CN106127427A - Multiple target transport path combined optimization method based on plague Epidemic Model - Google Patents

Abstract

Disclosed by the invention is a kind of multiple target transport path combined optimization method based on plague Epidemic Model, it is assumed that there is a kind of infectious disease being referred to as the plague in an ecosystem being made up of some individuals, propagates in plague infectious disease crowd；The crowd being uninfected by this infectious disease is referred to as susceptible person；After susceptible person infects this infectious disease but the person do not fallen ill is resurrectionist；Through after a period of time, resurrectionist starts the person of morbidity for sending out patient；The virus that it is internal can be passed to other people by resurrectionist and Fa patient；The person being cured in resurrectionist and Fa patient is healing person；In order to prevent the plague harm to crowd, crowd inoculates a vaccine at set intervals；Under plague infectious disease effect, everyone growth conditions will susceptible, expose, fall ill, cure random transition between these four states, utilize this random transition and the plague Epidemic Model global optimum of rapid solving multiple target transport path combinatorial optimization problem can solve scheme.

Description

Multiple target transport path combined optimization method based on plague Epidemic Model

Technical field

The present invention relates to intelligent optimization algorithm, be specifically related to a kind of multiple target transport path based on plague Epidemic Model Combined optimization method.

Background technology

Consider that the general type of multiple target transport path Combinatorial Optimization Model is as follows:

$\begin{array}{c}\min \{O_1{f}_1\left(X\right),O_2{f}_2\left(X\right),\mathrm{...},O_M{f}_M\left(X\right)\}\\ \begin{array}{cc}s.t.& \left\{\begin{array}{c}{g}_{i_a}\left(X\right)\≥0,i_a\∈I\\ h_{i_b}\left(X\right)=0,i_b\∈E\\ X\∈H\⋐R^n\end{array}\right.\end{array}\end{array}---\left(1\right)$

In formula:

(1)RⁿIt is that n ties up Euclidean space, the total number of variable that n is comprised by this Optimized model；

(2) X=(x₁, x₂..., x_m, x_m+1..., x_n) it is that a n ties up decision vector, wherein, front m variable x₁, x₂..., x_mIt is continuous Real-valued variable, is used for representing the flow shape parameter related in model；Rear n-m variable x_m+1..., x_nIt is 0,1 Integer type variable, is used for representing which website in n website must become some nodes in an optimum transport path, the most right In any x_j∈{x_m+1..., x_n, if x_j=1, then it represents that jth website is selected for a knot in this optimum transport path Point, if x_j=0, then it represents that jth website is the most selected；

(3)f₁(X), f₂(X) ..., f_M(X) it is M object function, is used for M the control mesh represented when transport path selects Mark requirement；

(4)O₁, O₂..., O_MFor the priority of M object function, priority order is required to meet O₁>O₂>…>O_M, i.e. mesh Scalar functions f₁(X) first require to minimize, next to that f₂(X), it is thirdly f₃(X), the like, finally require to reach That little is object function f_M(X)；

(5)Represent that website is when selecting required satisfied i-th_aIndividual inequality constraints condition；I be inequality about The set of bundle condition number；

(6)Represent that website is when selecting required satisfied i-th_bIndividual equality constraint；E is equality constraint bar The set of part numbering；

(7){f_i(X), i=1,2 ..., M},i_a∈I}、{i_bThe mathematic(al) representation of ∈ E} does not limit Condition processed；

(8) H is search volume, also known as solution space；

(9), when calculating, decision vector X is also referred to as trial solution；If trial solution X is unsatisfactory for constraints, then make f (X)=+ ∞。

Multiple target transport path Combinatorial Optimization Model formula (1) is commonly used to solve down-hole mine dust transport path optimization problem, thing Money Distribution path optimization problem, evacuating personnel routing problem, network route planning problem, etc..

F in multiple target transport path Combinatorial Optimization Model formula (1)_i(X)、Mathematic(al) representation Do not have restrictive condition, traditional Mathematics Optimization Method based on continuous He the property led cannot solve this problem.

At present, the common method solving multiple target transport path Combinatorial Optimization Model formula (1) is intelligent optimization algorithm.Existing Intelligent optimization algorithm have:

(1) genetic algorithm: this algorithm 1975 is by monograph " the Adaptation in of Univ Chicago USA Holland Natural andArtificial Systems " propose, be employed technical scheme comprise that and utilize Heredity theory structure individuality to enter Change method, thus optimization problem is solved." WMSNs based on genetic algorithm is many at document for Li Chengbo, Wang little Ming, Liu Qiang Path multiple-objection optimization routing algorithm, computer utility research, 2012, volume 29, the 6th phase, the 2277-2282 page " in, pin Demand to WMSNs Design of Routing Algorithm, according to ultimate principle and the Pareto Multipurpose Optimal Method of genetic algorithm, proposes WMSNs multipath multiple-objection optimization routing algorithm MMOR-GA；MMOR-GA is simulated emulation experiment, and result shows MMOR- GA algorithm can equalize the many qos parameters being effectively improved WMSNs route.Li Junliang, Li Jiying, hide flood control at document " based on something lost The military logistics transport project of propagation algorithm, naval aviation engineering college journal, 2015, volume 30, the 3rd phase, 291-295 Page " in, in transporting for military logistics, the combinatorial problem of vehicle loading and vehicle route is studied, and sets up vehicle loading and car The objective optimization model of combination of paths problem；By improved adaptive GA-IAGA to model solution, obtain more satisfied result, Can be under conditions of meeting the constraint of multi-vehicle-type multi items goods delivery, it is achieved haulage vehicle is minimum, vehicle load factor high, vehicle The target that transportation route is the shortest.Xu Hecan, Zhu rear people at document " Pareto genetic algorithm for solving multiple target band time window vehicle on road Footpath problem, logistlcs technology, 2015, volume 34,8 monthly magazines, the 166-170 page " in think that logistics distribution must simultaneously meet several Individual conflicting target, for this multi-objective optimization question, introduces Pareto optimal solution concept, establishes and describe this problem Mathematical model NSGAII, and propose to solve the Pareto genetic algorithm of VRPTW；Algorithm constructs non-domination solution by NSGAII, asks Go out to meet the most excellent solution that the minimum and total distance of number of vehicles is the shortest.Meng Yongchang, Yang Saini, Shi Peijun at document " based on changing Enter the road network emergency evacuation multiple-objection optimization of genetic algorithm, Wuhan University Journal information science version, 2014, volume 39, the 2nd Phase, the 201-205 page " in, actual demand based on road network emergency evacuation problem, propose with path flow as decision variable, with Discharge value is maximum, evacuation route is the shortest and reliability is up to the Model for Multi-Objective Optimization of target, having considered emergent dredging Ageing, the economy dissipated and safety, and design adaptive niche technology Pareto genetic algorithm model is solved.Tan Xiao Bravely, Lin Ying document " based on improve GACA algorithm Post disaster relief path planning, computer engineering and design, 2014, Volume 35, the 7th phase, the 2526-2530 page " in, as a example by earthquake, for feature and the need of calamity rear vehicle routing problem Ask, have studied rescue transit time, road risk and road and pay the multiobject appraisal procedures such as cost, set up based on this The Model for Multi-Objective Optimization of shake rear vehicle routing problem；Devise the genetic ant colony system hybrid algorithm of a kind of improvement； Strengthen the ability of searching optimum of algorithm by introducing the mutation operator of genetic algorithm, use minimax ant group algorithm realizes machine System carrys out the subpath of optimizing phase optimal solution；Simulation results on examples shows, this model and algorithm are feasible.

(2) ant group algorithm: this algorithm by Colorni A and Dorigo M et al. at document " Distributed Optimization by ant colonies, Proceedings of the 1^st Europe Conference on Artificial Life, 1991, the 134-142 page " middle proposition, be employed technical scheme comprise that simulation ant colony is looked for food Behavior is optimized solving of problem.Li Lin, Liu Shixin, Tang Jiafu are at the document " vehicle on road of band subscription time under B2C environment Footpath problem and multiple-objection optimization ant group algorithm, control theory and application, 2011, volume 28, the 1st phase, the 87-93 page " in, root The Vehicle Routing Problems of band subscription time is established according to the feature of logistics distribution under B2C (Business to Consumer) e-commerce environment (VRP) mathematical model, devises the ant group algorithm solving multiple-objection optimization, and each target has identical importance；In ant colony State transition probability in introduce subscription time window width and vehicle waiting time factor, produce during record optimization Pareto optimal solution, instructs the pheromone update strategy of ant colony by Pareto optimal solution set；Use the Solomon data of transformation Carry out emulation experiment, compare with result herein by Solomon optimal solution, the reasonability of experiment show model and The effectiveness of algorithm.Wu Zhaofu, Dong Wenyong " solve the evolutionary ant algorithm of Dynamic Vehicle Routing Problems, Wuhan University at document Journal (Edition), the 5th phase of volume 2007,53, the 571-575 page " in, on the basis of Evo-Ant algorithm, propose many mesh Target algorithm, i.e. utilize Evo-Ant algorithm to produce new solution, and utilize an extra memory space to deposit Pareto wait Choosing solves, and updates Pareto candidate solution by newly generated solution, eliminates the solution arranged, circulates successively, thus obtains approximation Pareto solves；In order to verify evolutionary ant algorithm, use 2 kinds of means of testing: a kind of is the test data of Solomon, another kind of It it is the test under simulated environment；Test result indicate that this algorithm has competitiveness very much.Xiao Le, Wu Xianglin, Zhen Tong are at document " the grain emergency route optimizing research of self adaptation Chaos Ant Colony Optimization, computer engineering and application, 2012, volume 48, the 24th Phase, the 28-31 page " in, for the grain emergency route optimization problem under risk management, will " risk in transit is minimum " and " transport Minimal time " as target, set up corresponding Optimized model；" max-min ant system " is utilized to solve, for avoiding Early it is absorbed in local optimum, proposes self adaptation chaos ant colony optimization algorithm；This algorithm utilizes efficient solution similarity to judge that ant colony is worked as Front state, according to circumstances carries out the overall situation and updates and chaotic disturbance, can be effectively improved the precision of optimal solution pheromone.Zhang Wei Deposit, the big straightforward words of Zheng, Wu Xiaodan document " based on ant colony PSO Algorithm multi-objective flexible scheduling problem, computer utility, 2007, volume 27, the 4th phase, the 936-939 page " in, by analyzing each target in Solving Multi-objective Flexible Job-shop Scheduling problem Mutual relation, the ant colony population derivation algorithm of a kind of master and slave hierarchical structure is proposed；In algorithm, main is ant group algorithm, Select work pieces process path process realizes equipment total load and the target of key equipment minimum loads；It is that population is calculated from level Method, realizes the target that the workpiece currency minimizes in the equipment scheduling under main processing route retrains；Then, bear with equipment Lotus and working procedure processing time design Formica fusca transition probability between operation available devices for heuristic information；Based on particle vectorized priority The magnitude relationship design coding/decoding method of weights realizes the operation scheduling on equipment.Finally, by emulation and comparative experiments, demonstrate The effectiveness of this algorithm.

(3) particle cluster algorithm: this algorithm by Eberhart R and Kennedy J at document " New optimizer using Particle swarm theory, MHS ' 95Proceedings of the Sixth International Symposium On Micro Machine and Human Science, IEEE, Piscataway, NJ, USA, nineteen ninety-five, the 38-43 page " in Propose, be employed technical scheme comprise that and utilize the group behavior imitating birds to be optimized solving of problem.Gao Xiaowei is at literary composition Offer " goods' transportation routing Study on Problems based on improvement QPSO algorithm, Computer Simulation, 2013, volume 30, the 8th phase, the 169-172 page " in, propose to turn to target, by weight coefficient with logistics transportation cost minimization and customer satisfaction maximum Model for Multi-Objective Optimization is converted into single object optimization model by converter technique, and the QPSO algorithm constructing improvement solves.Cao Jun, Tang Lun, Chen Qianbin, Lee Woon Jae document " Mobile routing selection scheme based on particle cluster algorithm, Guangdong communication technology, 2009, 1st phase, the 25-31 page " in give a kind of Mobile routing model, for meeting the network environment of Mobile routing, devise and make QoS The function of parameter moment change realizes；Then particle cluster algorithm is applied to the optimizing of realizing route in this model；Simulation result Show, be used for particle cluster algorithm in this Mobile routing model obtaining good convergence rate and optimizing result.Qiu Changwu, Wang Longmei, Huang Yanwen document " all-around mobile tow-armed robot continuous path task multiple objective programming based on long-pending formula decision-making, Robot, 2013, volume 35, the 2nd phase, the 178-185 page " in, analyze constrained OMDAR (all-around mobile both arms machine Device people) mathematical modeling of multiple target motion planning task of system and method for solving；At long-pending formula decision-making multi-objective optimization algorithm frame Under frame, OMDAR system continuous path motion planning demand is modeled as the single optimization object function of product form with related constraint, Use Gauss to cruise particle swarm optimization algorithm (GR-PSO), reliably and effectively achieve solving of problem.

