunteers to participate in the distribution of living goods and materials, and the problem of vehicle path optimization is involved. Unlike vehicle route optimization in traditional business models, where the driver is a volunteer of the community organization, the distance traveled per route should be as uniform as possible, the priority here being on fairness of the service side workload, which can also be understood as workload, and secondly the total cost of transportation. Meanwhile, the material transportation characteristics under an epidemic situation need to be considered, and the problem that a driver cannot participate in goods distribution due to going to a high-risk area in a short time exists. The existing path optimization method cannot meet the requirements under epidemic situations.
In view of the above, it is necessary to provide a new community material vehicle path optimization method based on the improved lion group algorithm in an epidemic situation to solve the above problems.
Disclosure of Invention
The invention aims to provide a community material vehicle path optimization method under an epidemic situation based on an improved lion group algorithm, and the method is used for solving the problem that the existing vehicle path optimization method cannot meet the requirement of optimizing vehicle paths in community material transportation under the epidemic situation, so that the fairness of workload and the high efficiency are guaranteed.
In order to achieve the aim, the invention provides a community material vehicle path optimization method under epidemic situation based on an improved lion group algorithm, which comprises the following steps:
step 1: establishing a path planning mathematical model and initializing algorithm parameters;
step 2: sequentially coding, randomly generating a primary lion group, calculating the individual initial fitness value of the lion group, sequencing the individuals by using a pareto non-dominated sequencing mechanism and individual crowding distance, and determining the primary lion king, the female lion and the young lion;
and step 3: detecting whether an external enemy invades, if so, checking whether an invader can dominate the current lion king, replacing the current lion king, and if not, driving;
and 4, step 4: using a lion group passage operator PO and the trial times maxtrial to realize the updating of the position of the lion group;
and 5: optimizing a workload balancing goal by using a balancing operator;
step 6: updating the best positions of the lion king and other individuals in the lion group, and re-determining the identity of the lion group individuals;
and 7: and (4) judging whether the iteration time T is equal to the maximum iteration time T of the algorithm, if not, T +1, returning to the step 3, repeating the steps 3 to 6 until T is equal to T, and recording the lion group history optimal individual.
As a further improvement of the present invention, the path planning mathematical model established in step 1 specifically includes:
Figure BDA0003505436390000021
Figure BDA0003505436390000022
Figure BDA0003505436390000023
and a constraint function:
Figure BDA0003505436390000024
Figure BDA0003505436390000025
w∈[0,m),w∈N +
Figure BDA0003505436390000031
wherein G ═ (V, E) is the distribution network; v is a set of nodes, where 0 denotes a distribution center and the remaining nodes denote customers; e is an arc set, E { (i, j) | i, j belongs to V, and i ≠ j }; k is a vehicle set, K ═ 1,2 k A decision variable of 0-1, 0 means that the kth vehicle cannot participate in the delivery for personal reasons of the driver, let num (Σ z) k 0) is w, which represents the number of drivers who cannot participate in the delivery, the actual number of vehicles is p-m-w; d ij Distance traveled for arc (i, j); r k As a set of sub-paths, R k ＝{r 1 ,r 2 ,......,r p }，r k Indicating a travel path of a k-th vehicle;
Figure BDA0003505436390000032
points are counted for the path;
Figure BDA0003505436390000033
indicating the ith customer point on the path; c is the maximum load of the delivery vehicle; q i Representing the demand of each customer point; y is ik A decision variable of 0-1, 1 indicating that customer point i is serviced by vehicle k; t represents the number of iterations; the first constraint function represents that the total demand of customer points served by each vehicle does not exceed the self load; the second constraint function indicates which vehicles in the vehicle set participate in the delivery; the third constraint function represents that the number of vehicles which cannot participate in distribution is less than the total number m of the vehicles and is a positive integer; the fourth constraint function indicates that a customer can only be serviced by one vehicle.
As a further improvement of the invention, the initialization algorithm parameters in the step 1 comprise the maximum iteration times T of the algorithm, the size P of the lion group, the ratio B of adult lion of the lion group and the intrusion factor lf.
As a further improvement of the present invention, the step 2 specifically includes:
step 21: real number coding is carried out on the distribution path, and then lion groups are initialized;
step 22: determining the sequence of the individuals sorted by pareto according to the respective crowding distance, enabling the individuals arranged at the forefront to become lion king, determining the number of adult lions according to the occupation ratio B of adult lions in the lion group, and determining the identities of other individuals according to the sequence of the individual arrangement.
