CN108053059A - With the method based on the intelligent group algorithm optimization Dynamic Traveling Salesman Problem for reusing strategy - Google Patents

With the method based on the intelligent group algorithm optimization Dynamic Traveling Salesman Problem for reusing strategy Download PDF

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CN108053059A
CN108053059A CN201711275295.3A CN201711275295A CN108053059A CN 108053059 A CN108053059 A CN 108053059A CN 201711275295 A CN201711275295 A CN 201711275295A CN 108053059 A CN108053059 A CN 108053059A
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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 kind of with the method based on the intelligent group algorithm optimization Dynamic Traveling Salesman Problem for reusing strategy.Traditional traveling salesman problem needs find the hamiltonian circuit of a Least-cost in a static search space.But in fact, some in real world can be using traveling salesman problem as model application be not necessarily all static.City gather and weight matrix in they the problem of models are dynamic changes.In dynamic environment, search result can be reused and learnt by the group under new environment in last environment.The search space of problem can be so reduced, so as to which algorithm be allowed to search more preferably path within the shorter time.The present invention propose it is a kind of more realistic meaning dynamic travelling salesman modeling method and by it is a kind of to historical search result re-use strategy, in an experiment, pass through that set environment is different degrees of to be changed come the dynamic property of test method, it was demonstrated that the present invention under different dynamic environment rationally effectively.

Description

With based on the intelligent group algorithm optimization Dynamic Traveling Salesman Problem for reusing strategy Method
Technical field
The present invention relates to dynamic travelling salesman modeling and intelligent Computation Technology fields, and in particular to a kind of with based on reuse plan The method of intelligent group algorithm optimization Dynamic Traveling Salesman Problem slightly.
Background technology
Traveling salesman problem (Traveling Salesman Problem, TSP) be considered as always just since proposition through The combinatorial optimization problem of allusion quotation, shop-assistant need to find one in a fixed non-directed graph G={ V, A, W } from a certain city knot Point sets out the other all city nodes of traversal once, eventually passes back to the shortest hamiltonian circuit of starting point, and wherein V represents one group Given node (in different problems model, the representative object of node is different), A represents the set of all nonoriented edges in figure, W It is the weighting matrix on non-directed graph G.The value of each element in matrix represent from two cities associated there away from From.The model of traveling salesman problem, which is successfully expanded to, solves line arrangement, machine scheduling and sequencing, Logistics System Design Etc. in a series of practical problems.At the same time, some are suggested and are successfully applied to quiet with targetedly algorithm in succession In the optimization of state scene.But in fact, some in real world can be using traveling salesman problem as model application be not necessarily all quiet State, that is to say, that they the problem of model in the node sets that include of non-directed graph G and weight matrix be dynamic change, this Have led to generation of the dynamic travelling salesman for topic.Dynamic Traveling Salesman Problem has very from reality, dynamic scene in reality More examples, such as school bus pick student's problem and the transmitting-receiving mail problem of postman.That is, when some students have spy When the different people that the origin of an incident cannot attend class or some are local does not have mail transmitting-receiving, there is no need to go to these places by school bus and postman.This It is indefinite that a little situations, which allow for their destination to be gone daily set,.On the other hand, it is if most short between two nodes (since the reasons such as road service system, traffic jam cause) when path is unreachable, shop-assistant needs to select the path of a suboptimum, this The traversal distance for having led to the two nodes changes (physical space is apart from constant).In both cases, shop-assistant Target be still to search out one in the destination node set of dynamic change to travel through other all presence from initial point Node once eventually passes back to the hamiltonian circuit of initial starting point in target collection.Due to the popularity of its dynamic scene and existing Reality not only great realistic meaning but also can help enterprise to reduce fortune the research of Dynamic Traveling Salesman Problem in logistic industry Defeated cost.In this case, a model to conform to the actual situation is designed for Dynamic Traveling Salesman Problem to solve to test its correlation Algorithm is necessary and with application value realistic.Since Dynamic Traveling Salesman Problem is based on traditional static traveling salesman problem A kind of extension, essence or combinatorial optimization problem, so equally some can be used to be usually used in solving combinatorial optimization problem Method solves.These algorithms are broadly divided into two kinds of deterministic algorithm and random algorithm.Deterministic algorithm, for example gradient method and climb Mountain method, branch and bound method etc., are easily trapped into local best points, cause the traversal path length of suboptimum.And some certainty are calculated Method excessively relies on the selection of initial search point, therefore is not often suitable for the optimization of Dynamic Traveling Salesman Problem.Opposite, it is random to calculate Method can widely scan for solution space, therefore than deterministic method more suitable for the optimization of Dynamic Traveling Salesman Problem. A kind of representative random algorithm, that is, evolution algorithm have attracted the concern of numerous researchers.The characteristics of evolution algorithm It is only to need the information of optimization aim with little need for any information of required problem.It is from the restricted hypothesis in search space Constraint, do not require such as continuity, the property led it is assumed that can be the problem of discrete, multipole value, higher-dimension containing noise Globally optimal solution is found with very high probability.Wherein, particle cluster algorithm is its important branch, is a kind of simulation nature Middle flock of birds and the random search algorithm of shoal of fish predation.Particle cluster algorithm is simple and practical since its update rule is clear, from propose with Just to have obtained the application of wide hair, such as dynamically distributes, medical graphical registration, machine learning and training, data mining and classification The fields of grade.Compared with other evolution algorithms, particle cluster algorithm has many advantages, such as fast convergence rate, the stable quality of solution.At present Particle cluster algorithm mainly for it is continuous it is empty under the problem of solve, many scholars were once attempted the particle cluster algorithm under continuous space It expands under discrete space.In these trials, a kind of is more successfully the particle group optimizing based on set and probability theory Algorithm.This algorithm regards entire discrete search space as a complete or collected works, any one feasible solution is all counted as this The a subset of complete or collected works, the speed of each particle under continuous space be defined as be one group of side with probability set. In optimization process, the update operation of continuous space medium velocity and position, which is all replaced by, is defined on speed that collection closes and position Update operation.This algorithm has easily extension, steady performance and has had been extended to some such as band time windows Routing problem optimization in.So this particle cluster algorithm based on set and probability theory is very suitable for dynamic travelling salesman and asks The solution of topic.In addition, a kind of simulation ant finds that the ant colony of the behavior in path is calculated during search of food by pheromones Method is suggested to Traveling Salesman Problem.There is ant group algorithm strong robustness, global search, parallel distributed to calculate, easily In other problems combine the advantages that, and its application field is more and more extensive, as Job-Shop problem, Vehicle Routing Problems, The problems such as Network route Problem, protein folding.These problems are all largely the combinatorial optimization problems of NP hardly possiblies, some are traditional Algorithm solution hard to find can not solve, and ant group algorithm provides effective means for the solution of these problems.So ant group algorithm It is very suitable for the solution of Dynamic Traveling Salesman Problem.Therefore also it is quite suitable for the optimization of Dynamic Traveling Salesman Problem.
