CN106126897A - Multiple target transport path optimization method based on HIV Infectious Dynamics - Google Patents

Abstract

Disclosed by the invention is a kind of multiple target transport path optimization method based on HIV Infectious Dynamics, it is assumed that an ecosystem is made up of several crowds；Inhibition of HIV is propagated in crowd, and people, by effectively contacting with the people of band inhibition of HIV, can infect this infectious disease；The crowd being uninfected by inhibition of HIV is referred to as susceptible person；After susceptible person infects inhibition of HIV, will not fall ill at once, its internal cell entry incubation period；Inhibition of HIV is in preclinical crowd and is referred to as inhibition of HIV carrier, and this type of people is divided into again two classes, and a class is not fall ill and sexual communication activity, and this kind of people becomes HIV sufferers through certain time with sequela, does not finally control because of acquired immune deficiency syndrome (AIDS) and dead；Another kind of is end morbidity always and losing property intercourse ability, the final natural death of this kind of people again；Under inhibition of HIV effect, everyone growth conditions generation change at random, utilize this change at random and HIV Epidemic Model can quickly try to achieve the overall optimal solution of multiple target transport path combinatorial optimization problem.

Description

Multiple target transport path optimization method based on HIV Infectious Dynamics

Technical field

The present invention relates to intelligent optimization algorithm, be specifically related to a kind of multiple target transport road based on HIV Infectious Dynamics Footpath optimization method.

Background technology

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

min{O₁f₁(X),O₂f₂(X),…,O_Mf_M(X)}

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

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 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},Mathematic(al) representation There is no 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 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 Optimized model formula (1)_i(X)、Mathematical table Reaching formula does not has 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.Xu Hecan, Zhu rear people at document, and " Pareto genetic algorithm for solving is many Target vehicle routing problem with time windows, logistlcs technology, 2015, volume 34,8 monthly magazines, the 166-170 page " in think logistics Dispensing must simultaneously meet several conflicting target, for this multi-objective optimization question, introduces Pareto optimal solution concept, Establish the mathematical model NSGAII describing this problem, and propose to solve the Pareto genetic algorithm of VRPTW；Experimental verification table Bright, Pareto genetic algorithm can effectively solve multiple target band time window logistics distribution.Meng Yongchang, Yang Saini, Shi Peijun exist Document " road network emergency evacuation multiple-objection optimization based on improved adaptive GA-IAGA, Wuhan University Journal information science version, 2014 Year, volume 39, the 2nd phase, the 201-205 page " in, actual demand based on road network emergency evacuation problem, propose with path flow For decision variable, maximum with discharge value, evacuation route is the shortest and reliability is up to the Model for Multi-Objective Optimization of target, comprehensively Consider ageing, economy and the safety of emergency evacuation, and design adaptive niche technology Pareto genetic algorithm to model Solve.Tan Xiaoyong, Lin Ying are in document " Post disaster relief path planning based on improvement GACA algorithm, computer engineering With design, 2014, volume 35, the 7th phase, the 2526-2530 page " in, as a example by earthquake, ask for calamity rear vehicle path optimization The feature of topic and demand, have studied rescue transit time, road risk and road and pay the multiobject appraisal procedures such as cost, with The Model for Multi-Objective Optimization of shake rear vehicle routing problem is established based on this；Owing to common ant group algorithm is solving vehicle Locally optimal solution easily it is absorbed in, to this end, devise the genetic ant colony system hybrid algorithm of a kind of improvement during routing problem；Example Simulation result 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.Wu Zhaofu, Dong Wenyong " solve dynamic vehicle at document The evolutionary ant algorithm of routing problem, Wuhan University Journal (Edition), the 5th phase of volume 2007,53, the 571-575 page " in, On the basis of Evo-Ant algorithm, propose multiobject algorithm, i.e. utilize Evo-Ant algorithm to produce new solution, and utilize One extra memory space deposits Pareto candidate solution, updates Pareto candidate solution by newly generated solution, eliminates and is propped up The solution joined, circulates successively, thus the Pareto obtaining approximation solves.Xiao Le, Wu Xianglin, Zhen Tong are in document " self adaptation chaos ant colony The grain emergency route optimizing research of algorithm, 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 " haulage time is minimum " conduct Target, sets up corresponding Optimized model；For avoiding being absorbed in too early local optimum, self adaptation chaos ant colony optimization algorithm is proposed.? Dimension is deposited, 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.

(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, in order to effectively carry out vehicle deploying, reduce logistics cost, improve the competitiveness of enterprise, propose with thing Stream cost of transportation minimizes and turns to target with customer satisfaction maximum, by weight coefficient converter technique by Model for Multi-Objective Optimization It is converted into single object optimization model, 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, the 1st phase, the 25-31 page " is given A kind of Mobile routing model, for meeting the network environment of Mobile routing, devises the function making the qos parameter moment change real Existing；Then particle cluster algorithm is applied to the optimizing of realizing route in this model.Qiu Changwu, Wang Longmei, Huang Yanwen are at document " base In the all-around mobile tow-armed robot continuous path task multiple objective programming of long-pending formula decision-making, robot, 2013, volume 35, 2nd phase, the 178-185 page " in, analyze the multiple target motion of constrained OMDAR (all-around mobile tow-armed robot) system The mathematical modeling of planning tasks and method for solving；Under long-pending formula decision-making multi-objective optimization algorithm framework, by continuous for OMDAR system rail Mark motion planning demand and related constraint are modeled as the single optimization object function of product form, use Gauss to cruise particle group optimizing Algorithm (GR-PSO), reliably and effectively achieves 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.Yin Limin, Li Xiang, Meng Tao, Yin Hang at document " based on changing Enter the transmission network planning of artificial fish-swarm algorithm, electric automatization, 2016, volume 38, the 2nd phase, the 48-51 page " in, Have studied extensive transmission network planning problem, establish consideration investment operating cost, cost of losses and overload expense Multiple-objection optimization mathematical model；For tradition fish-swarm algorithm initialize complicated, convergence rate is slow and relatively low the asking of convergence precision Topic, look for food at it, knock into the back during introduce Step-varied back propagation strategy with improve algorithm optimizing performance, and by improve artificial Fish-swarm algorithm is used for solving transmission network planning model.

(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.Cao Xianbin, Wang Bennian, Wang Xufa are in document " a kind of virus evolution type genetic algorithm, small-sized microcomputer system System, calendar year 2001, volume 21, the 1st phase, the 59-62 page " the VEGA algorithm that proposes is based on genetic algorithm, from biological virus Mechanism extracts some features of applicable improved adaptive GA-IAGA, individuality is divided into viremic individuals and host individual, two kinds of individualities Each own different behavior, has the most collaborative a kind of contact between the two, thus is greatly improved further through Infection Action Individual multiformity." multiple-objection optimization immunity based on Pareto is calculated at document for Zhai Yusheng, Cheng Zhihong, Chen Guangzhu, Li Liu Method, computer engineering and application, 2006, the 24th phase, the 27-29 page " in establish a kind of novel many based on Pareto Objective optimization immune algorithm (MOIA)；In algorithm, by the feasible solution correspondence antibody of optimization problem, the object function pair of optimization problem Answer antigen, Pareto optimal solution to be stored in memory cell to concentrate, and utilize the neighbouring exclusion algorithm being different from cluster that it is entered Row is constantly updated, and then obtains the Pareto optimal solution being evenly distributed.Li Lingjing, Chen Yun virtue at document, " knowledge based territory is many Objective optimization immune algorithm, computer engineering, 2010, volume 36, the 20th phase, the 161-163 page " in, for traditional immunization There is Premature Convergence and the problem of multiformity deficiency in algorithm, proposes the multi-objective Optimization Immune Algorithm in a kind of knowledge based territory； Select elite solution by initializing knowledge domain, utilize the border of this elite disaggregation adaptive updates knowledge domain, thus maintain algorithm Convergence and multifarious balance.Tang Jun, Zhao Xiaojuan " network base station plan optimization based on immune algorithm, computer engineering, 2010, volume 36, the 16th phase, the 169-170 page " in, for the deficiency of legacy network base station planning method, a kind of base is proposed Optimization method in immune algorithm；Using Multipurpose Optimal Method that base station planning problem carries out mathematical modeling, immune optimization is calculated Method uses concentration regulation select probability mechanism, neighbouring exclusion algorithm, recycling cross and the mutation operation of improvement, can guarantee that solution is many Sample and Pareto optimal solution set are evenly distributed on leading surface.Li Chunhua, Mao Zongyuan at document " based on Artificial Immune Algorithm Multi objective function optimization, computer measurement and control, 2005, volume 13, the 3rd phase, the 278-280 page " in, it is proposed that one Plant novel Artificial Immune Algorithm to be used for solving multi objective function optimization problem；Based on the good characteristic that natural immune system is intrinsic Algorithm is designed and has been analyzed.Long Wen, yellow Hamming, Li little Yong, Qin Bangyu are in document " multiple target City Integrated Emergency Response System addressing The immune algorithm of problem, Guangxi physics, 2008, volume 29, the 2nd phase, the 26-29 page " in, it is considered to during emergency location Cost and crash time factor, provide the mathematical model of a kind of multiple target city emergency Facility Location Problem；In view of conventional method Solve the difficulty of this model, propose a kind of multi-target immune algorithm as model solution method.Tao Yuan, Wu Gengfeng, Hu Min are at literary composition Offer " multi-target evolution immune algorithm based on Pareto, computer utility research, 2009, volume 26, the 5th phase, 1687- Page 1690 " in, propose a kind of new based on Pareto multi-target evolution immune algorithm (PMEIA)；Algorithm is at every generation glade Body is chosen optimum non-dominant antibody be saved in memory cell document；It is simultaneously introduced the Parzen window estimation technique and calculates memory cell Entropy, according to entropy, memory cell document is dynamically updated, makes algorithm towards preferable Pareto Optimal Boundary search.Leaf Cyanines document " TSP Study on Problems based on immunity-ant group algorithm, computer engineering, 2010, volume 36, the 24th phase, 156-157 page " in, accelerate convergence and the contradiction of precocious stagnation behavior for ant group algorithm, use for reference immune self regulation Mechanism keeps the multifarious ability of population, proposes immunity-ant group algorithm；This algorithm is according to the microcosmic multiformity solved, macroscopic view The concentration index of multiformity and arc dynamically adjusts Path selection probability and quantity of information more New Policy.