As a further improvement of the present invention, the real number encoding in step 21 specifically includes: firstly generating 0 representing the distribution center, 1-n representing all customer points needing distribution, randomly selecting the customer points to join, judging whether the constraint conditions of the path planning mathematical model are met, if not, inserting 0 representing the current sub-path to end, then opening up a sub-path, repeating the steps until all the customer points are joined, and finally ending with 0.
As a further improvement of the present invention, the step 3 specifically includes:
step 31: generating a random number r at the beginning of each generation, wherein r belongs to (0,1), comparing the size of r with an intrusion factor lf, if the size of r is smaller than that of the intrusion factor lf, representing that an external enemy invades, entering step 32, if the size of r is larger than that of the intrusion factor lf, not invading, ending step 31, and entering step 4;
step 32: a better individual is generated by a greedy insertion method to serve as an invader, and if the fitness value of the superior individual can dominate the current lion king, the superior individual is substituted for the lion king, otherwise, the superior individual is driven.
As a further improvement of the present invention, the greedy insertion method in step 32 specifically includes:
step 321: inputting a set of feasible solutions R * ＝{R 1 ,R 2 ,......,R m }，L←R * ；
Step 322: RL ← L, but not increased in the process
Figure BDA0003505436390000041
A subset of (a);
step 323: if the RL is not null, F ← RL is the optimal solution after pareto sorting and crowding distance judgment; if RL is empty, F ← L is the optimal solution after pareto sorting and crowding distance judgment;
step 324: and F is output.
As a further improvement of the present invention, step 4 specifically includes:
step 41: updating the positions of the lion groups by adopting a lion group passage operator PO, wherein the lion group movement strategy is as follows:
Figure BDA0003505436390000042
Figure BDA0003505436390000046
Figure BDA0003505436390000043
in the formula
Figure BDA0003505436390000044
Representing the best position of the individual i in the t generation, the first formula represents the position update strategy of the lion king, where g t Representing the optimal position of the individual in the lion group in the t generation; the second formula represents the location update strategy of the lion, wherein
Figure BDA0003505436390000045
Representing the optimal position of a random individual m in the female lion in the t generation; the third formula represents a position updating strategy of the young lion, wherein q is a random number between 0 and 1, q is not less than 1/3 and represents that the young lion moves towards the direction of the lion king, q is more than 1/3 and not more than 2/3 and moves towards the direction of the mother lion, q is more than 2/3 and not more than 1 and represents that the young lion is expelled and moves towards the opposite direction of the lion group;
step 42: the lion group position updating is realized by adopting the trial times maxtrial, and the formula of the trial times maxtrial is as follows:
Figure BDA0003505436390000051
Figure BDA0003505436390000052
as a further improvement of the present invention, said step 5 adopts three kinds of balancing operators to optimize the work load balancing goal:
equalization operator 1: path segment node reversal
Selecting the longest path of the current individual, generating a random positive integer i, j, and reversing the access sequence between the two nodes;
the balance operator 2: switching dual node
Selecting the longest path of the current solution, generating a random positive integer number i, j, and exchanging the access sequence of the two client points;
the equalization operator 3: removal and insertion
Selecting the longest path and the shortest path from the solution, removing the customer point which has the minimum influence on the path from the longest path, inserting the customer point into the shortest path and generating the minimum path growth, wherein the removed customer point meets the following formula:
Figure BDA0003505436390000054
assuming the removal point is w, the position of the addition point is represented as:
Figure BDA0003505436390000053
the results of the three balancing operators are accepted only when the constraint conditions of the path planning mathematical model are met and new individuals can dominate old individuals, and the three balancing operators are randomly selected.
As a further improvement of the present invention, the step 7 specifically includes: updating the best position of the individual i in the t generation and the best position of the lion group individual in the t generation, calculating whether the remainder of the t divided by 10 is 0 or not, wherein t is the iteration number, the remainder of the t divided by 10 is 0, then ranking the lion group by using pareto ranking and crowding distance judgment, re-determining the identity of the lion group individual, and if the remainder of the t divided by 10 is not 0, then no longer ranking the lion group.
