CN108053059B - Method for optimizing dynamic traveler problem by applying intelligent group algorithm based on reuse strategy - Google Patents

Method for optimizing dynamic traveler problem by applying intelligent group algorithm based on reuse strategy Download PDF

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CN108053059B
CN108053059B CN201711275295.3A CN201711275295A CN108053059B CN 108053059 B CN108053059 B CN 108053059B CN 201711275295 A CN201711275295 A CN 201711275295A CN 108053059 B CN108053059 B CN 108053059B
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张军
陈伟能
詹志辉
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South China University of Technology SCUT
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Abstract

The invention discloses a method for optimizing dynamic traveler problems by applying an intelligent group algorithm based on a reuse strategy. The traditional traveler problem is to find a least costly hamiltonian loop in a static search space. In practice, however, some applications in the real world that may be modeled by the traveler problem are not all static. The city set and weight matrix in their problem model are dynamically changing. In a dynamic environment, search results in the last environment may be reused and learned by a community in the new environment. Therefore, the search space of the problem can be reduced, and the algorithm can search a better path in a shorter time. The invention provides a dynamic traveler modeling method with more realistic significance and a strategy for reusing historical search results, and in an experiment, the dynamic performance of the method is tested by setting different degrees of change of the environment, so that the method is proved to be reasonable and effective under different dynamic environments.

Description

Method for optimizing dynamic traveler problem by applying intelligent group algorithm based on reuse strategy
Technical Field
The invention relates to the technical field of dynamic traveler modeling and intelligent calculation, in particular to a method for optimizing dynamic traveler problems by applying an intelligent group algorithm based on a reuse strategy.
Background
The Traveling Salesman Problem (TSP) has been considered as a classical combinatorial optimization Problem since its introduction, and salesmen needs to find a shortest hamiltonian loop from a certain city node to traverse all other city nodes once and finally back to the starting point in a fixed undirected graph G ═ V, a, W, where V denotes a given set of nodes (the nodes represent different objects in different Problem models), a denotes a set of all undirected edges in the graph, and W is a weighting matrix for the undirected graph G. The value of each element in the matrix represents the distance from the two cities with which it is associated. The model of the traveler problem has been successfully extended to address a range of practical problems, such as line scheduling, machine scheduling and sequencing, logistics system design, etc. At the same time, some targeted algorithms are proposed one after the other and successfully applied to the optimization of static scenes. However, in the real world, some applications that can be modeled by the traveler problem are not all static, that is, the set of nodes and the weight matrix contained in the undirected graph G in their problem model are dynamically changed, which results in the generation of the dynamic traveler problem. The dynamic traveler problem originates from the reality, and the dynamic scene thereof has many instances in the reality, such as a school bus pickup student problem and a mail delivery and receipt problem of a postman. That is, when some students have special events and are not sent or received by letters by people who cannot attend the class or in some places, school buses and postman do not need to go to these places. These situations make their daily set of destinations uncertain. On the other hand, if the shortest path between two nodes is not reachable (due to road failure, traffic jam, etc.), the salesperson needs to select a suboptimal path, which results in the change of the traversal distance of the two nodes (the physical space distance is not changed). In both cases, the goal of the salesperson is to find a hamiltonian loop from the initial point through all other nodes in the set of dynamically changing target nodes, back to the initial point once and for all. Due to the universality and the practicability of the dynamic scene, the research on the problems of the dynamic travelers is of great practical significance and can help enterprises reduce the transportation cost in the logistics industry. In this case, it is necessary to design a practical model for the problem of the dynamic traveler to test its associated solving algorithm and it has practical application value. Since the dynamic traveler problem is an extension of the traditional static traveler problem, and its nature is also a combinatorial optimization problem, it can be solved using some of the methods commonly used to solve combinatorial optimization problems. These algorithms are mainly classified into two kinds, deterministic algorithms and stochastic algorithms. Deterministic algorithms, such as gradient and hill climbing, branch-and-bound, etc., are prone to get into local optima, resulting in suboptimal path traversal lengths. Moreover, some deterministic algorithms are too dependent on the choice of initial search points and are therefore often not suitable for optimization