In sum, prior art can only solve the non-combined optimization problem in dimension the most much higher targeted delivery path, to dimension The highest extensive the solving of multiple target transport path combinatorial optimization problem of number has difficulties.

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 HIV The multiple target transport path combined optimization method of Infection Dynamics Model, is called for short TPO_HIV method；In TPO_HIV method, Use and the diverse mentality of designing of existing swarm intelligence algorithm, it is proposed that HIV Infection Dynamics Model is converted into and can ask Solve the conventional method of multiple target transport path combinatorial optimization problem；The operator constructed can fully reflect that HIV catches an illness kinetics The interaction relationship of model, thus embody the basic thought that HIV Infectious Dynamics is theoretical；TPO_HIV method method has There is global convergence.

In order to solve the problem that above-mentioned prior art exists, the present invention adopts the following technical scheme that

A kind of multiple target transport path optimization method based on pulse prophylactic immunization HIV model, is called for short TPO_HIV method, It is characterized in that: 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)}

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

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 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},Mathematic(al) representation There is no 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 mould Type:

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

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

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

Described TPO_HIV method, uses HIV Infectious Dynamics theoretical, it is assumed that to exist by some at certain ecosystem The crowd of individual's composition；One people is also known as body one by one；Each individuality is characterized by several features, and a feature is equivalent to One organ of human body；Propagating in inhibition of HIV crowd in this ecosystem, people is by having with the people of band inhibition of HIV Effect contact, can infect this infectious disease；What inhibition of HIV was attacked is the Partial Feature of human body；This ecosystem is uninfected by HIV The crowd of virus is referred to as susceptible person；After susceptible person infects inhibition of HIV, will not fall ill, its internal cell entry is hidden at once Phase；Internal inhibition of HIV is in preclinical crowd and is referred to as inhibition of HIV carrier；Inhibition of HIV carrier is divided into again two classes, and one Class is not fall ill and sexual communication activity, and this kind of people becomes HIV sufferers through certain time with sequela, finally because of AIDS Disease is not controlled and dead；Another kind of is end morbidity always and losing property intercourse ability, the final natural death of this kind of people again.One people because of Acquired immune deficiency syndrome (AIDS) is not controlled and dead or natural death, the ecosystem new person that can be born immediately to make up the people of this death so that Obtain the total number of persons in this ecosystem and keep constant.Under inhibition of HIV effect, everyone growth conditions will be at S state, I Random transition between these five states of state, A condition, Y state and Z condition；Described S state, represents sensitization, does not i.e. catch People's state in which of inhibition of HIV；Described I state, expression has been caught inhibition of HIV but has not been fallen ill and sexual communication activity now People's state in which, the people being in this state finally can develop into HIV sufferers；Described A condition, represents and has caught HIV Virus and people's state in which of having fallen ill；Described Y state, expression has been caught inhibition of HIV but has been ultimately failed to develop into AIDS People's state in which of patient；Described Z condition, represents and has caught inhibition of HIV but do not fall ill and asexual communication activity always People's state in which.This random transition is mapped to the search volume of optimization problem, it is meant that each trial solution is in search volume From a position transfer to another one position, it is achieved thereby that the random search to search volume.

The physical strength of individual is to be determined by the feature of this people, body constitution athlete energy continued growth, and has a delicate constitution People then stop growing.TPO_HIV method has that search capability is strong and the feature of global convergence, for multiple target transport path group Close solving of optimization problem and provide a solution.

There is pulse premunitive time lag HIV Infection Dynamics Model

Phase early 1980s, it has been found that a kind of epidemic diseases acquired immune deficiency syndrome (AIDS) (AIDS) threatening human life.According to Look into this disease be start from the fifties in non-to Caribbean, the latter stage seventies developed country start find.Owing to it is shied The infection velocity of people and the seriousness jeopardizing people's life have shaken the mankind, are therefore subject to this epiphytotics research in the whole world Pay attention to.The virulence factor definitely confirming this disease in 1984 is the third mankind's retrovirus retrovirus, i.e. mankind T-parent lymph sexually transmitted disease (STD) Poison III (HTLV-III), also referred to as human immune deficiency virus (HIV).Inhibition of HIV can hide 9～15 in human cell Year, say, that a people infected by inhibition of HIV, he will have the infective stage of 9-15 at premorbid, and this is also acquired immune deficiency syndrome (AIDS) One of major reason that infection velocity is fast.Owing to acquired immune deficiency syndrome (AIDS) infection velocity is fast, utilize mathematical model to describe acquired immune deficiency syndrome (AIDS), to reach Predicting future, the research finding control program etc. is subject to the people's attention in recent years.

Crowd in one ecosystem is divided into six classes:

S class: susceptible person, i.e. all entirety not contaminating patient in ecosystem, if this class people and inhibition of HIV carrier Make effectively contact, be easy for being infected and falling ill.

I class: inhibition of HIV carrier, but finally can develop into HIV sufferers, but do not fall ill and sexual communication activity now The entirety of crowd.

Y class: inhibition of HIV carrier, but ultimately fail to develop into the entirety of the crowd of HIV sufferers.

A class: HIV sufferers, has caught inhibition of HIV and the crowd that fallen ill.

Z class: inhibition of HIV carrier, but do not fall ill and the entirety of crowd of asexual communication activity always.

Assume: the constant increased numbers of (1) population is C；(2) being located at t in period, the total population of ecosystem is N (t)；(3) Total population is divided into two parts, and one is susceptible person S (t), and it two is inhibition of HIV carrier W (t), (4) inhibition of HIV carrier Be divided into again two classes, a class be inhibition of HIV carrier do not fall ill again and sexual communication activity be designated as I (t), these groups of people pass through Certain time becomes HIV sufferers A (t) with sequela；Another kind of is inhibition of HIV carrier Y (t), but this class people is the most not Morbidity and again losing property intercourse ability (as year waits for a long time), be designated as Z (t).Therefore, acquired immune deficiency syndrome (AIDS) infectious process can be expressed as follows:

$\left\{\begin{array}{c}\frac{dS\left(t\right)}{dt}=C-\mathrm{\λ}\mathrm{\σ}\[N\left(t\right)\]S\left(t\right)\frac{W\left(t\right)}{N\left(t\right)}-\mathrm{\μ}S\left(t\right)\\ \frac{dI\left(t\right)}{dt}=\mathrm{\λ}p\mathrm{\σ}\[N\left(t\right)\]S\left(t\right)\frac{W\left(t\right)}{N\left(t\right)}-({\mathrm{\α}}_I+\mathrm{\μ})I\left(t\right)\\ \frac{dY\left(t\right)}{dt}=\mathrm{\λ}(1-p)\mathrm{\σ}\[N\left(t\right)\]S\left(t\right)\frac{W\left(t\right)}{N\left(t\right)}-({\mathrm{\α}}_Y+\mathrm{\μ})Y\left(t\right)\\ \frac{dA\left(t\right)}{dt}={\mathrm{\α}}_{I}I\left(t\right)-(d+\mathrm{\μ})A\left(t\right)\\ \frac{dZ\left(t\right)}{dt}={\mathrm{\α}}_{Y}Y\left(t\right)-\mathrm{\μ}Z\left(t\right)\\ W\left(t\right)=I\left(t\right)+Y\left(t\right),N\left(t\right)=W\left(t\right)+S\left(t\right)\end{array}\right.---\left(3\right)$

In formula: t represents period；μ represents natural mortality rate, μ > 0；D represents acquired immune deficiency syndrome (AIDS) mortality rate, d > 0；σ [N (t)] represents Average spouse's number, σ [N (t)] > 0 in unit interval；P represents that susceptible person becomes acquired immune deficiency syndrome (AIDS) and sends out the probability of patient, p > 0；λ represents every A pair spouse infects the probability of acquired immune deficiency syndrome (AIDS), λ > 0；α_IAnd α_YIt is respectively by I class to A class with by the conversion coefficient of Y class to Z class, or Person is by I state to A condition with by the conversion coefficient of Y state to Z condition.

In order to simplify calculating, within the examination time limit, it is believed that total number of people N (t) in ecosystem remains constant. To formula (3) each both sides with divided by N (t), and make W (t)=I (t)+Y (t), i.e.

$\left\{\begin{array}{c}\frac{d\frac{S\left(t\right)}{N\left(t\right)}}{dt}=\frac{C}{N\left(t\right)}-\mathrm{\λ}\mathrm{\σ}\[N\left(t\right)\]\frac{S\left(t\right)}{N\left(t\right)}\frac{I\left(t\right)+Y\left(t\right)}{N\left(t\right)}-\mathrm{\μ}\frac{S\left(t\right)}{N\left(t\right)}\\ \frac{d\frac{I\left(t\right)}{N\left(t\right)}}{dt}=\mathrm{\λ}p\mathrm{\σ}\[N\left(t\right)\]\frac{S\left(t\right)}{N\left(t\right)}\frac{I\left(t\right)+Y\left(t\right)}{N\left(t\right)}-\left({\mathrm{\α}}_I+\mathrm{\μ}\right)\frac{I\left(t\right)}{N\left(t\right)}\\ \frac{d\frac{Y\left(t\right)}{N\left(t\right)}}{dt}=\mathrm{\λ}\left(1-p\right)\mathrm{\σ}\[N\left(t\right)\]\frac{S\left(t\right)}{N\left(t\right)}\frac{I\left(t\right)+Y\left(t\right)}{N\left(t\right)}-\left({\mathrm{\α}}_Y+\mathrm{\μ}\right)\frac{Y\left(t\right)}{N\left(t\right)}\\ \frac{d\frac{A\left(t\right)}{N\left(t\right)}}{dt}={\mathrm{\α}}_I\frac{I\left(t\right)}{N\left(t\right)}-\left(d+\mathrm{\μ}\right)\frac{A\left(t\right)}{N\left(t\right)}\\ \frac{d\frac{Z\left(t\right)}{N\left(t\right)}}{dt}={\mathrm{\α}}_Y\frac{Y\left(t\right)}{N\left(t\right)}-\mathrm{\μ}\frac{Z\left(t\right)}{N\left(t\right)}\\ \frac{I\left(t\right)+Y\left(t\right)}{N\left(t\right)}+\frac{S\left(t\right)}{N\left(t\right)}=1\end{array}\right.---\left(4\right)$

RatioRepresent that S class, I class, A class, Y class, Z class crowd are total people respectively Ratio shared in Kou.If S (t), I (t), A (t), Y (t), the implication of Z (t) are represented the number of S class, I class respectively by original Number, the number of A class, the number of Y class, the number of Z class change S class, I class, A class, Y class, Z class crowd respectively in total population Shared ratio, then formula (4) is the most rewritable is:

$\left\{\begin{array}{c}\frac{dS\left(t\right)}{dt}=C-\mathrm{\λ}\mathrm{\σ}S\left(t\right)\left(I\right(t)+Y(t\left)\right)-\mathrm{\μ}S\left(t\right)\\ \frac{dI\left(t\right)}{dt}=\mathrm{\λ}p\mathrm{\σ}S\left(t\right)\left(I\right(t)+Y(t\left)\right)-({\mathrm{\α}}_I+\mathrm{\μ})I\left(t\right)\\ \frac{dY\left(t\right)}{dt}=\mathrm{\λ}(1-p)\mathrm{\σ}S\left(t\right)\left(I\right(t)+Y(t\left)\right)-({\mathrm{\α}}_Y+\mathrm{\μ})Y\left(t\right)\\ \frac{dA\left(t\right)}{dt}={\mathrm{\α}}_{I}I\left(t\right)-(d+\mathrm{\μ})A\left(t\right)\\ \frac{dZ\left(t\right)}{dt}={\mathrm{\α}}_{Y}Y\left(t\right)-\mathrm{\μ}Z\left(t\right)\\ S\left(t\right)+I\left(t\right)+Y\left(t\right)=1\end{array}\right.---\left(5\right)$

In formula (5), the implication of C becomes the constant growth ratio of population；σ [N (t)] becomes the constant unrelated with N (t), no Harm makes σ=σ [N (t)].