The content of the invention
The purpose of the present invention is to solve drawbacks described above of the prior art, provide a kind of with based on reuse strategy The method of intelligent group algorithm optimization Dynamic Traveling Salesman Problem.
The purpose of the present invention can be reached by adopting the following technical scheme that：
A kind of method with the intelligent group algorithm optimization Dynamic Traveling Salesman Problem based on reuse strategy, the method Including：
S1, dynamic travelling salesman's model framework design procedure, dynamic travelling salesman's model are designed to a series of following states Change, the state change of search space will all be caused by accessing the variation of node set or the variation of weight matrix, each The state only change of corresponding access node set or the change of weight matrix, and from s in sequence S1Any two of beginning Shifting gears for adjacent state is self-consistentency, and the state change of search space is represented by：
S=s0s1s2s3…sk…sμ
Wherein, s0Represent original state, skK-th of state of search space is represented, μ represents what search space changed Number summation, from state skTo state sk+1Transformation show that search space changes；
The implementation steps that S2, routine weight value dynamic change, change, each specific state has one in weights A unique weight matrix is corresponding, in skWeight matrix under state is denoted asIt can represent as follows:
WhereinFor in state skThe middle sum for needing to access node, in the case where routine weight value dynamic changes, owns Needed in state the node set accessed size be it is constant, i.e.,From state skTo state sk+1It can represent such as Under：
Wherein Dc ∈ [Lb, Ub], Lb and Ub represent the upper and lower bound that weights change the factor respectively,WithRespectively It represents in state skWith in state sk+1In, the weights size from node i to node j,Be under original state from node i to knot The size of point j weights, randijBe forThe random number generated, Nc is the parameter between 0 to 1；
S3, the implementation steps that node dynamic changes are accessed, in the case where accessing node dynamic and changing, is needed in reset condition The node to be accessed is combined and is expressed asNode sum is accessed to be denoted asSucceeding state skThe middle node set for needing to access It is expressed asNode sum is accessed to be denoted asFrom state skTo sk+1Transformation in, some nodes can by temporarily from access tie Point setMiddle addition or deletion, it is assumed thatIn node set be：
ChangingBefore, model can generate one at random can just can negative integerMeet following two Condition：
Wherein, μ is status number, and Nr and Df are the range factors between 0 to 1, and Df is used for that two neighboring state is controlled to visit Asking that node set changes the size of degree, Nr is used for controlling the scope for accessing node set size, ifLess than 0, for Each existIn node, model can generate a random number rndiTo simulate nodeThe randomness of access, if It is present inThen nodeIt will be fromIn temporarily remove, ifMore than 0,In nodeIt will be added It is added toIn, in this way, in stateThe lower node for needing to access can be expressed as：
S4, optimization aim step, use cijAnd yijFollowing binary decision variable is represented respectively：
Wherein, xkIt represents in state skIn the minimal path value that finds, edgeijRepresent the side that node i and node j is formed, The target of optimization is in free position skIn to find all nodes and all existIn path cost minimum Hamilton return Road；
S5, policy implementation step is reused, by study to state skUntil beforeIt is all in secondary environment to be stored in Archive In best solution, this can be defined as from the process of reuse：
Wherein,It represents in stateThe history optimal feasible solution of middle all individuals of population, is being reused Before Archive, if environment happens is that dimension change, need to be adjusted the solution in Archive, after adjustment, State sk+1It is identical with each solution of Archive node set to be accessed, these particles can be reused state sk's In optimization, if environment is happens is that weights change, directly using the solution being stored in Archive.
