CN106953768A - A kind of network reliability model and mixing intelligent optimizing method - Google Patents

Abstract

The invention belongs to network communication technology field, disclose a kind of network reliability model and mixing intelligent optimizing method, network reliability model adds Survivabilities of Networks relevant evaluation index, design is optimized from two angles of survivability and survivability, and allow node to be failed with certain probability among optimization design, design is optimized to network topology structure, the single defect of existing reliability model restrictive condition is overcome, more improves and meets practical application scene.Optimization method of the present invention is poor for the local search ability of genetic algorithm, overall search ability is stronger, and ant group algorithm overall search ability is poor, the characteristics of local search ability is stronger, propose the integrated intelligent algorithm that genetic algorithm and ant group algorithm are combined, learn from other's strong points to offset one's weaknesses, overcome the defect of single intelligent algorithm inherently, improve the solution quality understood.

Description

A kind of network reliability model and mixing intelligent optimizing method

Technical field

The invention belongs to network communication technology field, a kind of network reliability model and mixing intelligent optimizing side are related generally to Method.

Background technology

Network system is real-life important system structure, such as power network, communication network, computer network all It is the infrastructure involved the interests of the state and the people, they all have network topology structure, its reliability performance directly influences social peace Complete and people's lives.Network system once breaks down, it will cause great to the living of people, economic and social safety etc. Influence.Therefore, the reliability of network is increasingly valued by people.Reliability can substantially go to consider in terms of three：Network Survivability, validity and survivability.The survivability of network refers to the network for having certain failure probability for node or link, Under randomness destruction, network can keep the probability of connection.Survivabilities of Networks is the reliability ginseng based on topological structure Number, does not consider the reliability of network edge and node, and measurement is that node in a network or side occur weathering or disliked Under conditions of meaning attack, network topology structure keeps the ability of connection.There are many documents both at home and abroad with regard to the anti-of network topology structure Ruining property, which is estimated, to be studied, and Main Conclusions has figure resistance degree, algebraic connectivity etc..Validity be then based on network performance can By property index, represent that network system meets the degree of communication service performance requirement under network components failure condition.Network is reliable Property optimization problem is a NP-Hard combinatorial problems, and it includes:1) using network reliability as constraints, minimization is invested into This；2) using cost of investment as constraints, maximize network reliability.Wherein, the former is the Hou Zheshi using operator as starting point Using user as starting point.

Existing more researcher deploys to study from the angle of survivability to network reliability at present.Integrity problem is It is NP-Hard problems to be certified as, and ordinary circumstance people can not obtain the optimal solution of problem.Basima Elshqeirat exist Topology design with minimal cost subject to network reliability constraint mono- Solve the problems, such as Network Topology Design under reliability restrictive condition based on dynamic programming in text.The algorithm is first with three inspirations Formula method produces k spanning tree sequence, and the k spanning tree sequence then produced using each heuristic correspondence produces excellent Change result.Berna Dengiz et al. are in A self-tuning heuristic for the design of The minimization under reliability restrictive condition is solved using self-adjusting heuristic in the texts of communication networks mono- The network reliability optimization problem of cost of investment.The above research is typically taken when optimizing solution to reliability model Heuristic or single intelligent algorithm, but because the latent defect of algorithm inherently, solving result is easily trapped into part most Excellent solution.When reliability model is analyzed, research all assumes that node is completely reliable in the past, carries out network reliability topological optimization and sets Meter, actually this does not meet actual conditions.In addition, the survivability problem of network is only considered in research in the past, with Full terminal reliability is directed to the survivability problem of network as network survivability metric objective, in model optimization research not Consider calculation of correlation index.

In summary, the problem of prior art is present be：Current reliability model does not consider node when model is set up The situation of failure, does not meet practical situation；Restrictive condition is single among model, and simply carrying out reliability from the angle of survivability opens up Optimization design is flutterred, the survivability energy of network is not considered, the network according to designed by optimizing existing reliability model out may Survival properties are preferably but survivability can be poor；Latent defect of the current reliability optimized algorithm due to algorithm inherently, it is required Optimum results are easily trapped into local optimum.

The content of the invention

The problem of existing for prior art, the invention provides a kind of network reliability model and mixing intelligent optimizing side Method.