At t in period, a people can be only in some class of S class, I class, A class, Y class, Z apoplexy due to endogenous wind；Because of S (t), I (t), A T (), Y (t), Z (t) represent that t in period belongs to the ratio of the crowd of S class, I class, A class, Y class, Z class respectively, therefore S (t), I (t), A T (), Y (t), Z (t) can regard a people as and belong to S class, I class, A class, Y class, the probability of Z class；When a people belong to S class, I class, When A class, Y class or Z class, mean that a people is in S state, I state, A condition, Y state or Z condition；S state, I state, A shape State, Y state and Z condition are abbreviated as S, I, A, Y and Z respectively.

Therefore, it can be applied to formula (5) anyone of crowd, i.e.

$\left\{\begin{array}{c}\frac{{\mathrm{dS}}_i\left(t\right)}{dt}=C-{\mathrm{\λ\σS}}_i\left(t\right)\left(I_i\left(t\right)+Y_i\left(t\right)\right)-{\mathrm{\μS}}_i\left(t\right)\\ \frac{{\mathrm{dI}}_i\left(t\right)}{dt}=\mathrm{\λ}p\mathrm{\σ}S\left(t\right)\left(I_i\left(t\right)+Y_i\left(t\right)\right)-({\mathrm{\α}}_I+\mathrm{\μ})I_i\left(t\right)\\ \frac{{\mathrm{dY}}_i\left(t\right)}{dt}=\mathrm{\λ}(1-p){\mathrm{\σS}}_i\left(t\right)\left(I_i\left(t\right)+Y_i\left(t\right)\right)-({\mathrm{\α}}_Y+\mathrm{\μ})Y_i\left(t\right)\\ \frac{{\mathrm{dA}}_i\left(t\right)}{dt}={\mathrm{\α}}_I{I}_i\left(t\right)-(d+\mathrm{\μ})A_i\left(t\right)\\ \frac{{\mathrm{dZ}}_i\left(t\right)}{dt}={\mathrm{\α}}_Y{Y}_i\left(t\right)-{\mathrm{\μZ}}_i\left(t\right)\\ S_i\left(t\right)+I_i\left(t\right)+Y_i\left(t\right)=1\end{array}\right.,i=1,2,...,N---\left(6\right)$

In formula, i is individual numbering；S_i(t)、I_i(t)、A_i(t)、Y_i(t)、Z_iT () represents that period, t individuality i was in S respectively State, I state, A condition, Y state and Z-shaped probability of state, and S_i(t) >=0, I_i(t) >=0, A_i(t) >=0, Y_i(t) >=0, Z_i(t) ≥0；

Formula (6) is in S state, I state, A condition, Y state and Z condition for everyone calculated in t crowd in period Probability.

Clock phase t parameter μ, d, σ, λ, p, C, α_IAnd α_YValue be respectively μ^t, d^t, σ^t, λ^t, p^t, C^t,For side Just calculate, change formula (6) into discrete recursive form, i.e.

$\left\{\begin{array}{c}{S}_i\left(t+1\right)=S_i\left(t\right)+C^t-{\mathrm{\λ}}^t{\mathrm{\σ}}^t{S}_i\left(t\right)\left(I_i\left(t\right)+Y_i\left(t\right)\right)-{\mathrm{\μ}}^t{S}_i\left(t\right)\\ I_i\left(t+1\right)=I_i\left(t\right)+{\mathrm{\λ}}^t{p}^t{\mathrm{\σ}}^{t}S\left(t\right)\left(I_i\left(t\right)+Y_i\left(t\right)\right)-\left({\mathrm{\α}}_I^t+{\mathrm{\μ}}^t\right)I_i\left(t\right)\\ Y_i\left(t+1\right)=Y_i\left(t\right)+{\mathrm{\λ}}^t\left(1-p^t\right){\mathrm{\σ}}^t{S}_i\left(t\right)\left(I_i\left(t\right)+Y_i\left(t\right)\right)-\left({\mathrm{\α}}_Y^t+{\mathrm{\μ}}^t\right)Y_i\left(t\right)\\ A_i\left(t+1\right)=A_i\left(t\right)+{\mathrm{\α}}_I^t{I}_i\left(t\right)-\left(d^t+{\mathrm{\μ}}^t\right)A_i\left(t\right)\\ Z_i\left(t+1\right)=Z_i\left(t\right)+{\mathrm{\α}}_Y^t{Y}_i\left(t\right)-{\mathrm{\μ}}^t{Z}_i\left(t\right)\\ S_i\left(t\right)+I_i\left(t\right)+Y_i\left(t\right)=1\end{array}\right.,i=1,2,...,N---\left(7\right)$

In formula (5), formula (6), parameter μ^t, d^t, σ^t, λ^t, p^t, C^t,Obtaining value method be μ^t=Rand (μ₀, μ₁), μ₀ And μ₁Represent μ^tThe lower limit of value and the upper limit, and meet μ₀>=0, μ₁>=0, μ₀≤μ₁；d^t=Rand (d₀, d₁), d₀And d₁Represent d^t The lower limit of value and the upper limit, and meet d₀>=0, d₁>=0, d₀≤d₁；σ^t=Rand (σ₀, σ₁), σ₀And σ₁Represent σ^tThe lower limit of value And the upper limit, and meet σ₀>=0, σ₁>=0, σ₀≤σ₁；λ^t=Rand (λ₀, λ₁), λ₀And λ₁Represent λ^tThe lower limit of value and the upper limit, and Meet λ₀>=0, λ₁>=0, λ₀≤λ₁；p^t=Rand (q₀, q₁), p₀And p₁Represent p^tThe lower limit of value and the upper limit, and meet p₀>=0, p₁>=0, p₀≤p₁；C^t=Rand (C₀, C₁), C₀And C₁Represent C^tThe lower limit of value and the upper limit, and meet C₀>=0, C₁>=0, C₀≤ C₁；a₀And a₁RepresentThe lower limit of value and the upper limit, and meet a₀>=0, a₁>=0, a₀≤a₁；b₀And b₁RepresentThe lower limit of value and the upper limit, and meet b₀>=0, b₁>=0, b₀≤b₁；Rand (A, B) represent that A and B is given constant, it is desirable to A≤B at one uniform random number of [A, B] interval generation；INT (w) represents Real number w round off is rounded.

Implementation method Scenario Design

Assume to there is, at certain 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 known as body one by one；Each individuality is characterized by n feature, and feature is equivalent to of human body Organ, i.e. for individual i, its characteristic feature is (x_i,1, x_i,2..., x_i,n), i=1,2 ..., N；Inhibition of HIV is in this ecosystem Propagating in crowd in system, people, by effectively contacting with the people of band inhibition of HIV, can infect this disease；Inhibition of HIV is attacked It it is the Partial Feature of human body；The crowd being uninfected by inhibition of HIV in this ecosystem is referred to as susceptible person；Susceptible person infects HIV After virus, will not fall ill at once, its internal cell entry incubation period；Internal inhibition of HIV is in preclinical crowd and is referred to as HIV Virus carrier；Inhibition of HIV carrier is divided into again two classes, and a class is not fall ill and sexual communication activity, and this kind of people is through one Fix time and become HIV sufferers with sequela, finally do not control because of acquired immune deficiency syndrome (AIDS) and dead；Another kind of is that fall ill and lose again in end always Going property intercourse ability, the final natural death of this kind of people；One people does not controls because of acquired immune deficiency syndrome (AIDS) and dead or natural death, ecosystem meeting One new person of birth makes up the people of this death immediately, so that the total number of persons in this ecosystem keeps constant.Sick at HIV Under toxic action, everyone growth conditions will between these five states of S state, I state, A condition, Y state and Z condition with Machine is changed.This random transition is mapped to the search volume of optimization problem, it is meant that each trial solution in search volume from one Position transfer is 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 determine, body constitution athlete can continued growth, people of weak constitution then stops 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 multiple target transport path combinatorial optimization problem formula (2).Good trial solution correspondence has higher HHI index The individuality that individuality, i.e. body constitution are strong, the trial solution correspondence of difference has the individuality of relatively low HHI index, the individuality i.e. having a delicate constitution.Right In 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, d^t, σ^t, λ^t, p^t, C^t,Use HIV Infectious Dynamics Model calculates the S of individual i respectively_i(t)、I_i(t)、A_i(t)、Y_i(t)、Z_i(t).Individual i period t be in S state, I state, A Which state in state, Y state and five states of Z condition, by S_i(t)、I_i(t)、A_i(t)、Y_i(t) and Z_iT () is formed Probability distribution determines, i.e. S_i(t)、I_i(t)、A_i(t)、Y_i(t) and Z_iT which value in () is the biggest, its corresponding state is selected In probability the biggest.Table 1 gives inhibition of HIV and propagates situation in crowd.