(4) fish-swarm algorithm: this algorithm is " a kind of autonomous based on animal at document by Li Xiaolei, Shao Zhijiang River and Qian Jixin et al. The optimizing chess formula of body: fish-swarm algorithm, the system engineering theory and practice, 2002, volume 22, o. 11th, the 32-38 page " in carry Go out, be employed technical scheme comprise that utilize fish in water look for food, knock into the back, optimization problem solution space is searched by the behavior such as clustering Rope, thus obtain the globally optimal solution of optimization problem.Liu Sheng, Li Gaoyun, Jiang Na are at document " the many mesh of the immune shoal of fish of SVM performance Mark optimizing research, intelligence system journal, 2010, volume 5, the 2nd phase, the 144-149 page " in think: the training essence of SVM algorithm Degree and training speed are 2 important indicators weighing its performance, set up SVM performance multiple target with these 2 indexs for target variable The mathematical model of optimization problem, uses the method being directly simultaneously optimized multiple targets to try to achieve the Pareto approximate solution of problem Collection；When solving Pareto and approximating disaggregation, the concentration mechanism in immunity principle is introduced in basic fish-swarm algorithm, form one and change The immune fish-swarm algorithm entered；With Nonlinear Dynamical System Simulation data as sample data, and use the immune fish-swarm algorithm of improvement The Pareto solving SVM performance multi-objective optimization question approximates disaggregation；Simulation result shows, is solving multi-objective optimization question Time, immunity fish-swarm algorithm has more preferable superiority relative to basic fish-swarm algorithm and genetic algorithm.Zhao Meiling, Zhou Genbao are at literary composition Offer " artificial fish-swarm algorithm and the application in multi-objected investment combination problem thereof, Agricultural University of the Inner Mongol's journal, 2014, the Volume 35, the 1st phase, the 152-154 page " in think: during capital investment, frequently refer to multi-objected investment combination problem, but Such issues that use traditional Algorithm for Solving is more complicated, proposes to utilize artificial fish-swarm algorithm to be optimized for this and solves, go forward side by side Row programming realization, the simulation experiment result indicates effective, the feasibility of this Algorithm for Solving problems.Yin Limin, Li Xiang, the Meng Great waves, Yin Hang document " based on improve artificial fish-swarm algorithm transmission network planning, electric automatization, 2016, the 38th Volume, the 2nd phase, the 48-51 page " in, have studied extensive transmission network planning problem, establish consideration investment running cost With, cost of losses and the multiple-objection optimization mathematical model of overload expense；Complicated, convergence speed is initialized for tradition fish-swarm algorithm The problem that degree is slow and convergence precision is relatively low, look for food at it, knock into the back during introduce Step-varied back propagation strategy with raising algorithm Optimizing performance, and be used for solving transmission network planning model by the artificial fish-swarm algorithm of improvement.To Garver-6 node and 18 bus test system carry out simulation calculation, verify the efficient feasibility of put forward model and algorithm.

(5) Artificial Immune Algorithm: this algorithm Shi Limao army, Luo An, virgin adjust raw in document " Artificial Immune Algorithm and application thereof Research, control theory and application, 2004, volume 21, the 2nd phase, the 153-158 page " middle proposition, this algorithm is to use for reference life section In, the concept of immunity and theoretical developments are got up, and the core of this algorithm is the structure of Immunity Operator, and Immunity Operator is logical Cross vaccination and select two steps of immunity to complete；Most of achievement of immune algorithm is based on Burnet proposition gram Grand selective theory.Based on Clonal Selection Principle, CASTRO D is at document " Learning and optimization using The clone selection principle, IEEE Transactions on Evolutionary Computation, 2002, volume 6, the 3rd phase, the 239-251 page " propose a kind of clonal selection algorithm, its core is to have employed ratio to replicate Operator and meristic variation operator, this algorithm easily produces the shortcoming that multiformity is poor, algorithm realizes process difficulty.JIAO Licheng, DU Haifeng is at document " Development and prospect ofthe artificial immune System, Acta Electronica Sinica, 2003, volume 31, the 10th phase, the 1540-1548 page " immunity is being selected On the basis of reason of selecting a good opportunity further investigation, it is proposed that self adaptation polyclone planning algorithm, self adaptation algorithm of dynamic clonal, immunodominance The multiple superior immune clonal selection algorithm such as clone algorithm.Cao Xianbin, Wang Bennian, Wang Xufa are in document " a kind of virus evolution type Genetic algorithm, small-sized microcomputer system, calendar year 2001, volume 21, the 1st phase, the 59-62 page " the VEGA algorithm that proposes be with Based on genetic algorithm, from biological virus mechanism, extract some features of applicable improved adaptive GA-IAGA, individuality is divided into disease Poison individuality and host individual, two kinds of each own different behaviors of individuality, there is one between the two further through Infection Action certainly Right collaborative contact, thus substantially increase the multiformity of individuality.Zhai Yusheng, Cheng Zhihong, Chen Guangzhu, Li Liu document " based on The multi-objective Optimization Immune Algorithm of Pareto, computer engineering and application, 2006, the 24th phase, the 27-29 page " in establish A kind of novel multi-objective Optimization Immune Algorithm (MOIA) based on Pareto；In algorithm, the feasible solution of optimization problem is corresponding Antibody, the object function correspondence antigen of optimization problem, Pareto optimal solution is stored in memory cell and concentrates, and utilization is different from It is constantly updated by the neighbouring exclusion algorithm of cluster, and then obtains the Pareto optimal solution being evenly distributed.Li Lingjing, Chen Yun Virtue document " multi-objective Optimization Immune Algorithm in knowledge based territory, computer engineering, 2010, volume 36, the 20th phase, the 161-163 page " in, there is Premature Convergence and the problem of multiformity deficiency for traditional immunization algorithm, propose a kind of based on knowing The multi-objective Optimization Immune Algorithm of the field of awareness；Select elite solution by initializing knowledge domain, utilize this elite disaggregation adaptive updates The border of knowledge domain, thus maintain Algorithm Convergence and multifarious balance；Test result shows, compares NSGAII, SPEAII Algorithm, this algorithm at runtime, multiformity and spreadability aspect there is greater advantage.Tang Jun, Zhao Xiaojuan are " based on immunity The network base station plan optimization of algorithm, computer engineering, 2010, volume 36, the 16th phase, the 169-170 page " in, for biography The deficiency of system network base station planing method, proposes a kind of optimization method based on immune algorithm；Use Multipurpose Optimal Method pair Base station planning problem carries out mathematical modeling, and immune optimization algorithm uses concentration regulation select probability mechanism, neighbouring exclusion algorithm, follows The mutation operation that ring intersects and improves, can guarantee that the multiformity of solution and Pareto optimal solution set are evenly distributed on leading surface； Simulation result shows, this algorithm can effectively obtain the base station distribution scheme of optimum, and coverage rate reaches 97.6%.Li Chunhua, hair Ancestor source document " multi objective function optimization based on Artificial Immune Algorithm, computer measurement and control, 2005, volume 13, the 3 phases, the 278-280 page " in, it is proposed that a kind of novel Artificial Immune Algorithm is used for solving multi objective function optimization problem；Base Algorithm designed in natural immune system intrinsic good characteristic and has been analyzed；Finally, algorithm is to 3 more complicated many mesh Mark problem is optimized, and optimum results can the Pareto optimum face of covering problem well.Long Wen, yellow Hamming, Li little Yong, Tan Nation remaining document " immune algorithm of multiple target City Integrated Emergency Response System location problem, Guangxi physics, 2008, volume 29, the 2nd phase, The 26-29 page " in, it is considered to cost during emergency location and crash time factor, provide a kind of multiple target city emergency and set Execute the mathematical model of location problem；In view of conventional method solves the difficulty of this model, a kind of multi-target immune algorithm conduct is proposed Model solution method, by example calculation, illustrates that this algorithm is effective.Tao Yuan, Wu Gengfeng, Hu Min document " based on The multi-target evolution immune algorithm of Pareto, computer utility research, 2009, volume 26, the 5th phase, the 1687-1690 page " In, propose a kind of new based on Pareto multi-target evolution immune algorithm (PMEIA)；Algorithm is chosen in every generation glade body Optimum non-dominant antibody is saved in memory cell document；It is simultaneously introduced the Parzen window estimation technique and calculates the entropy of memory cell, According to entropy, memory cell document is dynamically updated, make algorithm towards preferable Pareto Optimal Boundary search；Additionally, algorithm Carry out Immune Clone Selection based on point in object space distribution situation, be conducive to obtaining Pareto Optimal Boundary distributed more widely, and add Fast convergence rate；Compared with existing algorithm, PMEIA obtains very well in terms of convergence, multiformity and the distributivity solved Raising.Ye Jing document " TSP Study on Problems based on immunity-ant group algorithm, computer engineering, 2010, volume 36, 24 phases, the 156-157 page " in, accelerate convergence and the contradiction of precocious stagnation behavior for ant group algorithm, use for reference immune from My regulatory mechanism keeps the multifarious ability of population, proposes immunity-ant group algorithm；This algorithm is various according to the microcosmic solved Property, macroscopic view multiformity and the concentration index of arc dynamically adjust Path selection probability and quantity of information more New Policy；Symmetrical with several and Emulation experiment is carried out as a example by asymmetric TSP problem；Result shows, this algorithm has preferably local refinement than general ant group algorithm Ability, convergence and multiformity." logistics distribution center based on chaos Immune Evolutionary Algorithm is selected at document for Li Changbing, Du Maokang Location scheme, market modernizes, 2008, January (lower publication appearing once every ten days), the 109-110 page " in, it is used for solving by chaos Immune Evolutionary Algorithm The certainly Location Selection of Logistics Distribution Center problem under e-commerce environment；Chaos Immune Evolutionary Algorithm has preferable ability of searching optimum And convergence, it is possible to preferably solve the optimization problem of such complication system.Shi Yue, Guo Shaoyong, Qiu Xuesong at document " based on exempting from The power telecom network layout of roads method of epidemic disease algorithm, Beijing University of Post & Telecommunication's journal, 2014, volume 37, the 2nd phase, 14-17 Page " in, it is proposed that a kind of power telecom network layout of roads method based on immune algorithm, considered network economy, Reliability and service distribution factor；Construct network reliability function based on website cyclization rate, design in conjunction with service distribution situation The problem model of power telecom network layout of roads, and utilize immune algorithm to solve；The method uses multiple-objection optimization mould Type, can improve the motility of programme and comprehensive to a certain extent；Simulation result shows, in the face of different website cyclization In the case of rate constraint, the method is all provided that effective layout of roads scheme.

But, the individuality related in Artificial Immune Algorithm is gene, and Immunity Operator is by gene is carried out vaccine choosing Selecting and construct with two kinds of operations of vaccination, this algorithm has not yet been formed unified Computational frame so far, and most of AIA algorithms are basic On be the improvement to other intelligent algorithms particularly evolution algorithm.Additionally, Immunity Operator is little in AIA algorithm, want to expand Other operators need to relate to theory of immunity knowledge very professional and abstruse in life sciences, thus to non-life science It is extremely difficult for research worker.More it is essential that AIA algorithm cannot consider individual susceptible, expose, immune, sick with State Transferring between healing.Ask additionally, prior art can only solve the non-combined optimization in dimension the most much higher targeted delivery path Topic, has difficulties to extensive the solving of multiple target transport path combinatorial optimization problem that dimension is the highest.

Summary of the invention

In order to solve object function and constraints to need not the multiple target transport path combination of special restrictive condition excellent The extensive multiple target transport path combinatorial optimization problem that change problem, particularly dimension are the highest；The present invention provides a kind of based on Mus The multiple target transport path combined optimization method of epidemic disease Epidemic Model, is called for short TPO_SEIR method；In TPO_SEIR method, adopt By mentality of designing diverse with existing swarm intelligence algorithm, it is proposed that by premunitive for pulse time lag plague Epidemic Model It is converted into the conventional method that can solve multiple target transport path combinatorial optimization problem；The operator constructed can fully reflect pulse The interaction relationship of premunitive time lag plague Epidemic Model, thus embody the base that plague Infectious Dynamics is theoretical This thought；TPO_SEIR method has global convergence.