The present invention is achieved in that a kind of network reliability model, and the network reliability model is：

S.T.R(X)≥R₀ (2)

a_ij=a_ji=x_ij (4)

d_i>=2, i=1,2 ..., N (6)

L (G)=D (G)-A (G) (7)

λ₁≤λ₂≤…≤λ_N (8)

Formula (2-3) represents that the full Terminal Reliability of network is not less than the full Terminal Reliability of minimum requirements；Formula (4-6) represents net Node degree is both greater than the connected graph for being equal to that 2, i.e. network are a constraints of satisfaction 2 among network topological diagram；Formula (7-9) represents network Algebraic connectivity be not less than minimum requirements algebraic connectivity；Formula (10-12) represents that the figure resistance degree of network is wanted not less than minimum Seek figure resistance degree；

Wherein, the physical topology of network is G (V, E), node set V={ v_i| i=1,2 ... N } represent network equipment collection Close；Wherein, N represents the number of node in network；l_ijRepresent node v_iAnd v_jBetween link, and the collection of link is combined into E { l_ij| i,j∈N}；

F (X) represents object function；C^*Represent the figure resistance degree after normalization；Represent minimum requirements figure resistance degree；c_ijTable Show the link cost of i and j point-to-point transmissions；R (X) represents full Terminal Reliability；R₀Represent the full Terminal Reliability of minimum requirements；R_GRepresent Scheme resistance degree；x_ijRepresent link decisions variable, x_ij=1 expression node i and j have direct link connection, x_ij=0 represent node i and J is connected without direct link；X{x₁₂,x₁₃,…,x_ij,…,x_(N-1)NRepresent a kind of network topology link combinations；λ₀Represent minimum to want Seek algebraic connectivity；λ₂Representation algebra degree of communication；A (G) represents figure G adjacency matrix；a_ijRepresent the i-th of figure G adjacency matrix Row jth column element；D (G) represents figure G node degree diagonal matrix；d_ijRepresent the i-th row jth row of figure G node degree diagonal matrix Element；d_iRepresent node degree；L (G) represents figure G Laplacian Matrix；λ_iRepresent L (G) ith feature value；p_eRepresent link Reliability；p_vRepresent node point reliability.

It is described another object of the present invention is to provide a kind of mixing intelligent optimizing method of the network reliability model Optimization method comprises the following steps：

Step one, initialize:Initialization information element, link cost matrix, nodal information, link information, initial solution x_out； Given population scale pop, crossover probability p_c, mutation probability p_m, the maximum evolutionary generation g of heredity_max；Randomly generate and meet constraints Initial population, and make hereditary initial evolutionary generation g=0；

Step 2, by just when assessing the individual in population, by fitness function value and x maximum in population_outFitness Functional value is compared, if being more than, and its corresponding x is assigned into x_out；Otherwise, x_outKeep constant；

Step 3, by the roulette selection method of optimum maintaining strategy, is intersected and mutation operation；

Step 4, iterative algebra g=g+1；

Step 5, if g ＞ g_max, then stop, and export x_out, go to step six；Otherwise, two are gone to step；

Step 6, according to x_outValue fresh information element, and the another initial evolutionary generation t=0 of ant colony；

Step 7, ant colony search is carried out according to node transition rule；

Pheromones on link are updated by step 8；

Step 9, iterative algebra t=t+1 judges whether to meet end condition, if satisfaction, exports statistical information, program Terminate；Otherwise seven are gone to step.

Further, binary coding mode is used to population at individual, there is link between two nodes is represented with 1, otherwise Represented with 0；One chromosome of each X correspondences；For the network that node number is N, N is up among its map network topological diagram (N-1)/2 side, chromosome is defined as the bit string that length is equal to N (N-1)/2.

Further, object function and fitness function separately design for：

Object function：Z (X)=f (X)；

Fitness function:F (X)=C_max-f(X)；

Wherein, C_maxLink totle drilling cost when connecting entirely for network topology structure.

Further, using the roulette selection strategy of optimum maintaining strategy；First, by fitness function value in current population Highest individual is intactly copied in population of future generation；Then, by roulette selection strategy execution selection operation.

Further, the crossover operation is using single-point interleaved mode, random two parent chromosomes of selection from population, The interval random number p of regeneration one (0,1)_randomIf, p_randomLess than crossover probability p_c, then a gene location is randomly choosed As cross-point locations, crossover operation is carried out to two individuals, the chromosome after intersection is put into progeny population；If p_randomNo Less than crossover probability, then two individual holdings are constant, and parent individuality is copied directly in progeny population；Crossover probability p_cAnd evolution Function p associated algebraically i_c(i), computing formula：

p_c(i)=p_{c_min}+(p_{c_max}-p_{c_min})×i/g_max；

Wherein, p_c(i) crossover probability in the i-th generation, p are represented_{c_max}Represent the maximum crossover probability of setting, p_{c_min}Represent setting Minimum crossover probability, g_maxRepresent the maximum evolutionary generation of hereditary section sets among algorithm；

The mutation operation is using the method uniformly made a variation, for each gene in chromosome, generates (0, a 1) area Between random number p_random；If p_randomLess than mutation probability p_m, then the value on the gene location of this in chromosome is become another Virtual value；If p_randomNot less than mutation probability, then the value holding on gene location is constant；Mutation probability and genetic evolution algebraically i Associated function p_m(i), computing formula：

p_m(i)=p_{m_min}+(p_{m_max}-p_{m_min})×i/g_max；

Wherein, p_m(i) mutation probability in the i-th generation, p are represented_{m_max}Represent the maximum mutation probability of setting, p_{m_min}Represent setting Minimum mutation probability, g_maxRepresent the maximum evolutionary generation of hereditary section sets among algorithm.