of the dynamic traveler problem. In contrast, stochastic algorithms can search the solution space extensively and are therefore better suited to the optimization of the dynamic traveler problem than deterministic methods. A representative random algorithm, namely an evolutionary algorithm, attracts the attention of many researchers. The evolutionary algorithm is characterized by requiring little information about the problem sought and only information about the optimization objective. The method is not restricted by the search space restrictive hypothesis, does not require the hypothesis such as continuity, conductibility and the like, and can find the global optimal solution with high probability from discrete, multi-extremal and high-dimensional problems containing noise. The particle swarm algorithm is an important branch of the particle swarm algorithm and is a random search algorithm for simulating the predation of bird swarms and fish swarms in nature. The particle swarm algorithm has clear updating rule, is simple and practical, and has been widely applied in fields such as dynamic allocation, medical graph registration, machine learning and training, data mining and classification and the like. Compared with other evolutionary algorithms, the particle swarm algorithm has the advantages of high convergence speed, stable solution quality and the like. The existing particle swarm algorithm mainly solves the problem under the continuous space, and a few scholars try to expand the particle swarm algorithm under the continuous space to the discrete space. In these attempts, one of the more successful has been the particle swarm optimization algorithm based on set and probability theory. The algorithm treats the entire discrete search space as a full set, with any feasible solution being considered as a subset of the full set, and the velocity of each particle in continuous space being defined as a set of edges with probabilities. In the optimization process, the speed and position update operations in the continuous space are replaced with speed and position update operations defined on the set. This algorithm has the advantages of easy scalability, stable performance, etc. and has been extended to the optimization of some path problems such as time windowing. Therefore, the particle swarm optimization based on the set and probability theory is very suitable for solving the problem of the dynamic traveler. In addition, an ant colony algorithm simulating the behavior of ants finding paths through pheromones in the process of searching food is proposed to solve the problem of travelers. The ant colony algorithm has the advantages of strong robustness, global search, parallel distributed computation, easy combination of other problems and the like, and the application field of the ant colony algorithm is more and more extensive, such as the problems of workshop scheduling, vehicle path, network routing, protein folding and the like. Most of the problems are NP-difficult combined optimization problems, some traditional algorithms are difficult to solve or cannot be solved, and ant colony algorithm provides an effective means for solving the problems. Therefore, the ant colony algorithm is very suitable for solving the problem of the dynamic traveler. And therefore, the method is also very suitable for optimizing the dynamic traveler problem.
Disclosure of Invention
The invention aims to solve the defects in the prior art and provides a method for optimizing the dynamic traveler problem by applying an intelligent group algorithm based on a reuse strategy.
The purpose of the invention can be achieved by adopting the following technical scheme:
a method for optimizing dynamic traveler problems using an intelligent group algorithm based on a reuse strategy, said method comprising:
s1, a dynamic traveler model frame designing step, wherein the dynamic traveler model is designed to be a series of state changes, the change of the access node set or the change of the path weight value can lead to the state change of the search space, each state only corresponds to the change of the access node set or the change of the weight matrix, and the sequence S is composed of S1The change mode of any two adjacent states at the beginning is consistent, and the state change of the search space can be expressed as:
S＝s0s1s2s3...sk...sμ
wherein s is0Represents the initial state, skRepresenting the kth state of the search space, mu representing the sum of the times the search space has changed, from state skTo state sk+1Indicates that the search space has changed;
s2, dynamically changing path weight, wherein each specific state has a unique weight matrix corresponding to it under the condition of weight change, and S is the step of implementing dynamic change of path weightkThe weight matrix under the state is recorded as
Figure GDA0003047937700000041
Can be expressed as follows:
Figure GDA0003047937700000042
wherein
Figure GDA0003047937700000043
Is in a state skThe total number of nodes to be accessed in the node group is not changed in all the states under the condition that the path weight value is dynamically changed, namely the node group to be accessed in all the states is not changed in size
Figure GDA0003047937700000044
Slave state skTo state sk+1Can be expressed as follows:
Figure GDA0003047937700000045
wherein Dc ∈ [ Lb, Ub)]Lb and Ub represent the upper and lower limits of the weight change factor, respectively,
Figure GDA0003047937700000046
and
Figure GDA0003047937700000047