Further, the state change of the search space represents the search environment of optimization algorithm and changes, right It should be weight matrix and change or access node set and change, limitation of this variation can be described as follows：
Further, when the weight matrix of search space changes, state skIt is converted to sk+1Mode be：
Wherein, Dc ∈ [Lb, Ub], Lb and Ub represent the upper and lower bound that weights change the factor respectively,WithRespectively It represents in state skWith in state sk+1In weights size from node i to node j,Be under original state from node i to node The size of j weights, randijBe forThe random number generated, Nc is the parameter between 0 to 1；
When search space occurs to access node set change, from state skIt is converted to sk+1Mode is：
Wherein, wherein Nr and Df is the range factor between 0 to 1, and Df is used for controlling two neighboring conditional access node Gathering the size of change degree, Nr is used for controlling the scope for accessing node set size, ifLess than 0, for it is eachIn node, model can generate a random number rndiTo simulate nodeThe randomness of access, ifIt is present inThen nodeIt will be fromIn temporarily remove, ifMore than 0,In nodeIt will be added to In.
Further, the process being adjusted in the step S5 to the solution in Archive is as follows：
S501, each Archive individuals Ar is calculatediIn node number Ni；
S502, calculated by following formula will be temporarily from AriIt removes or to be added to AriIn node and by they It is stored in ΩiIn,
If S503,Illustrate that the nodal point number accessed increases, for each solution Ar in ArchiveiIt will ΩiIn each node according to the regular fashion of shortest path is made to be inserted into AriIn, otherwise, by AriNeutralize ΩiIdentical is every One node is directly deleted, and to delete the forerunner of node and successor node direct neighbor.
Further, the node accessed is needed to form complete or collected works, subsequent arbitrary shape in the step S3 in reset condition State skIt is middle to need the node set that accesses all to beSubset, accessing the size of node set, to correspond to population in new environment feasible The dimension of solution.
The present invention is had the following advantages compared with the prior art and effect：
1st, the present invention has carried out imperfectly mathematical modeling to the dynamic characteristic of traveling salesman problem.So that problem is being encoded and commented Estimate and existing Optimized model (particularly Swarm Intelligence Algorithm) is bonded in mode, this has established sturdy for the further research of problem Fundamentals of Mathematics.
2nd, the reuse strategy disclosed by the invention based on historical information, greatly reduces the search space of problem, improves The search efficiency of algorithm.Reasonable and effective important thinking is provided to solve this kind of dynamic problem.
3rd, the method disclosed by the invention for solving Dynamic Traveling Salesman Problem, can be applied to corresponding engineering and society In meeting problem, such as the optimization problem of communications and transportation circuit.This method will bring the key areas of production and living on considerable warp Ji and social value.
Description of the drawings
Fig. 1 is the basis of reality of dynamic model；
Fig. 2 is model dynamic schematic diagram；
Fig. 3 is the flow chart based on the set particle cluster algorithm optimization Dynamic Traveling Salesman Problem for reusing strategy；
Fig. 4 is the flow chart based on the ant group algorithm optimization Dynamic Traveling Salesman Problem for reusing strategy.
Specific embodiment
To make the purpose, technical scheme and advantage of the embodiment of the present invention clearer, below in conjunction with the embodiment of the present invention In attached drawing, the technical solution in the embodiment of the present invention is clearly and completely described, it is clear that described embodiment is Part of the embodiment of the present invention, instead of all the embodiments.Based on the embodiments of the present invention, those of ordinary skill in the art All other embodiments obtained without making creative work belong to the scope of protection of the invention.
Embodiment
Particle cluster algorithm based on set and ant group algorithm with reuse strategy are combined and apply to dynamic by the present embodiment In the optimization of travelling salesman.The content of the invention can be divided mainly into the modeling of dynamic travelling salesman and the reuse strategy of historical search information.
1) modeling of dynamic travelling salesman：
In part map shown in Fig. 1, one, which shares 12, accesses node (a-l), it is now assumed that there are two types of situations：
I) (traffic accident, road event when accident occurs for the original shortest path (red dotted portion) from h to a Barrier), red solid line part will become the current shortest path from h to a；
Ii) under certain conditions, since point l is without accessing, then original f, the access order of tri- nodes of i, l from f → l → I becomes f → i so as to directly skip node l.Based on both realities, they are modeled as dynamic trip by the present embodiment respectively The dynamic that the dynamic of routine weight value in problem of doing business changes and access node changes.In the case where routine weight value dynamic changes situation, The access weights on some sides of weight matrix are that dynamic changes in each calculated examples.For each edge, dynamic model can be It generates a random number randijIf randijMore than the current weights of pre-set parameter Nc and this edge and just Begin equal, then the weights of this edge can be multiplied by the factor more than 1；If randijLess than the current power of Nc and this edge Value and initial value differ, then the weights of this edge can be reset to initial value.In the case where accessing node dynamic and changing, in order to The successor states constructed from current state, dynamic model can be one integer that can just bearing within the specific limits of generation firstIfMore than 0, thenA city node can be removed from current accessed node set.Otherwise, the knot of identical quantity Point can be added to (not in current accessed node set) in current accessed node set.Under this design pattern, Mou Xiebian Weights and the node set that accesses of needs be all that dynamic changes, the mode changed is as shown in Figure 2.