Further, global renewal is carried out to pheromones on link according to formula：

τ_ij(new)=(1-p) τ_ij(old)+Δτ_ij；

If ant k have selected link (i, j)；

Wherein m is the quantity of ant, and Q represents pheromones intensity, Δ τ_ijFor pheromones on this circulation link (i, j) Increment, p is pheromones volatilization factor, τ_ij(old) it is the pheromone concentration on link (i, j) before this circulation, τ_ij(new) it is Pheromone concentration after this circulation on link (i, j).

Another object of the present invention is to provide a kind of network topology structure of the application network reliability model.

Advantages of the present invention and good effect are：Network reliability Optimized model proposed by the present invention adds network survivability Property relevant evaluation index, design is optimized from two angles of survivability and survivability, and allows among optimization design node Failed with certain probability, design is optimized to network topology structure, existing reliability model restrictive condition is overcome single Defect, more improve and meet practical application scene.Heredity proposed by the present invention and ant colony integrated intelligent algorithm MGACA, pin Local search ability to genetic algorithm (Genetic Algorithm, GA) is poor, and overall search ability is stronger, and ant colony is calculated Method (Ant Colony Optimization, ACO) overall search ability is poor, the characteristics of local search ability is stronger, by GA and ACO is combined, and is learnt from other's strong points to offset one's weaknesses, and overcomes the defect of single intelligent algorithm inherently, improves the solution quality understood.With it is existing Network reliability model method it is different, the present invention constructs a kind of new reliability model, and proposes genetic algorithm and ant The integrated intelligent algorithm that group's algorithm is combined searches out optimal network topology link allocation method.

Brief description of the drawings

Fig. 1 is the mixing intelligent optimizing method flow chart of network reliability model provided in an embodiment of the present invention.

Fig. 2 is that the mixing intelligent optimizing method of network reliability model provided in an embodiment of the present invention realizes flow chart.

Fig. 3 is that algorithm performance is contrasted when node number provided in an embodiment of the present invention is 10.

Fig. 4 is that algorithm performance is contrasted when node number provided in an embodiment of the present invention is 15.

Fig. 5 is that algorithm performance is contrasted when node number provided in an embodiment of the present invention is 14.

Comparative result schematic diagram when Fig. 6 is algebraic connectivity change provided in an embodiment of the present invention.

Embodiment

In order to make the purpose , technical scheme and advantage of the present invention be clearer, with reference to embodiments, to the present invention It is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, it is not used to Limit the present invention.

The application principle of the present invention is explained in detail below in conjunction with the accompanying drawings.

As shown in figure 1, the mixing intelligent optimizing method of network reliability model provided in an embodiment of the present invention is including following Step：

S101：Network node sum, link cost matrix, link reliability information, node reliability information etc. are inputted, just Beginning time genetic algorithm parameter；

S102：Randomly generate the initial population for meeting constraints；

S103：Individual fitness function is assessed in population；

S104：Using the roulette selection method of optimum maintaining strategy.First, by fitness function value in current population most High individual is intactly copied in population of future generation；Secondly, by roulette selection strategy execution selection operation；

S105：Intersect and make a variation；

S106：Judge whether current cycle time is less than maximum iteration：If current cycle time changes less than maximum Generation number, then cycle-index adds 1, and goes to step S103；If current cycle time is equal to maximum iteration, terminates heredity and calculate Method step, output result, and go to step S107；

S107：The result fresh information element exported according to genetic algorithm, initializes to the parameter in ant group algorithm, joins Number includes the maximum evolutionary generation of ant colony, globally optimal solution and iteration optimal solution etc.；

S108：The probability selection path that ant calculates according to state transition probability formula；

S109：Global renewal is carried out to the pheromones on link according to formula；

S110：Judge whether current cycle time is less than maximum iteration：If current cycle time changes less than maximum Generation number, then cycle-index adds 1, and goes to step S108；If current cycle time is equal to maximum iteration, terminate ant colony Search, exports statistical information, EP (end of program).

The application principle of the present invention is further described below in conjunction with the accompanying drawings.

1. technical scheme

1.1 degree of reiability indexs

(1) survivability is measured

The survivability of network refers to the network for having certain failure probability for node or link, in randomness destruction Under, the probability of network-in-dialing can be kept.Survivability is that the knowledge based on probability theory and graph theory puts forward, and describes randomness The influence of destruction and network topology structure to network reliability.