respectively represent at state skAnd in state sk+1In the above description, the weight from node i to node j,
Figure GDA0003047937700000048
is the weight from node i to node j in the initial state, randijIs that
Figure GDA0003047937700000049
Generating a random number, Nc is a preset parameter between 0 and 1;
s3, an implementation step of dynamic change of the access node set, wherein under the condition that the access node set is dynamically changed, the access node set needing to be accessed in the original state is represented as
Figure GDA00030479377000000410
Figure GDA00030479377000000411
Middle access node total numberIs composed of
Figure GDA00030479377000000412
Subsequent state skThe access node set needing to be accessed is expressed as
Figure GDA00030479377000000413
Figure GDA00030479377000000414
The total number of access nodes is recorded as
Figure GDA00030479377000000415
Slave state skTo sk+1In which some nodes are temporarily accessed from the node set
Figure GDA00030479377000000416
In case of addition or deletion, assume
Figure GDA00030479377000000417
The node set in (1) is:
Figure GDA0003047937700000051
at the transition
Figure GDA0003047937700000052
Previously, the model randomly generated a positive or negative integer
Figure GDA0003047937700000053
Figure GDA0003047937700000054
The following two conditions are satisfied:
Figure GDA0003047937700000055
Figure GDA0003047937700000056
where Nr and Df are both range factors between 0 and 1, Df is used to control the extent of change of two adjacent state access node sets, Nr is used to control the range of access node set size, if
Figure GDA0003047937700000057
Less than 0, for each at
Figure GDA0003047937700000058
The model generates a random number rndiTo simulate a node
Figure GDA0003047937700000059
Randomness of access if
Figure GDA00030479377000000510
Exist in
Figure GDA00030479377000000511
Then node
Figure GDA00030479377000000512
Will be selected from
Figure GDA00030479377000000513
Is temporarily removed if
Figure GDA00030479377000000514
Is greater than 0 and the content of the active ingredient,
Figure GDA00030479377000000515
node (2)
Figure GDA00030479377000000516
Will be added to
Figure GDA00030479377000000517
In this way, in the state
Figure GDA00030479377000000518
The following nodes to be accessed may be represented as:
Figure GDA00030479377000000519
s4, optimizing the target step by using cijAnd yijThe following binary decision variables are respectively represented:
Figure GDA00030479377000000520
Figure GDA00030479377000000521
Figure GDA00030479377000000522
wherein x iskIs shown in state skThe minimum path value, edge found inijRepresenting the edge formed by the node i and the node j, and the optimization is aimed at an arbitrary state skWherein all nodes to find a node are
Figure GDA00030479377000000523
The Hamiltonian loop with the minimum path cost;
s5, reusing strategy implementation step, learning state SkBefore that
Figure GDA00030479377000000524
The best solution in the sub-environment, all of which are stored in the external memory Archive, the process of this reuse can be defined as:
Figure GDA00030479377000000525
wherein the content of the first and second substances,
Figure GDA0003047937700000061
represents in a state
Figure GDA0003047937700000062
Before reusing the external memory Archive, if the environment is changed by the access node set, the solution in the external memory Archive needs to be adjusted, after the adjustment, the state sk+1These particles can be reused to the state s, identical to the set of nodes to be accessed by each solution of the external memory ArchivekIf the environment is changed by weight value, the solution stored in external memory Archive is directly used.
Further, the state change of the search space represents that the search environment of the optimization algorithm changes, and the change of the weight matrix or the change of the access node set corresponds to the following limitation:
Figure GDA0003047937700000063
Figure GDA0003047937700000064
further, when the weight matrix of the search space changes, state skTransition to sk+1The method comprises the following steps:
Figure GDA0003047937700000065
wherein Dc ∈ [ Lb, Ub)]Lb and Ub represent the upper and lower limits of the weight change factor, respectively,
Figure GDA0003047937700000066
and
Figure GDA0003047937700000067
respectively represent at state skAnd in state sk+1The weight value from node i to node j,
Figure GDA0003047937700000068
is the weight from node i to node j in the initial state, randijIs that
Figure GDA0003047937700000069
Generating a random number, Nc is a preset parameter between 0 and 1;
slave state s when a change in the set of access nodes occurs in the search spacekTransition to sk+1The method comprises the following steps:
Figure GDA00030479377000000610
wherein Nr and Df are both range factors between 0 and 1, Df is used to control the extent of change of two adjacent state access node sets, Nr is used to control the range of access node set size, if
Figure GDA00030479377000000611
Less than 0, for each at
Figure GDA00030479377000000612
The model generates a random number rndiTo simulate a node
Figure GDA0003047937700000071
Randomness of access if
Figure GDA0003047937700000072
Exist in
Figure GDA0003047937700000073
Then node
Figure GDA0003047937700000074
Will be selected from
Figure GDA0003047937700000075
Is temporarily removed if
Figure GDA0003047937700000076
Is greater than 0 and the content of the active ingredient,
Figure GDA0003047937700000077
node (2)
Figure GDA0003047937700000078
Will be added to
Figure GDA0003047937700000079
In (1).