In order to achieve the above object, the present invention adopts the following technical scheme that

A kind of multiple target transport path combined optimization method based on plague Epidemic Model, is called for short TPO_SEIR method, It is characterized in that: the general type setting multiple target transport path Combinatorial Optimization Model to be solved is as follows:

$\begin{array}{c}\min \{O_1{f}_1\left(X\right),O_2{f}_2\left(X\right),\mathrm{...},O_M{f}_M\left(X\right)\}\\ \begin{array}{cc}s.t.& \left\{\begin{array}{c}{g}_{i_a}\left(X\right)\≥0,i_a\∈I\\ h_{i_b}\left(X\right)=0,i_b\∈E\\ X\∈H\⋐R^n\end{array}\right.\end{array}\end{array}---\left(1\right)$

In formula:

(1)RⁿIt is that n ties up Euclidean space, the total number of variable that n is comprised by this Optimized model；

(2) X=(x₁, x₂..., x_m, x_m+1..., x_n) it is that a n ties up decision vector, wherein, front m variable x₁, x₂..., x_mIt is continuous Real-valued variable, is used for representing the flow shape parameter related in model；Rear n-m variable x_m+1..., x_nIt is 0,1 Integer type variable, is used for representing which website in n website must become some nodes in an optimum transport path, the most right In any x_j∈{x_m+1..., x_n, if x_j=1, then it represents that jth website is selected for a knot in this optimum transport path Point, if x_j=0, then it represents that jth website is the most selected；

(3)f₁(X), f₂(X) ..., f_M(X) it is M object function, is used for M the control mesh represented when transport path selects Mark requirement；

(4)O₁, O₂..., O_MFor the priority of M object function, priority order is required to meet O₁>O₂>…>O_M, i.e. mesh Scalar functions f₁(X) first require to minimize, next to that f₂(X), it is thirdly f₃(X), the like, finally require to reach That little is object function f_M(X)；

(5)Represent that website is when selecting required satisfied i-th_aIndividual inequality constraints condition；I be inequality about The set of bundle condition number；

(6)Represent that website is when selecting required satisfied i-th_bIndividual equality constraint；E is equality constraint bar The set of part numbering；

(7){f_i(X), i=1,2 ..., M},i_a∈I}、{i_bThe mathematic(al) representation of ∈ E} does not limit Condition processed；

(8) H is search volume, also known as solution space；

(9), when calculating, decision vector X is also referred to as trial solution；If trial solution X is unsatisfactory for constraints, then make f (X)=+ ∞；

Multiple target transport path Combinatorial Optimization Model formula (1) is converted into following single goal transport path Combinatorial Optimization mould Type:

$\begin{array}{c}\min \{F\left(X\right)=\underset{k=1}{\overset{M}{\Σ}}{O}_k{f}_k\left(X\right)\}\\ \begin{array}{cc}s.t.& \left\{\begin{array}{c}{g}_{i_a}\left(X\right)\≥0,i_a\∈I\\ h_{i_b}\left(X\right)=0,i_b\∈E\\ X\∈H\⋐R^n\end{array}\right.\end{array}\end{array}---\left(2\right)$

In formula, O_k=10^M-k；K is the numbering of object function；

Described TPO_SEIR method, uses and has pulse premunitive time lag plague Infectious Dynamics theory, use There is pulse premunitive time lag plague Infectious Dynamics theoretical, it is assumed that exist by some individual's groups at certain ecosystem The crowd become, everyone characterizes by several features, and a feature is equivalent to an organ of human body；This ecosystem is deposited A kind of be referred to as the plague infectious disease, people by effectively contacting with viruliferous mouse, as bitten by it, eat by mistake its meat or Eat by mistake by the food of its manure contamination, this disease can be infected, this infectious disease can among crowd wide-scale distribution；This infectious disease Attack is the Partial Feature of human body；The crowd being uninfected by this infectious disease in this ecosystem is referred to as susceptible person；Susceptible person feels After catching this infectious disease, will not fall ill at once, its internal cell entry incubation period；Internal virus is in preclinical crowd and claims For resurrectionist；Virus can be passed to other people effectively contacted with it by resurrectionist；Resurrectionist after incubation period can fall ill, this type of Person is for sending out patient；Send out patient and the virus that it is internal can be passed to other people effectively contacted with it；Resurrectionist and Fa patient can To be cured by therapeutic treatment；Resurrectionist and Fa patient are referred to as healing person after being cured；In order to prevent this infectious disease to crowd Harm, crowd inoculates a vaccine at set intervals, and the people of inoculated vaccine 100% will not be successfully obtained immunity；Success Vaccinated crowd self will not catch an illness within a period of time, more will not give other people by virus disseminating；The most successfully inoculate The crowd of vaccine is still that susceptible person；The immunocompetence that the people of successful vaccination is obtained can cease to be in force automatically over time And immunocompetence of dying；The people not carrying out immunity or immunocompetence of dying can catch this infectious disease again.At this ecosystem In infectious disease effect under, everyone growth conditions will susceptible, expose, fall ill, cure between these four states random Conversion.This random transition is mapped to the search volume of optimization problem, it is meant that each trial solution in search volume from a position Put and transfer to another one position, it is achieved thereby that the random search to search volume.The physical strength of individual is by this people Feature determines, body constitution athlete energy continued growth, people of weak constitution then stops growing.This optimization method has search Ability is strong and the feature of global convergence, provides one solution party for solving of multiple target transport path combinatorial optimization problem Case.

There is pulse premunitive time lag plague Epidemic Model

Crowd in the ecosystem being made up of people is divided into four classes:

S class: susceptible person (susceptible) class, i.e. all entirety not contaminating patient in ecosystem, if this class people Pestivirus person effectively contacts with band, is easy for being infected and falling ill.

E class: resurrectionist (exposed) class, i.e. made with band pestivirus person in ecosystem effective contact but also The entirety of the crowd not fallen ill, this class crowd is potential patient.

I class: send out patient (infective) class, i.e. caught the plague in ecosystem and still the crowd of period of disease, If this class crowd effectively contacts with the crowd of susceptible person's class, it is easy for pestivirus to be transmitted to susceptible person.

R class: healing person (recovered) class, i.e. represents the healing person after catching an illness, and these people temporarily will not fall ill, but Catch an illness if effectively contacting also can reappear with band pestivirus person after a predetermined time.

Consider that there is pulse premunitive time lag plague Infection Dynamics Model:

$\left\{\begin{array}{cc}\left.\begin{array}{c}\frac{dS\left(t\right)}{dt}=\mathrm{\μ}-\mathrm{\β}I\left(t\right)(1+vI(t\left)\right)S\left(t\right)-\mathrm{\μ}S\left(t\right)-q\mathrm{\μ}I\left(t\right)\\ \frac{dI\left(t\right)}{dt}=-{\mathrm{\βe}}^{-\mathrm{\μ}\mathrm{\τ}}I(t-\mathrm{\τ})(1+vI(t-\mathrm{\τ}\left)S\right(t-\mathrm{\τ}\left)\right)+{\mathrm{q\μe}}^{-\mathrm{\μ}\mathrm{\τ}}I(t-\mathrm{\τ})-(r+\mathrm{\μ})I\left(t\right)\\ \frac{dR\left(t\right)}{dt}=rI\left(t\right)-\mathrm{\μ}R\left(t\right)\\ E\left(t\right)=1-S\left(t\right)-I\left(t\right)-R\left(t\right)\end{array}\right\}& t\≠kT\\ \left.\begin{array}{c}S\left(t^{+}\right)=S\left(t\right)-b\mathrm{\μ}\left(S\right(t)+E(t)+R(t\left)\right)-bp\mathrm{\μ}I\left(t\right)\\ E\left(t^{+}\right)=E\left(t\right)\\ I\left(t^{+}\right)=I\left(t\right)\\ R\left(t^{+}\right)=R\left(t\right)+b\mathrm{\μ}\left(S\right(t)+E(t)+R(t\left)\right)+bp\mathrm{\μ}I\left(t\right)\end{array}\right\}& t=kT\end{array}\right.---\left(3\right)$

In formula: t represents period；S (t), E (t), I (t), R (t) represent that t in period belongs to S class, E class, I class, R class people respectively The ratio of group, S (t) >=0, E (t) >=0, I (t) >=0, R (t) >=0, S (t)+E (t)+I (t)+R (t)=1；μ represents natality；β Represent linear infectious rate, β > 0；ν represents Nonlinear Incidence Rate, ν >=0；Q represents vertical infection rate, q > 0；P represents that level infects Rate, p > 0；R represents cure rate, r > 0；B represents immune success rate ratio, b > 0；τ represents length incubation period, τ > 0；V represents that immunity has Effect time duration, V > 0；T represents transfer period；K is positive integer, k=1,2 ....

At t in period, a people can be only in some class of S class, E class, I class, R apoplexy due to endogenous wind；Because of S (t), E (t), I (t), R T () represents that t in period belongs to S class, E class, I class, the ratio of R class crowd respectively, therefore S (t), E (t), I (t), R (t) can regard one as Individual belongs to S class, E class, I class and the probability of R class；When a people belongs to S class, E class, I class or R class, mean that at a people In S state, E-state, I state or R state；Described S state refers to the individual state do not caught an illness, and is called for short sensitization；Described E shape State refers to that the individual state infectd plague infectious disease but also do not fallen ill, abbreviation latency, described I state refer to that individuality is After infecing plague infectious disease and be in morbidity state, be called for short morbidity state, described R state is cured after referring to Personal State, be called for short healing state.S state, E-state, I state and R state are abbreviated as S, E, I and R respectively.

Therefore, it can be applied to formula (3) anyone of crowd, i.e.

$\begin{array}{c}\left\{\begin{array}{cc}\left.\begin{array}{c}\frac{{\mathrm{dS}}_i\left(t\right)}{dt}=\mathrm{\μ}-{\mathrm{\βI}}_i\left(t\right)(1+{\mathrm{vI}}_i(t\left)\right)S_i\left(t\right)-{\mathrm{\μS}}_i\left(t\right)-{\mathrm{q\μI}}_i\left(t\right)\\ \frac{{\mathrm{dI}}_i\left(t\right)}{dt}=-{\mathrm{\βe}}^{-{\mathrm{\μ\τ}}_i}{I}_i(t-\mathrm{\τ})(1+{\mathrm{vI}}_i(t-\mathrm{\τ}\left)S_i\right(t-\mathrm{\τ}\left)\right)+{\mathrm{q\μe}}^{-{\mathrm{\μ\τ}}_i}{I}_i(t-\mathrm{\τ})-(r+\mathrm{\μ})I_i\left(t\right)\\ \frac{{\mathrm{dR}}_i\left(t\right)}{dt}={\mathrm{rI}}_i\left(t\right)-{\mathrm{\μR}}_i\left(t\right)\\ E_i\left(t\right)=1-S_i\left(t\right)-I_i\left(t\right)-R_i\left(t\right)\end{array}\right\}& t\≠kT\\ \left.\begin{array}{c}{S}_i\left(t^{+}\right)=S_i\left(t\right)-b\mathrm{\μ}\left(S_i\right(t)+E_i(t)+R_i(t\left)\right)-{\mathrm{bp\μI}}_i\left(t\right)\\ E_i\left(t^{+}\right)=E_i\left(t\right)\\ I_i\left(t^{+}\right)=I_i\left(t\right)\\ R_i\left(t^{+}\right)=R_i\left(t\right)+b\mathrm{\μ}\left(S_i\right(t)+E_i(t)+R_i(t\left)\right)+{\mathrm{bp\μI}}_i\left(t\right)\end{array}\right\}& t=kT\end{array}\right.,i=1,\\ 2,\mathrm{...},N\end{array}---\left(4\right)$

Formula (4) is at the general of S state, E-state, I state and R state for everyone calculated in t crowd in period Rate.

Clock phase t parameter μ, and the value of β, ν, q, p, r, m is respectively μ^t, β^t, ν^t, q^t, p^t, r^t, m^t；For convenience of calculating, will Formula (4) changes discrete recursive form into, i.e.