The present invention is full Terminal Reliability for the Measure Indexes selection of survivability, i.e., among probability graph, any two section There is the probability of normal operation link between point, survival ability of the whole network in the case of unit failure can be weighed.

(2) survivability is measured

Survivabilities of Networks is the dependability parameter based on topological structure, and the node in network and the reliability on side are not considered, Weigh be node in a network or weathering or under conditions of deliberately being attacked, network topology structure holding occurs for side The ability of connection.The survivability of network refers at least need the key node or critical link that destroy many small numbers, caused whole Network is split into several subnets or disappearance critical path, so that the ability of the communication between interrupt unit node.Survivability is ground Study carefully the topological structure intrinsic mainly by analyzing network, primary metric parameter is figure resistance degree, algebraic connectivity etc..The present invention Using algebraic connectivity, scheme Measure Indexes of the resistance degree as Survivabilities of Networks.

1) algebraic connectivity

If G (V, E) is a undirected simple graph.Figure G adjacency matrix be designated as A (G), make D (G) be G Vertex Degree it is diagonal Matrix, defines G Laplacian Matrix L (G)=D (G)-A (G), if L (G) eigenvalue λ₁,λ₂,…λ_NMeet λ₁≤λ₂ ≤…≤λ_N。λ₂Referred to as G algebraic connectivity, is designated as α (G).

2) figure resistance degree

If G (V, E) is a undirected simple graph.Figure G adjacency matrix be designated as A (G), make D (G) be G Vertex Degree it is diagonal Matrix, defines G Laplacian Matrix L (G)=D (G)-A (G), if L (G) eigenvalue λ₁,λ₂,…λ_NMeet λ₁≤λ₂ ≤…≤λ_N.Wherein, N is network node number, R_GReferred to as scheme resistance degree, computing formula is as follows.

1.2 reliability optimization models

If the physical topology of given network is G (V, E), node set V={ v_i| i=1,2 ... N } represent network equipment collection Close.Wherein, N represents the number of node in network；l_ijRepresent node v_iAnd v_jBetween link, and the collection of link is combined into E { l_ij| i,j∈N}。

The implication of variable symbol is as follows：

f(X)：Object function；

C^*：Figure resistance degree after normalization；

：Minimum requirements figure resistance degree；

c_ij：The link cost of i and j point-to-point transmissions；

R(X)：Full Terminal Reliability；

R₀：The full Terminal Reliability of minimum requirements；

R_G：Scheme resistance degree；

x_ij：Link decisions variable, x_ij=1 expression node i and j have direct link connection, x_ij=0 represent node i and j without Direct link is connected；

X：{x₁₂,x₁₃,…,x_ij,…,x_(N-1)NA kind of network topology link combinations；

λ₀：Minimum requirements algebraic connectivity；

λ₂：Algebraic connectivity；

A(G):Scheme G adjacency matrix；

a_ij：Scheme the i-th row jth column element of G adjacency matrix；

D(G):Scheme G node degree diagonal matrix；

d_ij：Scheme the i-th row jth column element of G node degree diagonal matrix；

d_i：Node degree；

L(G)：Scheme G Laplacian Matrix；

λ_i：L (G) characteristic value；

p_e：Link reliability；

p_v：Node point reliability；

Model hypothesis condition：

(1) network node number is given and corresponding reliability is to determine；

(2) cost and reliability of each of the links are to determine；

(3) each of the links is two-way, and can only have a link between node i and node j；

(4) each of the links has two states, i.e. normal and failure, and link failure is statistical iteration；

(5) each node has two states, i.e. normal and failure, and node failure is statistical iteration；

(6) system is unrepairable；

Based on above description, present invention construction reliability optimization model shown below.

S.T.R(X)≥R₀Formula (2)

a_ij=a_ji=x_ijFormula (4)

d_i>=2, i=1,2 ..., N formulas (6)

L (G)=D (G)-A (G) formula (7)

λ₁≤λ₂≤…≤λ_NFormula (8)

Formula (2-3) represents that the full Terminal Reliability of network is not less than the full Terminal Reliability of minimum requirements；Formula (4-6) represents net Node degree is both greater than the connected graph for being equal to that 2, i.e. network are a constraints of satisfaction 2 among network topological diagram；Formula (7-9) represents network Algebraic connectivity be not less than minimum requirements algebraic connectivity；Formula (10-12) represents that the figure resistance degree of network is wanted not less than minimum Seek figure resistance degree.