Further, the process of adjusting the solution in Archive in step S5 is as follows:
s501, calculating Ar of each Archive individualiNumber of nodes N ini；
S502, calculating the temporary secondary Ar by the following formulaiIs removed or is to be added to AriAnd store them in omegaiIn (1),
Figure GDA00030479377000000710
s503, if
Figure GDA00030479377000000711
Accounting for the increase in the number of nodes accessed, Ar is solved for each solution in ArchiveiWill omegaiEach node in (1) is inserted into Ar in a regular manner that minimizes the pathiIn otherwise, Ar isiNeutralization omegaiEach of the same nodes is directly deleted and the predecessor and successor nodes of the deleted node are made to be immediately adjacent.
Further, in the step S3, the nodes to be accessed in the original state form a complete set, and the following arbitrary state SkMiddle needThe node sets to be accessed are all
Figure GDA00030479377000000712
The size of the set of access nodes corresponds to the dimension of the feasible solution of the population in the new environment.
Compared with the prior art, the invention has the following advantages and effects:
1. the invention completely and mathematically models the dynamic characteristics of the traveler problem. The problem is attached to the existing optimization model (particularly a group intelligent algorithm) in a coding and evaluation mode, and a solid mathematical foundation is laid for further research of the problem.
2. The reuse strategy based on the historical information disclosed by the invention greatly reduces the search space of the problem and improves the search efficiency of the algorithm. Provides a reasonable and effective important idea for solving the dynamic problems.
3. The method for solving the problem of the dynamic traveler can be applied to corresponding engineering and social problems, such as optimization of transportation lines. The method brings considerable economic and social values to important fields of production and life.
Drawings
FIG. 1 is a realistic basis for a dynamic model;
FIG. 2 is a schematic diagram of model dynamics;
FIG. 3 is a flow chart of a reuse strategy based aggregated particle swarm optimization to optimize a dynamic traveler problem;
FIG. 4 is a flow chart of ant colony algorithm optimization of dynamic traveler problem based on reuse strategy.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Examples
The embodiment combines the set-based particle swarm algorithm and the ant swarm algorithm with the reuse strategy and applies the combination to the optimization of the dynamic traveler. The invention content can be mainly divided into modeling of dynamic travelers and reuse strategies of historical search information.
1) Modeling of dynamic travelers:
in the partial map shown in fig. 1, there are a total of 12 access nodes (a-l), and two cases are now assumed:
i) when an accident (traffic accident, road fault) occurs on the original shortest path from h to a (red dotted line part), the red solid line part will become the current shortest path from h to a;
ii) in some cases, since point l does not need to be visited, the visiting order of the three nodes of original f, i, l changes from f → l → i to f → i to directly skip node l. Based on these two reality cases, the present embodiment models them as dynamic changes in path weights and dynamic changes in access nodes in the dynamic traveler problem, respectively. In the case of dynamic changes in path weights, the access weights for certain edges of the weight matrix in each compute instance are dynamically changed. For each edge, the dynamic model generates a random number rand for itijIf randijIf the current weight of the edge is smaller than the preset parameter Nc and equal to the initial weight, the weight of the edge is multiplied by a factor larger than 1; if randijGreater than Nc and the current weight and initial value of the edge are not equal, the weight of the edge is reset to the initial value. In the case of dynamic change of access node, in order to construct the subsequent state from the current state, the dynamic model will first generate an integer that can be positive or negative within a certain range
Figure GDA0003047937700000091
If it is not
Figure GDA0003047937700000092
Less than 0, then
Figure GDA0003047937700000093
The individual city node is removed from the current set of access nodes. Otherwise, the same number of nodes (not in the current access node set) will be added to the current access node set. In this design mode, the weights of some edges and the node sets to be accessed are dynamically changed, and the change mode is shown in fig. 2.