$\begin{array}{c}\{\begin{array}{c}{S}_i(t+1)=S_i\left(t\right)+{\mathrm{\μ}}^t-{\mathrm{\β}}^t{I}_i\left(t\right)(1+v^t{I}_i(t\left)\right)S_i\left(t\right)-{\mathrm{\μ}}^t{S}_i\left(t\right)-q^t{\mathrm{\μ}}^t{I}_i\left(t\right)\\ I_i(t+1)=I_i\left(t\right)+-{\mathrm{\β}}^{-{\mathrm{\μ}}^t{\mathrm{\τ}}_i}{I}_i(t-{\mathrm{\τ}}_i)(1+v^t{I}_i(t-{\mathrm{\τ}}_i\left)S_i\right(t-{\mathrm{\τ}}_i\left)\right)+d^t{\mathrm{\μ}}^t{e}^{-{\mathrm{\μ}}^t{\mathrm{\τ}}_i}{I}_i(t-{\mathrm{\τ}}_i)-(r^t+{\mathrm{\μ}}^t)I_i\left(t\right)\\ R_i(t+1)=R_i\left(t\right)+r^t{I}_i\left(t\right)-{\mathrm{\μ}}^t{R}_i\left(t\right)\\ E_i(t+1)=1-S_i(t+1)-I_i(t+1)-R_i(t+1)\end{array},i=1,\\ 2,\mathrm{...},N;t\≠kT\end{array}---\left(5\right)$

$\{\begin{array}{c}{S}_i(t+1)=S_i\left(t\right)-b^t{\mathrm{\μ}}^t\left(S_t\right(t)+E_i(t)+R_i(t\left)\right)-b^t{p}^t{\mathrm{\μ}}^t{I}_i\left(t\right)\\ E_i(t+1)=E_i\left(t\right)\\ I_i(t+1)=I_i\left(t\right)\\ R_i(t+1)=R_i\left(t\right)+b^t{\mathrm{\μ}}^t\left(S_i\right(t)+E_i(t)+R_i(t\left)\right)+b^t{p}^t{\mathrm{\μ}}^t{I}_i\left(t\right)\end{array},i=1,2,\mathrm{...},N;t=kT---\left(6\right)$

In formula (5), formula (6), S_i(t)、E_i(t)、I_i(t)、R_iT () represents that period, t individuality i belonged to S class, E class, I respectively Class, the probability of R class crowd, S_i(t) >=0, E_i(t) >=0, I_i(t) >=0, R_i(t) >=0, S_i(t)+E_i(t)+I_i(t)+R_i(t)=1； Parameter μ^t, β^t, ν^t, q^t, p^t, r^t, m^t, τ_iObtaining value method be μ^t=Rand (μ₀, μ₁), μ₀And μ₁Represent μ^tThe lower limit of value and upper Limit, and meet μ₀>=0, μ₁>=0, μ₀≤μ₁；β^t=Rand (β₀, β₁), β₀And β₁Represent β^tThe lower limit of value and the upper limit, and meet β₀ >=0, β₁>=0, β₀≤β₁；ν^t=Rand (ν₀, ν₁), v₀And v₁Represent v^tThe lower limit of value and the upper limit, and meet ν₀>=0, ν₁>=0, ν₀≤ν₁；q^t=Rand (q₀, q₁), q₀And q₁Represent q^tThe lower limit of value and the upper limit, and meet q₀>=0, q₁>=0, q₀≤q₁；p^t= Rand(p₀, p₁), p₀And p₁Represent p^tThe lower limit of value and the upper limit, and meet p₀>=0, p₁>=0, p₀≤p₁；r^t=Rand (r₀, r₁), r₀And r₁Represent r^tThe lower limit of value and the upper limit, and meet r₀>=0, r₁>=0, r₀≤r₁；b^t=Rand (b₀, b₁), b₀And b₁ Represent b^tThe lower limit of value and the upper limit, and meet b₀>=0, b₁>=0, b₀≤b₁；τ_i=INT (Rand (τ₀, τ₁)), τ₀, τ₁Represent τ_i The lower limit of value and the upper limit, and meet τ₀>=0, τ₁>=0, τ₀≤τ₁；V_i=INT (Rand (V₀, V₁)), V₀, V₁Represent V_iValue Lower limit and the upper limit, and meet V₀>=0, V₁>=0, V₀≤V₁；Rand (A, B) represent [A, B] interval produce one be uniformly distributed with Machine number, A and B is given constant, it is desirable to A≤B；Real number w round off is rounded by INT (w) expression.

Implementation method Scenario Design

The plague, has another name called core pestilence, is that Yersinia pestis borrows Mus flea-borne deadly infectious disease, and fatality rate is high, Ren Leili In history, Zeng Sanci is very popular, for a kind of disease of natural focus being widely current between wild rodent.Before the human world is popular, General the most popular between Mus.The Rat plague source of infection (reservoir) has field rodent, suslik, Vulpes, wolf, cat, leopard etc., wherein Citellus Most important with Marmota.Rattusflauipectus, Rattus norvegicus and rattus rattus in home mouse is the important source of infection of human plague.

Assume to there is, at an ecosystem Z, the crowd being made up of N number of people.In crowd, everyone represents by numbering is exactly 1, 2 ..., N；One people is also called body one by one；Each individuality is characterized by n feature, and a feature is equivalent to the one of human body Individual organ, i.e. for individual i, its characteristic feature is (x_i,1, x_i,2..., x_i,n), i=1,2 ..., N；This ecosystem exists A kind of plague infectious disease, people is by effectively contacting with viruliferous mouse, as bitten, eat by mistake its meat by it or eating by mistake by it The food of manure contamination, can infect this disease, this infectious disease can among crowd wide-scale distribution；This infectious disease attack be The Partial Feature of human body；The crowd being uninfected by this infectious disease in this ecosystem is referred to as susceptible person；Susceptible person infects this biography After catching an illness, will not fall ill, its internal pestivirus enters incubation period at once；Internal virus is in preclinical crowd and is referred to as sudden and violent Dew person；Pestivirus can be passed to other people effectively contacted with it by resurrectionist；Resurrectionist after incubation period can fall ill, this type of Person is for sending out patient；Send out patient and the pestivirus that it is internal can be passed to other people effectively contacted with it；Resurrectionist and morbidity Person can be cured by therapeutic treatment；Resurrectionist and Fa patient are referred to as healing person after being cured；In order to prevent this infectious disease pair The harm of crowd, crowd inoculates a vaccine at set intervals, and the people of inoculated vaccine 100% will not be successfully obtained immunity； The crowd of successful vaccination self will not catch an illness within a period of time, and pestivirus more will not be broadcast to other people；No The crowd of successful vaccination is still that susceptible person；The immunocompetence that the people of successful vaccination is obtained over time can Cease to be in force automatically and immunocompetence of dying；The people not carrying out immunity or immunocompetence of dying can catch this infectious disease again.At this Under plague infectious disease effect in ecosystem, everyone growth conditions in this ecosystem Z will susceptible, expose, Fall ill, cure random transition between these four states.This random transition is mapped to the search volume of optimization problem, it is meant that every Individual trial solution in search volume from a position transfer to another one position, it is achieved thereby that searching at random search volume Rope.The physical strength of individual is to be determined by the feature of this people, and body constitution athlete energy continued growth, people of weak constitution is then Stop growing.

Above-mentioned scene is mapped to the search procedure to multiple target transport path combinatorial optimization problem formula (2) globally optimal solution In, its implication is as described below.

The search volume H of multiple target transport path combinatorial optimization problem formula (2) is corresponding with ecosystem Z, this ecosystem In system, body corresponds to a trial solution of multiple target transport path combinatorial optimization problem formula (2) one by one, corresponding to individuality Souning out disaggregation is exactly X={X₁, X₂..., X_N, X_i=(x_i,1, x_i,2..., x_i,n), i=1,2 ..., N.One feature of individual i Corresponding to optimization problem trial solution X_i(X_i∈ X) a variable, feature j of i.e. individual i and trial solution X_iVariable x_i,jRelatively Should, so the characteristic number of individual i and trial solution X_iVariable number identical, be all n.Therefore, individual i and trial solution X_iIt is of equal value general Read.Individual physical strength represents with crowd health index HHI (Human Health Index, HHI), and HHI exponent pair should Target function value in optimization problem formula (2).Good trial solution correspondence has the individuality of higher HHI index, i.e. body constitution is strong Individuality, the trial solution correspondence of difference has the individuality of relatively low HHI index, the individuality i.e. having a delicate constitution.For optimization problem formula (2), The HHI index calculation method of individual i is:

At t in period, the μ of automated randomized generation crowd^t, β^t, ν^t, q^t, p^t, r^t, b^t, τ_i, use plague Epidemic Model respectively Calculate susceptible rate S of individual i_i(t), exposure E_i(t), rate I of catching an illness_i(t) and cure rate R_i(t).Individual i period t be in S Which state in state, E-state, I state and four states of R state, by S_i(t)、E_i(t)、I_i(t) and R_iT () is formed Probability distribution determines, i.e. S_i(t)、E_i(t)、I_i(t) and R_iT which value in () is the biggest, selected general of its corresponding state Rate is the biggest.Table 1 gives plague infectious disease and propagates situation in crowd.

The legal state conversion of table 1 plague Epidemic Model

Possible S, E, I, R State Transferring of each individuality has 4 × 4=16 kind, but legal state conversion only 9 kinds, such as table 1 Shown in.Except 9 kinds in table 1 are in addition to legal State Transferring, and other kinds of State Transferring is the most illegal.9 kinds of legal shapes Available 9 operators of state conversion describe, i.e. S-S, S-E, E-E, E-I, E-R, I-I, I-R, R-R, R-S.

Due to when phase in office, the μ of crowd in ecosystem^t, β^t, ν^t, q^t, p^t, r^t, b^t, τ^tIt is all random, the most individual The growth conditions of body i will between tetra-states of S, E, I, R random transition.This random transition is mapped to the search of optimization problem Space, it is meant that each trial solution in search volume from a position transfer to another one position, it is achieved thereby that to search The random search in space.

In random search procedure, if the HHI index that the HHI index of t individuality i in period is higher than t-1 in its period, then individual i will Continued growth, this mean individual i from globally optimal solution increasingly close to；Otherwise, if the HHI index of t individuality i in period less than or etc. In the HHI index of t-1 in its period, then individual i will stop growing, and this means that individual i stays the position at t-1 in period place not Dynamic.The poorest this random searching strategy makes this algorithm have global convergence.

Characterizing population group gathers generation method

Period t, it is as follows that characterizing population group gathers generation method:

(1) advantage population PS is produced^u: from the crowd being in state u, random choose goes out L individuality, these people's The HHI index HHI index than current individual i is high, forms advantage population PS^u, u ∈ { S, E, I, R}；L is also called to other The number of individuals that individuality is exerted one's influence；

(2) classification population CS is produced^u: from the crowd being in state u, random choose goes out L individuality, forms classification Population CS^u, u ∈ { S, E, I, R}；

Evolutive operators

(1) S-S operator.What this operator described is the individuality being in sensitization, does not catches the situation of infectious disease yet.Will Set PS^SIn proprietary feature j randomly choosed and state value weighted sum thereof pass to the character pair j of current individual i, Make individual i also by set PS^SThe impact of middle crowd, i.e. for being in the individual i of state S, has

If j≤m, then

$v_{i,j}(t+1)=\left\{\begin{array}{cc}\underset{s\∈{\mathrm{PS}}^S}{\Σ}{\mathrm{\α}}_s{x}_{s,j}\left(t\right)& \left|{\mathrm{PS}}^S\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{PS}}^S\right|=0\end{array}\right.---\left(8\right)$

If j > m, then

$v_{i,j}(t+1)=\left\{\begin{array}{cc}most({\mathrm{PS}}^S,j)& \left|{\mathrm{PS}}^S\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{PS}}^S\right|=0\end{array}\right.---\left(9\right)$

In formula: v_i,j(t+1) it is the state value of feature j of t+1 individuality i in period；x_s,jT () is feature j of t individuality s in period State value；α_sFor affecting constant, α_s=Rand (0.4,0.6)；most(PS^S, j) it is meant that: as set PS^SIn jth The state value of feature be the number of 1 more than the number that state value is 0 of jth feature time, most (PS^S, j)=1；As set PS^S In the number that state value is 1 of jth feature less than the number that state value is 0 of jth feature time, most (PS^S, j)= 0；As set PS^SIn the number that state value is 1 of jth feature equal to the number that state value is 0 of jth feature time, most(PS^S, value j) randomly selects among both 0 or 1.