1.3 mixing intelligent optimizing algorithms

The present invention is poor for the local search ability of genetic algorithm (Genetic Algorithm, GA), ability of searching optimum It is relatively strong, and ant group algorithm (Ant Colony OptimizationACO) overall search ability is poor, local search ability is stronger The characteristics of, GA and ACO are combined, learnt from other's strong points to offset one's weaknesses, construction integrated intelligent algorithm MGACA (Mixed Gene and Ant Colony Algorithm).Its basic ideas is that algorithm early stage carries out global search using genetic algorithm, utilizes genetic algorithm Global convergence, rapidity, randomness, its Search Results produce the initial information element distribution of relevant issues.The algorithm later stage uses Ant group algorithm, in the case where there is initial information element distribution, makes full use of ant group algorithm positive feedback, concurrency, refinement solution effect The features such as rate is high.

The step that implements of the optimization method of inventive network reliability model is：

(1) initialize:Initialization information element, link cost matrix, nodal information, link information, initial solution x_outDeng；Give Determine population scale pop, crossover probability p_c, mutation probability p_m, the maximum evolutionary generation g of heredity_max；Randomly generate and meet constraints Initial population, and make hereditary initial evolutionary generation g=0；

(2) press just when assessing each individual in population, by fitness function value and x maximum in population_outFitness Functional value is compared, if being more than, and its corresponding x is assigned into x_out；Otherwise, x_outKeep constant；

(3) the roulette selection method of optimum maintaining strategy is pressed, is intersected and mutation operation；

(4) iterative algebra g=g+1；

(5) if g ＞ g_max, then stop, and export x_out, turn (6)；Otherwise, turn (2)；

(6) according to x_outValue fresh information element, and the another initial evolutionary generation t=0 of ant colony；

(7) ant colony search is carried out according to node transition rule；

(8) Pheromone update；

(9) iterative algebra t=t+1, judges whether to meet end condition, if meeting, exports statistical information, program knot Beam；Otherwise turn (7)；

As shown in Fig. 2 the optimization method of inventive network reliability model to implement step as follows：

Step 1：Network node sum, link cost matrix, link reliability information, node reliability information etc. are inputted, Initialize genetic algorithm parameter.

Step 2：Randomly generate the initial population for meeting constraints

The present invention uses binary coding bit string to population at individual, and there is link between two nodes is represented with 1, is otherwise used 0 represents.One chromosome of each X correspondences, chromosome uses binary coding.For the network that node number is N, its correspondence net It is up to N (N-1)/2 side in network figure, therefore chromosome is defined as the bit string that length is equal to N (N-1)/2.

The coding form for representing this network is：

[x₁₂ x₁₃ x₁₄ x₁₅ x₂₃ x₂₄ x₂₅ x₃₄ x₃₅ x₄₅]

[1 1 0 1 1 0 1 1 0 1]

Step 3：Individual fitness function is assessed in population

Fitness function is a kind of standard judged the quality of genetic algorithm solution, and fitness function value is that heredity is entered The Main Basiss of row selection operation, for the minimization cost optimization model in the present invention, object function and fitness function point It is not designed as：

Object function：Z (X)=f (X)；

Fitness function:F (X)=C_max-f(X)；

Wherein C_maxLink totle drilling cost when connecting entirely for network topology structure.

Step 4：Selection operation

The present invention uses the roulette selection strategy of optimum maintaining strategy.First, by fitness function value in current population Highest individual is intactly copied in population of future generation；Secondly, by roulette selection strategy execution selection operation；The strategy Advantage is the individual that obtained result is the highest fitness occurred in successive dynasties population when Genetic Algorithms are terminated.

Step 5：Intersect and make a variation

1) crossover operation

So the present invention uses single-point interleaved mode.Its concrete operations is two parent dyeing of random selection from population Body, the interval random number p of regeneration one (0,1)_randomIf, p_randomLess than crossover probability p_c, then a gene is randomly choosed Position carries out crossover operation to two individuals, the chromosome after intersection is put into progeny population as cross-point locations；If p_randomNot less than crossover probability, then two individual holdings are constant, and parent individuality is copied directly in progeny population.

With the gradually increase of genetic evolution algebraically, the individual in population is become better and better.To keep individual many in population Sample, it is to avoid optimum results are absorbed in local optimum, overcomes Premature convergence, makes crossover probability p_cWith controllability, make p_cWith The increase of evolutionary generation and gradually increase.Therefore, a crossover probability p is set up among algorithm_cIt is associated with evolutionary generation i Function p_c(i), computing formula is as follows：

p_c(i)=p_{c_min}+(p_{c_max}-p_{c_min})×i/g_max

Wherein, p_c(i) crossover probability in the i-th generation, p are represented_{c_max}Represent the maximum crossover probability of setting, p_{c_min}Represent setting Minimum crossover probability, g_maxRepresent the maximum evolutionary generation of hereditary section sets among algorithm.

