CN112804597A - Multi-objective optimization method for multicast routing of self-adaptive optical network - Google Patents

Abstract

The invention discloses a multi-target optimization method for multicast routing of an Adaptive optical network, which adopts an improved NSGA-II algorithm MRWA _ AOSNSGA-II with an Adaptive Operator Selection strategy, wherein the optimization target comprises the use cost of multicast network resources, end-to-end delay and channel utilization rate, QoS constraints such as end-to-end delay, available bandwidth and packet loss rate are met, and Adaptive Operator Selection (AOS) adaptively selects a proper Operator in the algorithm process to improve the solving performance of the algorithm and generate a better group of non-dominated optical network multicast routing.

Description

Multi-objective optimization method for multicast routing of self-adaptive optical network

Technical Field

The invention relates to the field of multicast routing wavelength allocation, in particular to a multi-objective optimization method for a multicast routing of an adaptive optical network.

Background

In IP networks, the multicast problem has been solved well, resulting in many efficient multicast routing algorithms. With the rapid development of Wavelength Division Multiplexing (WDM) technology and the increasing of multicast services, how to efficiently merge the WDM technology and the multicast technology, it is a great challenge to implement multicast services in the optical domain in the current optical network development. From the current research, multicast routing is a hot issue of optical networks, which mainly explores how to find a suitable path for a given multicast service request (e.g. a service source and several destination receivers) to solve the problem of data service multicast.

The latest research progress is to model the QoS (quality of service) multicast routing in WDM as a multi-objective optimization problem, and a multi-objective optimization meta-heuristic algorithm is adopted to solve the problem [10 ]. In the document [1], a hybrid evolutionary algorithm combining a genetic algorithm and a minimization of area (GA-MDF) based route allocation and a fast non-dominated sorting genetic algorithm is used for solving a multi-target RWA network design problem. The genetic tabu algorithm combining the genetic algorithm and the tabu search algorithm is used in the document [2] to solve the problem of the minimum cost QoS multicast routing wavelength.

Document [3] solves the problem of routing wavelength allocation in wavelength division multiplexed networks using genetic algorithms. Zhang et al [4,5] propose a multi-objective genetic algorithm based on non-dominated sorting algorithm to solve the QoS-based routing wavelength problem, and then propose a self-adaptive multi-objective genetic algorithm based on decomposition idea to solve the RWA problem in WDM network [6 ]. Wu et al [7] propose a multi-neighbor-based iterative tabu search algorithm, which includes three neighbors with a uniform incremental evaluation method. In document [8], using an algorithm based on multi-population parallel genetic simulated annealing, the routing aims to find a multicast tree with minimum cost, and the wavelength allocation aims to minimize the delay of the multicast tree by minimizing the number of wavelength conversions. Xing et al [9] propose a multi-granularity evolution algorithm MEQGA of a quantum genetic algorithm based on a quantum revolving gate strategy to solve the problem of multicast routing in a WDM network, allow different chromosomes in a same generation population to have different rotation angle step values for updating, and simultaneously propose a self-adaptive quantum mutation operation capable of effectively avoiding local search.

The existing methods in the literature for solving the problem of routing wavelength allocation in wavelength division multiplexing networks have incomplete optimization targets. In addition, various optical network optimization operators in the literature have advantages and disadvantages, and how to select the optimization operators in a self-adaptive manner is a problem to be solved.

There are a large number of heuristic algorithms in the past literature, and these algorithms generally only use a single certain QoS performance parameter as an optimization target (for example, minimizing the cost of multicast trees or minimizing the number of wavelength allocations), and do not comprehensively consider various QoS requirements, so that a solution that is optimal for a certain QoS performance parameter may be a poor solution for another performance parameter, while some solutions that are better for other performance parameters are ignored because they are not optimization targets.

The operators of the multi-objective evolutionary algorithm are not simple to select, because some operators are only effective in problems with specific properties, such as linear separability, and these operators may have parameters that need to be adjusted, which results in a difficult and time-consuming process, because not only the correct combination of multi-objective evolutionary algorithm and operators is found, but also their parameters are adjusted, and it may happen that the optimal parameters at the beginning of the search may be suboptimal parameters at the end of the search.