2) The reuse strategy is as follows:
in the dynamic traveler problem, the search space of the optimization algorithm is dynamically changed, and the optimal values in different environments, although different, more or less delete, add or regroup some edges, thereby sharing some path subsets composed of common edges. These path subsets can be reused and learned by the optimization algorithm in the new environment. Therefore, repeated searching can be avoided, the searching speed of the algorithm is increased, and the algorithm can search the Hamiltonian loop with smaller path sum in shorter time. In the aggregate particle swarm algorithm, when the environment changes, the historical optimal solution pbest of each particle in the swarm will be stored in an external memory Archive, the size of which is fixed. When the amount of newly added particles pbest exceeds the Archive size, coverage occurs. In design, the size of an Archive is an integral multiple of the size of a population, so before historical optimal solutions pbest of population particles in the Archive are reused, the historical optimal solutions pbest are sorted according to fitness values, and only popsize (the size of the population) with the best fitness value can be selected as the historical optimal solution pbest of a new population. In the ant colony algorithm, after the pheromone matrix in the new environment is initialized, all the pheromones on the edges belonging to the best popsize historical optimal solutions pbest are increased by an increment, the increment enables the values of the pheromones on the edges to be higher than those of the pheromones on other edges, and thus the edge belonging to the global optimal value of the new environment has a higher probability to be selected.
A method for optimizing dynamic traveler problems by using an intelligent group algorithm based on a reuse strategy comprises the following steps:
s1, designing a dynamic traveler model framework;
dynamic traveler model framework design from initial state s0And starting. In an initial state s0And the accessed nodes and the weight matrix are not changed, which is consistent with the data test case under the traditional static model. The subsequent series of states is represented as follows:
S＝s0s1s2s3...sk...sμ
wherein s iskRepresenting the kth state of the search space and μ representing the total number of environmental changes. Slave state skTo state sk+1The transition of (d) indicates that the search space has changed. Changes in the search space represent changes in the search environment of the optimization algorithm. This change is either a change in the weight matrix or a change in the set of access nodes. The limitations of this variation can be described as follows:
Figure GDA0003047937700000101
Figure GDA0003047937700000102
s2, implementation of dynamic change of path weights:
in the case of weight change, each particular state has a unique weight matrix corresponding thereto, at skThe weight matrix under the state is recorded as
Figure GDA0003047937700000103
Can be expressed as follows:
Figure GDA0003047937700000104
wherein
Figure GDA0003047937700000111
Is in the shape ofState skThe total number of nodes that need to be accessed. In the case of dynamic change of the path weight, the size of the node set to be accessed in all the states is not changed, i.e. the node set needs to be accessed in all the states is not changed
Figure GDA0003047937700000112
Slave state skTo state sk+1Can be expressed as follows:
Figure GDA0003047937700000113
wherein Dc ∈ [ Lb, Ub)]Lb and Ub represent the upper and lower limits of the weight change factor, respectively,
Figure GDA0003047937700000114
and
Figure GDA0003047937700000115
respectively represent at state skAnd in state sk+1In the above description, the weight from node i to node j,
Figure GDA0003047937700000116
is the weight from node i to node j in the initial state, randijIs that
Figure GDA0003047937700000117
A random number, Nc, is generated as a parameter between 0 and 1 set in advance.
S3, implementation mode of dynamic change of access nodes:
in the case of dynamic change of access node, the combination of nodes needing access in original state is expressed as
Figure GDA0003047937700000118
The total number of access nodes is recorded as
Figure GDA0003047937700000119
Subsequent state skThe node set needing to be accessed is expressed as
Figure GDA00030479377000001110
The total number of access nodes is recorded as
Figure GDA00030479377000001111
Slave state skTo sk+1In which some nodes are temporarily accessed from the node set
Figure GDA00030479377000001112
To be added or deleted. Suppose that
Figure GDA00030479377000001113
The node set in (1) is:
Figure GDA00030479377000001114
at the transition
Figure GDA00030479377000001115
Previously, the model randomly generated a positive or negative integer
Figure GDA00030479377000001116
Figure GDA00030479377000001117
The following two conditions are satisfied:
Figure GDA00030479377000001118
Figure GDA00030479377000001119
where Nr and Df are both range factors between 0 and 1, Df is used to control the degree of change of two adjacent state access node sets, and Nr is used to control the range of access node set sizes. If it is not
Figure GDA00030479377000001120
Less than 0, for each at
Figure GDA00030479377000001121
The model generates a random number rndiTo simulate a node
Figure GDA00030479377000001122
Randomness of access. If it is not
Figure GDA00030479377000001123
Exist in
Figure GDA00030479377000001124
Then node
Figure GDA00030479377000001125
Will be selected from
Figure GDA00030479377000001126
Is temporarily removed. If it is not
Figure GDA00030479377000001127
Is greater than 0 and the content of the active ingredient,
Figure GDA00030479377000001128
node (2)
Figure GDA00030479377000001129
Will be added to
Figure GDA00030479377000001130
In (1). Thus in the state
Figure GDA00030479377000001131
The following nodes to be accessed may be represented as:
Figure GDA00030479377000001132
in this case, it is preferable that the air conditioner,the nodes needing to be accessed in the original state form a complete set, and the subsequent arbitrary state skThe node sets needing to be accessed are
Figure GDA0003047937700000121
A subset of (a). The size of the set of access nodes corresponds to the dimension of the feasible solution of the population in the new environment.