The conversion of S state, I state, A condition, Y state and Z condition that each individuality is possible has 5 × 5=25 kind, but legal State Transferring only has 11 kinds, as shown in table 1.Except 11 kinds in table 1 are in addition to legal State Transferring, and other kinds of state turns Change the most illegal.11 kinds of legal State Transferring can describe with 11 operators, i.e. S-S, S-I, S-Y, I-I, I-A, A-A, A-S, Y-Y、Y-Z、Z-Z、Z-S。

Due to when phase in office, the μ of crowd in ecosystem^t, d^t, σ^t, λ^t, p^t, C^t,It is all random, therefore The growth conditions of individual i will between five states of S, I, Y, A, Z random transition.This random transition is mapped to optimization problem Search volume, it is meant that each trial solution in search volume from a position transfer to another one position, it is achieved thereby that right The random search of search volume.

The legal state conversion of table 1HIV Infection Dynamics Model

Paying special attention to, state D in table 1 represents dead state；Remain often in order to ensure the total number of persons in ecosystem Number, might as well suppose people's death, and be just born a new person immediately；Then, state transfer A → D, Z → D can regard A → S, Z as →S；In table 1, D (S) is meant that and regards state D as state S.

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, and these are individual The HHI index HHI index than current individual i high, form advantage population PS^u, u ∈ { S, I, Y, A, Z}；L be also called to The number of individuals that other 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, I, Y, A, Z}；

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, makes p_a=Rand (0,1), has

If j≤m, then

$v_{i,j}\left(t+1\right)=\left\{\begin{array}{cc}\left.\begin{array}{cc}\underset{k\&Element;{\mathrm{PS}}^S}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)& p_a<0.5\\ \underset{k\&Element;{\mathrm{PS}}^S}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)-\underset{k\&Element;{\mathrm{PS}}^S}{\mathrm{\&Sigma;}}{\mathrm{\&beta;}}_k{x}_{k,j}\left(t\right)& p_a\&GreaterEqual;0.5\end{array}\right\}& \left|{\mathrm{PS}}^S\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{PS}}^S\right|=0\end{array}\right.---\left(9\right)$

If j > m, then

$v_{i,j}(t+1)=\left\{\begin{array}{cc}most\left({\mathrm{PS}}^S,j\right)& \left|{\mathrm{PS}}^S\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{PS}}^S\right|=0\end{array}\right.---\left(10\right)$

In formula: v_i,j(t+1) it is the state value of feature j of t+1 individuality i in period；x_k,jT () is feature j of t individuality k in period State value；α_kAnd β_kFor affecting constant, α_k=Rand (0.5,0.9), β_k=Rand (0.4,0.8)；most(PS^S, implication j) It is: as set PS^SIn the number that state value is 1 of jth feature more than the number that state value is 0 of jth feature time, most(PS^S, j)=1；As set PS^SIn the number that state value is 1 of jth feature be 0 less than the state value of jth feature Number time, most (PS^S, j)=0；As set PS^SIn the number that state value is 1 of jth feature equal to jth feature When state value is the number of 0, most (PS^S, value j) randomly selects among both 0 or 1.

(2) S-I operator.What this operator described is the individuality being in sensitization, by effectively contacting with I class crowd The situation of inhibition of HIV on after stain.Because this inhibition of HIV can be propagated interpersonal, therefore allow feature j of L I class people and state thereof Value weighted sum is transmitted to the character pair j of the susceptible individual i not caught an illness so that it is catch inhibition of HIV.I.e. for being in state S Individual i, makes p_a=Rand (0,1), has

If j≤m, then

$v_{i,j}(t+1)=\left\{\begin{array}{cc}\left.\begin{array}{cc}\underset{k\&Element;{\mathrm{CS}}^I}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)& p_a<0.5\\ \underset{k\&Element;{\mathrm{CS}}^I}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)-\underset{k\&Element;{\mathrm{CS}}^I}{\mathrm{\&Sigma;}}{\mathrm{\&beta;}}_k{x}_{k,j}\left(t\right)& p_a\&GreaterEqual;0.5\end{array}\right\}& \left|{\mathrm{CS}}^I\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^I\right|=0\end{array}\right.---\left(11\right)$

If j > m, then

$v_{i,j}(t+1)=\left\{\begin{array}{cc}most\left({\mathrm{CS}}^I,j\right)& \left|{\mathrm{CS}}^I\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^I\right|=0\end{array}\right.---\left(12\right)$

(3) S-Y operator.What this operator described is the individuality being in sensitization, by effectively contacting with Y class crowd The situation of inhibition of HIV on after stain.Because this inhibition of HIV can be propagated interpersonal, therefore allow feature j of L Y class people and state thereof Value weighted sum is transmitted to the character pair j of the susceptible individual i not caught an illness so that it is catch inhibition of HIV.I.e. for being in state S Individual i, makes p_a=Rand (0,1), has

If j≤m, then

$v_{i,j}\left(t+1\right)=\left\{\begin{array}{cc}\left.\begin{array}{cc}\underset{k\&Element;{\mathrm{CS}}^Y}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)& p_a<0.5\\ \underset{k\&Element;{\mathrm{CS}}^Y}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)-\underset{k\&Element;{\mathrm{CS}}^Y}{\mathrm{\&Sigma;}}{\mathrm{\&beta;}}_k{x}_{k,j}\left(t\right)& p_a\&GreaterEqual;0.5\end{array}\right\}& \left|{\mathrm{CS}}^Y\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^Y\right|=0\end{array}\right.---\left(13\right)$

If j > m, then

$v_{i,j}(t+1)=\left\{\begin{array}{cc}most\left({\mathrm{CS}}^Y,j\right)& \left|{\mathrm{CS}}^Y\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^Y\right|=0\end{array}\right.---\left(14\right)$

(4) I-I operator.What this operator described is that the individuality being in I state is internal at it because not arriving inhibition of HIV incubation period Do not have started the situation of outbreak.L is allowed to be in I state but feature j of its HHI index people higher than current individual i and shape thereof State value weighted sum passes to the character pair j of the current individual i being in I state so that it is body constitution strengthens.I.e. for being in state I Individual i, make p_a=Rand (0,1), has

If j≤m, then

$v_{i,j}\left(t+1\right)=\left\{\begin{array}{cc}\left.\begin{array}{cc}\underset{k\&Element;{\mathrm{PS}}^I}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)& p_a<0.5\\ \underset{k\&Element;{\mathrm{PS}}^I}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)-\underset{k\&Element;{\mathrm{PS}}^I}{\mathrm{\&Sigma;}}{\mathrm{\&beta;}}_k{x}_{k,j}\left(t\right)& p_a\&GreaterEqual;0.5\end{array}\right\}& \left|{\mathrm{PS}}^I\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{PS}}^I\right|=0\end{array}\right.---\left(15\right)$

If j > m, then

$v_{i,j}(t+1)=\left\{\begin{array}{cc}most\left({\mathrm{PS}}^I,j\right)& \left|{\mathrm{PS}}^I\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{PS}}^I\right|=0\end{array}\right.---\left(16\right)$

(5) I-A operator.What this operator described is that the individuality being in I state is internal at it because having arrived inhibition of HIV incubation period Starting the situation of outbreak, hereafter, this individuality becomes HIV sufferers.Feature j of L A class people and state value weighted sum thereof is allowed to pass Give the character pair j of the current individual i being in I state so that it is become HIV sufferers, i.e. for being in the current of state I Individual i, makes p_a=Rand (0,1), has

If j≤m, then

$v_{i,j}\left(t+1\right)=\left\{\begin{array}{cc}\left.\begin{array}{cc}\underset{k\&Element;{\mathrm{CS}}^A}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)& p_a<0.5\\ \underset{k\&Element;{\mathrm{CS}}^A}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)-\underset{k\&Element;{\mathrm{CS}}^A}{\mathrm{\&Sigma;}}{\mathrm{\&beta;}}_k{x}_{k,j}\left(t\right)& p_a\&GreaterEqual;0.5\end{array}\right\}& \left|{\mathrm{CS}}^A\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^A\right|=0\end{array}\right.---\left(17\right)$

If j > m, then

$v_{i,j}(t+1)=\left\{\begin{array}{cc}most\left({\mathrm{CS}}^A,j\right)& \left|{\mathrm{CS}}^A\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^A\right|=0\end{array}\right.---\left(18\right)$

(6) A-A operator.What this operator described is the individuality being in A condition, at present still in the situation of A condition.Allow L Individual allowing is in A condition but its HHI index feature j of people higher than current individual i and state value weighted sum thereof are passed to and be in A shape The character pair j of the current individual i of state so that it is body constitution strengthens.I.e. for being in the individual i of state A, make p_a=Rand (0,1), Have

If j≤m, then

$v_{i,j}\left(t+1\right)=\left\{\begin{array}{cc}\left.\begin{array}{cc}\underset{k\&Element;{\mathrm{PS}}^A}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)& p_a<0.5\\ \underset{k\&Element;{\mathrm{PS}}^A}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)-\underset{k\&Element;{\mathrm{PS}}^A}{\mathrm{\&Sigma;}}{\mathrm{\&beta;}}_k{x}_{k,j}\left(t\right)& p_a\&GreaterEqual;0.5\end{array}\right\}& \left|{\mathrm{PS}}^A\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{PS}}^A\right|=0\end{array}\right.---\left(19\right)$

If j > m, then

$v_{i,j}(t+1)=\left\{\begin{array}{cc}most\left({\mathrm{PS}}^A,j\right)& \left|{\mathrm{PS}}^A\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{PS}}^A\right|=0\end{array}\right.---\left(20\right)$

(7) A-S operator.What this operator described is the individuality being in A condition, dead because acquired immune deficiency syndrome (AIDS) outbreak fails to cure Dying, but after this individual death, have the most again the situation that a newborn individual occurs in this ecosystem, this is equivalent to this individuality and obtains Must live again.L individual feature j being in S state and state value weighted sum thereof is allowed to pass to the individuality being currently in A condition The character pair j of i so that it is obtain and live again.I.e. for being in the current individual i of state A, make p_a=Rand (0,1), has

If j≤m, then

$v_{i,j}\left(t+1\right)=\left\{\begin{array}{cc}\left.\begin{array}{cc}\underset{k\&Element;{\mathrm{CS}}^S}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)& p_a<0.5\\ \underset{k\&Element;{\mathrm{CS}}^S}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)-\underset{k\&Element;{\mathrm{CS}}^S}{\mathrm{\&Sigma;}}{\mathrm{\&beta;}}_k{x}_{k,j}\left(t\right)& p_a\&GreaterEqual;0.5\end{array}\right\}& \left|{\mathrm{CS}}^S\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^S\right|=0\end{array}\right.---\left(21\right)$

