【晶体结构算法】基于晶体结构算法求解单目标优化问题附Matlab源码

1 简介

Metaheuristics are computational procedures that intelligently lead the search process through the efficient exploration of the search space associated with an optimization problem. With the progressive outburst of problems with large data sets in various fields, there is an ongoing quest for enhancing existing metaheuristic algorithms as well as developing new ones with greater accuracy and efficiency. In general, a powerful and efficient metaheuristic algorithm is based on a rich inspiration source, implemented effectively through a precise mathematical model. Aiming to develop a highly efficient, nature-inspired optimization algorithm, here we propose a novel metaheuristic called Crystal Structure Algorithm (CryStAl). This method is chiefly inspired by the principles underlying the formation of crystal structures from the addition of the basis to the lattice points, which is a natural phenomenon that can be seen in the symmetric arrangement of constituents (i.e. atoms, molecules, or ions) in crystalline minerals such as quartz. A total number of 239 mathematical functions which are categorized into four different groups are utilized to evaluate the overall performance of the proposed method. To validate the results of this novel algorithm, 12 different classical and modern metaheuristic algorithms are selected from the literature. The minimum, mean, and standard deviation values alongside the number of function evaluations for CryStAl and the other metaheuristics for a specific tolerance are calculated and presented accordingly. The obtained results, further supported by a complete statistical analysis, demonstrated that the proposed algorithm is capable of providing very competitive results, outperforming the other metaheuristics in most cases.

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2 部分代码

% ----------------------------------------------------------------------- %%% [1] Talatahari, S. , et al. "Crystal Structure Algorithm (CryStAl): A Metaheuristic Optimization Method." IEEE Access PP.99(2021):1-1. for Unconstrained Benchmark Problems​%%clc;clear all;                                                              %% Get Required Problem InformationObjFuncName = @(x) Sphere(x); % @CostFunction ;Var_Number = 100 ; % Number of variables ;LB = -10 *ones(1,Var_Number) ;  % Lower bound of variable ;UB = 10 *ones(1,Var_Number) ;  % Upper bound of variable ;%% Get Required Algorithm ParametersMaxIteation = 1000 ; % Maximum number of Iterations ;Cr_Number = 10 ; % Maximum number of initial Crystals ;%% Outputs:% BestCr        (Best solution)% BestFitness     (final Best fitness)% Conv_History    (Convergence History Curve)%% Updating the Size of ProblemParametersif length(LB)==1    LB=repmat(LB,1,Var_Number);endif length(UB)==1    UB=repmat(UB,1,Var_Number);end%% Initialization% Initializing the Position of first probsval(i)                Fun_eval(i)=Fun_evalNew(i2);                Crystal(i,:)=NewCrystal(i2,:);            end            % Updation the Number of Function Evalutions            Eval_Number=Eval_Number+1;        end    end % End of One Iteration    Iter=Iter+1;   % The best Crystal    [BestFitness,idbest]=min(Fun_eval);    Crb=Crystal(idbest,:);    BestCr=Crb;    Conv_History(Iter)=BestFitness;    % Show Iteration Information    disp(['Iteration ' num2str(Iter) ': Best Cost = ' num2str(Conv_History(Iter))]);end % End of Main Loopingsemilogy(Conv_History)​​

3 仿真结果

4 参考文献

[1] Talatahari, S. , et al. "Crystal Structure Algorithm (CryStAl): A Metaheuristic Optimization Method." IEEE Access PP.99(2021):1-1.

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