(2) S-E operator.What this operator described is the individuality being in sensitization, by with expose or caught an illness Crowd contacts the situation of infectious disease on after stain.Because this infectious disease can be propagated interpersonal, therefore L is allowed to expose or caught an illness Feature j of people and state value weighted sum be transmitted to the character pair j of the susceptible individual i not caught an illness so that it is expose.I.e. for It is in the individual i of state S, has

If j≤m, then

$v_{i,j}(t+1)=\left\{\begin{array}{cc}\underset{s\∈{\mathrm{CS}}^E\∪{\mathrm{CS}}^I}{\Σ}{\mathrm{\α}}_s{x}_{s,j}\left(t\right)& \left|{\mathrm{CS}}^E\∪{\mathrm{CS}}^I\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^E\∪{\mathrm{CS}}^I\right|=0\end{array}\right.---\left(10\right)$

If j > m, then

$v_{i,j}(t+1)=\left\{\begin{array}{cc}most({\mathrm{CS}}^E\∪{\mathrm{CS}}^I,j)& \left|{\mathrm{CS}}^E\∪{\mathrm{CS}}^I\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^E\∪{\mathrm{CS}}^I\right|=0\end{array}\right.---\left(11\right)$

(3) E-E operator.What this operator described is the individuality being in exposed state, does not arrives because of incubation period to be still in and hides The situation of phase.L is allowed to have exposed but feature j of its HHI index people higher than current individual i and state value weighted sum thereof are passed to The character pair j of the individual i exposed so that it is body constitution strengthens, and i.e. for being in the individual i of state E, has

If j≤m, then

$v_{i,j}(t+1)=\left\{\begin{array}{cc}\underset{s\∈{\mathrm{PS}}^E}{\Σ}{\mathrm{\α}}_s{x}_{s,j}\left(t\right)& \left|{\mathrm{PS}}^E\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{PS}}^E\right|=0\end{array}\right.---\left(12\right)$

If j > m, then

$v_{i,j}(t+1)=\left\{\begin{array}{cc}most({\mathrm{PS}}^E,j)& \left|{\mathrm{PS}}^E\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{PS}}^E\right|=0\end{array}\right.---\left(13\right)$

(4) E-I operator.What this operator described is that the individuality being in exposed state is because having arrived the feelings starting morbidity incubation period Shape.L individual feature j fallen ill and state value weighted sum thereof is allowed to pass to the character pair j of the individual i exposed so that it is Morbidity.I.e. for being in the individual i of state E, have

If j≤m, then

$v_{i,j}(t+1)=\left\{\begin{array}{cc}\underset{s\∈{\mathrm{CS}}^I}{\Σ}{\mathrm{\α}}_s{x}_{s,j}\left(t\right)& \left|{\mathrm{CS}}^I\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^I\right|=0\end{array}\right.---\left(14\right)$

If j > m, then

$v_{i,j}(t+1)=\left\{\begin{array}{cc}most({\mathrm{CS}}^I,j)& \left|{\mathrm{CS}}^I\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^I\right|=0\end{array}\right.---\left(15\right)$

(5) E-R operator.What this operator described is the individuality being in exposed state, makes it recover by vaccination Situation.L individual feature j cured and state value weighted sum thereof is allowed to pass to the correspondence of the individual i being in exposed state Feature j so that it is cure, i.e. for being in the individual i of state E, have

If j≤m, then

$v_{i,j}(t+1)=\left\{\begin{array}{cc}\underset{s\∈{\mathrm{CS}}^R}{\Σ}{\mathrm{\α}}_s{x}_{s,j}\left(t\right)& \left|{\mathrm{CS}}^R\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^R\right|=0\end{array}\right.---\left(16\right)$

If j > m, then

$v_{i,j}(t+1)=\left\{\begin{array}{cc}most({\mathrm{CS}}^R,j)& \left|{\mathrm{CS}}^R\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^R\right|=0\end{array}\right.---\left(17\right)$

(6) I-I operator.What this operator described is the individuality being in morbidity state, at present still in the feelings of morbidity state Shape.Allow L allow fall ill but feature j of its HHI index people higher than current individual i and state value weighted sum thereof are passed to and fallen ill The character pair j of individual i so that it is body constitution strengthens.I.e. for being in the individual i of state I, have

If j≤m, then

$v_{i,j}(t+1)=\left\{\begin{array}{cc}\underset{s\∈{\mathrm{PS}}^I}{\Σ}{\mathrm{\α}}_s{x}_{s,j}\left(t\right)& \left|{\mathrm{PS}}^I\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{PS}}^I\right|=0\end{array}\right.---\left(18\right)$

If j > m, then

$v_{i,j}(t+1)=\left\{\begin{array}{cc}most({\mathrm{PS}}^I,j)& \left|{\mathrm{PS}}^I\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{PS}}^I\right|=0\end{array}\right.---\left(19\right)$

(7) I-R operator.What this operator described is the individuality being in morbidity state, makes it by treatment or vaccination The situation recovered.Allow L feature j having cured individuality and state value weighted sum thereof pass to the character pair j of current individual i, make It is cured.I.e. for being in the individual i of state I, have

If j≤m, then

$v_{i,j}(t+1)=\left\{\begin{array}{cc}\underset{s\∈{\mathrm{CS}}^R}{\Σ}{\mathrm{\α}}_s{x}_{s,j}\left(t\right)& \left|{\mathrm{CS}}^R\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^R\right|=0\end{array}\right.---\left(20\right)$

If j > m, then

$v_{i,j}(t+1)=\left\{\begin{array}{cc}most({\mathrm{CS}}^R,j)& \left|{\mathrm{CS}}^R\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^R\right|=0\end{array}\right.---\left(21\right)$

(8) R-R operator.What this operator described is the individuality being in healing state, at present still in the feelings curing state Shape.L is allowed to have cured but feature j of its HHI index people higher than current individual i and state value weighted sum thereof are passed to and cured The character pair j of individual i so that it is body constitution strengthens.I.e. for the individual i of state R, have

If j≤m, then

$v_{i,j}(t+1)=\left\{\begin{array}{cc}\underset{s\∈{\mathrm{PS}}^R}{\Σ}{\mathrm{\α}}_s{x}_{s,j}\left(t\right)& \left|{\mathrm{PS}}^R\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{PS}}^R\right|=0\end{array}\right.---\left(22\right)$

If j > m, then

$v_{i,j}(t+1)=\left\{\begin{array}{cc}most({\mathrm{PS}}^R,j)& \left|{\mathrm{PS}}^R\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{PS}}^R\right|=0\end{array}\right.---\left(23\right)$

(9) R-S operator.What this operator described is the individuality being in healing state, transfers to easily because immunocompetence loses The situation of sense state.L individual feature j being in sensitization and state value weighted sum thereof is allowed to pass to the right of current individual i Answer feature j so that it is transfer sensitization to.I.e. for being in the individual i of state R, have

If j≤m, then

$v_{i,j}(t+1)=\left\{\begin{array}{cc}\underset{s\∈{\mathrm{CS}}^S}{\Σ}{\mathrm{\α}}_s{x}_{s,j}\left(t\right)& \left|{\mathrm{CS}}^S\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^S\right|=0\end{array}\right.---\left(24\right)$

If j > m, then

$v_{i,j}(t+1)=\{\begin{array}{cc}most({\mathrm{CS}}^S,)& \left|{\mathrm{CS}}^S\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^S\right|=0\end{array}---\left(25\right)$

(10) accretive operatos.What this operator described is the growth of crowd, i.e.

In formula:

X_i(t)=(x_{I, 1}(t), x_{I, 2}(t) ..., x_{I, n}(t))；

V_i(t+1)=(v_{I, 1}(t+1), v_{I, 2}(t+1) ..., v_{I, n}(t+1))；

In formula, HHI (V_i(t+1))、HHI(X_i(t)) calculate by formula (7)；

The structure of TPO_SEIR method

Described TPO_SEIR method includes including following steps:

(S1) initialize: a) make t=0 in period；The all parameters related in this optimization method are initialized by table 2；B) exist Search volume H randomly chooses the trial solution { X corresponding to individuality₁(0),X₂(0),…,X_N(0)}；C) V (i)=0 is made, i=1, 2 ..., N；V (i) > 0 represents individual i vaccination success, and V (i)=0 represents that individual i vaccination is unsuccessful or does not inoculates；

The obtaining value method of table 2 parameter

(S2) calculate: CalculateR_i(0)=1-S_i(0)-E_i(0)-I_i (0), i=1,2 ..., N；

In formula, S_i(0), E_i(0), I_i(0), R_i(0) represent that period 0, individual i was in S state, E-state, I state and R respectively Shape probability of state；Rand (A, B) represents that A and B is given constant, at one uniform random number of [A, B] interval generation Seek A≤B；Constant for stochastic generation；

(S3) the SEIR state of individual i, SEIR are calculated_i(0)=SEIR (S_i(0),E_i(0),I_i(0),R_i(0)), i=1, 2 ..., N；Wherein SEIR_i(0) individual i state in which in period 0 is represented；Function SEIR_i(0)=SEIR (S_i(0),E_i(0),I_i (0),R_i(0)), it is used for determining which kind of state individual i will be in.

(S4) making t in period from 0 to G, circulation performs step (S5)～step (S22), and wherein G is evolutionary period number；

(S5) calculate: μ^t=Rand (μ₀, μ₁), β^t=Rand (β₀, β₁), ν^t=Rand (ν₀, ν₁), q^t=Rand (q₀, q₁), p^t=Rand (p₀, p₁), r^t=Rand (r₀, r₁), b^t=Rand (b₀, b₁)；

(S6) for all u ∈, { S, E, I, R} generate characterizing population group and gather PS^u、CS^u；

(S7) making i from 1 to N, circulation performs following step (S8)～step (S19)；

(S8) τ is calculated_i=INT (Rand (τ₀, τ₁)), V_i=INT (Rand (V₀, V₁))；If t can not be divided exactly by T, then by formula (5) S is calculated_i(t+1)、E_i(t+1)、I_iAnd R (t+1)_i(t+1)；Otherwise, if t can be divided exactly by T, then q is made₀=Rand (0,1), if q₀≤Q₀, then S is calculated by formula (6)_i(t+1)、E_i(t+1)、I_iAnd R (t+1)_i, and make V (i)=t+1 (t+1)；Otherwise by formula (5) Calculate S_i(t+1)、E_i(t+1)、I_iAnd R (t+1)_i(t+1)；Wherein Q₀The maximum of immunocompetence it is successfully obtained for crowd's vaccination Probability；

(S9) making j from 1 to n, circulation performs following step (S10)～step (S17)；

(S10) calculate: p₀=Rand (0,1), wherein p₀The infected disease of feature for individual i is attacked and affected reality Border probability；

(S11) if p₀≤E₀, then step (S12)～(S15), wherein E are performed₀For crowd because of infectious disease transmission by shadow The maximum of probability rung；Otherwise, (S16) is gone to step；

(S12) if SEIR_i(t)=S, then

If SEIR_i(t+1)=S, then perform S-S operator as j≤m by formula (8), obtain v_i,j(t+1)；As j > m time by formula (9) perform S-S operator, obtain v_i,j(t+1)；

If SEIR_i(t+1)=E, and V (i)=0, then make LP (i)=t+1, performs S-E operator as j≤m by formula (10), Obtain v_i,j(t+1)；As j > m time by formula (11) perform S-E operator, obtain v_i,j(t+1)；

Otherwise, v is made_i,j(t+1)=x_i,j(t), SEIR_i(t+1)=SEIR_i(t)；

(S13) if SEIR_i(t)=E, then

If SEIR_i(t+1)=E, then perform E-E operator as j≤m by formula (12), obtain v_i,j(t+1)；As j > m time press Formula (13) performs E-E operator, obtains v_i,j(t+1)；

If SEIR_i(t+1)=I, and (t+1-LP (i)) > τ_i, then perform E-I operator as j≤m by formula (14), obtain v_i,j (t+1)；As j > m time by formula (15) perform E-I operator, obtain v_i,j(t+1)；

If SEIR_i(t+1)=R, then perform E-R operator as j≤m by formula (16), obtain v_i,j(t+1)；As j > m time press Formula (17) performs E-R operator, obtains v_i,j(t+1)；

Otherwise, v is made_i,j(t+1)=x_i,j(t), SEIR_i(t+1)=SEIR_i(t)；

(S14) if SEIR_i(t)=I, then

If SEIR_i(t+1)=I, then perform I-I operator as j≤m by formula (18), obtain v_i,j(t+1)；As j > m time press Formula (19) performs I-I operator, obtains v_i,j(t+1)；

If SEIR_i(t+1)=R, then perform I-R operator as j≤m by formula (20), obtain v_i,j(t+1)；As j > m time press Formula (21) performs I-R operator, obtains v_i,j(t+1)；

Otherwise, v is made_i,j(t+1)=x_i,j(t), SEIR_i(t+1)=SEIR_i(t)；

(S15) if SEIR_i(t)=R, then

If SEIR_i(t+1)=R, then perform R-R operator as j≤m by formula (22), obtain v_i,j(t+1)；As j > m time press Formula (23) performs R-R operator, obtains v_i,j(t+1)；

If SEIR_i(t+1)=S, and (t+1-V (i)) > V_i, then make V (i)=0, and perform R-S as j≤m by formula (24) Operator, obtains v_i,j(t+1)；As j > m time by formula (25) perform R-S operator, obtain v_i,j(t+1)；

Otherwise, v is made_i,j(t+1)=x_i,j(t), SEIR_i(t+1)=SEIR_i(t)；

(S16) if p > E₀, then v is made_i,j(t+1)=x_i,j(t), SEIR_i(t+1)=SEIR_i(t)；

(S17) make j=j+1, if j≤n, then go to step (S10), otherwise go to step (S18)；

(S18) perform accretive operatos by formula (26), obtain X_i(t+1)；

(S19) make i=i+1, if i≤N, then go to step (S8), otherwise go to step (S20)；

(S20) if newly obtained globally optimal solution X^*t+1And the error between the globally optimal solution that the last time obtains meets Minimum requirements ε, then go to step (S23), otherwise goes to step (S21)；

(S21) newly obtained globally optimal solution X is preserved^*t+1；

(S22) make t=t+1, if t≤G, then go to step (S5), otherwise go to step (S23)；

(S23) terminate.