If j > m, then

$v_{i,j}(t+1)=\left\{\begin{array}{cc}most\left({\mathrm{CS}}^S,j\right)& \left|{\mathrm{CS}}^S\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^S\right|=0\end{array}\right.---\left(22\right)$

(8) Y-Y operator.What this operator described is the individuality being in Y state, at present still in the situation of Y state.Allow L Individual it is in Y state but its HHI index feature j of people higher than current individual i and state value thereof are passed to after being weighted processing It is in the character pair j of the current individual i of Y state so that it is body constitution strengthens.I.e. for being in the current individual i of Y state, order p_a=Rand (0,1), has

If j≤m, then

$v_{i,j}\left(t+1\right)=\left\{\begin{array}{cc}\left.\begin{array}{cc}\underset{k\&Element;{\mathrm{PS}}^Y}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)& p_a<0.5\\ \underset{k\&Element;{\mathrm{PS}}^Y}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)-\underset{k\&Element;{\mathrm{PS}}^Y}{\mathrm{\&Sigma;}}{\mathrm{\&beta;}}_k{x}_{k,j}\left(t\right)& p_a\&GreaterEqual;0.5\end{array}\right\}& \left|{\mathrm{PS}}^Y\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{PS}}^Y\right|=0\end{array}\right.---\left(23\right)$

If j > m, then

$v_{i,j}(t+1)=\left\{\begin{array}{cc}most\left({\mathrm{PS}}^Y,j\right)& \left|{\mathrm{PS}}^Y\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{PS}}^Y\right|=0\end{array}\right.---\left(24\right)$

(9) Y-Z operator.What this operator described is the individuality being in Y state, and becoming because of the property lost intercourse ability cannot Propagate the situation of the Z class people of inhibition of HIV.L is allowed to pass after being in individual feature j of Z condition and the weighted process of state value thereof Give the character pair j of the individual i being currently in Y state so that it is transfer Z condition to.I.e. it is in the current of Y state for being in Individual i, makes p_a=Rand (0,1), has

If j≤m, then

$v_{i,j}\left(t+1\right)=\left\{\begin{array}{cc}\left.\begin{array}{cc}\underset{k\&Element;{\mathrm{CS}}^Z}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)& p_a<0.5\\ \underset{k\&Element;{\mathrm{CS}}^Z}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)-\underset{k\&Element;{\mathrm{CS}}^Z}{\mathrm{\&Sigma;}}{\mathrm{\&beta;}}_k{x}_{k,j}\left(t\right)& p_a\&GreaterEqual;0.5\end{array}\right\}& \left|{\mathrm{CS}}^Z\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^Z\right|=0\end{array}\right.---\left(25\right)$

If j > m, then

$v_{i,j}(t+1)=\left\{\begin{array}{cc}most\left({\mathrm{CS}}^Z,j\right)& \left|{\mathrm{CS}}^Z\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^Z\right|=0\end{array}\right.---\left(26\right)$

(10) Z-Z operator.What this operator described is the individuality being in Z condition, at present still in the situation of Z condition.Allow L Individual it is in Z condition but its HHI index feature j of people higher than current individual i and state value thereof are passed to after being weighted processing It is in the character pair j of the current individual i of Z condition so that it is body constitution strengthens.I.e. for being in the current individual i of Z condition, order p_a=Rand (0,1), has

If j≤m, then

$v_{i,j}\left(t+1\right)=\left\{\begin{array}{cc}\left.\begin{array}{cc}\underset{k\&Element;{\mathrm{PS}}^Z}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)& p_a<0.5\\ \underset{k\&Element;{\mathrm{PS}}^Z}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)-\underset{k\&Element;{\mathrm{PS}}^Z}{\mathrm{\&Sigma;}}{\mathrm{\&beta;}}_k{x}_{k,j}\left(t\right)& p_a\&GreaterEqual;0.5\end{array}\right\}& \left|{\mathrm{PS}}^Z\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{PS}}^Z\right|=0\end{array}\right.---\left(27\right)$

If j > m, then

$v_{i,j}(t+1)=\left\{\begin{array}{cc}most\left({\mathrm{PS}}^Z,j\right)& \left|{\mathrm{PS}}^Z\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{PS}}^Z\right|=0\end{array}\right.---\left(28\right)$

(11) Z-S operator.What this operator described is the individual natural death being in Z condition, but after this individual death, should Having the most again the situation that a newborn individual occurs in ecosystem, this is equivalent to the acquisition of this individuality and lives again.L is allowed to be in S The character pair j of the individual i being currently in Z condition is passed to after individual feature j of state and the weighted process of state value thereof, Make it obtain to live again.I.e. for being in the current individual i of state Z, make p_a=Rand (0,1), has

If j≤m, then

$v_{i,j}\left(t+1\right)=\left\{\begin{array}{cc}\left.\begin{array}{cc}\underset{k\&Element;{\mathrm{CS}}^S}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)& p_a<0.5\\ \underset{k\&Element;{\mathrm{CS}}^S}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)-\underset{k\&Element;{\mathrm{CS}}^S}{\mathrm{\&Sigma;}}{\mathrm{\&beta;}}_k{x}_{k,j}\left(t\right)& p_a\&GreaterEqual;0.5\end{array}\right\}& \left|{\mathrm{CS}}^S\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^S\right|=0\end{array}\right.---\left(29\right)$

If j > m, then

$v_{i,j}(t+1)=\left\{\begin{array}{cc}most\left({\mathrm{CS}}^S,j\right)& \left|{\mathrm{CS}}^S\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^S\right|=0\end{array}\right.---\left(30\right)$

(12) 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))；

The structure of TPO_HIV method

Described TPO_HIV method includes including following steps:

(S1) initialize: a) make t=0；The all parameters related in this optimization method are initialized by table 2；B) in search Space H randomly chooses the trial solution { X corresponding to individuality₁(0),X₂(0),…,X_N(0)}。

The obtaining value method of table 2 parameter

(S2) calculate:Calculate A_i(0)=Rand (0,1), Z_i(0)=Rand (0,1), i=1, 2 ..., N.

In formula, S_i(0), I_i(0), A_i(0), Y_i(0), Z_i(0) represent that period 0, individual i was in S state, I state, A shape respectively State, Y state and Z-shaped probability of state；Constant for stochastic generation.

(S3) the HIV state of individual i, HIV are calculated_i(0)=HIV (S_i(0),I_i(0),Y_i(0)), i=1,2 ..., N；Its In, HIV_i(0) individual i state in which is represented；Function HIV_i(0)=HIV (S_i(0),I_i(0),Y_i(0)), it is used for determining individual i Which kind of state will be in.

(S4) making t in period from 0 to G, circulation performs step (S5)～step (S23), and wherein G is evolutionary period number.

(S5) calculate: μ^t=Rand (μ₀, μ₁), d^t=Rand (d₀, d₁), p^t=Rand (p₀, p₁), λ^t=Rand (λ₀, λ₁), σ^t=Rand (σ₀, σ₁), C^t=Rand (C₀, C₁),

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

(S7) making i from 1 to N, circulation performs following step (S8)～step (S20)；

(S8) S is calculated by formula (7)_i(t+1)、I_i(t+1)、Y_i(t+1)、A_iAnd Z (t+1)_i(t+1)；

(S9) making j from 1 to n, circulation performs following step (S10)～step (S18)；

(S10) calculate: p₀=Rand (0,1), wherein p₀Feature for individual i is attacked and affected reality by inhibition of HIV Border probability；

(S11) if p₀≤E₀, then step (S12)～(S16), wherein E are performed₀For crowd because inhibition of HIV propagates by shadow The maximum of probability rung；Otherwise, (S17) is gone to step；

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

If HIV_i(t+1)=S, then perform S-S operator as j≤m by formula (9), obtain v_i,j(t+1)；As j > m time by formula (10) perform S-S operator, obtain v_i,j(t+1)；

If HIV_i(t+1)=I, then perform S-I operator as j≤m by formula (11), obtain v_i,j(t+1)；As j > m time by formula (12) perform S-I operator, obtain v_i,j(t+1)；

If HIV_i(t+1)=Y, then perform S-Y operator as j≤m by formula (13), obtain v_i,j(t+1)；As j > m time by formula (14) perform S-Y operator, obtain v_i,j(t+1)；

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

(S13) if HIV_i(t)=I, then

If HIV_i(t+1)=I, then perform I-I operator as j≤m by formula (15), obtain v_i,j(t+1)；As j > m time by formula (16) perform I-I operator, obtain v_i,j(t+1)；

If HIV_i(t+1)=A, then perform I-A operator as j≤m by formula (17), obtain v_i,j(t+1)；As j > m time by formula (18) perform I-A operator, obtain v_i,j(t+1)；

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

(S14) if HIV_i(t)=Y, then

If HIV_i(t+1)=Y, then perform Y-Y operator as j≤m by formula (19), obtain v_i,j(t+1)；As j > m time by formula (20) perform Y-Y operator, obtain v_i,j(t+1)；

If HIV_i(t+1)=Z, then perform Y-Z operator as j≤m by formula (21), obtain v_i,j(t+1)；As j > m time by formula (22) perform Y-Z operator, obtain v_i,j(t+1)；

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

(S15) if HIV_i(t)=A, then

If HIV_i(t+1)=A, then perform A-A operator as j≤m by formula (23), obtain v_i,j(t+1)；As j > m time by formula (24) perform A-A operator, obtain v_i,j(t+1)；

If HIV_i(t+1)=S, then perform A-S operator as j≤m by formula (25), obtain v_i,j(t+1)；As j > m time by formula (26) perform A-S operator, obtain v_i,j(t+1)；

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

(S16) if HIV_i(t)=Z, then

If HIV_i(t+1)=Z, then perform Z-Z operator as j≤m by formula (27), obtain v_i,j(t+1)；As j > m time by formula (28) perform Z-Z operator, obtain v_i,j(t+1)；

If HIV_i(t+1)=S, then perform Z-S operator as j≤m by formula (29), obtain v_i,j(t+1)；As j > m time by formula (30) perform Z-S operator, obtain v_i,j(t+1)；

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

(S17) if p > E₀, then v is made_i,j(t+1)=x_i,j(t), HIV_i(t+1)=HIV_i(t)；

(S18) make j=j+1, if j≤n, then go to step (S10), otherwise go to step (S19)；

(S19) perform accretive operatos by formula (31), obtain X_i(t+1)；

(S20) make i=i+1, if i≤N, then go to step (S8), otherwise go to step (S21)；

(S21) 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 (S24), otherwise goes to step (S22)；

(S22) newly obtained globally optimal solution X is preserved^*t+1；

(S23) make t=t+1, if t≤G, then go to step (S5), otherwise go to step (S24)；

(S24) terminate.