Note:

[1]L.Pakorn,C.Chalermpol,and W.Naruemon.2010.Solving multi-objective routing and wavelength assignment in WDM network using hybrid evolutionary computation approach.Computer Communications 33,18(Dec.2010),2246–2259.

[2]Alaa M.Allakany,Tarek M.Mahmoud,Koji Okamura,and Moheb R.Girgis.2015.Multiple constraints QoS multicast routing optimization algorithm based on Genetic Tabu Search Algorithm.Advances in Computer Science:an International Journal 4,3(May.2015).

[3]LI Ying-Qiu,ZR Dong,MH Chen.Genetic Algorithm for Routing and Wavelength Assignment in DWDM Optical Networks.Computer Engineering&Design,2010,31(2):295-294

[4]Hongyi Zhang,Zhidong Shen,Changsheng Zhang.A Non-Dominated Sorting Genetic Algorithm for The QoS Based Routing and Wavelength Allocation Problem.Journal of Convergence Information Technology,2013,8(3):560-567

[5]Changsheng Zhang,ZhongLin Li,Xiaohong Zhang,Bin Zhang.Two multi-objective genetic algorithms for the QoS based routing and wavelength allocation problem in WDM network.Optik-International Journal for Light and Electron Optics,2013,pp.2734–2739

[6]Changsheng Zhang,Mingkang Ren,Bin ZhangCollege.A self-adaptive multi-objective genetic algorithm for the QoS based routing andwavelength allocation problem in WDM network.Optik-International Journal for Light and Electron Optics,2013,4571–4575

[7]Xinyun Wu,Shengfeng Yan,XinWan,Zhipeng Lü.Multi-neighborhood based iterated tabu search for routing and wavelength assignment problem.Journal of Combinatorial Optimization,2016,32(2):445-468

[8]Hui Cheng,Xingwei Wang,Shengxiang Yang,and Min Huang.2009.A multi-population parallel genetic simulated annealing-based QoS routing and wavelength assignment integration algorithm for multicast in optical networks.Applied Soft Computing 9,2(Mar.2009),677–684.

[9]Huanlai Xing,Xin Liu,Xing Jin,Lin Bai,and Yuefeng Ji.2009.A multi-granularity evolution based Quantum Genetic Algorithm for QoS multicast routing problem in WDM networks.Computer Communications 32,2(Feb.2009),386-393.

[10]Ying Xu,Yan Zhou.2018.A Steady-State NSGA-II based Multi-Objective Multicast Routing Algorithm for Optical Networks.In Proceedings of The Genetic and Evolutionary Computation Conference(GECOO 2018),July 15-19th,Kyoto,2018.

disclosure of Invention

The technical problem to be solved by the invention is to provide a self-adaptive optical network multicast routing multi-target optimization method aiming at the defects of the prior art, adaptively select a proper operator, improve the solving performance of an algorithm and generate a better group of non-dominated optical network multicast and routing.

In order to solve the technical problems, the technical scheme adopted by the invention is as follows: a multi-objective optimization method for multicast routing of an adaptive optical network comprises the following steps:

1) establishing a spare route set ROUTES;

2) establishing and evaluating an initial population by using the spare routing set ROUTES;

3) judging whether an algorithm ending condition is reached, if so, ending; otherwise, entering step 4);

4) selecting operators from an operator pool by using an operator selection strategy based on bandit and creating filial generations;

5) adopting a loop elimination strategy based on an MPH algorithm to cut off filial generations;

6) evaluating the offspring and merging the offspring into the initial population to obtain an updated population;

7) calculating operator credit values by using a credit allocation strategy based on Pareto contribution for the updated population, assigning the credit values to operators, and generating optical network multicast and routing;

8) and adding 1 to the iteration number, and returning to the step 3).