The invention has the beneficial effects that: according to the method, a position updating strategy of an original lion group algorithm is improved, lion group position updating is achieved by using lion group passage operators and trial times, a balancing operator is used for optimizing a work load balancing target, and the problem that the existing vehicle path optimization method cannot meet the requirement of optimizing vehicle paths in community material transportation under epidemic conditions, so that the fairness of work load is guaranteed, and the high efficiency is guaranteed.
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FIG. 1 is a step diagram of the present invention.
Fig. 2 is a flow chart of the algorithm of the present invention.
Fig. 3 is a schematic diagram of crowding distance.
Fig. 4 is a schematic diagram after pareto sorting.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in detail with reference to the accompanying drawings and specific embodiments.
As shown in fig. 1 and 2, the invention discloses a community material vehicle path optimization method under epidemic situation based on an improved lion group algorithm, which specifically comprises the following steps:
step 1: and establishing a path planning mathematical model and initializing algorithm parameters.
G ═ V, E) is the distribution network;
v is a node set, where 0 denotes a distribution center and the remaining nodes denote customers; e is an arc set, E { (i, j) | i, j belongs to V, and i ≠ j };
k is a vehicle set, K ═ 1,2 k Decision variable of 0-1, 0 means that the kth vehicle cannot participate in delivery for personal reasons of the driver, let num (Σ z) k 0) is w, which indicates the number of drivers who cannot participate in the delivery, and the actual number of vehicles is p-m-w;
d ij distance traveled for arc (i, j); r k As a set of sub-paths, R k ＝{r 1 ,r 2 ,......,r p }，r k Indicating a travel path of a k-th vehicle;
Figure BDA0003505436390000061
points are counted for the path;
Figure BDA0003505436390000071
indicating the ith customer point on the path; c is the maximum load of the delivery vehicle; q i Representing the demand of each customer point; y is ik A decision variable of 0-1, 1 indicating that customer point i is serviced by vehicle k; t is the number of iterations.
The basic assumption is made according to the distribution situation in an epidemic situation: all customer nodes in the distribution network are served and are served only once by one vehicle, one vehicle corresponding to one driver. Meanwhile, the transportation of living goods and materials for communities affected by epidemic situations does not have some attributes in the traditional business mode, and the client does not have strict time requirements, so that a time window mechanism and the client service time are not set in the model.
The path planning mathematical model is established as follows:
set of subpaths R k Travel distance of the kth vehicle:
Figure BDA0003505436390000072
objective function 1, minimizing the difference between the longest sub-path and the shortest sub-path in the same solution:
Figure BDA0003505436390000073
objective function 2, minimizing total path length:
Figure BDA0003505436390000074
constraint function:
Figure BDA0003505436390000075
Figure BDA0003505436390000076
w∈[0,m),w∈N +
Figure BDA0003505436390000077
the first constraint function represents that the total demand of customer points served by each vehicle does not exceed the self load; a second constraint function representing which vehicles in the set of vehicles participate in the delivery; the third constraint function represents that the number of vehicles which cannot participate in distribution is less than the total number m of the vehicles and is a positive integer; the fourth constraint function indicates that a customer can only be serviced by one vehicle.
And then initializing algorithm parameters, including the maximum iteration number T of the algorithm, the size P of the lion group, the ratio B of the adult lion of the lion group and an intrusion factor lf.
Step 2: sequentially coding, randomly generating a primary lion group, calculating the individual initial fitness value of the lion group, sequencing the individuals by using a pareto non-dominated sequencing mechanism and individual crowding distance, and determining the primary lion king, the female lion and the young lion;
the step 2 specifically comprises the following steps:
step 21: the sequential coding is carried out by adopting a real number coding mode, wherein 0 represents a distribution center, 1-n represent customer points, for example, an individual of the sequential coding 01350260 represents that a first vehicle sequentially serves the 1 st, 3 rd and 5 th customer points, and a second vehicle sequentially serves the 2 nd and 6 th customer points. After the coding is finished, the lion group is initialized, and the process is as follows: firstly, 0 representing the distribution center is generated, customer points are randomly selected to be added, whether constraint conditions are met or not is judged, if the constraint conditions are not met, 0 is inserted to represent that the current sub-path is ended, then a sub-path is created, the steps are repeated until all the customer points are added, and finally the steps are ended with 0.
Step 22: determining the sequence of the individuals sorted by pareto according to the respective crowding distance, enabling the individuals arranged at the forefront to become lion king, determining the number of adult lions according to the occupation ratio B of adult lions in the lion group, and determining the identities of other individuals according to the sequence of the individual arrangement.