Function HIV (p_S, p_I, p_Y) it is defined as follows:

HIV(p_S, p_I, p_Y)//p_S, p_I, p_YState S of being respectively, the probability that I, Y occur

Calculate: w=Rand (0,1)；

If w≤p_S, then state S is returned；

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

If p_S+p_I<w≤p_S+p_I+p_Y, then state Y is returned；

Beneficial effect

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

1, disclosed by the invention is the multiple target transport path optimization method of a kind of HIV Infection Dynamics Model, i.e. TPO_HIV method.In the method, use HIV Infectious Dynamics theoretical, it is assumed that to exist by several at certain ecosystem The crowd of people's composition；One people is also known as body one by one；Each individuality is characterized by several features, and a feature is equivalent to people One organ of body；Propagating in inhibition of HIV crowd in this ecosystem, people is carried out effectively by the people with band inhibition of HIV Contact, can infect this infectious disease；What inhibition of HIV was attacked is the Partial Feature of human body；This ecosystem is uninfected by HIV sick The crowd of poison is referred to as susceptible person；After susceptible person infects inhibition of HIV, will not fall ill at once, its internal cell entry incubation period； Internal inhibition of HIV is in preclinical crowd and is referred to as inhibition of HIV carrier；Inhibition of HIV carrier is divided into again two classes, and a class is Not falling ill and sexual communication activity, this kind of people becomes HIV sufferers through certain time with sequela, finally because of acquired immune deficiency syndrome (AIDS) not Control and dead；Another kind of is end morbidity always and losing property intercourse ability, the final natural death of this kind of people again.One people is because of AIDS Disease is not controlled and dead or natural death, and the ecosystem new person that can be born immediately is to make up the people of this death, so that should Total number of persons in ecosystem keeps constant.Under inhibition of HIV effect, everyone growth conditions will S state, I state, Random transition between these five states of A condition, Y state and Z condition.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.The physical strength of individual is to be determined by the feature of this people, body constitution athlete energy continued growth, and body constitution Weakling then stops growing.This optimization method has that search capability is strong and the feature of global convergence, for multiple target transport road Solving of footpath combinatorial optimization problem provides a solution.

2, the search capability of TPO_HIV method is the strongest.TPO_HIV method include S-S operator, S-I operator, S-Y operator, I-I operator, I-A operator, A-A operator, A-S operator, Y-Y operator, Y-Z operator, Z-Z operator, Z-S operator, these operators are significantly Add its search capability.

3, model parameter value is simple.Random method is used to determine the HIV Infection Dynamics Model in TPO_HIV method In parameter and S-S operator, S-I operator, S-Y operator, I-I operator, I-A operator, A-A operator, A-S operator, Y-Y operator, Y-Z Relevant parameter in operator, Z-Z operator, Z-S operator, had both been greatly reduced parameter input number, and had made again model more can express reality Border situation.

4, the S-S operator in TPO_HIV method, S-I operator, S-Y operator, I-I operator, I-A operator, A-A operator, A-S Operator, Y-Y operator, Y-Z operator, Z-Z operator, Z-S operator are by utilizing HIV Infection Dynamics Model to construct , completely without relevant to actual optimization problem to be solved, therefore TPO_HIV method has universality.

5, in TPO_HIV method, S-S operator, I-I operator, Y-Y operator, A-A operator, Z-Z operator can make HHI index High individuality transmits strong characteristic information to the individuality that HHI index is low so that the direction that the individual physical ability that HHI index is low is become better is sent out Exhibition；S-I operator, S-Y operator, I-A operator, A-S operator, Y-Z operator, Z-S operator can make to be in different conditions individuality it Between exchange information, the individual weighted feature information obtaining other individualities can be made again, thus reduce individuality and be absorbed in local optimum Probability.Therefore, TPO_HIV method can fully realize the information exchange between individuality from multiple angles, and this is to expanding hunting zone Significant.

6, attack because of virus is little Partial Feature of crowd every time, when the individual exchange features being in different conditions is believed During breath, relating only to little a part of feature and participate in computing, individual most features are not involved in computing；While it is true, but Its HHI index remains to be improved very well.Owing to processed characteristic number is greatly decreased, so when solving complicated optimum problem, Particularly during high-dimensional optimization, convergence rate can be substantially improved.

7, the evolutionary process involved by TPO_HIV method embodies the natural mortality rate of the crowd being in different conditions, Chinese mugwort Grow sick mortality rate, average spouse's number in the unit interval, susceptible person become that acquired immune deficiency syndrome (AIDS) sends out the probability of patient, a pair spouse infects AIDS Sick probability, inhibition of HIV carrier to acquired immune deficiency syndrome (AIDS) send out patient and become without inhibition of HIV contagion probability person between conversion coefficient Isoparametric complicated situation of change.

8, evolutionary process has Markov characteristic.From S-S operator, S-I operator, S-Y operator, I-I operator, I-A operator, A- A operator, A-S operator, Y-Y operator, Y-Z operator, Z-Z operator, the definition of Z-S operator are known, the generation of any one new trial solution is only Relevant with the current state of this trial solution, 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_HIV 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_HIV 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 3TPO_HIV method

2) TPO_HIV method has global convergence.Calculate from from S-S operator, S-I operator, S-Y operator, I-I operator, I-A Son, A-A operator, A-S operator, Y-Y operator, Y-Z operator, Z-Z operator, the definition of Z-S operator are known, the life of any one new trial solution Become only the most relevant with the current state of this trial solution, and be that how to develop the course of current state unrelated before this trial solution, Show that the evolutionary process of TPO_HIV method has Markov characteristic；Know from the definition of accretive operatos, the evolution of TPO_HIV method Process has " the poorest " characteristic；These 2 TPO_HIV method can have global convergence, its relevant proof and document " SIS Epidemic model-based optimization, Journal of Computational Science, the 2014, the 5th Volume, the 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 pattern (2).

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

(3) run TPO_HIV 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

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

$f_2\left(X\right)=\underset{i=1}{\overset{n-3}{\&Sigma;}}(x_i^2-20cos(2{\mathrm{\&pi;x}}_i)+20)+(150x_{n-2}+80x_{n-1}+x_n)$

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 4TPO_HIV method relevant parameter

(5) using TPO_HIV 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 [1.124817E-8,3.643792E-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 optimization method based on HIV Infectious Dynamics, is called for short TPO_HIV method, its feature It is: the general type setting multiple target transport path Combinatorial Optimization Model to be solved is as follows:

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

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 that equality constraint is compiled Number 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:

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

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

Described TPO_HIV method is assumed to there is, at certain ecosystem, the crowd being made up of some individuals；One people is also known as one Individual；Each individuality is characterized by several features, and a feature is equivalent to an organ of human body；Inhibition of HIV is raw at this Propagating in the intrasystem crowd of state, people, by effectively contacting with the people of band inhibition of HIV, can infect this infectious disease；HIV is sick What poison was attacked is the Partial Feature of human body；The crowd being uninfected by inhibition of HIV in this ecosystem is referred to as susceptible person；Susceptible person feels After catching inhibition of HIV, will not fall ill at once, its internal cell entry incubation period；Internal inhibition of HIV is in preclinical crowd It is referred to as inhibition of HIV carrier；Inhibition of HIV carrier is divided into again two classes, and a class is not fall ill and sexual communication activity, this kind of people's warp Spending certain time becomes HIV sufferers with sequela, does not finally control because of acquired immune deficiency syndrome (AIDS) and dead；Another kind of be always end morbidity and Losing property intercourse ability again, the final natural death of this kind of people；One people does not controls because of acquired immune deficiency syndrome (AIDS) and dead or natural death, ecosystem The system new person that can be born immediately is to make up the people of this death, so that the total number of persons in this ecosystem keeps constant；? Under inhibition of HIV effect, everyone growth conditions will be in these five states of S state, I state, A condition, Y state and Z condition Between random transition；Described S state, represents sensitization, does not i.e. catch people's state in which of inhibition of HIV；Described I state, Expression has been caught inhibition of HIV but has not been fallen ill and people's state in which of sexual communication activity now, and the people being in this state can be HIV sufferers can be developed into eventually；Described A condition, represents the people's state in which having caught inhibition of HIV and fallen ill；Described Y state, expression has been caught inhibition of HIV but has been ultimately failed to develop into people's state in which of HIV sufferers；Described Z condition, table Show and catch inhibition of HIV but do not fall ill and people's state in which of asexual communication activity always；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；S state, I state, A condition, Y state and Z condition be abbreviated as respectively S, I, A, Y and Z；

Individual physical strength represents with crowd health index HHI, and HHI index corresponds to multiple target transport path Combinatorial Optimization The target function value of problem formula (2)；Good trial solution correspondence has an individuality of higher HHI index, and the individuality that i.e. body constitution is strong is poor Trial solution correspondence there is the individuality of relatively low HHI index, the individuality i.e. having a delicate constitution；For optimization problem formula (2), individual i's HHI index calculation method 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_HIV method comprises the steps:

(S1) initialize: a) make t=0 in period；The all parameters related in this optimization method are initialized by table 2；B) in search Space H randomly chooses the trial solution { X corresponding to individuality₁(0),X₂(0),…,X_N(0)}；

The obtaining value method of table 2 parameter

(S2) calculate:Calculate A_i(0)=Rand (0,1), Z_i(0)=Rand (0,1), i=1, 2 ..., N；

In formula, S_i(0), I_i(0), A_i(0), Y_i(0), Z_i(0) represent that period 0, individual i was in S state, I state, A condition, Y respectively State and Z-shaped probability of state；Rand (A, B) represents that A and B is given at one uniform random number of [A, B] interval generation Constant, it is desirable to A≤B；Constant for stochastic generation；

(S3) the HIV state of individual i: HIV is calculated_i(0)=HIV (S_i(0),I_i(0),Y_i(0)), i=1,2 ..., N；Wherein HIV_i (0) individual i state in which is represented；

Function HIV_i(0)=HIV (S_i(0),I_i(0),Y_i(0)) it is used for determining which kind of state individual i will be in；

Function HIV (p_S, p_I, p_Y) it is defined as follows:

HIV(p_S, p_I, p_Y)//p_S, p_I, p_YState S of being respectively, the probability that I, Y occur

Calculate: w=Rand (0,1)；

If w≤p_S, then state S is returned；

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

If p_S+p_I<w≤p_S+p_I+p_Y, then state Y is returned；

(S4) making t in period from 0 to G, circulation performs step (S5)～step (S23), and wherein G is evolutionary period number；

(S5) calculate: μ^t=Rand (μ₀, μ₁), d^t=Rand (d₀, d₁), p^t=Rand (p₀, p₁), λ^t=Rand (λ₀, λ₁), σ^t= Rand(σ₀, σ₁), C^t=Rand (C₀, C₁),In formula, μ^t, d^t, σ^t, λ^t, p^t, C^t,It is parameter μ respectively, d, σ, λ, p, C, α_IAnd α_YValue at t in period；μ represents natural mortality rate, μ > 0；d Represent acquired immune deficiency syndrome (AIDS) mortality rate, d > 0；Average spouse's number, σ > 0 in the σ representation unit time；P represents that susceptible person becomes acquired immune deficiency syndrome (AIDS) morbidity The probability of person, p > 0；λ represents that every a pair spouse infects the probability of acquired immune deficiency syndrome (AIDS), λ > 0；α_IAnd α_YIt is respectively by state I to state A With the conversion coefficient by state Y to state Z；μ₀And μ₁Represent μ^tThe lower limit of value and the upper limit, and meet μ₀>=0, μ₁>=0, μ₀≤ μ₁；d₀And d₁Represent d^tThe lower limit of value and the upper limit, and meet d₀>=0, d₁>=0, d₀≤d₁；σ₀And σ₁Represent σ^tThe lower limit of value and The upper limit, and meet σ₀>=0, σ₁>=0, σ₀≤σ₁；；λ₀And λ₁Represent λ^tThe lower limit of value and the upper limit, and meet λ₀>=0, λ₁>=0, λ₀ ≤λ₁；p₀And p₁Represent p^tThe lower limit of value and the upper limit, and meet p₀>=0, p₁>=0, p₀≤p₁；C₀And C₁Represent C^tThe lower limit of value And the upper limit, and meet C₀>=0, C₁>=0, C₀≤C₁；a₀And a₁RepresentThe lower limit of value and the upper limit, and meet a₀>=0, a₁>=0, a₀≤a₁；b₀And b₁RepresentThe lower limit of value and the upper limit, and meet b₀>=0, b₁>=0, b₀≤b₁；

(S6) for all u ∈, { S, I, Y, A, Z} generate characterizing population group and gather PS^u、CS^u；Wherein, period t, characterizing population group gather 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, and the HHI of these individualities refers to The number HHI index than current individual i is high, forms advantage population PS^u, u ∈ { S, I, Y, A, Z}；L is also called to other individual The number of individuals exerted one's influence；

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, I, Y, A, Z}；

(S7) making i from 1 to N, circulation performs following step (S8)～step (S20)；

(S8) S is calculated by formula (7)_i(t+1)、I_i(t+1)、Y_i(t+1)、A_iAnd Z (t+1)_i(t+1)；

$\left\{\begin{array}{c}{S}_i\left(t+1\right)=S_i\left(t\right)+C^t-{\mathrm{\&lambda;}}^t{\mathrm{\&sigma;}}^t{S}_i\left(t\right)\left(I_i\left(t\right)+Y_i\left(t\right)\right)-{\mathrm{\&mu;}}^t{S}_i\left(t\right)\\ I_i\left(t+1\right)=I_i\left(t\right)+{\mathrm{\&lambda;}}^t{p}^t{\mathrm{\&sigma;}}^{t}S\left(t\right)\left(I_i\left(t\right)+Y_i\left(t\right)\right)-\left({\mathrm{\&alpha;}}_I^t+{\mathrm{\&mu;}}^t\right)I_i\left(t\right)\\ Y_i\left(t+1\right)=Y_i\left(t\right)+{\mathrm{\&lambda;}}^t\left(1-p^t\right){\mathrm{\&sigma;}}^t{S}_i\left(t\right)\left(I_i\left(t\right)+Y_i\left(t\right)\right)-\left({\mathrm{\&alpha;}}_Y^t+{\mathrm{\&mu;}}^t\right)Y_i\left(t\right)\\ A_i\left(t+1\right)=A_i\left(t\right)+{\mathrm{\&alpha;}}_I^t{I}_i\left(t\right)-\left(d^t+{\mathrm{\&mu;}}^t\right)A_i\left(t\right)\\ Z_i\left(t+1\right)=Z_i\left(t\right)+{\mathrm{\&alpha;}}_Y^t{Y}_i\left(t\right)-{\mathrm{\&mu;}}^t{Z}_i\left(t\right)\\ S_i\left(t\right)+I_i\left(t\right)+Y_i\left(t\right)=1\end{array}\right.,i=1,2,...,N---\left(7\right)$

In formula, S_i(t), I_i(t), A_i(t), Y_i(t), Z_iT () represents that period, t individuality i was in S state, I state, A condition, Y respectively State and Z-shaped probability of state, and S_i(t) >=0, I_i(t) >=0, A_i(t) >=0, Y_i(t) >=0, Z_i(t)≥0；

Formula (7) derives from having pulse premunitive time lag HIV Infection Dynamics Model formula (6):

$\left\{\begin{array}{c}\frac{{\mathrm{dS}}_i\left(t\right)}{dt}=C-{\mathrm{\&lambda;\&sigma;S}}_i\left(t\right)\left(I_i\left(t\right)+Y_i\left(t\right)\right)-{\mathrm{\&mu;S}}_i\left(t\right)\\ \frac{{\mathrm{dI}}_i\left(t\right)}{dt}=\mathrm{\&lambda;}p\mathrm{\&sigma;}S\left(t\right)\left(I_i\left(t\right)+Y_i\left(t\right)\right)-({\mathrm{\&alpha;}}_I+\mathrm{\&mu;})I_i\left(t\right)\\ \frac{{\mathrm{dY}}_i\left(t\right)}{dt}=\mathrm{\&lambda;}(1-p){\mathrm{\&sigma;S}}_i\left(t\right)\left(I_i\left(t\right)+Y_i\left(t\right)\right)-({\mathrm{\&alpha;}}_Y+\mathrm{\&mu;})Y_i\left(t\right)\\ \frac{{\mathrm{dA}}_i\left(t\right)}{dt}={\mathrm{\&alpha;}}_I{I}_i\left(t\right)-(d+\mathrm{\&mu;})A_i\left(t\right)\\ \frac{{\mathrm{dZ}}_i\left(t\right)}{dt}={\mathrm{\&alpha;}}_Y{Y}_i\left(t\right)-{\mathrm{\&mu;Z}}_i\left(t\right)\\ S_i\left(t\right)+I_i\left(t\right)+Y_i\left(t\right)=1\end{array}\right.,i=1,2,...,N---\left(6\right)$

(S9) making j from 1 to n, circulation performs following step (S10)～step (S18)；

(S10) calculate: p₀=Rand (0,1), wherein p₀Feature for individual i is attacked by inhibition of HIV and affected reality is general Rate；

(S11) if p₀≤E₀, then step (S12)～(S16), wherein E are performed₀Affected because inhibition of HIV propagates for crowd Maximum of probability；Otherwise, (S17) is gone to step；

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

If HIV_i(t+1)=S, then perform S-S operator as j≤m by formula (9), obtain v_i,j(t+1)；As j > m time hold by formula (10) Row S-S operator, obtains v_i,j(t+1)；

$v_{i,j}\left(t+1\right)=\left\{\begin{array}{cc}\left.\begin{array}{cc}\underset{k\&Element;{\mathrm{PS}}^S}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)& p_a<0.5\\ \underset{k\&Element;{\mathrm{PS}}^S}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)-\underset{k\&Element;{\mathrm{PS}}^S}{\mathrm{\&Sigma;}}{\mathrm{\&beta;}}_k{x}_{k,j}\left(t\right)& p_a\&GreaterEqual;0.5\end{array}\right\}& \left|{\mathrm{PS}}^S\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{PS}}^S\right|=0\end{array}\right.---\left(9\right)$

$v_{i,j}(t+1)=\left\{\begin{array}{cc}most\left({\mathrm{PS}}^S,j\right)& \left|{\mathrm{PS}}^S\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{PS}}^S\right|=0\end{array}\right.---\left(10\right)$

In formula: v_i,j(t+1) it is the state value of feature j of t+1 individuality i in period；x_k,jT () is the shape of feature j of t individuality k in period State value；p_aFor select probability, p_a=Rand (0,1)；α_kAnd β_kFor affecting constant, α_k=Rand (0.5,0.9), β_k=Rand (0.4,0.8)；most(PS^S, j) it is meant that: as set PS^SIn the number that state value is 1 of jth feature more than jth When the state value of feature is the number of 0, most (PS^S, j)=1；As set PS^SIn the number that state value is 1 of jth feature During less than the number that state value is 0 of jth feature, most (PS^S, j)=0；As set PS^SIn the state value of jth feature Be 1 number equal to the number that state value is 0 of jth feature time, most (PS^S, value j) is selected among both 0 or 1 at random Take；

If HIV_i(t+1)=I, then perform S-I operator as j≤m by formula (11), obtain v_i,j(t+1)；As j > m time by formula (12) Perform S-I operator, obtain v_i,j(t+1)；

$v_{i,j}(t+1)=\left\{\begin{array}{cc}\left.\begin{array}{cc}\underset{k\&Element;{\mathrm{CS}}^I}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)& p_a<0.5\\ \underset{k\&Element;{\mathrm{CS}}^I}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)-\underset{k\&Element;{\mathrm{CS}}^I}{\mathrm{\&Sigma;}}{\mathrm{\&beta;}}_k{x}_{k,j}\left(t\right)& p_a\&GreaterEqual;0.5\end{array}\right\}& \left|{\mathrm{CS}}^I\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^I\right|=0\end{array}\right.---\left(11\right)$

$v_{i,j}(t+1)=\left\{\begin{array}{cc}most\left({\mathrm{CS}}^I,j\right)& \left|{\mathrm{CS}}^I\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^I\right|=0\end{array}\right.---\left(12\right)$

If HIV_i(t+1)=Y, then perform S-Y operator as j≤m by formula (13), obtain v_i,j(t+1)；As j > m time by formula (14) Perform S-Y operator, obtain v_i,j(t+1)；