2) strategy is reused：
In Dynamic Traveling Salesman Problem, the search space of optimization algorithm is dynamic change, the optimal value in varying environment Although different, some sides are all more or less deleted, add or recombinate to these optimal values, so as to share some by common edge The subsets of paths formed.These subsets of paths can be reused and learnt by the optimization algorithm under new environment.It so can be with It avoids repeat search and accelerates the search speed of algorithm, so as to which algorithm be allowed to search path summation smaller within the shorter time Hamiltonian circuit.In particle cluster algorithm is gathered, when environment changes, the history optimal solution of each particle in population Pbest will be saved in an external memory Archive, and the size of Archive is fixed.When the particle newly added in When the quantity of pbest is more than Archive sizes, covering will be generated.In the design, the size of Archive is Population Size Integral multiple, so in Archive is reused before the history optimal solution pbest of population particle, these history optimal solution pbest meetings It is ranked up according to fitness value, only the best popsize of fitness value (size of population) is a can just be chosen as new population History optimal solution pbest.In ant group algorithm, the Pheromone Matrix in new environment is upon initialization, all to belong to best Popsize history optimal solution pbest side on pheromones can all be increased an increment, this increment can cause these While upper pheromones value than it is other while it is high, the side for so belonging to the global optimum of new environment has higher probability and is chosen It selects.
It is a kind of to include following step with the method based on the intelligent group algorithm optimization Dynamic Traveling Salesman Problem for reusing strategy Suddenly：
S1, the design of dynamic travelling salesman model framework；
Dynamic travelling salesman model framework is designed from original state s0Start.In original state s0Under, the node and weights of access Matrix does not all change, this is consistent with the data test use-case under traditional static models.A series of subsequent shapes State represents as follows：
S=s0s1s2s3…sk…sμ
Wherein, skK-th of state of search space is represented, μ represents the total degree of environment change.From state skTo state sk+1 Transformation show that search space is changed.The search environment that the change of search space represents optimization algorithm changes. Or it is this change be weight matrix change or be access node set change.The limitation of this variation can be with It is described as follows：
The embodiment that S2, routine weight value dynamic change：
Change in weights, there are one each specific states, and unique weight matrix is corresponding, in sk Weight matrix under state is denoted asIt can represent as follows:
WhereinFor in state skThe middle sum for needing to access node.In the case where routine weight value dynamic changes, own Needed in state the node set accessed size be it is constant, i.e.,From state skTo state sk+1It can represent such as Under：
Wherein Dc ∈ [Lb, Ub], Lb and Ub represent the upper and lower bound that weights change the factor respectively,WithRespectively It represents in state skWith in state sk+1In, the weights size from node i to node j,Be under original state from node i to knot The size of point j weights, randijBe forThe random number generated, Nc is the parameter between 0 to 1.
S3, the embodiment that node dynamic changes is accessed：
In the case where accessing node dynamic and changing, the node accessed is needed to combine in reset condition and is expressed asIt accesses Node sum is denoted asSucceeding state skThe middle node set for needing to access is expressed asNode sum is accessed to be denoted as From state skTo sk+1Transformation in, some nodes can by temporarily from access node setMiddle addition or deletion.Assuming thatIn Node set be：
ChangingBefore, model can generate one at random can just can negative integerMeet following two Condition：
Wherein, Nr and Df is the range factor between 0 to 1, and Df is used for controlling two neighboring conditional access node set The size of change degree, Nr are used for controlling the scope for accessing node set size.IfLess than 0, for it is each In node, model can generate a random number rndiTo simulate nodeThe randomness of access.IfIt is present inThen nodeIt will be fromIn temporarily remove.IfMore than 0,In nodeIt will be added to In.In this way, in stateThe lower node for needing to access can be expressed as：
In this case, the node accessed is needed to form complete or collected works, subsequent free position s in reset conditionkMiddle needs The node set of access is allSubset.The size for accessing node set corresponds to the dimension of population feasible solution in new environment.
S4, optimization aim：
Use cijAnd yijFollowing binary decision variable is represented respectively
Wherein, xkIt represents in state skIn the minimal path value that finds, edgeijRepresent the side that node i and node j is formed. The target of optimization is in free position skIn to find all nodes and all existIn path cost minimum Hamilton return Road.
S5, tactful specific embodiment is reused：
In strategy is reused, the algorithm of invention will learn to state skUntil beforeIt is all in secondary environment to be stored in Best solution in Archive.This can be defined as from the process of reuse：
Wherein,It represents in stateThe history optimal feasible solution of middle all individuals of population.It is reusing Before Archive, if environment, happens is that dimension change, needs to carry out the solution in Archive some adjustment, adjustment walks It is rapid as follows：
S501, each Archive individuals Ar is calculatediIn node number Ni；
S502, calculated by following formula will be temporarily from AriIt removes or to be added to AriIn node and by they It is stored in ΩiIn,
If S503,Illustrate that the nodal point number accessed increases.For each solution Ar in ArchiveiIt will ΩiIn each node according to the regular fashion of shortest path is made to be inserted into AriIn.Otherwise, by AriNeutralize ΩiIdentical is every One node is directly deleted, and to delete the forerunner of node and successor node direct neighbor.
After this adjustment is carried out, state sk+1Be with each solution of Archive node set to be accessed it is identical, so State s can be reused by allowing for these particleskOptimization in.If environment directly uses happens is that weights change The solution being stored in Archive.