2) mutation operation

The main function of mutation operation is to increase the diversity of individuals of population, and it is various that uniform variation can increase individual well Property, so algorithm proposed by the present invention is using the method uniformly made a variation.Its basic operation is：For each base in chromosome Cause, the interval random number p of generation one (0,1)_random.If p_randomLess than mutation probability p_m, by the gene location of this in chromosome On value be changed into another virtual value；If p_randomNot less than mutation probability, then the value holding on gene location is constant.

Equally, to avoid Premature Convergence, algorithm proposed by the present invention makes the value of mutation probability have certain controllability, built Found the mutation probability function p associated with genetic evolution algebraically i_m(i), computing formula is as follows：

p_m(i)=p_{m_min}+(p_{m_max}-p_{m_min})×i/g_max

Wherein, p_m(i) mutation probability in the i-th generation, p are represented_{m_max}Represent the maximum mutation probability of setting, p_{m_min}Represent setting Minimum mutation probability, g_maxRepresent the maximum evolutionary generation of hereditary section sets among algorithm.

Step 6：Judge whether current cycle time is less than maximum iteration：If current cycle time changes less than maximum Generation number, then cycle-index adds 1, and goes to step 3；If current cycle time is equal to maximum iteration, terminate genetic algorithm Step, exports x_out, and go to step 7.

Step 7：According to x_outValue fresh information element, and the parameter in ant group algorithm is initialized, parameter includes ant The maximum evolutionary generation of group, globally optimal solution and iteration optimal solution etc..

Step 8：The probability selection path that ant calculates according to state transition probability formula.

Step 9：Global renewal is carried out to the pheromones on link according to formula.

τ_ij(new)=(1-p) τ_ij(old)+Δτ_ij；

If ant k have selected link (i, j)；

Wherein m is the quantity of ant, and Q represents pheromones intensity, Δ τ_ijFor pheromones on this circulation link (i, j) Increment, p is pheromones volatilization factor, τ_ij(old) it is the pheromone concentration on link (i, j) before this circulation, τ_ij(new) it is Pheromone concentration after this circulation on link (i, j).

Step 10：Judge whether current cycle time is less than maximum iteration：If current cycle time is less than maximum Iterations, then cycle-index adds 1, and goes to step 8；If current cycle time is equal to maximum iteration, terminate ant colony Search, exports statistical information, EP (end of program).

The application effect of the present invention is explained in detail with reference to emulation.

Condition set by Computer Simulation of the present invention is as follows：

Experimental situation：Software test and emulation are carried out under Microsoft Windows XP operating system environments, is owned Emulation is all run in Hewlett-Packard's computer (four cores, CPU frequency 3.30GHz, internal memory 4GB), and Imitation Development Platform is JDK1.7.0_25+Eclipse, source code is write using Java language.

In order to embody performance of the MGACA algorithms under different scenes, choose three typical telecommunications networks and tested, one The network for being N=10 for node number, secondly being the network that node number is interior N=15.This corresponding net of two groups of test problems Network topology link maximum number be respectively 45,105, the coded system that problem is used forBinary coding bit string, this Search space corresponding to two groups of test problem solutions is respectively 245,2105, so that different search is crossed in the test of algorithm Space, it is ensured that the general properties of test of heuristics.Finally, a kind of emulation topology knot conventional to node number N=14 classics Structure NSFnet topologys re-start the optimization of reliability Topology connection, verify the actual applicability suggested plans.

Other simulated environment parameter configurations are：Link reliability ρ_e=0.95, node point reliability p_v=0.98, each link into This (unit:Member) it is the integer randomly generated between [1,100], R₀=0.95, λ_o=0.7,Crossover probability lower limit For 0.5, the upper limit is 0.9, and heredity maximum evolutionary generation and the maximum evolutionary generation of ant colony are set to 6000, population scale and ant Number is set to 50, and pheromones volatilization factor is set to ρ=0.5.

In order to be able to the performance of preferably testing algorithm, for each test problem, by MGACA algorithms and it is recently proposed STH (Self-tuning Heuristic) algorithm is analyzed, to verify the performance of MGACA algorithms.

In order to be able to preferably compare the optimization performance of two kinds of algorithms, for each test problem, two kinds of algorithms are by calculating Machine carries out 10 random experiments, takes 10 simulation results to be contrasted and analyzed as output data.

The Optimization Solution quality of algorithm refers to the height for being eventually found solution quality, for Optimized model of the present invention, Ensure under conditions of reliability requirement, the solution correspondence target function value found out is smaller, then the solution effect of algorithm is better.

In following simulation result figure, the longitudinal axis of accompanying drawing 3 to 5 represents network cost, characterizes algorithm optimization and solves matter The ability of amount；The transverse axis of accompanying drawing 3 to 5 represents experiment number；The transverse axis representation algebra degree of communication of accompanying drawing 6.