Because the path planning model has two objective functions which are not a dimension and cannot be processed by a weighting method, the individuals with calculated fitness values need to be ranked by using pareto ranking and individual crowding distance values, and then initial identities of the individuals are determined.
The dominant concept of the pareto non-dominant sorting machine seed production is as follows: assuming that f1 and f2 are the values of two objective functions, if individual 1 has at least one objective better than individual 2 and all objectives of individual 1 are not worse than individual 2, then individual 1 dominates individual 2. I.e. two solutions x, y, x ═ x 1 ,x 2 ),y＝(y 1 ,y 2 )：
Figure BDA0003505436390000081
Crowding distance: the crowding distance is used to calculate the distance between an individual in a pareto optimal solution set and other individuals in the solution set. The larger the crowding distance is, the better the diversity of lion groups is
Referring to FIG. 3, five points in the graph represent a pareto optimal solution set, and the crowding distance of the point n is the average side length of the quadrilateral in the graph
Figure BDA0003505436390000091
The procedure for pareto ranking is:
the pareto rating is first defined: in a given solution set of a multi-objective problem, all pareto optimal solutions, i.e. the rank definitions of non-inferior solutions, are first positioned to 1; a pareto optimal solution set of rank 1 ensures that all solutions are not dominated by any other solution. Then, the level 1 solution is eliminated from the solution set, and of the remaining solutions, all pareto optimal solutions, whose pareto level is set to 2, are followed by analogy. Please refer to fig. 4, which is a simplified diagram of the pareto sorting.
Determining the sequence of the individuals sorted by pareto according to the respective crowding distance, wherein the individuals ranked at the forefront become lion king, determining the number of adult lions according to the size of the parameter B, and determining the identities of other individuals according to the sequence of the individuals.
And step 3: and detecting whether an external enemy invades, if so, checking whether the invader can dominate the current lion king, replacing the current lion king, and if not, driving.
The step 3 specifically comprises the following steps:
step 31: and (3) generating a random number r at the beginning of each generation, belonging to (0,1), comparing the size of r with the intrusion factor lf, if the size of r is smaller than the size of r, representing that an external enemy intrudes, entering a step 32, if the size of r is larger than the size of r, not intruding, ending the step 31, and entering a step 4.
Step 32: a better individual is generated by a greedy insertion method to serve as an invader, and if the fitness value of the superior individual can dominate the current lion king, the superior individual is substituted for the lion king, otherwise, the superior individual is driven.
The design idea of the greedy insertion method is derived from a greedy algorithm, and each step of the algorithm reaches the current optimum in the state of the previous step, so that the result approaches the global optimum.
The flow of greedy insertion is as follows:
step 321: inputting a set of feasible solutions R * ＝{R 1 ,R 2 ,......,R m }，L←R * ；
Step 322: RL ← L, but not increased in the process
Figure BDA0003505436390000105
A subset of (a);
step 323: if the RL is not null, F ← RL is the optimal solution after pareto sorting and crowding distance judgment; if RL is null, F ← L is the optimal solution after pareto sorting and crowding distance judgment;
step 324: and F is output.
F is the current optimal solution.
And 4, step 4: lion group position updating is achieved using the lion group passage operator PO and the number of attempts maxtrial.
The step 4 specifically comprises the following steps:
step 41: the lion group position updating method adopts the lion group passage operator PO to update the lion group position, and because the method aims to solve the problem of vehicle path, and non-integers can be obtained after the encoded solution is substituted into the original algorithm formula, the position updating formula in the lion group algorithm needs to be designed according to specific problems. And the position in the original algorithm is updated too randomly, and the relevance with the position of the previous generation is not large. Therefore, a lion group passage operator PO is provided.
Taking the lion king as an example,
Figure BDA0003505436390000101
represents the best position of the ith lion in the t generation, and is set as 1-5-4-7-2-3-6, g t The best positions of all the lions in the t generation are shown and set as 5-6-1-2-4-3-7, two tangent point positions i, j i, j epsilon (0, n) are randomly selected, i ≠ j, n is the total number of customer points, and the two tangent point positions are assumed to be 2 and 6.