The particle rapidity and location updating rule that particle cluster algorithm based on set uses are represented by：
Wherein, ω is inertia weight, and c is accelerator coefficient, fi(d) learning object of the d dimensions of i-th of particle is represented, it should Object can be other particles in oneself or population.Learning object depends on the corresponding parameter of each particle Pci,PciIt is represented by：
A random number will be generated per one-dimensional d for each particle, if this random number is more than Pci, then can be to The d dimension study of oneself pbest.Otherwise it can tie up to the d of the pbest of other particles and learn.When environment changes, Popsize optimal solution in Archive will be selected as the pbest of new population, then can later during by for In generation, is absorbed in local optimum to prevent population from excessively receiving the attraction of these pbest in optimization process.Based on reuse strategy The flow chart for gathering particle cluster algorithm optimization Dynamic Traveling Salesman Problem is as shown in Figure 3.
In ant group algorithm, when environment changes, the Pheromone Matrix of ant colony will be reinitialized.In pheromones After matrix completes initialization, the pheromones on all sides for belonging to the popsize optimal solution in Archive will be held One autoincrementing operation of row, this operation can be expressed as：
τij=τij+α·τ0
Wherein τijRepresent edgeijThe amount of upper current pheromones, τ0It is the path acquired under new environment by greedy algorithm Inverse, α be pheromones decay factor.Flow chart based on the ant group algorithm optimization Dynamic Traveling Salesman Problem for reusing strategy is such as Shown in Fig. 4.In all test cases of dynamic model, the maximum iteration in each environment isIn order to the greatest extent may be used Different degrees of environment changes in the simulation reality of energy, and the relative parameters setting of dynamic model is as follows：
Parameter Value
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 relative parameters setting of dynamic set particle cluster algorithm is as follows：
The relative parameters setting of Dynamic Ant Algorithm is as follows：
In order to verify reuse strategy validity, the optimum results that two kinds of algorithms are all introduced with reuse strategy are imitated respectively True test.The results show that reuse the introducing of strategy so that two kinds of dynamic algorithms interior at the same time to have found path shorter Solution, and for Dynamic Ant Algorithm, solution of the dynamic set particle cluster algorithm in most examples can be found more Good solution.This proves to serve as the pbest of population and pheromones increment in new environment based on the best a part of solution of selection history The method for reusing of operation is very effective in the optimization problem of dynamic travelling salesman.
Above-described embodiment is the preferable embodiment of the present invention, but embodiments of the present invention and from above-described embodiment Limitation, other any Spirit Essences without departing from the present invention with made under principle change, modification, replacement, combine, simplification, Equivalent substitute mode is should be, is included within protection scope of the present invention.

Claims (5)

  1. It is 1. a kind of with the method based on the intelligent group algorithm optimization Dynamic Traveling Salesman Problem for reusing strategy, which is characterized in that The method includes：
    S1, dynamic travelling salesman's model framework design procedure, dynamic travelling salesman's model are designed to a series of changing for following states Become, the state change of search space, each state will all be caused by accessing the variation of node set or the variation of weight matrix The only change of the corresponding change or weight matrix for accessing node set, and from s in sequence S1Any two of beginning is adjacent Shifting gears for state be self-consistentency, the state change of search space is represented by：
    S=s0s1s2s3…sk…sμ
    Wherein, s0Represent original state, skK-th of state of search space is represented, μ represents the number that search space changes Summation, from state skTo state sk+1Transformation show that search space changes；
    The implementation steps that S2, routine weight value dynamic change, change in weights, and there are one only for each specific state One weight matrix is corresponding, in skWeight matrix under state is denoted asIt can represent as follows:
    WhereinFor in state skThe middle sum for needing to access node, in the case where routine weight value dynamic changes, institute is stateful It is middle need the node set size that accesses be it is constant, i.e.,From state skTo state sk+1It can represent as follows：
