【智能优化算法-灰狼算法】基于非支配排序灰狼优化器（NS-GWO）算法求解多目标优化算法附matlab代码

1 内容介绍

1.1 灰狼算法介绍

2 仿真代码

%% Non Sorted Grey Wolf Algorithm (NSGWO) % NSGWO is developed by Pradeep Jangir %% Objective Function % The objective function description contains information about the % objective function. M is the dimension of the objective space, D is the % dimension of decision variable space, LB and UB are the % range for the variables in the decision variable space. User has to % define the objective functions using the decision variables. Make sure to % edit the function 'evaluate_objective' to suit your needs. clc clear all D = 30; % Number of decision variables M = 2; % Number of objective functions K=M+D; LB = ones(1, D).*0; % LB - A vector of decimal values which indicate the minimum value for each decision variable. UB = ones(1, D).*1; % UB - Vector of maximum possible values for decision variables. Max_iteration = 100; % Set the maximum number of generation (GEN) SearchAgents_no = 100; % Set the population size (Search Agent) ishow = 10; %% Initialize the population % Population is initialized with random values which are within the % specified range. Each chromosome consists of the decision variables. Also % the value of the objective functions, rank and crowding distance % information is also added to the chromosome vector but only the elements % of the vector which has the decision variables are operated upon to % perform the genetic operations like corssover and mutation. chromosome = initialize_variables(SearchAgents_no, M, D, LB, UB);

%% Sort the initialized population % Sort the population using non-domination-sort. This returns two columns % for each individual which are the rank and the crowding distance % corresponding to their position in the front they belong. At this stage % the rank and the crowding distance for each chromosome is added to the % chromosome vector for easy of computation. intermediate_chromosome = non_domination_sort_mod(chromosome, M, D);

%% Perform Selection % Once the intermediate population is sorted only the best solution is % selected based on it rank and crowding distance. Each front is filled in % ascending order until the addition of population size is reached. The % last front is included in the population based on the individuals with % least crowding distance % Select NP fittest solutions using non dominated and crowding distance % sorting and store in population Population = replace_chromosome(intermediate_chromosome, M,D,SearchAgents_no); %% Start the evolution process % The following are performed in each generation % * Select the parents which are fit for reproduction % * Perfrom crossover and Mutation operator on the selected parents % * Perform Selection from the parents and the offsprings % * Replace the unfit individuals with the fit individuals to maintain a % constant population size. Pareto = NSGWO(D,M,LB,UB,Population,SearchAgents_no,Max_iteration,ishow); save Pareto.txt Pareto -ascii; % save data for future use %% Plot data if M == 2 plot_data2(M,D,Pareto) elseif M == 3 plot_data_TCQ(M,D,Pareto); end

%% function f = initialize_variables(N, M, D, LB, UB) % This function initializes the population. Each individual has the % following at this stage % * set of decision variables % * objective function values % % where, % NP - Population size % M - Number of objective functions % D - Number of decision variables % min_range - A vector of decimal values which indicate the minimum value % for each decision variable. % max_range - Vector of maximum possible values for decision variables.

min = LB; max = UB;

% K is the total number of array elements. For ease of computation decision % variables and objective functions are concatenated to form a single % array. For crossover and mutation only the decision variables are used % while for selection, only the objective variable are utilized.

K = M + D; f=zeros(NP,K);

%% Initialize each individual in population % For each chromosome perform the following (N is the population size) for i = 1 : NP % Initialize the decision variables based on the minimum and maximum % possible values. V is the number of decision variable. A random % number is picked between the minimum and maximum possible values for % the each decision variable. for j = 1 : D f(i,j) = min(j) + (max(j) - min(j))*rand(1); end % end for j % For ease of computation and handling data the chromosome also has the % vlaue of the objective function concatenated at the end. The elements % D + 1 to K has the objective function valued. % The function evaluate_objective takes one individual at a time, % infact only the decision variables are passed to the function along % with information about the number of objective functions which are % processed and returns the value for the objective functions. These % values are now stored at the end of the individual itself. f(i,D + 1: K) = evaluate_objective(f(i,1:D)); end % end for i

%% Zitzler1 function (ZDT3)
function f = zdt3 (x)
% Number of objective is 2.
% Number of variables is 30. Range x [0,1]
f = [];
n=length(x);
g=1+9*sum(x(2:n))/(n-1);
f(1)=x(1);
f(2)=1-sqrt(x(1)/g)-(x(1)/g)*sin(10*pi*x(1));

min = LB; max = UB;

K = M + D; f=zeros(NP,K);

%% function f = evaluate_objective(x) % Function to evaluate the objective functions for the given input vector % x. x is an array of decision variables and f(1), f(2), etc are the % objective functions. The algorithm always minimizes the objective % function hence if you would like to maximize the function then multiply % the function by negative one. M is the numebr of objective functions and % D is the number of decision variables. % This functions is basically written by the user who defines his/her own % objective function. Make sure that the M and D matches your initial user % input. % A set of testing function is stored in folder TEST %% Retrieve function from folder TEST f = zdt1(x); % change the name of function we can use different functions end

3 运行结果

4 参考文献

[1]姜飞. 基于灰狼优化算法的多目标柔性作业车间动态调度研究[D]. 江苏大学.

[2]颜曙林. 基于非支配排序的多目标优化算法改进研究. 2016.

[3]张涛, 余利, 冯朕,等. 基于多目标差分灰狼算法的配电网无功优化方法:, CN109768573A[P]. 2019.

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