$v_{i,j}\left(t+1\right)=\left\{\begin{array}{cc}\left.\begin{array}{cc}\underset{k\&Element;{\mathrm{CS}}^Y}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)& p_a<0.5\\ \underset{k\&Element;{\mathrm{CS}}^Y}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)-\underset{k\&Element;{\mathrm{CS}}^Y}{\mathrm{\&Sigma;}}{\mathrm{\&beta;}}_k{x}_{k,j}\left(t\right)& p_a\&GreaterEqual;0.5\end{array}\right\}& \left|{\mathrm{CS}}^Y\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^Y\right|=0\end{array}\right.---\left(13\right)$

$v_{i,j}(t+1)=\left\{\begin{array}{cc}most\left({\mathrm{CS}}^Y,j\right)& \left|{\mathrm{CS}}^Y\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^Y\right|=0\end{array}\right.---\left(14\right)$

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

(S13) if HIV_i(t)=I, then

If HIV_i(t+1)=I, then perform I-I operator as j≤m by formula (15), obtain v_i,j(t+1)；As j > m time by formula (16) Perform I-I operator, obtain v_i,j(t+1)；

$v_{i,j}\left(t+1\right)=\left\{\begin{array}{cc}\left.\begin{array}{cc}\underset{k\&Element;{\mathrm{PS}}^I}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)& p_a<0.5\\ \underset{k\&Element;{\mathrm{PS}}^I}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)-\underset{k\&Element;{\mathrm{PS}}^I}{\mathrm{\&Sigma;}}{\mathrm{\&beta;}}_k{x}_{k,j}\left(t\right)& p_a\&GreaterEqual;0.5\end{array}\right\}& \left|{\mathrm{PS}}^I\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{PS}}^I\right|=0\end{array}\right.---\left(15\right)$

$v_{i,j}(t+1)=\left\{\begin{array}{cc}most\left({\mathrm{PS}}^I,j\right)& \left|{\mathrm{PS}}^I\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{PS}}^I\right|=0\end{array}\right.---\left(16\right)$

If HIV_i(t+1)=A, then perform I-A operator as j≤m by formula (17), obtain v_i,j(t+1)；As j > m time by formula (18) Perform I-A operator, obtain v_i,j(t+1)；

$v_{i,j}\left(t+1\right)=\left\{\begin{array}{cc}\left.\begin{array}{cc}\underset{k\&Element;{\mathrm{CS}}^A}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)& p_a<0.5\\ \underset{k\&Element;{\mathrm{CS}}^A}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)-\underset{k\&Element;{\mathrm{CS}}^A}{\mathrm{\&Sigma;}}{\mathrm{\&beta;}}_k{x}_{k,j}\left(t\right)& p_a\&GreaterEqual;0.5\end{array}\right\}& \left|{\mathrm{CS}}^A\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^A\right|=0\end{array}\right.---\left(17\right)$

$v_{i,j}(t+1)=\left\{\begin{array}{cc}most\left({\mathrm{CS}}^A,j\right)& \left|{\mathrm{CS}}^A\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^A\right|=0\end{array}\right.---\left(18\right)$

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

(S14) if HIV_i(t)=Y, then

If HIV_i(t+1)=Y, then perform Y-Y operator as j≤m by formula (19), obtain v_i,j(t+1)；As j > m time by formula (20) Perform Y-Y operator, obtain v_i,j(t+1)；

$v_{i,j}\left(t+1\right)=\left\{\begin{array}{cc}\left.\begin{array}{cc}\underset{k\&Element;{\mathrm{PS}}^A}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)& p_a<0.5\\ \underset{k\&Element;{\mathrm{PS}}^A}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)-\underset{k\&Element;{\mathrm{PS}}^A}{\mathrm{\&Sigma;}}{\mathrm{\&beta;}}_k{x}_{k,j}\left(t\right)& p_a\&GreaterEqual;0.5\end{array}\right\}& \left|{\mathrm{PS}}^A\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{PS}}^A\right|=0\end{array}\right.---\left(19\right)$

$v_{i,j}(t+1)=\left\{\begin{array}{cc}most\left({\mathrm{PS}}^A,j\right)& \left|{\mathrm{PS}}^A\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{PS}}^A\right|=0\end{array}\right.---\left(20\right)$

If HIV_i(t+1)=Z, then perform Y-Z operator as j≤m by formula (21), obtain v_i,j(t+1)；As j > m time by formula (22) Perform Y-Z operator, obtain v_i,j(t+1)；

$v_{i,j}\left(t+1\right)=\left\{\begin{array}{cc}\left.\begin{array}{cc}\underset{k\&Element;{\mathrm{CS}}^S}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)& p_a<0.5\\ \underset{k\&Element;{\mathrm{CS}}^S}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)-\underset{k\&Element;{\mathrm{CS}}^S}{\mathrm{\&Sigma;}}{\mathrm{\&beta;}}_k{x}_{k,j}\left(t\right)& p_a\&GreaterEqual;0.5\end{array}\right\}& \left|{\mathrm{CS}}^S\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^S\right|=0\end{array}\right.---\left(21\right)$

$v_{i,j}(t+1)=\left\{\begin{array}{cc}most\left({\mathrm{CS}}^S,j\right)& \left|{\mathrm{CS}}^S\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^S\right|=0\end{array}\right.---\left(22\right)$

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

(S15) if HIV_i(t)=A, then

If HIV_i(t+1)=A, then perform A-A operator as j≤m by formula (23), obtain v_i,j(t+1)；As j > m time by formula (24) Perform A-A operator, obtain v_i,j(t+1)；

$v_{i,j}\left(t+1\right)=\left\{\begin{array}{cc}\left.\begin{array}{cc}\underset{k\&Element;{\mathrm{PS}}^Y}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)& p_a<0.5\\ \underset{k\&Element;{\mathrm{PS}}^Y}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)-\underset{k\&Element;{\mathrm{PS}}^Y}{\mathrm{\&Sigma;}}{\mathrm{\&beta;}}_k{x}_{k,j}\left(t\right)& p_a\&GreaterEqual;0.5\end{array}\right\}& \left|{\mathrm{PS}}^Y\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{PS}}^Y\right|=0\end{array}\right.---\left(23\right)$

$v_{i,j}(t+1)=\left\{\begin{array}{cc}most\left({\mathrm{PS}}^Y,j\right)& \left|{\mathrm{PS}}^Y\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{PS}}^Y\right|=0\end{array}\right.---\left(24\right)$

If HIV_i(t+1)=S, then perform A-S operator as j≤m by formula (25), obtain v_i,j(t+1)；As j > m time by formula (26) Perform A-S operator, obtain v_i,j(t+1)；

$v_{i,j}\left(t+1\right)=\left\{\begin{array}{cc}\left.\begin{array}{cc}\underset{k\&Element;{\mathrm{CS}}^Z}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)& p_a<0.5\\ \underset{k\&Element;{\mathrm{CS}}^Z}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)-\underset{k\&Element;{\mathrm{CS}}^Z}{\mathrm{\&Sigma;}}{\mathrm{\&beta;}}_k{x}_{k,j}\left(t\right)& p_a\&GreaterEqual;0.5\end{array}\right\}& \left|{\mathrm{CS}}^Z\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^Z\right|=0\end{array}\right.---\left(25\right)$

$v_{i,j}(t+1)=\left\{\begin{array}{cc}most\left({\mathrm{CS}}^Z,j\right)& \left|{\mathrm{CS}}^Z\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^Z\right|=0\end{array}\right.---\left(26\right)$

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

(S16) if HIV_i(t)=Z, then

If HIV_i(t+1)=Z, then perform Z-Z operator as j≤m by formula (27), obtain v_i,j(t+1)；As j > m time by formula (28) Perform Z-Z operator, obtain v_i,j(t+1)；

$v_{i,j}\left(t+1\right)=\left\{\begin{array}{cc}\left.\begin{array}{cc}\underset{k\&Element;{\mathrm{PS}}^Z}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)& p_a<0.5\\ \underset{k\&Element;{\mathrm{PS}}^Z}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)-\underset{k\&Element;{\mathrm{PS}}^Z}{\mathrm{\&Sigma;}}{\mathrm{\&beta;}}_k{x}_{k,j}\left(t\right)& p_a\&GreaterEqual;0.5\end{array}\right\}& \left|{\mathrm{PS}}^Z\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{PS}}^Z\right|=0\end{array}\right.---\left(27\right)$

$v_{i,j}(t+1)=\left\{\begin{array}{cc}most\left({\mathrm{PS}}^Z,j\right)& \left|{\mathrm{PS}}^Z\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{PS}}^Z\right|=0\end{array}\right.---\left(28\right)$

If HIV_i(t+1)=S, then perform Z-S operator as j≤m by formula (29), obtain v_i,j(t+1)；As j > m time by formula (30) Perform Z-S operator, obtain v_i,j(t+1)；

$v_{i,j}\left(t+1\right)=\left\{\begin{array}{cc}\left.\begin{array}{cc}\underset{k\&Element;{\mathrm{CS}}^S}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)& p_a<0.5\\ \underset{k\&Element;{\mathrm{CS}}^S}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_k{x}_{k,j}\left(t\right)-\underset{k\&Element;{\mathrm{CS}}^S}{\mathrm{\&Sigma;}}{\mathrm{\&beta;}}_k{x}_{k,j}\left(t\right)& p_a\&GreaterEqual;0.5\end{array}\right\}& \left|{\mathrm{CS}}^S\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^S\right|=0\end{array}\right.---\left(29\right)$

$v_{i,j}(t+1)=\left\{\begin{array}{cc}most\left({\mathrm{CS}}^S,j\right)& \left|{\mathrm{CS}}^S\right|>0\\ x_{i,j}\left(t\right)& \left|{\mathrm{CS}}^S\right|=0\end{array}\right.---\left(30\right)$

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

(S17) if p > E₀, then v is made_i,j(t+1)=x_i,j(t), HIV_i(t+1)=HIV_i(t)；

(S18) make j=j+1, if j≤n, then go to step (S10), otherwise go to step (S19)；

(S19) perform accretive operatos by formula (31), 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 (3)；

(S20) make i=i+1, if i≤N, then go to step (S8), otherwise go to step (S21)；

(S21) 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 (S24), otherwise go to step (S22)；

(S22) newly obtained globally optimal solution X is preserved^*t+1；

(S23) make t=t+1, if t≤G, then go to step (S5), otherwise go to step (S24)；

(S24) terminate.