The specific implementation process of the step 1) comprises the following steps: first, a uniformly distributed coefficient vector w in M dimension is generated₁,w₂,...,w_MIs equal to the number of QoS parameters that need to be considered by w, where w_iIs the ith row of the coefficient vector; 1,2, … …, M; second, the QoS parameters associated with each edge are normalized, let w_iWeighting and summing with the normalized QoS parameter matrix to obtain a weight graph G_iUsing Dijkstra algorithm at G_iTo each destination node d_jFinally, these paths are stored in the ith row and the jth column of the backup route set ROUTES.

The specific implementation process of the step 2) comprises the following steps: initializing a population P by using the spare routing set ROUTES; randomly generating an integer between 1 and | M | for each allele of each chromosome of the population P to obtain a new chromosome, namely a child; in the generation of the t generation offspring population P_oIn the process of (2), an operator o is selected_k，k∈[1,K]K is the total number of operators, and the operators are used for acting on the parent gamma selected from the parent population to obtain offspring

Updating the pareto frontier PF of the current population, and obtaining offspring

Adding the offspring population P_oIs an operator o_kAllocating credits c_k,t(ii) a When the filial generation population P_oNumber and parent population P_tWhen the numbers are the same, the two are merged, and a new generation population P is obtained by using a fast non-dominated sorting and crowding distance comparison operator_t+1。

In step 4), the specific implementation process of selecting an operator from the operator pool by using a bandit-based operator selection strategy comprises: at each time point t, an operator is selected that maximizes the function:

wherein C is a scaling factor;

is an empirical quality estimate of the kth operator; n is_kIndicating the number of times the operator k was selected in the iterations so far.

In step 4), the following operator combinations are set as the operator configuration in the operator pool:

a binomial crossover operator + a Gaussian mutation operator; two-point crossover operator + Gaussian mutation operator; binomial crossover operator + uniform mutation operator; two-point crossover operators and uniform mutation operators; binomial crossover operator + non-uniform mutation operator; two-point crossover operator + non-uniform mutation operator.

The specific implementation process of the step 5) comprises the following steps: multicast tree T_kOnly one source node s is included during initialization, and Z is initialized to

For storing connections to T_kThe distance T is selected from the remaining destination nodes_kDestination node d with minimum cost path_iThen d is_iAnd this least cost path is added to T_kAnd d is_iAddingTo Z; repeating the above process until all destination nodes are added to Z, and obtaining the pruned filial generation.

In step 7), the operator credit value c is calculated using the following formula_i,t，

Wherein the content of the first and second substances,

the decay factor D ∈ [0, 1]]；Reward_iIs a prize value; rank_iIs the rank value.

Compared with the prior art, the invention has the beneficial effects that: the invention adopts an improved NSGA-II algorithm MRWA _ AOSNSGA-II with a self-Adaptive Operator Selection strategy, the optimization targets comprise the use cost of multicast network resources, end-to-end delay and channel utilization rate, QoS constraints such as end-to-end delay, available bandwidth and packet loss rate are met, the Adaptive Operator Selection (AOS) adaptively selects a proper Operator in the algorithm process, the solving performance of the algorithm can be improved, and a better group of non-dominated optical network multicast routing is generated.

Drawings

FIG. 1 is a flow chart of the method of the present invention;

FIG. 2 is a diagram illustrating the establishment of a backup route set according to the present invention;

FIG. 3 is a flow chart of the MPH algorithm;

FIG. 4 is a chromosome representation and alternate route set;

FIG. 5 is a binomial crossover operator;

FIG. 6 is a two-point crossover operator;

FIG. 7 is a uniform mutation operator;

FIG. 8 is a non-uniform mutation operator;

FIG. 9 is a flow chart of a credit allocation strategy based on Pareto contribution;

FIG. 10 is a flowchart of a bandit-based operator selection strategy;

FIG. 11 is a box plot of H values;

fig. 12 is a comparison of Pareto fronts.