Position 1: 1-5/4-7-2-3/6
Position 2: 5-6/1-2-4-3/7
Starting from the second tangent point in the position 1, the new solution is 7-5-6-1-2-4-3, the part between the two tangent points in the position 1 is stored, 4-7-2-3 is remained, the repeated part in the new solution is removed, 5-6-1 is remained in the new solution, and the same part which is remained in the new solution is filled in from the second tangent point in the position 1, namely 6-1-4-7-2-3-5.
The improved lion group moving strategy is as follows:
Figure BDA0003505436390000102
Figure BDA0003505436390000103
Figure BDA0003505436390000104
in the formula
Figure BDA0003505436390000111
Representing the best position of the individual i in the t generation, the first formula represents the position update strategy of the lion king, where g t Representing the optimal position of the individual in the lion group in the t generation; the second formula represents the location update strategy of the lion, wherein
Figure BDA0003505436390000112
Representing the optimal position of a random individual m in the female lion in the t generation; the third formula represents the position updating strategy of the young lion, wherein q is a random number between 0 and 1, q is not less than 1/3 and represents that the young lion moves towards the direction of the lion king, q is more than 1/3 and not more than 2/3 and moves towards the direction of the mother lion, q is more than 2/3 and not more than 1 and represents that the young lion is expelled and moves towards the opposite direction of the lion group.
Step 42: lion group location updates are implemented using the number of attempts maxtrial.
The invention simulates the predation movement of the lion group by using the idea of reinforcement learning, and for the reinforcement learning, the probability density of high return value obtained by actions usually made in the state of high return value is high, while for the algorithm of the invention, the position update adopted by the point near the local optimum value is more likely to be close to the extreme point. Since the main task in the algorithm is to find local optimum is the female lion, some individuals in the female lion have a high probability density of finding local extreme points.
The number of tries maxtrial is introduced here, which is such a value that the parent lion closest to the local extremum in each generation has multiple try opportunities, and the number of tries decreases gradually as the number of generations increases, thereby accelerating convergence of the algorithm. The formula for the number of tries maxtrial is:
Figure BDA0003505436390000113
Figure BDA0003505436390000114
and 5: a balancing operator is used to optimize the workload balancing objective.
Three kinds of balancing operators are designed in the algorithm to optimize the workload balancing target.
Equalization operator 1: path segment node reversal
Selecting the longest path of the current individual, generating a random positive integer i, j, and reversing the access sequence between the two nodes;
an exemplary case: if i is 3 and j is 7, the path part node is 5-7-6-4-1-3-2-8, and the access sequence between the two nodes is reversed to be 5-7-3-1-4-6-2-8.
The balance operator 2: switching dual node
Selecting the longest path of the current solution, generating a random positive integer number i, j, and exchanging the access sequence of the two client points;
an exemplary case: when i is 2 and j is 5, the path part node is 5-7-6-4-1-3-2-8, and the access sequence between the two nodes is reversed to be 5-1-6-4-7-3-2-8.
The equalization operator 3: removal and insertion
Unlike the two operators above, this operation involves two paths, selecting the longest and shortest paths from the solution, removing the customer points in the longest path that have the least impact on that path, inserting them into the shortest path and producing the smallest path growth, the removed customer points satisfying the following formula:
Figure BDA0003505436390000122
assuming the removal point is w, the position of the addition point is represented as:
Figure RE-GDA0003722523190000122
the results after the operation of the three kinds of balancing operators are accepted only when the constraint conditions of the path planning mathematical model are met and the new individual can dominate the old individual, and the three kinds of balancing operators are randomly selected.
Step 6: updating the optimal position of the individual i in the t generation and the optimal position of the lion group individual in the t generation, calculating whether the remainder of the iteration number t divided by 10 is 0 or not, wherein t is the iteration number, the remainder of the t divided by 10 is 0, sorting the lion groups by using pareto sorting and congestion distance judgment, re-determining the identity of the lion group individual, and no longer re-sorting the lion groups when the remainder of the t divided by 10 is not 0
And 7: and (4) judging whether the iteration time T is equal to the maximum iteration time T of the algorithm, if not, T +1, returning to the step 3, repeating the step 3 to the step 6 until T is equal to T, and recording the history optimal individual of the lion group, namely the optimal path.
In conclusion, the position updating strategy of the original lion group algorithm is improved, the lion group position updating is realized by using the lion group passage operator and the trial frequency, the workload balancing target is optimized by using the balancing operator, and the problem that the existing vehicle path optimization method cannot meet the requirement of optimizing the vehicle path in community material transportation under the epidemic situation, so that the fairness of the workload and the high efficiency are guaranteed.