    <mrow> <msub> <mi>&amp;delta;</mi> <mrow> <msub> <mi>ijs</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mrow> </msub> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&amp;delta;</mi> <mrow> <msub> <mi>ijs</mi> <mi>k</mi> </msub> </mrow> </msub> <mo>&amp;CenterDot;</mo> <mi>D</mi> <mi>c</mi> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>if&amp;delta;</mi> <mrow> <msub> <mi>ijs</mi> <mi>k</mi> </msub> </mrow> </msub> <mo>=</mo> <msub> <mi>&amp;delta;</mi> <mrow> <msub> <mi>ijs</mi> <mn>0</mn> </msub> </mrow> </msub> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mi> </mi> <mi>N</mi> <mi>c</mi> <mo>&gt;</mo> <msub> <mi>rand</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&amp;delta;</mi> <mrow> <msub> <mi>ijs</mi> <mn>0</mn> </msub> </mrow> </msub> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>if&amp;delta;</mi> <mrow> <msub> <mi>ijs</mi> <mi>k</mi> </msub> </mrow> </msub> <mo>&amp;NotEqual;</mo> <msub> <mi>&amp;delta;</mi> <mrow> <msub> <mi>ijs</mi> <mn>0</mn> </msub> </mrow> </msub> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mi> </mi> <mi>N</mi> <mi>c</mi> <mo>&lt;</mo> <msub> <mi>rand</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>
    Wherein Dc ∈ [Lb, Ub], Lb and Ub represent the upper and lower bound that weights change the factor respectively,WithIt represents respectively In state skWith in state sk+1In, the weights size from node i to node j,It is from node i to node j under original state The size of weights, randijBe forThe random number generated, Nc is the parameter between 0 to 1；
    S3, the implementation steps that node dynamic changes are accessed, in the case where accessing node dynamic and changing, needs to visit in reset condition The node asked is combined and is expressed asNode sum is accessed to be denoted asSucceeding state skIt is middle that the node set accessed is needed to represent ForNode sum is accessed to be denoted asFrom state skTo sk+1Transformation in, some nodes can by temporarily from access nodal set It closesMiddle addition or deletion, it is assumed thatIn node set be：
    <mrow> <msub> <mi>V</mi> <mrow> <mn>1</mn> <msub> <mi>s</mi> <mi>k</mi> </msub> </mrow> </msub> <mo>=</mo> <mo>{</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>i</mi> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mi>N</mi> <msub> <mi>s</mi> <mi>k</mi> </msub> </msub> <mo>}</mo> </mrow>
    ChangingBefore, model can generate one at random can just can negative integerMeet following two Part：
    <mrow> <msub> <mi>N</mi> <msub> <mi>s</mi> <mi>k</mi> </msub> </msub> <mo>&amp;Element;</mo> <mo>&amp;lsqb;</mo> <msub> <mi>N</mi> <msub> <mi>s</mi> <mn>0</mn> </msub> </msub> <mo>&amp;CenterDot;</mo> <mi>N</mi> <mi>r</mi> <mo>,</mo> <msub> <mi>N</mi> <msub> <mi>s</mi> <mn>0</mn> </msub> </msub> <mo>&amp;rsqb;</mo> <mo>,</mo> <mrow> <mo>(</mo> <mi>k</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>&amp;mu;</mi> <mo>)</mo> </mrow> </mrow>
    <mrow> <mo>|</mo> <msub> <mi>N</mi> <msub> <mi>s</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </msub> <mo>-</mo> <msub> <mi>N</mi> <msub> <mi>s</mi> <mi>k</mi> </msub> </msub> <mo>|</mo> <mo>&amp;GreaterEqual;</mo> <msub> <mi>N</mi> <msub> <mi>s</mi> <mn>0</mn> </msub> </msub> <mo>&amp;CenterDot;</mo> <mi>D</mi> <mi>f</mi> <mrow> <mo>(</mo> <mo>|</mo> <msub> <mi>N</mi> <msub> <mi>s</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </msub> <mo>-</mo> <msub> <mi>N</mi> <msub> <mi>s</mi> <mi>k</mi> </msub> </msub> <mo>|</mo> <mo>=</mo> <mo>|</mo> <msub> <mi>Dr</mi> <msub> <mi>s</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </msub> <mo>|</mo> <mo>)</mo> </mrow> </mrow>
    Wherein, μ is status number, and Nr and Df are the range factors between 0 to 1, and Df is used for controlling two neighboring conditional access knot Point set changes the size of degree, and Nr is used for controlling the scope for accessing node set size, ifLess than 0, for each In node, model can generate a random number rndiTo simulate nodeThe randomness of access, ifIn the presence of InThen nodeIt will be fromIn temporarily remove, ifMore than 0,In nodeIt will be added toIn, in this way, in stateThe lower node for needing to access can be expressed as：
    <mrow> <msub> <mi>V</mi> <mrow> <mn>1</mn> <msub> <mi>s</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mrow> </msub> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mo>{</mo> <msub> <mi>V</mi> <mrow> <mn>1</mn> <msub> <mi>s</mi> <mi>k</mi> </msub> </mrow> </msub> <mo>-</mo> <mo>{</mo> <msubsup> <mi>V</mi> <mrow> <mn>1</mn> <msub> <mi>s</mi> <mi>k</mi> </msub> </mrow> <mrow> <msub> <mi>rnd</mi> <mi>i</mi> </msub> </mrow> </msubsup> <mo>}</mo> <mo>|</mo> <mi>i</mi> <mo>&amp;Element;</mo> <mo>&amp;lsqb;</mo> <mn>1</mn> <mo>,</mo> <mo>|</mo> <msub> <mi>Dr</mi> <msub> <mi>s</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </msub> <mo>|</mo> <mo>&amp;rsqb;</mo> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mi> </mi> <msubsup> <mi>V</mi> <mrow> <mn>1</mn> <msub> <mi>s</mi> <mi>k</mi> </msub> </mrow> <mrow> <msub> <mi>rnd</mi> <mi>i</mi> </msub> </mrow> </msubsup> <mo>&amp;Element;</mo> <msub> <mi>V</mi> <mrow> <mn>1</mn> <msub> <mi>s</mi> <mi>k</mi> </msub> </mrow> </msub> <mo>}</mo> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>i</mi> <mi>f</mi> <mi> </mi> <msub> <mi>Dr</mi> <msub> <mi>s</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </msub> <mo>&lt;</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>{</mo> <msub> <mi>V</mi> <mrow> <mn>1</mn> <msub> <mi>s</mi> <mi>k</mi> </msub> </mrow> </msub> <mo>&amp;cup;</mo> <mo>{</mo> <msubsup> <mi>V</mi> <mrow> <mn>2</mn> <msub> <mi>s</mi> <mi>k</mi> </msub> </mrow> <mrow> <msub> <mi>rnd</mi> <mi>i</mi> </msub> </mrow> </msubsup> <mo>}</mo> <mo>|</mo> <mi>i</mi> <mo>&amp;Element;</mo> <mo>&amp;lsqb;</mo> <mn>1</mn> <mo>,</mo> <mo>|</mo> <msub> <mi>Dr</mi> <msub> <mi>s</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </msub> <mo>|</mo> <mo>&amp;rsqb;</mo> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mi> </mi> <msubsup> <mi>V</mi> <mrow> <mn>2</mn> <msub> <mi>s</mi> <mi>k</mi> </msub> </mrow> <mrow> <msub> <mi>rnd</mi> <mi>i</mi> </msub> </mrow> </msubsup> <mo>&amp;Element;</mo> <msub> <mi>V</mi> <mrow> <mn>2</mn> <msub> <mi>s</mi> <mi>k</mi> </msub> </mrow> </msub> <mo>}</mo> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>i</mi> <mi>f</mi> <mi> </mi> <msub> <mi>Dr</mi> <msub> <mi>s</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </msub> <mo>&gt;</mo> <mn>0</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>
    S4, optimization aim step, use cijAnd yijFollowing binary decision variable is represented respectively：
    <mrow> <mi>f</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mrow> <mi>s</mi> <mi>k</mi> </mrow> </msub> </munderover> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <msub> <mi>s</mi> <mi>k</mi> </msub> </msub> </munderover> <msub> <mi>c</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <msub> <mi>&amp;delta;</mi> <mrow> <msub> <mi>ijs</mi> <mi>k</mi> </msub> </mrow> </msub> </mrow>
    Wherein, xkIt represents in state skIn the minimal path value that finds, edgeijRepresent the side that node i and node j is formed, optimization Target is in free position skIn to find all nodes and all existIn path cost minimum hamiltonian circuit；
    S5, policy implementation step is reused, by study to state skUntil beforeIt is all in secondary environment to be stored in Archive most Good solution, this can be defined as from the process of reuse：
    Wherein,It represents in stateThe history optimal feasible solution of middle all individuals of population, reuse Archive it Before, if environment happens is that dimension change, need to be adjusted the solution in Archive, after adjustment, state sk+1With Each solution of Archive node set to be accessed is identical, these particles can be reused state skOptimization in, such as Fruit environment is happens is that weights change, then directly using the solution being stored in Archive.
  2. It is 2. according to claim 1 with the side based on the intelligent group algorithm optimization Dynamic Traveling Salesman Problem for reusing strategy Method, which is characterized in that the search environment that the state change of the search space represents optimization algorithm changes, and corresponds to Weight matrix changes or accesses node set and changes, and the limitation of this variation can be described as follows：
    <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>&amp;mu;</mi> </munderover> <msub> <mi>T</mi> <mi>k</mi> </msub> <mo>&amp;Element;</mo> <mo>{</mo> <mn>0</mn> <mo>,</mo> <mi>&amp;mu;</mi> <mo>}</mo> <mo>.</mo> </mrow>
  3. It is 3. according to claim 2 with the side based on the intelligent group algorithm optimization Dynamic Traveling Salesman Problem for reusing strategy Method, which is characterized in that
    When the weight matrix of search space changes, state skIt is converted to sk+1Mode be：
    <mrow> <msub> <mi>&amp;delta;</mi> <mrow> <msub> <mi>ijs</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mrow> </msub> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&amp;delta;</mi> <mrow> <msub> <mi>ijs</mi> <mi>k</mi> </msub> </mrow> </msub> <mo>&amp;CenterDot;</mo> <mi>D</mi> <mi>c</mi> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>if&amp;delta;</mi> <mrow> <msub> <mi>ijs</mi> <mi>k</mi> </msub> </mrow> </msub> <mo>=</mo> <msub> <mi>&amp;delta;</mi> <mrow> <msub> <mi>ijs</mi> <mn>0</mn> </msub> </mrow> </msub> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mi> </mi> <mi>N</mi> <mi>c</mi> <mo>&gt;</mo> <msub> <mi>rand</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&amp;delta;</mi> <mrow> <msub> <mi>ijs</mi> <mn>0</mn> </msub> </mrow> </msub> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>if&amp;delta;</mi> <mrow> <msub> <mi>ijs</mi> <mi>k</mi> </msub> </mrow> </msub> <mo>&amp;NotEqual;</mo> <msub> <mi>&amp;delta;</mi> <mrow> <msub> <mi>ijs</mi> <mn>0</mn> </msub> </mrow> </msub> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mi> </mi> <mi>N</mi> <mi>c</mi> <mo>&lt;</mo> <msub> <mi>rand</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>
    Wherein, Dc ∈ [Lb, Ub], Lb and Ub represent the upper and lower bound that weights change the factor respectively,WithIt represents respectively In state skWith in state sk+1In weights size from node i to node j,It is to be weighed under original state from node i to node j The size of value, randijBe forThe random number generated, Nc is the parameter between 0 to 1；
    When search space occurs to access node set change, from state skIt is converted to sk+1Mode is：