S4, optimizing the target:
by cijAnd yijBinary decision variables respectively expressed as follows
Figure GDA0003047937700000122
Figure GDA0003047937700000123
Figure GDA0003047937700000124
Wherein x iskIs shown in state skThe minimum path value, edge found inijRepresenting the edge formed by node i and node j. The goal of the optimization is to be at an arbitrary state skWherein all nodes to find a node are
Figure GDA0003047937700000125
The hamiltonian loop with the smallest path cost.
S5, specific implementation of the reuse strategy:
in the reuse strategy, the inventive algorithm will learn to state skBefore that
Figure GDA0003047937700000126
All the best solutions in the Secondary Environment are saved in Archive. This process of reuse can be defined as:
Figure GDA0003047937700000127
wherein the content of the first and second substances,
Figure GDA0003047937700000128
represents in a state
Figure GDA0003047937700000129
And (4) historical optimal feasible solutions of all individuals in the middle population. Before the Archive is reused, if the environment is changed by the access node set, some adjustment to the solution in Archive is needed, and the adjustment steps are as follows:
s501, calculating Ar of each Archive individualiNumber of nodes N ini；
S502, calculating the temporary secondary Ar by the following formulaiIs removed or is to be added to AriAnd store them in omegaiIn (1),
Figure GDA00030479377000001210
s503, if
Figure GDA0003047937700000131
Illustrating an increase in the number of nodes accessed. For each solution Ar in ArchiveiWill omegaiEach node in (1) is inserted into Ar in a regular manner that minimizes the pathiIn (1). Otherwise, Ar is addediNeutralization omegaiEach of the same nodes is directly deleted and the predecessor and successor nodes of the deleted node are made to be immediately adjacent.
After this adjustment, the state sk+1The same set of nodes to be accessed for each solution of Archive is used, so that the particles can be reused to state skIn the optimization of (2). If the environment is a weight change, the solution saved in Archive is used directly.
The particle velocity and location update rule used by the set-based particle swarm algorithm can be expressed as:
Figure GDA0003047937700000132
Figure GDA0003047937700000133
where ω is the inertial weight, c is the acceleration coefficient, fi(d) The learning object in dimension d representing the ith particle may be itself or another particle in the population. The learning object depends on the corresponding parameter Pc of each particlei,PciCan be expressed as:
Figure GDA0003047937700000134
for each dimension d of each particle, a random number is generated if the random number is greater than PciThen learn from the d-th dimension of its pbest. Otherwise it will learn to the d-th dimension of pbest of the other particle. When the environment changes, the optimal popsize solutions in Archive will be selected as pbest of the new population and then replaced in the later process to prevent the population from getting into local optimality by receiving excessive attraction of pbest in the optimization process. A flowchart of a reuse strategy-based aggregate particle swarm optimization for optimizing the dynamic traveler problem is shown in fig. 3.
In the ant colony algorithm, the pheromone matrix of the ant colony is reinitialized when the environment changes. After the initialization of the pheromone matrix is completed, all pheromones on the edges belonging to the optimal popsize solutions in Archive are executed with an increment operation, which can be expressed as:
τij＝τij+α·τ0
wherein tau isijRepresents edgeijThe amount of the above current pheromone, τ0Is the reciprocal of the path obtained by the greedy algorithm under the new environment, and alpha is the decay factor of the pheromone. Ant colony algorithm based on reuse strategyA flow chart for optimizing the dynamic traveler problem is shown in fig. 4. In all test cases of the dynamic model, the maximum number of iterations in each environment is
Figure GDA0003047937700000141
In order to simulate the environment changes of different degrees in reality as much as possible, the relevant parameters of the dynamic model are set as follows:
parameter(s) Value taking
Nc {0.75,0.65,0.55}
Lb 1.0
Ub {1.5,2.0}
{Nr,Df} {0.8,0.05},{0.7,0.1},{0.6,0.15}
The relevant parameters of the dynamic particle swarm optimization are set as follows:
Figure GDA0003047937700000142
the relevant parameters of the dynamic ant colony algorithm are set as follows:
Figure GDA0003047937700000143
Figure GDA0003047937700000151
in order to verify the effectiveness of the reuse strategy, simulation tests are respectively carried out on the optimization results of the reuse strategy introduced by the two algorithms. The result shows that the introduction of the reuse strategy enables two dynamic algorithms to find a solution with a shorter path in the same time, and compared with the dynamic ant colony algorithm, the solution of the dynamic ensemble particle swarm algorithm in most of the examples can find a better solution. This demonstrates that the reuse approach of pbest and pheromone delta operations acting as groups of particles in the new environment based on the best part of the selection history is very effective in the optimization problem for dynamic travelers.