Although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the spirit and scope of the present invention.

Claims (10)

1. A community material vehicle path optimization method under epidemic situation based on an improved lion group algorithm is characterized by comprising the following steps:
step 1: establishing a path planning mathematical model and initializing algorithm parameters;
step 2: sequentially coding, randomly generating a primary lion group, calculating the individual initial fitness value of the lion group, sequencing the individuals by using a pareto non-dominated sequencing mechanism and individual crowding distance, and determining the primary lion king, the female lion and the young lion;
and step 3: detecting whether an external enemy invades, if so, checking whether an invader can dominate the current lion king, replacing the current lion king, and if not, driving;
and 4, step 4: using a lion group passage operator PO and the trial times maxtrial to realize the updating of the position of the lion group;
and 5: optimizing a workload balancing goal by using a balancing operator;
step 6: updating the best positions of the lion king and other individuals in the lion group, and re-determining the identity of the lion group individuals;
and 7: and (4) judging whether the iteration time T is equal to the maximum iteration time T of the algorithm, if not, T +1, returning to the step 3, repeating the steps 3 to 6 until T is equal to T, and recording the lion group history optimal individual.
2. The improved lion group algorithm-based community material vehicle path optimization method under epidemic situation according to claim 1, characterized in that: the path planning mathematical model established in the step 1 is specifically:
Figure FDA0003505436380000011
Figure FDA0003505436380000012
Figure FDA0003505436380000013
and a constraint function:
Figure FDA0003505436380000021
Figure FDA0003505436380000022
w∈[0,m),w∈N +
Figure FDA0003505436380000023
wherein G ═ (V, E) is the distribution network; v is a node set, where 0 denotes a distribution center and the remaining nodes denote customers; e is an arc set, E { (i, j) | i, j belongs to V, and i ≠ j }; k is a vehicle set, K ═ 1,2 k A decision variable of 0-1, 0 means that the kth vehicle cannot participate in the delivery for personal reasons of the driver, let num (Σ z) k 0) is w, which represents the number of drivers who cannot participate in the delivery, the actual number of vehicles is p-m-w; d is a radical of ij Distance traveled for arc (i, j); r k As a set of sub-paths, R k ＝{r 1 ,r 2 ,......,r p }，r k Indicating a travel path of a k-th vehicle;
Figure FDA0003505436380000024
points are counted for the path;
Figure FDA0003505436380000025
indicating the ith customer point on the path; c is the maximum load of the delivery vehicle; q i Representing the demand of each customer point; y is ik A decision variable of 0-1, 1 indicating that customer point i is serviced by vehicle k; t represents the number of iterations; the first constraint function represents that the total demand of customer points served by each vehicle does not exceed the self load; a second constraint function representing which vehicles in the set of vehicles participate in the delivery; the third constraint function represents that the number of vehicles which cannot participate in distribution is less than the total number m of the vehicles and is a positive integer; the fourth constraint function indicates that a customer can only be serviced by one vehicle.
3. The improved lion group algorithm-based community material vehicle path optimization method under epidemic situation according to claim 1, characterized in that: the initialization algorithm parameters in the step 1 comprise the maximum iteration times T of the algorithm, the size P of the lion group, the ratio B of adult lion of the lion group and an intrusion factor lf.
4. The method for optimizing the community material vehicle path under epidemic situation based on the improved lion group algorithm as claimed in claim 1, wherein the step 2 specifically comprises:
step 21: real number coding is carried out on the distribution path, and then lion groups are initialized;
step 22: determining the sequence of the individuals sorted by pareto according to the respective crowding distance, enabling the individuals arranged at the forefront to become lion king, determining the number of adult lions according to the occupation ratio B of the adult lions in the lion group, and determining the identities of other individuals according to the sequence of the individuals.
5. The method for optimizing the community material vehicle path under epidemic situation based on the improved lion group algorithm as claimed in claim 4, wherein the real number encoding in the step 21 is specifically as follows: firstly generating 0 representing the distribution center, 1-n representing all customer points needing distribution, randomly selecting the customer points to join, judging whether the constraint conditions of the path planning mathematical model are met, if not, inserting 0 representing the current sub-path to end, then opening up a sub-path, repeating the steps until all the customer points are joined, and finally ending with 0.