    <mrow> <msub> <mi>V</mi> <mrow> <mn>1</mn> <msub> <mi>s</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mrow> </msub> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mo>{</mo> <msub> <mi>V</mi> <mrow> <mn>1</mn> <msub> <mi>s</mi> <mi>k</mi> </msub> </mrow> </msub> <mo>-</mo> <mo>{</mo> <msubsup> <mi>V</mi> <mrow> <mn>1</mn> <msub> <mi>s</mi> <mi>k</mi> </msub> </mrow> <mrow> <msub> <mi>rnd</mi> <mi>i</mi> </msub> </mrow> </msubsup> <mo>}</mo> <mo>|</mo> <mi>i</mi> <mo>&amp;Element;</mo> <mo>&amp;lsqb;</mo> <mn>1</mn> <mo>,</mo> <mo>|</mo> <msub> <mi>Dr</mi> <msub> <mi>s</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </msub> <mo>|</mo> <mo>&amp;rsqb;</mo> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mi> </mi> <msubsup> <mi>V</mi> <mrow> <mn>1</mn> <msub> <mi>s</mi> <mi>k</mi> </msub> </mrow> <mrow> <msub> <mi>rnd</mi> <mi>i</mi> </msub> </mrow> </msubsup> <mo>&amp;Element;</mo> <msub> <mi>V</mi> <mrow> <mn>1</mn> <msub> <mi>s</mi> <mi>k</mi> </msub> </mrow> </msub> <mo>}</mo> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>i</mi> <mi>f</mi> <mi> </mi> <msub> <mi>Dr</mi> <msub> <mi>s</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </msub> <mo>&lt;</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>{</mo> <msub> <mi>V</mi> <mrow> <mn>1</mn> <msub> <mi>s</mi> <mi>k</mi> </msub> </mrow> </msub> <mo>&amp;cup;</mo> <mo>{</mo> <msubsup> <mi>V</mi> <mrow> <mn>2</mn> <msub> <mi>s</mi> <mi>k</mi> </msub> </mrow> <mrow> <msub> <mi>rnd</mi> <mi>i</mi> </msub> </mrow> </msubsup> <mo>}</mo> <mo>|</mo> <mi>i</mi> <mo>&amp;Element;</mo> <mo>&amp;lsqb;</mo> <mn>1</mn> <mo>,</mo> <mo>|</mo> <msub> <mi>Dr</mi> <msub> <mi>s</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </msub> <mo>|</mo> <mo>&amp;rsqb;</mo> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mi> </mi> <msubsup> <mi>V</mi> <mrow> <mn>2</mn> <msub> <mi>s</mi> <mi>k</mi> </msub> </mrow> <mrow> <msub> <mi>rnd</mi> <mi>i</mi> </msub> </mrow> </msubsup> <mo>&amp;Element;</mo> <msub> <mi>V</mi> <mrow> <mn>2</mn> <msub> <mi>s</mi> <mi>k</mi> </msub> </mrow> </msub> <mo>}</mo> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>i</mi> <mi>f</mi> <mi> </mi> <msub> <mi>Dr</mi> <msub> <mi>s</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </msub> <mo>&gt;</mo> <mn>0</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>
    Wherein, wherein Nr and Df is the range factor between 0 to 1, and Df is used for controlling two neighboring conditional access node set The size of change degree, Nr are used for controlling the scope for accessing node set size, ifLess than 0, for it is each In node, model can generate a random number rndiTo simulate nodeThe randomness of access, ifIt is present inThen nodeIt will be fromIn temporarily remove, ifMore than 0,In nodeIt will be added toIn.
  4. It is 4. according to claim 1 with the side based on the intelligent group algorithm optimization Dynamic Traveling Salesman Problem for reusing strategy Method, which is characterized in that the process being adjusted in the step S5 to the solution in Archive is as follows：
    S501, each Archive individuals Ar is calculatediIn node number Ni；
    S502, calculated by following formula will be temporarily from AriIt removes or to be added to AriIn node and they are stored In ΩiIn,
    <mrow> <msub> <mi>&amp;Omega;</mi> <mi>i</mi> </msub> <mo>=</mo> <msub> <mi>Ar</mi> <mi>i</mi> </msub> <msub> <mi>&amp;Theta;V</mi> <mrow> <mn>1</mn> <msub> <mi>s</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mrow> </msub> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mo>{</mo> <mi>t</mi> <mo>:</mo> <mi>t</mi> <mo>&amp;NotElement;</mo> <msub> <mi>Ar</mi> <mi>i</mi> </msub> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mi> </mi> <mi>t</mi> <mo>&amp;Element;</mo> <msub> <mi>V</mi> <mrow> <mn>1</mn> <msub> <mi>s</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mrow> </msub> <mo>}</mo> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>i</mi> <mi>f</mi> <mi> </mi> <msub> <mi>N</mi> <msub> <mi>s</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </msub> <mo>&gt;</mo> <msub> <mi>N</mi> <mi>i</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>{</mo> <mi>t</mi> <mo>:</mo> <mi>t</mi> <mo>&amp;Element;</mo> <msub> <mi>Ar</mi> <mi>i</mi> </msub> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mi> </mi> <mi>t</mi> <mo>&amp;NotElement;</mo> <msub> <mi>V</mi> <mrow> <mn>1</mn> <msub> <mi>s</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mrow> </msub> <mo>}</mo> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>i</mi> <mi>f</mi> <mi> </mi> <msub> <mi>N</mi> <msub> <mi>s</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </msub> <mo>&lt;</mo> <msub> <mi>N</mi> <mi>i</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>
    If S503,Illustrate that the nodal point number accessed increases, for each solution Ar in ArchiveiBy ΩiIn Each node according to the regular fashion of shortest path is made to be inserted into AriIn, otherwise, by AriNeutralize ΩiEach identical Node is directly deleted, and to delete the forerunner of node and successor node direct neighbor.
  5. It is 5. according to claim 1 with the side based on the intelligent group algorithm optimization Dynamic Traveling Salesman Problem for reusing strategy Method, which is characterized in that the node accessed is needed to form complete or collected works, subsequent free position s in the step S3 in reset conditionk It is middle to need the node set that accesses all to beSubset, the size for accessing node set corresponds to population feasible solution in new environment Dimension.
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