Detailed Description

(1) MOMWRA problem modeling:

assume that the all-optical network physical topology is represented as an undirected graph G (V, E, W). The vertex set V represents nodes in the network, the edge set E represents a set of bidirectional optical fiber links E which are interconnected among the nodes, the set belongs to the E, and W is the number of wavelengths which can be used by the optical fiber links. For each link E E, respectively using B (E), DL (E), W (E), and PL (E) to represent the available bandwidth, time delay, available wavelength number, and packet loss rate of the link E. Let the set Λ ═ λ be assumed₁,λ₂,...,λ_kIs the set of wavelengths available for the optical network,

representing the set of wavelengths available on link e. Given a multicast request R (s, D, DL_R,B_R,PL_R) Wherein s ∈ V denotes a source node,

representing a set of destination nodes, DL_RFor time-delay constraints, B_RFor available bandwidth constraints, PL_RIs a packet loss rate constraint. T (s, D, λ) represents a multicast tree with s as a source node and D as a destination node set with λ, i.e. a solution to the problem, D_i∈D。

Representing the movement from a source node s to a destination node d_iThe delay, the available bandwidth and the packet loss rate of a path belonging to the D are defined as follows.

P_T(s,d_i) Delay of (2):

P_T(s,d_i) Available bandwidth of (a):

P_T(s,d_i) The packet loss rate of (1):

according to the above definitions, the delay, available bandwidth, and packet loss rate of the multicast tree T (s, D) are defined as follows.

Delay of T (s, D):

available bandwidth of T (s, D):

packet loss rate of T (s, D):

to define the cost of network resource usage, the following definitions are given:

(a) cost of wavelength usage

For each link e and wavelength λ, the non-negative weight w (e, λ)_i) Indicating the use of λ on link e_iThe cost of (2).

The weight value w (e, lambda)_i) Denotes λ for infinity_iIs invalid on link e. The cost of using the multicast tree T (s, D) for the wavelengths is as shown in equation (7).

(b) Cost of wavelength conversion

For each node v, the wavelength λ_pAnd λ_qDefinition of C_v(λ_p,λ_q) Represented at node v, wavelength λ_pConversion to lambda_qAt a cost of, ifWavelength conversion at node v is not effective, C_v(λ_p,λ_q) Is infinite, if the two wavelengths are the same, then C_v(λ_p,λ_q) 0. The cost of wavelength conversion for the multicast tree T (s, D) is as shown in equation (8).

(c) Cost of photodisruption

C (v) is the cost of replicating a signal once from the splitter at vertex v, which is the product of c (v) and the number of times n the optical signal is replicated at vertex v, defined as equation (9).

Thus, the cost of network resource usage can be defined as equation (10).

The proposed momtra problem is defined as follows.

1) Minimizing multicast tree delay definition:

f₁(T)＝Minimize(DL(T(s,D))) (11)

2) minimizing network resource usage cost definition:

3) minimization of channel reuse definition:

where Λ is the set of wavelengths, b_wIndicating the wavelength requirements of the current data stream,

indicating the capacity of the wavelength lambda on the link e,

represents a binary variable whose value is 1 if and only if the link e uses the wavelength λ to transmit data on the tree T, and whose value is 0 otherwise.

Meanwhile, the following constraint conditions need to be met:

DL(T(s,D))≤DL_R (14)

B(T(s,D))≥B_R (15)

PL(T(s,D))≤PL_R (16)

(2) alternate routing strategy

The backup route set is created in advance, and the process of creating the backup route set is as shown in fig. 2, and first, a coefficient vector w with uniform distribution in | M | dimension is generated₁,w₂,...,w_MIs equal to the number of QoS parameters that need to be considered by w, where w_iIs the ith row of the coefficient vector. Second, the QoS parameters associated with each edge are normalized because they have different value ranges. Next, let w_iWeighting and summing with the normalized QoS parameter matrix to obtain a weight graph G_iUsing Dijkstra algorithm at G_iTo each destination node d_jFinally, these paths are stored in the ith row and the jth column of the backup path set ROUTES.

After the standby route set is established, the idea of the routing strategy is as follows: in the operation of the algorithm, the number of genes in the chromosome is equal to the number of destination nodes, and each gene points to a unit in ROUTES, which stores a path from the source node to the destination node represented by the gene.