The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.

Claims (5)

1. A method for optimizing dynamic traveler problems by using an intelligent group algorithm based on a reuse strategy is characterized by comprising the following steps:
s1, a dynamic traveler model frame designing step, wherein the dynamic traveler model is designed to be a series of state changes, the change of the access node set or the change of the path weight value can lead to the state change of the search space, each state only corresponds to the change of the access node set or the change of the weight matrix, and the sequence S is composed of S1The change mode of any two adjacent states at the beginning is consistent, and the state change of the search space can be expressed as:
S＝s0s1s2s3...sk...sμ
wherein s is0Represents the initial state, skRepresenting the kth state of the search space, mu representing the sum of the times the search space has changed, from state skTo state sk+1Indicates that the search space has changed;
s2, dynamically changing path weight, wherein each specific state has a unique weight matrix corresponding to it under the condition of weight change, and S is the step of implementing dynamic change of path weightkThe weight matrix under the state is recorded as
Figure FDA0003047937690000011
Can be expressed as follows:
Figure FDA0003047937690000012
wherein
Figure FDA0003047937690000013
Is in a state skThe total number of nodes to be accessed in the node group is not changed in all the states under the condition that the path weight value is dynamically changed, namely the node group to be accessed in all the states is not changed in size
Figure FDA0003047937690000014
Slave state skTo state sk+1Can be expressed as follows:
Figure FDA0003047937690000021
wherein Dc ∈ [ Lb, Ub)]Lb and Ub represent the upper and lower limits of the weight change factor, respectively,
Figure FDA0003047937690000022
and
Figure FDA0003047937690000023
respectively represent at state skAnd in state sk+1In (1), the weight from node i to node j，
Figure FDA0003047937690000024
Is the weight from node i to node j in the initial state, randijIs that
Figure FDA0003047937690000025
Generating a random number, Nc is a preset parameter between 0 and 1;
s3, an implementation step of dynamic change of the access node set, wherein under the condition that the access node set is dynamically changed, the access node set needing to be accessed in the original state is represented as
Figure FDA0003047937690000026
Figure FDA0003047937690000027
The total number of access nodes is recorded as
Figure FDA0003047937690000028
Subsequent state skThe access node set needing to be accessed is expressed as
Figure FDA0003047937690000029
Figure FDA00030479376900000210
The total number of access nodes is recorded as
Figure FDA00030479376900000211
Slave state skTo sk+1In which some nodes are temporarily accessed from the node set
Figure FDA00030479376900000212
In case of addition or deletion, assume
Figure FDA00030479376900000213
In (1)The node set is as follows:
Figure FDA00030479376900000214
at the transition
Figure FDA00030479376900000215
Previously, the model randomly generated a positive or negative integer
Figure FDA00030479376900000216
Figure FDA00030479376900000217
The following two conditions are satisfied:
Figure FDA00030479376900000218
Figure FDA00030479376900000219
where Nr and Df are both range factors between 0 and 1, Df is used to control the extent of change of two adjacent state access node sets, Nr is used to control the range of access node set size, if
Figure FDA00030479376900000220
Less than 0, for each at
Figure FDA00030479376900000221
The model generates a random number rndiTo simulate a node
Figure FDA00030479376900000222
Randomness of access if
Figure FDA00030479376900000223
Exist in
Figure FDA00030479376900000224
Then node
Figure FDA00030479376900000225
Will be selected from
Figure FDA00030479376900000226
Is temporarily removed if
Figure FDA00030479376900000227
Is greater than 0 and the content of the active ingredient,
Figure FDA00030479376900000228
node (2)
Figure FDA00030479376900000229
Will be added to
Figure FDA00030479376900000230
In this way, in the state
Figure FDA00030479376900000231
The following nodes to be accessed may be represented as:
Figure FDA00030479376900000232
s4, optimizing the target step by using cijAnd yijThe following binary decision variables are respectively represented:
Figure FDA0003047937690000031
Figure FDA0003047937690000032
Figure FDA0003047937690000033
wherein x iskIs shown in state skThe minimum path value, edge found inijRepresenting the edge formed by the node i and the node j, and the optimization is aimed at an arbitrary state skWherein all nodes to find a node are
Figure FDA0003047937690000034
The Hamiltonian loop with the minimum path cost;
s5, reusing strategy implementation step, learning state SkBefore that
Figure FDA0003047937690000035
The best solution in the sub-environment, all of which are stored in the external memory Archive, the process of this reuse can be defined as:
Figure FDA0003047937690000036
wherein the content of the first and second substances,
Figure FDA0003047937690000037
represents in a state
Figure FDA0003047937690000038
Before the Archive is reused, if the environment is changed by the access node set, the solution in the Archive of the external memory needs to be adjusted, and after the adjustment, the state sk+1These particles can be reused to the state s, identical to the set of nodes to be accessed by each solution of the external memory ArchivekIn case of environmental occurrenceIf the weights change, the solution saved in the external memory Archive is used directly.