Accompanying drawing 3,4 and 5 gives the Comparative result of different node number MGACA algorithms and STH algorithms, from three figures all As can be seen that the result of MGACA algorithms is better than STH algorithms.

Table 1 give the solution mass ratio of algorithm compared with.It can be seen that what MGACA was found out by the test result in table 1 Solution, either the average value of preferably solution, worst solution or solution is all best.Therefore, MGACA algorithms find out majorization of solutions quality It is higher, demonstrate the validity of put forward algorithm.Table 2 gives these three test problems final prioritization scheme.

The Algorithm for Solving mass ratio of table 1 compared with

The prioritization scheme of table 2

Under same test scene, algorithm is also due to the difference of constraints, the result differed greatly. In order to test influence of the different parameters to MGACA algorithm performances, we are provided with difference to node number for 10 test problem Influence of the minimum requirements algebraic connectivity to network cost.Accompanying drawing 6 gives simulation result and compared.It can be seen that net Network cost increases with the increase of the two, and the corresponding network cost of MGACA algorithms network cost corresponding compared with STH algorithms is low.

Presently preferred embodiments of the present invention is the foregoing is only, is not intended to limit the invention, all essences in the present invention Any modification, equivalent and improvement made within refreshing and principle etc., should be included within the scope of the present invention.

Claims (7)

1. a kind of network reliability model, it is characterised in that the network reliability model is：

$\begin{array}{cc}Min& f\left(X\right)=\underset{i=1}{\overset{N-1}{\Σ}}\underset{j=i+1}{\overset{N}{\Σ}}{c}_{ij}\·x_{ij}\end{array}---\left(1\right)$

S.T. R(X)≥R₀ (2)

$R\left(X\right)=1-\[\underset{i=1}{\overset{N}{\Σ}}{(1-p_e)}^{d_i}\underset{j=1}{\overset{i-1}{\Π}}\[1-{(1-p_e)}^{d_j-a_{ij}}\]+p_e^{\frac{\underset{i=1}{\overset{N}{\Σ}}{d}_i}{2}}(1-p_v)\underset{i=0}{\overset{N-1}{\Σ}}{p_v}^i\]---\left(3\right)$

a_ij=a_ji=x_ij (4)

$d_i=\underset{j=1}{\overset{N}{\Σ}}{a}_{ij},i=1,2,...,N---\left(5\right)$

d_i>=2, i=1,2 ..., N (6)

L (G)=D (G)-A (G) (7)

λ₁≤λ₂≤…≤λ_N (8)

$\frac{{\mathrm{\λ}}_2}{N}\≥{\mathrm{\λ}}_0---\left(9\right)$

$R_G=N\underset{i=2}{\overset{N}{\Σ}}\frac{1}{{\mathrm{\λ}}_i}---\left(10\right)$

$C^{*}=\frac{N-1}{R_G}---\left(11\right)$

$C^{*}\≥C_0^{*}---\left(12\right)$

Formula 2- formulas 3 represent that the full Terminal Reliability of network is not less than the full Terminal Reliability of minimum requirements；Formula 4- formulas 6 represent that network is opened up Flutter node degree among figure and be both greater than the connected graph for being equal to that 2, i.e. network are a constraints of satisfaction 2；Formula 7- formulas 9 represent the generation of network Number degree of communication is not less than minimum requirements algebraic connectivity；Formula 10- formulas 12 represent that the figure resistance degree of network is not less than minimum requirements figure Resistance degree；

Wherein, the physical topology of network is G (V, E), node set V={ v_i| i=1,2 ... N } represent sets of network devices；Its In, N represents the number of node in network；l_ijRepresent node v_iAnd v_jBetween link, and the collection of link is combined into E { l_ij|i,j∈ N}；

F (X) represents object function；C^*Represent the figure resistance degree after normalization；Represent minimum requirements figure resistance degree；c_ijRepresent i With the link cost of j point-to-point transmissions；R (X) represents full Terminal Reliability；R₀Represent the full Terminal Reliability of minimum requirements；R_GExpression figure is supported Anti- degree；x_ijRepresent link decisions variable, x_ij=1 expression node i and j have direct link connection, x_ij=0 represent node i and j without Direct link is connected；X{x₁₂,x₁₃,…,x_ij,…,x_(N-1)NRepresent a kind of network topology link combinations；λ₀Represent minimum requirements Algebraic connectivity；λ₂Representation algebra degree of communication；A (G) represents figure G adjacency matrix；a_ijRepresent the i-th row of figure G adjacency matrix Jth column element；D (G) represents figure G node degree diagonal matrix；d_ijRepresent the i-th row jth row member of figure G node degree diagonal matrix Element；d_iRepresent node degree；L (G) represents figure G Laplacian Matrix；λ_iRepresent L (G) ith feature value；p_eRepresent that link is reliable Degree；p_vRepresent node point reliability.