(3) Loop elimination strategy based on MPH algorithm

The MPH algorithm is to find the shortest path from a node to a local tree by using a shortest path algorithm, and then connect the node to the local tree through the shortest path, and the algorithm complexity is O (m)n²) And n and m represent the number of nodes and the number of canonical points in the graph, respectively. MPH Algorithm flow diagram As shown in FIG. 3, multicast Tree T_kOnly one source node s is included during initialization, and Z is initialized to

For storing connections to T_kThen, a distance T is selected among the remaining destination nodes_kDestination node d with minimum cost path_iThen d is_iAnd this least cost path is added to T_kAnd d is_iTo Z. The above steps are repeated until all destination nodes are added to Z.

(4) Chromosome coding mode

And adopting a decimal coding mechanism, wherein the number of genes in each chromosome is the number of destination nodes, and the allele of each gene is an integer from 1 to the column number of the alternative path set ROUTES. For example, in a network G with 15 nodes, when the source node is 1, the destination node set is {3, 5, 7, 9, 11, 13}, and there are 6 destination nodes, the relationship between the corresponding chromosome and ROUTES is shown in fig. 4.

(5) Operator pool setting

Due to the restrictions of the encoding method of the chromosome caused by the specificity of the solution, the allele of each gene in the chromosome must be an integer between 1 and the number of rows | R | of the alternative route set ROUTES after the operator operation in the operator pool. With the above limitations, a binomial crossover operator and a two-point crossover operator are selected as crossover operators in an operator pool, and a uniform mutation operator, a non-uniform mutation operator and a gaussian mutation operator are selected as mutation operators in the operator pool, and the five operators are defined as follows:

1) binomial crossover operator

Wherein v isⁱAnd xⁱIs parent, uⁱFor the child solution resulting from the intersection operation, j ∈ [ 1.,n]Denotes the gene index in the chromosome, n is the number of genes in the chromosome, and rand is from [0, 1]]A uniform random number selected from among CR ∈ [0, 1]]To cross probability, j_randIs an integer randomly selected from the set S ═ { 1.., n }. A schematic diagram of the binomial crossover is given in fig. 5.

2) Two-point intersection operator

Two-point crossing means that two crossing points are randomly set in two chromosomes paired with each other, and then a part of genes between the two crossing points is exchanged. FIG. 6 is a schematic diagram of a two-point intersection, where t₁And t₂Are two cross points randomly selected on the chromosome.

3) Uniform mutation operator

The uniform mutation operator is suitable for the initial stage of the algorithm and can increase the diversity of the population. The uniform mutation operation is to replace the original gene values of each gene in the chromosome with a small probability by random numbers uniformly distributed in a certain range. The specific operation process of uniform mutation is that each gene on the chromosome is designated as a mutation point in turn, and then the mutation probability p is used for each mutation point_mAnd a random number is taken from the value range of the corresponding gene to replace the original gene value.

Suppose a chromosome in a population is represented as x ═ x₁x₂...x_k...x_n]Wherein x is_j(j∈[1,n]) Is a gene on the chromosome of an individual, and n is the number of genes in the chromosome. If x_kIs a variation point and has a value range of

Then the new gene x 'of the mutation point'_kThe values of (A) are:

wherein γ ∈ [0, 1]]Is a random number uniformly distributed, j belongs to [1]Represents the gene index in the chromosome, and rand is from [0, 1]]A uniform random number, p, selected from_mIs the mutation probability, j_randAnd rounding the selected integer from the set S ═ 1.. multidot.n } so as to ensure that the obtained gene value is an integer, and if the gene value obtained by mutation is out of range, performing out-of-range processing, namely setting the gene value as a boundary value of the value range. FIG. 7 is a schematic diagram of uniform variation.

4) Non-uniform mutation operator

The non-uniform mutation is a dynamic mutation operator, the operator is in a uniform search space at the beginning, and the search process is more concentrated in a certain key area along with the operation of an algorithm. Suppose a chromosome in a population is represented as x ═ x₁x₂...x_k...x_n]Wherein x is_j(j∈[1,n]) Is a gene on the chromosome of an individual, and n is the number of genes in the chromosome. If x_kIs a variation point and has a value range of