Function SEIR (p_S, p_E, p_I, p_R) it is defined as follows:

SEIR(p_S, p_E, p_I, p_R)//p_S, p_E, p_I, p_RState S of being respectively, the probability that E, I, R occur

Calculate: w=Rand (0,1)；

If w≤p_S, then state S is returned；

If p_S<w≤p_S+p_E, then state E is returned；

If p_S+p_E<w≤p_S+p_E+p_I, then state I is returned；

If p_S+p_E+p_I<w≤p_S+p_E+p_I+p_R, then state R is returned；

Beneficial effect

Compared to the prior art the present invention, has the advantage that

1, disclosed by the invention is that a kind of transport path with pulse premunitive time lag plague Epidemic Model is excellent Change method, i.e. TPO_SEIR method.In the method, employing has pulse premunitive time lag plague Infectious Dynamics reason Opinion, it is assumed that there is the crowd being made up of some individuals at certain ecosystem, everyone is characterized by several features, one Feature is equivalent to an organ of human body；There is a kind of plague infectious disease in this ecosystem, people is by entering with viruliferous mouse Row effectively contact, as bitten, eat by mistake its meat by it or eating by mistake by the food of its manure contamination, can infect this disease, this biography Catch an illness and understand wide-scale distribution among crowd；What this infectious disease was attacked is the Partial Feature of human body；This ecosystem is uninfected by The crowd of this infectious disease is referred to as susceptible person；After susceptible person infects this infectious disease, will not fall ill at once, its internal pestivirus Enter incubation period；Internal pestivirus is in preclinical crowd and is referred to as resurrectionist；Pestivirus can be passed to other by resurrectionist The people effectively contacted with it；Resurrectionist after incubation period can fall ill, and this type of person is for sending out patient；Sending out patient can be internal by it Pestivirus passes to other people effectively contacted with it；Resurrectionist and Fa patient can be cured by therapeutic treatment；Resurrectionist It is referred to as healing person with sending out after patient is cured；In order to prevent the harm to crowd of this infectious disease, crowd inoculates at set intervals Vaccine, the people of inoculated vaccine 100% will not be successfully obtained immunity；The crowd of successful vaccination within a period of time from Body will not be caught an illness, and pestivirus more will not be broadcast to other people；The crowd not having successful vaccination is still that susceptible person；Become The immunocompetence that the vaccinated people of merit is obtained can cease to be in force automatically and immunocompetence of dying over time；Do not exempt from The people of epidemic disease or immunocompetence of dying can catch this infectious disease again.Under infectious disease effect in this ecosystem, everyone Growth conditions will susceptible, expose, fall ill, cure random transition between these four states.This random transition is mapped to excellent The search volume of change problem, it is meant that each trial solution in search volume from a position transfer to another one position, thus Achieve the random search to search volume.The physical strength of individual is to be determined by the feature of this people, body constitution athlete's energy Continued growth, people of weak constitution then stops growing.This optimization method has that search capability is strong and the feature of global convergence, A solution is provided for solving of multiple target transport path combinatorial optimization problem.

2, the search capability of TPO_SEIR method is the strongest.TPO_SEIR method includes S-S operator, S-E operator, E-E calculation Son, E-I operator, E-R operator, I-I operator, I-R operator, R-R operator, R-S operator, these operators are added significantly to its search energy Power.

3, model parameter value is simple.Use random method determine in TPO_SEIR method to have pulse premunitive Parameter in time lag plague Infection Dynamics Model and S-S operator, S-E operator, E-E operator, E-I operator, E-R operator, I-I Relevant parameter in operator, I-R operator, R-R operator, R-S operator, had both been greatly reduced parameter input number, had made again model more Practical situation can be expressed.

4, the S-S operator in TPO_SEIR method, S-E operator, E-E operator, E-I operator, E-R operator, I-I operator, I-R Operator, R-R operator, R-S operator by utilizing plague Infection Dynamics Model to construct, completely without with want The actual optimization problem solved is correlated with, and therefore TPO_SEIR method has universality.

5, in TPO_SEIR method, S-S operator, E-E operator, I-I operator, R-R operator can make the individuality that HHI index is high The individuality low to HHI index transmits strong characteristic information so that the individual physical ability that HHI index is low develops toward the good aspect；S-E calculates Son, E-I operator, E-R operator, I-R operator, R-S operator can make to be in and exchange information between the individuality of different conditions, can make again The individual weighted feature information obtaining other individualities, thus reduce individuality and be absorbed in the probability of local optimum；Pulse prophylactic immunization There is the characteristic making individuality jump out locally optimal solution trap.Therefore, TPO_SEIR method can fully realize individuality from multiple angles Between information exchange, this to expand hunting zone significant.

6, attack because of pestivirus is little Partial Feature of crowd every time, as the individual exchange spy being in different conditions During reference breath, relating only to little a part of feature and participate in computing, individual most features are not involved in computing；Although such as This, but its HHI index remains to be improved very well.Owing to processed characteristic number is greatly decreased, so when solving complex optimization Problem, particularly during high-dimensional optimization, convergence rate can be substantially improved.

7, the evolutionary process involved by TPO_SEIR method embodies the natality of the crowd being in different conditions, linearly passes Dye rate, Nonlinear Incidence Rate, vertical infection rate, horizontal infectious rate, cure rate, epidemic disease success rates, length incubation period and immunity have The isoparametric complicated situation of change of effect time duration.

8, evolutionary process has Markov characteristic.From S-S operator, S-E operator, E-E operator, E-I operator, E-R operator, I- I operator, I-R operator, R-R operator, the definition of R-S operator are known, the generation of any one new trial solution is current with this trial solution State is relevant, and be that how to develop the course of current state unrelated before this trial solution.

9, evolutionary process has " the poorest " characteristic.Just know from the definition of accretive operatos.

10, be suitable to solve higher-dimension multiple target transport path combinatorial optimization problem.When being iterated calculating, the most only process The 1/1000～1/100 of species characteristic number, is greatly reduced so that calculating time complexity, and this method is suitable to solve the many mesh of higher-dimension Mark transport path combinatorial optimization problem.

11, the feature of TPO_SEIR method of the present invention is as follows:

1) time complexity is relatively low.It is as shown in table 3 that the time complexity of TPO_SEIR method calculates process, and its time is complicated Spend and evolutionary period number G, crowd size N, total number of variable n and the time complexity of each operator and other auxiliary operation phases Close.

The time complexity computational chart of table 3 TPO_SEIR method

2) TPO_SEIR method has global convergence.Calculate from S-S operator, S-E operator, E-E operator, E-I operator, E-R Son, I-I operator, I-R operator, R-R operator, the definition of R-S operator are known, generation and this trial solution of any one new trial solution Current state is relevant, and be that how to develop the course of current state unrelated before this trial solution, show TPO_SEIR method Evolutionary process there is Markov characteristic；Knowing from the definition of accretive operatos, the evolutionary process of TPO_SEIR method has " the most not Difference " characteristic；These 2 TPO_SEIR method can have global convergence, its relevant proof and document " SIS epidemic Model-based optimization, Journal of Computational Science, volume 2014,5,32-50 Page " similar, the present invention repeats no more.

Detailed description of the invention

Below in conjunction with instantiation, the present invention is described in further detail.

(1) determine actual optimization problem to be solved, this problem is changed into the canonical form described by Optimized model formula (1) Formula.Then, the method weighted by object function, Optimized model formula (1) is changed into single goal transport path Combinatorial Optimization mould Canonical form described by type (2).

(2) method as described by table 2 determines the parameter of TPO_SEIR method.

(3) run TPO_SEIR method to solve.

(4) for following actual optimization problem, seeking n=100, overall situation when 200,400,600,800,1000,1200 is Excellent solution.

min{f₁(X),f₂(X)}

s.t.-10≤x_i≤ 10, i=1,2 ..., n-3；x_n-2+x_n-1+x_n≥1；x_n-2, x_n-1, x_n=0 or 1

$f_1\left(X\right)=\underset{i=1}{\overset{n-3}{\mathrm{\&Sigma;}}}(x_i^2-10\cos \left(2\mathrm{\&pi;}{x}_i\right)+10)+(100x_{n-2}+50x_{n-1}+x_n)$

$f_1\left(X\right)=\underset{i=1}{\overset{n-3}{\&Sigma;}}(x_i^2-10cos(2{\mathrm{\&pi;x}}_i)+10)+(100x_{n-2}+50x_{n-1}+x_n)$

A) method weighted by object function, changes into the canonical form of single-object problem by this optimization problem, The i.e. form of Optimized model formula (2):

Minf (X)=10f₁(X)+f₂(X)

s.t.-10≤x_i≤ 10, i=1,2 ..., n-3；x_n-2+x_n-1+x_n≥1；x_n-2, x_n-1, x_n=0 or 1

B) method as described by table 2 determines the parameter of algorithm, as shown in table 4.

The obtaining value method of table 4 TPO_SEIR method relevant parameter

(5) using TPO_SEIR algorithm to solve, acquired results is as shown in table 5.

Table 5 result of calculation

(6) optimal solution tried to achieve is at x_iWithin [1.113471E-8,4.025455E-8], i=1,2 ..., n-3；x_n-2 =0, x_n-1=0, x_n=1.

Claims (1)

1. a multiple target transport path combined optimization method based on plague Epidemic Model, is called for short TPO_SEIR method, its It is characterised by: the general type setting multiple target transport path Combinatorial Optimization Model to be solved is as follows:

min{O₁f₁(X),O₂f₂(X),…,O_Mf_M(X)}

$\begin{array}{cc}s.t.& \left\{\begin{array}{c}{g}_{i_a}\left(X\right)\&GreaterEqual;0,i_a\&Element;I\\ h_{i_b}\left(X\right)=0,i_b\&Element;E\\ X\&Element;H\&Subset;R^n\end{array}\right.\end{array}---\left(1\right)$

In formula:

(1)RⁿIt is that n ties up Euclidean space, the total number of variable that n is comprised by this Optimized model；

(2) X=(x₁, x₂..., x_m, x_m+1..., x_n) it is that a n ties up decision vector, wherein, front m variable x₁, x₂..., x_mIt is even Continuous Real-valued variable, is used for representing the flow shape parameter related in model；Rear n-m variable x_m+1..., x_nIt it is 0,1 integer type Variable, is used for representing which website in n website must become some nodes in an optimum transport path, i.e. for arbitrarily x_j∈{x_m+1..., x_n, if x_j=1, then it represents that jth website is selected for a node in this optimum transport path, if x_j =0, then it represents that jth website is the most selected；

(3)f₁(X), f₂(X) ..., f_M(X) it is M object function, is used for representing that M control target when transport path selects is wanted Ask；

(4)O₁, O₂..., O_MFor the priority of M object function, priority order is required to meet O₁>O₂>…>O_M, i.e. target letter Number f₁(X) first require to minimize, next to that f₂(X), it is thirdly f₃(X), the like, finally requirement minimizes It is object function f_M(X)；

(5)Represent that website is when selecting required satisfied i-th_aIndividual inequality constraints condition；I is inequality constraints bar The set of part numbering；

(6)Represent that website is when selecting required satisfied i-th_bIndividual equality constraint；E is equality constraint numbering Set；

(7){f_i(X), i=1,2 ..., M},Mathematic(al) representation do not have Restrictive condition；

(8) H is search volume, also known as solution space；

(9), when calculating, decision vector X is also referred to as trial solution；If trial solution X is unsatisfactory for constraints, then make f (X)=+ ∞；

Multiple target transport path Combinatorial Optimization Model formula (1) is converted into following single goal transport path Combinatorial Optimization Model:

$\min \{F\left(X\right)=\underset{k=1}{\overset{M}{\&Sigma;}}{O}_k{f}_k\left(X\right)\}$