2. a kind of mixing intelligent optimizing method of network reliability model as claimed in claim 1, it is characterised in that the mixing Intelligent optimization method comprises the following steps：

Step one, initialize:Initialization information element, link cost matrix, nodal information, link information, initial solution x_out；It is given Population scale pop, crossover probability p_c, mutation probability p_m, the maximum evolutionary generation g of heredity_max；Randomly generate and meet the first of constraints Beginning population, and make hereditary initial evolutionary generation g=0；

Step 2, by just when assessing the individual in population, by fitness function value and x maximum in population_outFitness function Value is compared, if being more than, and its corresponding x is assigned into x_out；Otherwise, x_outKeep constant；

Step 3, by the roulette selection method of optimum maintaining strategy, is intersected and mutation operation；

Step 4, iterative algebra g=g+1；

Step 5, if g ＞ g_max, then stop, and export x_out, go to step six；Otherwise, two are gone to step；

Step 6, according to x_outValue fresh information element, and the another initial evolutionary generation t=0 of ant colony；

Step 7, ant colony search is carried out according to node transition rule；

Step 8, Pheromone update；

Step 9, iterative algebra t=t+1 judges whether to meet end condition, if satisfaction, exports statistical information, program knot Beam；Otherwise seven are gone to step.

3. mixing intelligent optimizing method as claimed in claim 2, it is characterised in that binary coding side is used to population at individual There is link between formula, two nodes to be represented with 1, otherwise represented with 0；One chromosome of each X correspondences；It is for node number N (N-1)/2 side is up among N network, its map network topological diagram, chromosome is defined as length and is equal to N's (N-1)/2 Bit string.

4. mixing intelligent optimizing method as claimed in claim 2, it is characterised in that object function and fitness function are set respectively It is calculated as：

Object function：Z (X)=f (X)；

Fitness function:F (X)=C_max-f(X)；

Wherein C_maxNetwork totle drilling cost when all being connected for network topology structure link.

5. mixing intelligent optimizing method as claimed in claim 2, it is characterised in that selected using the roulette of optimum maintaining strategy Select strategy；First, fitness function value highest individual in current population is intactly copied in population of future generation；Then, By roulette selection strategy execution selection operation.

6. mixing intelligent optimizing method as claimed in claim 2, it is characterised in that the crossover operation uses single-point intersection side Formula, randomly chooses two parent chromosomes, the interval random number p of regeneration one (0,1) from population_randomIf, p_randomIt is small In crossover probability p_c, then a gene location is randomly choosed as cross-point locations, and crossover operation is carried out to two individuals, will be intersected Chromosome afterwards is put into progeny population；If p_randomNot less than crossover probability, then two individual holdings are constant, and parent individuality is straight Connect and copy in progeny population；Crossover probability p_cThe function p being associated with evolutionary generation i_c(i), computing formula：

p_c(i)=p_{c_min}+(p_{c_max}-p_{c_min})×i/g_max；

Wherein, p_c(i) crossover probability in the i-th generation, p are represented_{c_max}Represent the maximum crossover probability of setting, p_{c_min}Represent setting most Small crossover probability, g_maxRepresent the maximum evolutionary generation of hereditary section sets among algorithm；

The mutation operation is using the method uniformly made a variation, and for each gene in chromosome, generation one (0,1) is interval Random number p_random；If p_randomLess than mutation probability p_m, then the value on the gene location of this in chromosome is become into another has Valid value；If p_randomNot less than mutation probability, then the value holding on gene location is constant；Mutation probability and genetic evolution algebraically i phases The function p of association_m(i), computing formula：

p_m(i)=p_{m_min}+(p_{m_max}-p_{m_min})×i/g_max；

Wherein, p_m(i) mutation probability in the i-th generation, p are represented_{m_max}Represent the maximum mutation probability of setting, p_{m_min}Represent setting most Small mutation probability, g_maxRepresent the maximum evolutionary generation of hereditary section sets among algorithm.

7. mixing intelligent optimizing method as claimed in claim 2, it is characterised in that the pheromones on link are entered according to formula Row global information element updates：

τ_ij(new)=(1-p) τ_ij(old)+Δτ_ij；

${\mathrm{\Δ\τ}}_{ij}=\underset{k=1}{\overset{m}{\Σ}}{\mathrm{\Δ\τ}}_{ij}^k;$

Wherein m is the quantity of ant, and Q represents pheromones intensity, Δ τ_ijFor the increasing of pheromones on this circulation link (i, j) Amount, p is pheromones volatilization factor, τ_ij(old) it is the pheromone concentration on link (i, j) before this circulation, τ_ij(new) it is this Pheromone concentration after secondary circulation on link (i, j).