Then the new gene x 'of the mutation point'_kThe values of (A) are:

wherein gamma is randomly 0 or 1, p_mIs the mutation probability. Δ (t, y) represents [0, y ]]A random number in the range conforming to a non-uniform distribution requires that as the number of iterations t increases, the probability that Δ (t, y) is close to 0 also increases gradually. Δ (t, y) can be defined as follows: Δ (t, y) ═ y (1-r)^(1-t/T)b) Wherein r is [0, 1]]A random number is uniformly distributed in the range, T is the maximum iteration number, and b is a system parameter which determines the degree of dependence of random number disturbance on the iteration number T. The rounding is to ensure that the obtained gene value is an integer, and if the gene value obtained by mutation is out of range, the out-of-range processing is carried out, namely the gene value is set as the boundary value of the value range. FIG. 8 is a diagram of non-uniform variations.

5) Gauss mutation operator

Gaussian variation is another method for improving the local search performance of genetic algorithm on key search areasA variation operation method, wherein Gaussian variation operation refers to that when variation operation is performed, coincidence mean value is mu and variance is sigma²A random number of the normal distribution of (a) replaces the original gene value. From the characteristics of the normal distribution, it is known that the gaussian variation is also an important search for a local region near the original individual. The specific process of gaussian variation is similar to uniform variation.

When the Gaussian variation is realized, the random numbers Q conforming to the normal distribution can be composed of random numbers r conforming to the uniform distribution_i(i ═ 1, 2.., 12) then N (μ, σ) is satisfied²) A random number Q of a normal distribution can be derived from:

suppose a chromosome in a population is represented as x ═ x₁x₂...x_k...x_n]Wherein x is_j(j∈[1,n]) Is a gene on the chromosome of an individual, and n is the number of genes in the chromosome. If x_kIs a variation point and has a value range of

And assume that

Then the new gene x 'of the mutation point'_kThe values of (A) are:

the rounding is to ensure that the obtained gene value is an integer, and if the gene value obtained by mutation is out of range, the out-of-range processing is carried out, namely the gene value is set as the boundary value of the value range.

According to the above definitions of crossover operators and mutation operators, the following operator combinations are set as the operator configurations in the operator pool:

a)op₁: binomial crossover operator + Gaussian mutation operator

b)op₂: two arePoint crossover operator + Gaussian mutation operator

c)op₃: binomial crossover operator + uniform mutation operator

d)op₄: two-point crossover operator + uniform mutation operator

e)op₅: binomial crossover operator + non-uniform mutation operator

f)op₆: two-point crossover operator + non-uniform mutation operator

(6) Credit allocation strategy based on pareto frontier contribution

According to the operator o_iGenerated offspring solution

The contribution to the pareto front PF rewards the operator. If an operator o_iThe solution generated

The operator is rewarded by entering the current pareto frontier PF either because it continuously approaches the pareto optimal solution by replacing one or more existing solutions in the current PF solution set, or by increasing the diversity of the current PF while not replacing any solution in the PF. Since the pareto frontier PF may be solved with the offspring

Is updated so that each child solution is generated, the credit value for each operator must be recalculated, which allocation of credits will favor operators that significantly improve the PF over those that incrementally improve the PF. The operator o is measured here by the following formula_iInfluence produced during search, where n_PFIndicating the number of solutions in the current PF.

All Reward obtained_iThe values are arranged in a reverse order to order Rank_iAs a sequence of operators iNumber (n). To give the best operator more opportunities to select, we introduce the decay factor D ∈ [0, 1]]Will Reward_iIs converted into

Next, we shall credit c_i,tAnd (3) assigning to an operator i:

(7) bandit-based operator selection strategy

The ith operator having an empirical quality estimate

And a number n of times depending on it has been used previously_iThe confidence interval of (c). At each point in time t, a separate arm will be chosen that can maximize the function:

where C is a scale factor used to balance the development of the best operator with the exploration of other operators. n is_iIndicating the number of times operator i was selected in the iteration so far. When the algorithm starts we give each operator the same probability to be selected.