6. The method for optimizing the community material vehicle path under epidemic situation based on the improved lion group algorithm as claimed in claim 1, wherein the step 3 specifically comprises:
step 31: generating a random number r at the beginning of each generation, wherein r belongs to (0,1), comparing the size of r with an intrusion factor lf, if the size of r is smaller than the size of r, representing that an external enemy invades, entering a step 32, if the size of r is larger than the size of r, not invading, ending the step 31, and entering a step 4;
step 32: a better individual is generated by a greedy insertion method to serve as an invader, and if the fitness value of the superior individual can dominate the current lion king, the superior individual is substituted for the lion king, otherwise, the superior individual is driven.
7. The method for optimizing the community material vehicle path under epidemic situation based on the improved lion group algorithm as claimed in claim 6, wherein the greedy insertion method in the step 32 comprises the following specific processes:
step 321: inputting a set of feasible solutions R * ＝{R 1 ,R 2 ,......,R m }，L←R * ；
Step 322: RL ← L, but not increased in the process
Figure FDA0003505436380000031
A subset of (a);
step 323: if the RL is not null, F ← RL is the optimal solution after pareto sorting and crowding distance judgment; if RL is null, F ← L is the optimal solution after pareto sorting and crowding distance judgment;
step 324: and F is output.
8. The method for optimizing the community material vehicle path under epidemic situation based on the improved lion group algorithm as claimed in claim 1, wherein the step 4 specifically comprises:
step 41: updating the position of the lion group by adopting a lion group passage operator PO, wherein the lion group movement strategy is as follows:
Figure FDA0003505436380000041
Figure FDA0003505436380000042
Figure FDA0003505436380000043
in the formula
Figure FDA0003505436380000044
Representing the best position of the individual i in the t generation, the first formula represents the lion king position update strategy, where g t Representing the optimal position of the individual in the lion group in the t generation; the second formula represents the location update strategy of the lion, wherein
Figure FDA0003505436380000045
Representing the optimal position of a random individual m in the female lion in the t generation; the third formula represents the position updating strategy of the young lion, wherein q is a random number between 0 and 1, q is not less than 1/3 and represents that the young lion moves towards the direction of the lion king, q is more than 1/3 and not more than 2/3 and moves towards the direction of the mother lion, q is more than 2/3 and not more than 1 and represents that the young lion is expelled and moves towards the opposite direction of the lion group;
step 42: the lion group position updating is realized by adopting the trial times maxtrial, and the formula of the trial times maxtrial is as follows:
Figure FDA0003505436380000046
Figure FDA0003505436380000047
9. the improved lion group algorithm-based community material vehicle path optimization method under epidemic situation according to claim 1, characterized in that: step 5 adopts three balancing operators to optimize the workload balancing goal:
equalization operator 1: path segment node reversal
Selecting the longest path of the current individual, generating a random positive integer i, j, and reversing the access sequence between the two nodes;
the balance operator 2: switching dual node
Selecting the longest path of the current solution, generating a random positive integer number i, j, and exchanging the access sequence of the two client points;
the equalization operator 3: removal and insertion
Selecting the longest path and the shortest path from the solution, removing the customer point which has the smallest influence on the path in the longest path, inserting the customer point into the shortest path and generating the smallest path growth, wherein the removed customer point meets the following formula:
Figure FDA0003505436380000051
assuming the removal point is w, the position of the addition point is represented as:
Figure FDA0003505436380000052
the results of the three kinds of balancing operators are accepted only when the constraint conditions of the path planning mathematical model are met and new individuals can dominate old individuals, and the three kinds of balancing operators are selected randomly.
10. The method for optimizing the community material vehicle path under epidemic situation based on the improved lion group algorithm as claimed in claim 1, wherein the step 7 is specifically as follows: updating the best position of the individual i in the t generation and the best position of the lion group individual in the t generation, calculating whether the remainder of the t divided by 10 is 0 or not, wherein t is the iteration number, the remainder of the t divided by 10 is 0, then ranking the lion group by using pareto ranking and crowding distance judgment, re-determining the identity of the lion group individual, and if the remainder of the t divided by 10 is not 0, then no longer ranking the lion group.
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Cited By (1)

* Cited by examiner, † Cited by third party
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116029639A (en) * 2023-02-22 2023-04-28 南京信息工程大学 Vehicle path planning method based on mixed wolf particle swarm algorithm

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