$\begin{array}{cc}s.t.& \left\{\begin{array}{c}{g}_{i_a}\left(X\right)\&GreaterEqual;0,i_a\&Element;I\\ h_{i_b}\left(X\right)=0,i_b\&Element;E\\ X\&Element;H\&Subset;R^n\end{array}\right.\end{array}---\left(2\right)$

In formula, O_k=10^M-k；K is the numbering of object function；

Described TPO_SEIR method, uses and has pulse premunitive time lag plague Infectious Dynamics theory, it is assumed that one There is the crowd being made up of some individuals in individual ecosystem, everyone is characterized by several features, and a feature is equivalent to One organ of human body；There is a kind of infectious disease being referred to as the plague in this ecosystem, people is by having with viruliferous mouse Effect contact, is bitten by it, eats its meat by mistake or eat by mistake by the food of its manure contamination, can infect this disease, this infectious disease meeting Wide-scale distribution among crowd；What this infectious disease was attacked is the Partial Feature of human body；This ecosystem is uninfected by this infection Sick crowd is referred to as susceptible person；After susceptible person infects this infectious disease, will not fall ill, its internal cell entry is hidden at once Phase；Internal virus is in preclinical crowd and is referred to as resurrectionist；Pestivirus can be passed to other and effectively contact with it by resurrectionist People；Resurrectionist after incubation period can fall ill, and this type of person is for sending out patient；Send out patient can be passed to by the pestivirus that it is internal Other people effectively contacted with it；Resurrectionist and Fa patient are cured by therapeutic treatment；After resurrectionist and Fa patient are cured It is referred to as healing person；In order to prevent the harm to crowd of this infectious disease, crowd inoculates a vaccine, inoculated epidemic disease at set intervals The people of Seedling 100% will not be successfully obtained immunity；The crowd of successful vaccination self will not catch an illness within a period of time, more will not Pestivirus is broadcast to other people；The crowd not having successful vaccination is still that susceptible person；The people institute of successful vaccination The immunocompetence obtained can cease to be in force automatically and immunocompetence of dying over time；Do not carry out immunity or immunocompetence of dying People can again catch this infectious disease；Under this infectious disease effect, everyone growth conditions in this ecosystem will be Susceptible, expose, fall ill, cure random transition between these four states；The search that this random transition is mapped to optimization problem is empty Between, it is meant that each trial solution in search volume from a position transfer to another one position, it is achieved thereby that to search sky Between random search；

Crowd in above-mentioned ecosystem is divided into four classes:

S class: susceptible person's class, i.e. all entirety not contaminating patient in ecosystem, if this class people makees with band pestivirus person Effectively contact, is easy for being infected and falling ill；

E class: resurrectionist's class, has i.e. made effective crowd's contacted but also do not fall ill with band pestivirus person in ecosystem Entirety, this class crowd is potential patient；

I class: send out patient's class, i.e. caught the plague in ecosystem and still the crowd of period of disease, if this class crowd with The crowd of susceptible person's class effectively contacts, and is easy for pestivirus to be transmitted to susceptible person；

R class: healing person's class, i.e. represents the healing person after catching an illness, and these people temporarily will not fall ill, but after a predetermined time Catch an illness if effectively contacting also can reappear with band pestivirus person；

At t in period, a people can be only in some class of S class, E class, I class, R apoplexy due to endogenous wind；Because of S (t), E (t), I (t), R (t) point Not Biao Shi period t belong to S class, E class, I class, the ratio of R class crowd, therefore S (t), E (t), I (t), R (t) can regard a people as Belong to S class, E class, I class and the probability of R class；When a people belongs to S class, E class, I class or R class, mean that a people is in S shape State, E-state, I state or R state；Described S state refers to the individual state do not caught an illness, and is called for short sensitization；Described E-state is Refer to that the individual state infectd plague infectious disease but also do not fallen ill, abbreviation latency, described I state refer to that individuality infects After upper plague infectious disease and be in morbidity state, be called for short morbidity state, shape that described R state has been cured after referring to Personal State, is called for short healing state；S state, E-state, I state and R state are abbreviated as S, E, I and R respectively；

The physical strength of individual is to be determined by the feature of this people, body constitution athlete energy continued growth, and people of weak constitution Then stop growing；One people is also called body one by one；Individual physical strength represents with crowd health index HHI, HHI index Target function value corresponding to optimization problem formula (2)；Good trial solution correspondence has the individuality of higher HHI index, i.e. body constitution is strong Strong individuality, the trial solution correspondence of difference has the individuality of relatively low HHI index, the individuality i.e. having a delicate constitution；For optimization problem formula (2), the HHI index calculation method of individual i is:

In formula, X_iFor the trial solution corresponding to individual i；N is the individual sum in crowd；I is individual numbering；

Described TPO_SEIR method comprises the steps:

(S1) initialize:

A) t=0 in period is made；The all parameters related in this optimization method are initialized by table 2；

B) trial solution { X corresponding to individuality is randomly choosed at search volume H₁(0),X₂(0),…,X_N(0)}；

C) V (i)=0 is made, i=1,2 ..., N；V (i) > 0 represents individual i vaccination success, and V (i)=0 represents individual i inoculation Vaccine is unsuccessful or does not inoculates；

The obtaining value method of table 2 parameter

(S2) calculate:CalculateR_i(0)=1-S_i(0)-E_i(0)-I_i(0), i= 1,2 ..., N；

In formula, S_i(0), E_i(0), I_i(0), R_i(0) represent that period 0, individual i was in S state, E-state, I state and R state respectively Probability；Rand (A, B) represents that A and B is given constant, it is desirable to A at one uniform random number of [A, B] interval generation ≤B；Constant for stochastic generation；

(S3) the SEIR state of individual i, SEIR are calculated_i(0)=SEIR (S_i(0),E_i(0),I_i(0),R_i(0)), i=1,2 ..., N；Wherein SEIR_i(0) individual i state in which in period 0 is represented；

Function SEIR_i(0)=SEIR (S_i(0),E_i(0),I_i(0),R_i(0)), it is used for determining which kind of state individual i will be in；Letter Number SEIR (p_S, p_E, p_I, p_R) it is defined as follows:

SEIR(p_S, p_E, p_I, p_R)//p_S, p_E, p_I, p_RState S of being respectively, the probability that E, I, R occur

Calculate: w=Rand (0,1)；

If w≤p_S, then state S is returned；

If p_S<w≤p_S+p_E, then state E is returned；

If p_S+p_E<w≤p_S+p_E+p_I, then state I is returned；

If p_S+p_E+p_I<w≤p_S+p_E+p_I+p_R, then state R is returned；

(S4) making t in period from 0 to G, circulation performs step (S5)～step (S22), and wherein G is evolutionary period number；

(S5) calculate: μ^t=Rand (μ₀, μ₁), β^t=Rand (β₀, β₁), ν^t=Rand (ν₀, ν₁), q^t=Rand (q₀, q₁), p^t= Rand(p₀, p₁), r^t=Rand (r₀, r₁), b^t=Rand (b₀, b₁)；

In formula: μ^t, β^t, ν^t, q^t, p^t, r^t, b^tBeing respectively parameter μ, β, ν, q, p, r, b are in the value of t in period；μ represents natality；β Represent linear infectious rate, β > 0；ν represents Nonlinear Incidence Rate, ν >=0；Q represents vertical infection rate, q > 0；P represents that level infects Rate, p > 0；R represents cure rate, r > 0；B represents immune success rate ratio, b > 0；μ₀And μ₁Represent μ^tThe lower limit of value and the upper limit, and full Foot μ₀>=0, μ₁>=0, μ₀≤μ₁；β₀And β₁Represent β^tThe lower limit of value and the upper limit, and meet β₀>=0, β₁>=0, β₀≤β₁；v₀And v₁ Represent v^tThe lower limit of value and the upper limit, and meet ν₀>=0, ν₁>=0, ν₀≤ν₁；q₀And q₁Represent q^tThe lower limit of value and the upper limit, and Meet q₀>=0, q₁>=0, q₀≤q₁；p₀And p₁Represent p^tThe lower limit of value and the upper limit, and meet p₀>=0, p₁>=0, p₀≤p₁；r₀With r₁Represent r^tThe lower limit of value and the upper limit, and meet r₀>=0, r₁>=0, r₀≤r₁；b₀And b₁Represent b^tThe lower limit of value and the upper limit, And meet b₀>=0, b₁>=0, b₀≤b₁；

(S6) for all u ∈, { S, E, I, R} generate characterizing population group and gather PS^u、CS^u；Wherein, characterizing population group's set of t in period PS^u、CS^uGeneration method is as follows:

A) advantage population PS is produced^u: from the crowd being in state u, random choose goes out L individuality, the HHI index of these people HHI index than current individual i is high, forms advantage population PS^u, u ∈ { S, E, I, R}；L is also called to other individual applying The number of individuals of impact；

B) classification population CS is produced^u: from the crowd being in state u, random choose goes out L individuality, forms classification people's cluster Close CS^u, u ∈ { S, E, I, R}；

(S7) making i from 1 to N, circulation performs following step (S8)～step (S19)；

(S8) τ is calculated_i=INT (Rand (τ₀, τ₁)), V_i=INT (Rand (V₀, V₁))；If t can not be divided exactly by T, then by formula (5) Calculate S_i(t+1)、E_i(t+1)、I_iAnd R (t+1)_i(t+1)；Otherwise, if t can be divided exactly by T, then q is made₀=Rand (0,1), if q₀≤ Q₀, then S is calculated by formula (6)_i(t+1)、E_i(t+1)、I_iAnd R (t+1)_i, and make V (i)=t+1 (t+1)；Otherwise calculate by formula (5) S_i(t+1)、E_i(t+1)、I_iAnd R (t+1)_i(t+1)；Wherein Q₀It is successfully obtained the most general of immunocompetence for crowd's vaccination Rate；

$\begin{array}{c}\{\begin{array}{c}{S}_i(t+1)=S_i\left(t\right)+{\mathrm{\&mu;}}^t-{\mathrm{\&beta;}}^t{I}_i\left(t\right)(1+v^t{I}_i(t\left)\right)S_i\left(t\right)-{\mathrm{\&mu;}}^t{S}_i\left(t\right)-q^t{\mathrm{\&mu;}}^t{I}_i\left(t\right)\\ I_i(t+1)=I_i\left(t\right)+-{\mathrm{\&beta;}}^{-{\mathrm{\&mu;}}^t{\mathrm{\&tau;}}_i}{I}_i(t-{\mathrm{\&tau;}}_i)(1+v^t{I}_i(t-{\mathrm{\&tau;}}_i\left)S_i\right(t-{\mathrm{\&tau;}}_i\left)\right)+d^t{\mathrm{\&mu;}}^t{e}^{-{\mathrm{\&mu;}}^t{\mathrm{\&tau;}}_i}{I}_i(t-{\mathrm{\&tau;}}_i)-(r^t+{\mathrm{\&mu;}}^t)I_i\left(t\right)\\ R_i(t+1)=R_i\left(t\right)+r^t{I}_i\left(t\right)-{\mathrm{\&mu;}}^t{R}_i\left(t\right)\\ E_i(t+1)=1-S_i(t+1)-I_i(t+1)-R_i(t+1)\end{array},i=1,\\ 2,\mathrm{...},N;t\&NotEqual;kT\end{array}---\left(5\right)$

$\{\begin{array}{c}{S}_i(t+1)=S_i\left(t\right)-b^t{\mathrm{\&mu;}}^t\left(S_t\right(t)+E_i(t)+R_i(t\left)\right)-b^t{p}^t{\mathrm{\&mu;}}^t{I}_i\left(t\right)\\ E_i(t+1)=E_i\left(t\right)\\ I_i(t+1)=I_i\left(t\right)\\ R_i(t+1)=R_i\left(t\right)+b^t{\mathrm{\&mu;}}^t\left(S_i\right(t)+E_i(t)+R_i(t\left)\right)+b^t{p}^t{\mathrm{\&mu;}}^t{I}_i\left(t\right)\end{array},i=1,2,\mathrm{...},N;t=kT---\left(6\right)$

In formula (5), formula (6): S_i(t)、E_i(t)、I_i(t)、R_iT () represents that period, t individuality i belonged to S class, E class, I class, R class respectively The probability of crowd, S_i(t) >=0, E_i(t) >=0, I_i(t) >=0, R_i(t) >=0, S_i(t)+E_i(t)+I_i(t)+R_i(t)=1；τ_iRepresent Length incubation period of individual i, τ_i>0；τ₀, τ₁Represent τ_iThe lower limit of value and the upper limit, and meet τ₀>=0, τ₁>=0, τ₀≤τ₁；V_iTable Show immunity effectively time duration, the V of individual i_i>0；V₀, V₁Represent V_iThe lower limit of value and the upper limit, and meet V₀>=0, V₁≥ 0, V₀≤V₁；T represents transfer period；K is positive integer, k=1,2 ...；Real number w round off is rounded by INT (w) expression；