(8) MRWA _ AOSNSGA-II algorithm

When the algorithm starts, a backup route set ROUTES is established, the number of rows of the ROUTES is | M |, then a population P is initialized, and the initialization mode is as follows: an integer between 1 and | M | is randomly generated for each allele of each chromosome. Next, the pareto frontier PF of the current population is calculated. When the algorithm enters the main circulation stage, the filial population P of the generation t is generated_oIn the process of (2), an operator o is selected according to an operator selection strategy_i(i∈[1,K]K is the total number of operators), the operators are used to act on the parent gamma selected from the parent population to obtain offspring

Updating the pareto frontier PF of the current population, and obtaining offspring

Adding the offspring population P_oUsing credit allocation strategy as operator o_iAllocating credits c_i,t. When the filial generation population P_oNumber and parent population P_tWhen the numbers are the same, the two are merged, and a new generation population P is obtained by using a fast non-dominated sorting and crowding distance comparison operator_t+1. The pseudo code of the algorithm is shown in algorithm 4.3.

The effectiveness of the solution was verified using four different sized networks, including a true optical network Europe net, and three randomly generated networks Random _ N1, Random _ N2, Random _ N3. The Europe net contains 28 nodes and 41 edges. Random _ N1 is composed of 40 nodes and 153 edges, Random _ N2 is composed of 70 nodes and 280 edges, and Random _ N3 is composed of 100 nodes and 603 edges. Each link in these networksContaining 10 wavelength channels. Each optical node is assumed to have wavelength conversion capability, meaning that different wavelengths may be used in the same transport service. Twelve test cases were generated for testing these algorithms according to the optical network above, and table 1 is the detailed information of these test cases. In each test case, the maximum suitable evaluation value per run is defined as

Wherein G is_nodes，G_edgesAnd G_perRespectively representing the number of nodes of the network, the number of edges and the percentage of the target node in each test case to the total nodes. All algorithms were run on a Core (i7),3.40GHz,8GB RAM computer, with each algorithm run 20 times on each test case.

Table 1 network tested.

To prove the effectiveness of the proposed algorithm MRWA _ AOSNSGA-II, the algorithms were compared in three sets of experiments: (1) in order to verify the effectiveness of the algorithm in solving the MOMRWA problem, the algorithm is compared with three multi-objective optimization algorithms for solving the MRWA problem, wherein the algorithms are respectively a multi-objective optimization algorithm based on decomposition, a multi-objective optimization algorithm based on enhanced pareto and a multi-objective optimization algorithm based on rapid non-dominant ordering, and are respectively represented by MRWA _ MOEA/D, MRWA _ SPEA2 and MRWA _ NSGA-II.

TABLE 2 comparison of H indicators

TABLE 3 comparison of overlay (C) indicators

(MRWA_MOEA/D(I)，MRWA_SPEA2(II)，MRWA_NSGA-II(III)，and MRWA_AOSNSGA-II(IV))

(2) To verify the validity of the adaptive operator selection strategy addition, the algorithm MRWA _ AOSNSGA-II (VII) is compared with an algorithm using only a single operator, which is respectively denoted as MRWA _ NSGA-II_op1(I)、MRWA_NSGA-II_op2(II)、MRWA_NSGA-II_op3(III)、MRWA_NSGA-II_op4(IV)、MRWA_NSGA-II_op5(V)、MRWA_NSGA-II_op6(VI)

(3) TABLE 4 Single operator comparison with coverage (C) index for MRWA _ AOSNSGA-II

(4) To verify the validity of the proposed credit allocation strategy based on pareto contributions and the bandit-based operator selection strategy, the algorithm is compared with algorithms using different credit allocation strategies and operator selection strategies. Selecting a comparative credit allocation policy herein as based on the dominant child vs parent type of creditUsing an allocation strategy, denoted by OP, which rewards operators that can produce child solutions that dominate their parents; the operator selection strategies for comparison herein are Random selection strategy (Random), Probabilistic Matching (PM), and adaptive tracking (AP). The algorithms to be compared are respectively MRWA _ NSGA-II_Random(I)、MRWA_NSGA-II_OP+PM(II)、MRWA_NSGA-II_OP+AP(III) is shown.