2. The method of claim 1, wherein the state change of the search space represents a change of a search environment of the optimization algorithm, and the change of the state corresponds to a change of a weight matrix or a change of an access node set, and the change can be described as follows:
Figure FDA0003047937690000039
Figure FDA00030479376900000310
3. the method for optimizing dynamic traveler problem using intelligent group algorithm based on reuse strategy according to claim 2,
state s when the weight matrix of the search space changeskTransition to sk+1The method comprises the following steps:
Figure FDA0003047937690000041
wherein Dc ∈ [ Lb, Ub)]Lb and Ub represent the upper and lower limits of the weight change factor, respectively,
Figure FDA0003047937690000042
and
Figure FDA0003047937690000043
respectively represent at state skAnd in state sk+1The weight value from node i to node j,
Figure FDA0003047937690000044
is the weight from node i to node j in the initial state, randijIs that
Figure FDA0003047937690000045
Generating a random number, Nc is a preset parameter between 0 and 1;
slave state s when a change in the set of access nodes occurs in the search spacekTransition to sk+1The method comprises the following steps:
Figure FDA0003047937690000046
wherein Nr and Df are both range factors between 0 and 1, Df is used to control the extent of change of two adjacent state access node sets, Nr is used to control the range of access node set size, if
Figure FDA0003047937690000047
Less than 0, for each at
Figure FDA0003047937690000048
The model generates a random number rndiTo simulate a node
Figure FDA0003047937690000049
Randomness of access if
Figure FDA00030479376900000410
Exist in
Figure FDA00030479376900000411
Then node
Figure FDA00030479376900000412
Will be selected from
Figure FDA00030479376900000413
Is temporarily removed if
Figure FDA00030479376900000414
Is greater than 0 and the content of the active ingredient,
Figure FDA00030479376900000415
node (2)
Figure FDA00030479376900000416
Will be added to
Figure FDA00030479376900000417
In (1).
4. The method for optimizing the dynamic traveler problem by using the intelligent group algorithm based on the reuse strategy as claimed in claim 1, wherein the adjusting the solution in the external memory Archive in step S5 is as follows:
s501, calculating Ar of each external memory Archive individualiNumber of nodes N ini；
S502, calculating the temporary secondary Ar by the following formulaiIs removed or is to be added to AriAnd store them in omegaiIn (1),
Figure FDA00030479376900000418
s503, if
Figure FDA0003047937690000051
Accounting for the increase in the number of nodes accessed, Ar is solved for each of the external memories ArchiveiWill omegaiEach node in (1) is inserted into Ar in a regular manner that minimizes the pathiIn otherwise, Ar isiNeutralization omegaiEach identical node is deleted directly, and a predecessor of the deleted node is madeDirectly adjacent to the successor node.
5. The method for optimizing dynamic traveler problem by using intelligent group algorithm based on reuse strategy as claimed in claim 1, wherein the nodes to be visited in original state in step S3 form a complete set, and any subsequent state SkThe node sets needing to be accessed are
Figure FDA0003047937690000052
The size of the set of access nodes corresponds to the dimension of the feasible solution of the population in the new environment.
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