Formula (5) and formula (6) come from and have pulse premunitive time lag plague Epidemic Model formula (4):

$\left\{\begin{array}{cc}\left.\begin{array}{c}\frac{{\mathrm{dS}}_i\left(t\right)}{dt}=\mathrm{\&mu;}-{\mathrm{\&beta;I}}_i\left(t\right)(1+{\mathrm{vI}}_i(t\left)\right)S_i\left(t\right)-{\mathrm{\&mu;S}}_i\left(t\right)-{\mathrm{q\&mu;I}}_i\left(t\right)\\ \frac{{\mathrm{dI}}_i\left(t\right)}{dt}=-{\mathrm{\&beta;e}}^{-{\mathrm{\&mu;\&tau;}}_i}{I}_i(t-\mathrm{\&tau;})(1+{\mathrm{vI}}_i(t-\mathrm{\&tau;}\left)S_i\right(t-\mathrm{\&tau;}\left)\right)+{\mathrm{q\&mu;e}}^{-{\mathrm{\&mu;\&tau;}}_i}{I}_i(t-\mathrm{\&tau;})-(r+\mathrm{\&mu;})I_i\left(t\right)\\ \frac{{\mathrm{dR}}_i\left(t\right)}{dt}={\mathrm{rI}}_i\left(t\right)-{\mathrm{\&mu;R}}_i\left(t\right)\\ E_i\left(t\right)=1-S_i\left(t\right)-I_i\left(t\right)-R_i\left(t\right)\end{array}\right\}& t\&NotEqual;kT\\ \left.\begin{array}{c}{S}_i\left(t^{+}\right)=S_i\left(t\right)-b\mathrm{\&mu;}\left(S_i\right(t)+E_i(t)+R_i(t\left)\right)-{\mathrm{bp\&mu;I}}_i\left(t\right)\\ E_i\left(t^{+}\right)=E_i\left(t\right)\\ I_i\left(t^{+}\right)=I_i\left(t\right)\\ R_i\left(t^{+}\right)=R_i\left(t\right)+b\mathrm{\&mu;}\left(S_i\right(t)+E_i(t)+R_i(t\left)\right)+{\mathrm{bp\&mu;I}}_i\left(t\right)\end{array}\right\}& t=kT\end{array}\right.,i=1,$

$2,...,N---\left(4\right)$

In formula, τ represents length incubation period, τ > 0；

(S9) making j from 1 to n, circulation performs following step (S10)～step (S17)；

(S10) calculate: p₀=Rand (0,1), wherein p₀The infected disease of feature for individual i is attacked and affected reality is general Rate；

(S11) if p₀≤E₀, then step (S12)～(S15), wherein E are performed₀Affected because of infectious disease transmission for crowd Maximum of probability；Otherwise, (S16) is gone to step；

(S12) if SEIR_i(t)=S, then

If SEIR_i(t+1)=S, then perform S-S operator as j≤m by formula (8), obtain v_i,j(t+1)；As j > m time hold by formula (9) Row S-S operator, obtains v_i,j(t+1)；

$v_{i,j}(t+1)=\left\{\begin{array}{cc}\underset{s\&Element;{\mathrm{PS}}^S}{\&Sigma;}{\mathrm{\&alpha;}}_s{x}_{s,j}\left(t\right)& \left|{\mathrm{PS}}^S\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{PS}}^S\right|=0\end{array}\right.---\left(8\right)$

$v_{i,j}(t+1)=\left\{\begin{array}{cc}most({\mathrm{PS}}^S,j)& \left|{\mathrm{PS}}^S\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{PS}}^S\right|=0\end{array}\right.---\left(9\right)$

In formula: v_i,j(t+1) it is the state value of feature j of t+1 individuality i in period；x_s,jT () is the shape of feature j of t individuality s in period State value；α_sFor affecting constant, α_s=Rand (0.4,0.6)；most(PS^S, j) it is meant that: as set PS^SIn jth feature The number that state value is 1 more than the number that state value is 0 of jth feature time, most (PS^S, j)=1；As set PS^SIn The state value of jth feature be the number of 1 less than the number that state value is 0 of jth feature time, most (PS^S, j)=0；When Set PS^SIn the number that state value is 1 of jth feature equal to the number that state value is 0 of jth feature time, most (PS^S, value j) randomly selects among both 0 or 1；

If SEIR_i(t+1)=E, and V (i)=0, then make LP (i)=t+1, performs S-E operator as j≤m by formula (10), obtains v_i,j(t+1)；As j > m time by formula (11) perform S-E operator, obtain v_i,j(t+1)；

$v_{i,j}(t+1)=\left\{\begin{array}{cc}\underset{s\&Element;{\mathrm{CS}}^E\&cup;{\mathrm{CS}}^I}{\&Sigma;}{\mathrm{\&alpha;}}_s{x}_{s,j}\left(t\right)& \left|{\mathrm{CS}}^E\&cup;{\mathrm{CS}}^I\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^E\&cup;{\mathrm{CS}}^I\right|=0\end{array}\right.---\left(10\right)$

$v_{i,j}(t+1)=\left\{\begin{array}{cc}most({\mathrm{CS}}^E\&cup;{\mathrm{CS}}^I,j)& \left|{\mathrm{CS}}^E\&cup;{\mathrm{CS}}^I\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^E\&cup;{\mathrm{CS}}^I\right|=0\end{array}\right.---\left(11\right)$

Otherwise, v is made_i,j(t+1)=x_i,j(t), SEIR_i(t+1)=SEIR_i(t)；

(S13) if SEIR_i(t)=E, then

If SEIR_i(t+1)=E, then perform E-E operator as j≤m by formula (12), obtain v_i,j(t+1)；As j > m time by formula (13) Perform E-E operator, obtain v_i,j(t+1)；

$v_{i,j}(t+1)=\left\{\begin{array}{cc}\underset{s\&Element;{\mathrm{PS}}^E}{\&Sigma;}{\mathrm{\&alpha;}}_s{x}_{s,j}\left(t\right)& \left|{\mathrm{PS}}^E\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{PS}}^E\right|=0\end{array}\right.---\left(12\right)$

$v_{i,j}(t+1)=\left\{\begin{array}{cc}most({\mathrm{PS}}^E,j)& \left|{\mathrm{PS}}^E\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{PS}}^E\right|=0\end{array}\right.---\left(13\right)$

If SEIR_i(t+1)=I, and (t+1-LP (i)) > τ_i, then perform E-I operator as j≤m by formula (14), obtain v_i,j(t+ 1)；As j > m time by formula (15) perform E-I operator, obtain v_i,j(t+1)；

$v_{i,j}(t+1)=\left\{\begin{array}{cc}\underset{s\&Element;{\mathrm{CS}}^I}{\&Sigma;}{\mathrm{\&alpha;}}_s{x}_{s,j}\left(t\right)& \left|{\mathrm{CS}}^I\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^I\right|=0\end{array}\right.---\left(14\right)$

$v_{i,j}(t+1)=\left\{\begin{array}{cc}most({\mathrm{CS}}^I,j)& \left|{\mathrm{CS}}^I\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^I\right|=0\end{array}\right.---\left(15\right)$

If SEIR_i(t+1)=R, then perform E-R operator as j≤m by formula (16), obtain v_i,j(t+1)；As j > m time by formula (17) Perform E-R operator, obtain v_i,j(t+1)；

$v_{i,j}(t+1)=\left\{\begin{array}{cc}\underset{s\&Element;{\mathrm{CS}}^R}{\&Sigma;}{\mathrm{\&alpha;}}_s{x}_{s,j}\left(t\right)& \left|{\mathrm{CS}}^R\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^R\right|=0\end{array}\right.---\left(16\right)$

$v_{i,j}(t+1)=\left\{\begin{array}{cc}most({\mathrm{CS}}^R,j)& \left|{\mathrm{CS}}^R\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^R\right|=0\end{array}\right.---\left(17\right)$

Otherwise, v is made_i,j(t+1)=x_i,j(t), SEIR_i(t+1)=SEIR_i(t)；

(S14) if SEIR_i(t)=I, then

If SEIR_i(t+1)=I, then perform I-I operator as j≤m by formula (18), obtain v_i,j(t+1)；As j > m time by formula (19) Perform I-I operator, obtain v_i,j(t+1)；

$v_{i,j}(t+1)=\left\{\begin{array}{cc}\underset{s\&Element;{\mathrm{PS}}^I}{\&Sigma;}{\mathrm{\&alpha;}}_s{x}_{s,j}\left(t\right)& \left|{\mathrm{PS}}^I\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{PS}}^I\right|=0\end{array}\right.---\left(18\right)$

$v_{i,j}(t+1)=\left\{\begin{array}{cc}most({\mathrm{PS}}^I,j)& \left|{\mathrm{PS}}^I\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{PS}}^I\right|=0\end{array}\right.---\left(19\right)$

If SEIR_i(t+1)=R, then perform I-R operator as j≤m by formula (20), obtain v_i,j(t+1)；As j > m time by formula (21) Perform I-R operator, obtain v_i,j(t+1)；

$v_{i,j}(t+1)=\left\{\begin{array}{cc}\underset{s\&Element;{\mathrm{CS}}^R}{\&Sigma;}{\mathrm{\&alpha;}}_s{x}_{s,j}\left(t\right)& \left|{\mathrm{CS}}^R\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^R\right|=0\end{array}\right.---\left(20\right)$

$v_{i,j}(t+1)=\left\{\begin{array}{cc}most({\mathrm{CS}}^R,j)& \left|{\mathrm{CS}}^R\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^R\right|=0\end{array}\right.---\left(21\right)$

Otherwise, v is made_i,j(t+1)=x_i,j(t), SEIR_i(t+1)=SEIR_i(t)；

(S15) if SEIR_i(t)=R, then

If SEIR_i(t+1)=R, then perform R-R operator as j≤m by formula (22), obtain v_i,j(t+1)；As j > m time by formula (23) Perform R-R operator, obtain v_i,j(t+1)；

$v_{i,j}(t+1)=\left\{\begin{array}{cc}\underset{s\&Element;{\mathrm{PS}}^R}{\&Sigma;}{\mathrm{\&alpha;}}_s{x}_{s,j}\left(t\right)& \left|{\mathrm{PS}}^R\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{PS}}^R\right|=0\end{array}\right.---\left(22\right)$

$v_{i,j}(t+1)=\left\{\begin{array}{cc}most({\mathrm{PS}}^R,j)& \left|{\mathrm{PS}}^R\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{PS}}^R\right|=0\end{array}\right.---\left(23\right)$

If SEIR_i(t+1)=S, and (t+1-V (i)) > V_i, then make V (i)=0, and perform R-S operator as j≤m by formula (24), Obtain v_i,j(t+1)；As j > m time by formula (25) perform R-S operator, obtain v_i,j(t+1)；

$v_{i,j}(t+1)=\left\{\begin{array}{cc}\underset{s\&Element;{\mathrm{CS}}^S}{\&Sigma;}{\mathrm{\&alpha;}}_s{x}_{s,j}\left(t\right)& \left|{\mathrm{CS}}^S\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^S\right|=0\end{array}\right.---\left(24\right)$

$v_{i,j}(t+1)=\{\begin{array}{cc}most({\mathrm{CS}}^S,j)& \left|{\mathrm{CS}}^S\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^S\right|=0\end{array}---\left(25\right)$

Otherwise, v is made_i,j(t+1)=x_i,j(t), SEIR_i(t+1)=SEIR_i(t)；

(S16) if p > E₀, then v is made_i,j(t+1)=x_i,j(t), SEIR_i(t+1)=SEIR_i(t)；

(S17) make j=j+1, if j≤n, then go to step (S10), otherwise go to step (S18)；

(S18) perform accretive operatos by formula (26), obtain X_i(t+1)；

In formula:

X_i(t)=(x_i,1(t),x_i,2(t),…,x_i,n(t))；

V_i(t+1)=(v_i,1(t+1),v_i,2(t+1),…,v_i,n(t+1))；

In formula, HHI (V_i(t+1))、HHI(X_i(t)) calculate by formula (7)；

(S19) make i=i+1, if i≤N, then go to step (S8), otherwise go to step (S20)；

(S20) if newly obtained globally optimal solution X^*t+1And the error between the globally optimal solution that the last time obtains meets minimum Require ε, then go to step (S23), otherwise go to step (S21)；

(S21) newly obtained globally optimal solution X is preserved^*t+1；

(S22) make t=t+1, if t≤G, then go to step (S5), otherwise go to step (S23)；

(S23) terminate.