(5) TABLE 5 comparison of H values

(6)

(7) TABLE 6 overlay (C) index comparison

(8)(MRWA_NSGA-II_Random(I)，MRWA_NSGA-II_OP+PM(II)，MRWA_NSGA-II_OP+AP(III)，，MRWA_AOSNSGA-II(IV))。

Claims (7)

1. A multi-objective optimization method for multicast routing of an adaptive optical network is characterized by comprising the following steps:

1) establishing a spare route set ROUTES;

2) establishing and evaluating an initial population by using the spare routing set ROUTES;

3) judging whether an algorithm ending condition is reached, if so, ending; otherwise, entering step 4);

4) selecting operators from an operator pool by using an operator selection strategy based on bandit and creating filial generations;

5) adopting a loop elimination strategy based on an MPH algorithm to cut off filial generations;

6) evaluating the offspring and merging the offspring into the initial population to obtain an updated population;

7) calculating operator credit values by using a credit allocation strategy based on Pareto contribution for the updated population, assigning the credit values to operators, and generating optical network multicast and routing;

8) and adding 1 to the iteration number, and returning to the step 3).

2. The adaptive optical network multicast routing multi-objective optimization method according to claim 1, wherein the specific implementation process of step 1) includes: first, a uniformly distributed coefficient vector w in M dimension is generated₁,w₂,...,w_MIs equal to the number of QoS parameters that need to be considered by w, where w_iIs the ith row of the coefficient vector; 1,2, … …, M; second, the QoS parameters associated with each edge are normalized, let w_iWeighting and summing with the normalized QoS parameter matrix to obtain a weight graph G_iUsing Dijkstra algorithm at G_iTo each destination node d_jFinally, these paths are stored in the ith row and the jth column of the backup route set ROUTES.

3. The adaptive optical network multicast routing multi-objective optimization method according to claim 2, wherein the specific implementation process of step 2) includes: initializing a population P by using the spare routing set ROUTES; randomly generating an integer between 1 and | M | for each allele of each chromosome of the population P to obtain a new chromosome, namely a child; in the generation of the t generation offspring population P_oIn the process of (2), an operator o is selected_k，k∈[1,K]K is the total number of operators, and the operators are used for acting on the parent gamma selected from the parent population to obtainTo offspring

Updating the pareto frontier PF of the current population, and obtaining offspring

Adding the offspring population P_oIs an operator o_kAllocating credits c_k,t(ii) a When the filial generation population P_oNumber and parent population P_tWhen the numbers are the same, the two are merged, and a new generation population P is obtained by using a fast non-dominated sorting and crowding distance comparison operator_t+1。

4. The adaptive optical network multicast routing multi-objective optimization method according to claim 1, wherein in step 4), the specific implementation process of selecting an operator from the operator pool by using a bandit-based operator selection strategy includes: at each time point t, an operator is selected that maximizes the function:

wherein C is a scaling factor;

is an empirical quality estimate of the kth operator; n is_kIndicating the number of times the operator k was selected in the iterations so far.

5. The adaptive optical network multicast routing multi-objective optimization method according to claim 1, wherein in step 4), the following operator combinations are set as the operator configuration in the operator pool:

a binomial crossover operator + a Gaussian mutation operator; two-point crossover operator + Gaussian mutation operator; binomial crossover operator + uniform mutation operator; two-point crossover operators and uniform mutation operators; binomial crossover operator + non-uniform mutation operator; two-point crossover operator + non-uniform mutation operator.

6. The adaptive optical network multicast routing multi-objective optimization method according to claim 1, wherein the specific implementation process of step 5) includes: multicast tree T_kOnly one source node s is included during initialization, and Z is initialized to

For storing connections to T_kThe distance T is selected from the remaining destination nodes_kDestination node d with minimum cost path_iThen d is_iAnd this least cost path is added to T_kAnd d is_iTo Z; repeating the above process until all destination nodes are added to Z, and obtaining the pruned filial generation.

7. The adaptive optical network multicast routing multi-objective optimization method according to claim 1, wherein in step 7), the operator credit value c is calculated by using the following formula_i,t，

Wherein the content of the first and second substances,

the decay factor D ∈ [0, 1]]；Reward_iIs a prize value; rank_iIs the rank value.

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