💥1 概述
参考文献：
提出了基于自适应适应度-距离平衡选择的随机分形搜索（FDB-SFS）算法。对实验研究中提出的方法的结果进行了统计评估，并与文献中竞争优化算法的结果进行了比较。对比表明，所提出的FDB-SFS算法在寻找最优解方面优于其他算法，并且收敛速度更快达到最优解。根据实验研究结果，所提出的FDB-SFS算法在OPF问题中的优化成本比AO、GBO、GPC、HGS、HHO、RUN、TSO、LSHADE、LSHADE-EPSIN、LSHADE-CNEPSIN、LSHADE-SPACMA和MadDE优化算法好5.7362%、0.0954%、7.6244、0.1785%、2.4329%、1.7408%、1.95317%、3.5486%、2.2007%和1.5203%。
📚2 运行结果
部分代码：
function []=case_1() [nPop, dimension, maxIteration, lbArray, ubArray] = problem_terminate(); S.Start_Point = nPop; S.Maximum_Diffusion = 0; S.Walk = 1; % *Important S.Ndim = dimension; S.Lband = lbArray; S.Uband = ubArray; S.Maximum_Generation = maxIteration; P = zeros(S.Start_Point,S.Ndim); %Creating random points in considered search space========================= point = repmat(S.Lband,S.Start_Point,1) + rand(S.Start_Point, S.Ndim).* ... (repmat(S.Uband - S.Lband,S.Start_Point,1)); %========================================================================== %Calculating the fitness of first created points=========================== FirstFit = zeros(1,S.Start_Point); for i = 1 : size(point,1) FirstFit(i) = problem(point(i,:)); end [Sorted_FitVector, Indecis] = sort(FirstFit); point = point(Indecis,:);%sorting the points based on obtaind result %========================================================================== %Finding the Best point in the group======================================= BestPoint = point(1, :); fbest = Sorted_FitVector(1);%saving the first best fitness %========================================================================== nfeval = 1; %Starting Optimizer======================================================== while ( ( nfeval < S.Maximum_Generation) ) New_Point = point; FitVector = Sorted_FitVector; %diffusion process occurs for all points in the group if S.Maximum_Diffusion>0 for i = 1 : S.Start_Point %creating new points based on diffusion process [NP, fit] = Diffusion_Process(point(i,:),Sorted_FitVector(i),S,nfeval,BestPoint,fhd, fNumber); New_Point(i,:) = NP; FitVector(i) = fit; nfeval = nfeval + 1; if nfeval >= S.Maximum_Generation S.Start_Point = 0; break; end end end fit = FitVector'; [~, sortIndex] = sort(fit); Pa = zeros(1,S.Start_Point); %Starting The First Updating Process==================================== for i=1:1:S.Start_Point Pa(sortIndex(i)) = (S.Start_Point - i + 1) / S.Start_Point; end RandVec1 = randperm(S.Start_Point); RandVec2 = randperm(S.Start_Point); FDBIndex = fitnessDistanceBalance( point, fit); for i = 1 : S.Start_Point for j = 1 : size(New_Point,2) if rand > Pa(i) if Sigmoid_Func_1_Increase(S.Maximum_Generation, nfeval) P(i,j) = New_Point(FDBIndex,j) - rand*(New_Point(RandVec2(i),j) - New_Point(i,j)); else P(i,j) = New_Point(RandVec1(i),j) - rand*(New_Point(RandVec2(i),j) - New_Point(i,j)); end else P(i,j)= New_Point(i,j); end end end P = Bound_Checking(P,S.Lband,S.Uband);%for checking bounds for i = 1 : S.Start_Point Fit_FirstProcess = problem(P(i,:)); if Fit_FirstProcess<=fit(i) New_Point(i,:)=P(i,:); fit(i)=Fit_FirstProcess; end nfeval = nfeval + 1; if nfeval >= S.Maximum_Generation S.Start_Point = 0; break; end end FitVector = fit; %====================================================================== [Sorted_FitVector,SortedIndex] = sort(FitVector); New_Point = New_Point(SortedIndex,:); BestPoint = New_Point(1,:);%first point is the best pbest = New_Point(1,:); fbest = FitVector(1); point = New_Point; %Starting The Second Updating Process================================== Pa = sort(SortedIndex/S.Start_Point, 'descend'); for i = 1 : S.Start_Point if rand > Pa(i) %selecting two different points in the group R1 = ceil(rand*size(point,1)); R2 = ceil(rand*size(point,1)); while R1 == R2 R2 = ceil(rand*size(point,1)); end if rand < .5 ReplacePoint = point(i,:) - rand * (point(R2,:) - BestPoint); else ReplacePoint = point(i,:) + rand * (point(R2,:) - point(R1,:)); end ReplacePoint = Bound_Checking(ReplacePoint,S.Lband,S.Uband); replaceFit = problem(ReplacePoint); if replaceFit < Sorted_FitVector(i) point(i,:) = ReplacePoint; Sorted_FitVector(i) = replaceFit; end if replaceFit < fbest pbest = ReplacePoint; fbest = replaceFit; BestPoint = pbest; end nfeval = nfeval + 1; if nfeval >= S.Maximum_Generation break; end end end end bestFitness=fbest; bestSolution=pbest; fprintf('Best Fitness: %d\n', bestFitness); disp('Best Solution:'); disp(bestSolution); end function p = Bound_Checking(p,lowB,upB) for i = 1 : size(p,1) upper = double(gt(p(i,:),upB)); lower = double(lt(p(i,:),lowB)); up = find(upper == 1); lo = find(lower == 1); if (size(up,2)+ size(lo,2) > 0 ) for j = 1 : size(up,2) p(i, up(j)) = (upB(up(j)) - lowB(up(j)))*rand()... + lowB(up(j)); end for j = 1 : size(lo,2) p(i, lo(j)) = (upB(lo(j)) - lowB(lo(j)))*rand()... + lowB(lo(j)); end end end end function [createPoint, fitness] = Diffusion_Process(Point,Fitness,S,g,BestPoint, fhd, fNumber) %calculating the maximum diffusion for each point NumDiffiusion = S.Maximum_Diffusion; New_Point = zeros(S.Maximum_Diffusion+1,S.Ndim); fitness = zeros(1,S.Maximum_Diffusion+1); New_Point(1,:) = Point; fitness(1) = Fitness; %Diffiusing Part******************************************************* for i = 1 : NumDiffiusion %consider which walks should be selected. if rand < S.Walk GeneratePoint = normrnd(BestPoint, (log(g)/g)*(abs((Point - BestPoint))), [1 size(Point,2)]) + (randn*BestPoint - randn*Point); % E艧itlik (11) else GeneratePoint = normrnd(Point, (log(g)/g)*(abs((Point - BestPoint))),[1 size(Point,2)]); % E艧itlik (12) end New_Point(i+1,:) = GeneratePoint; end %check bounds of New Point New_Point = Bound_Checking(New_Point,S.Lband,S.Uband); %sorting fitness for i = 2 : size(New_Point,1) fitness(i) = problem(New_Point(i,:)); end [fit_value,fit_index] = sort(fitness); fitness = fit_value(1,1); New_Point = New_Point(fit_index,:); createPoint = New_Point(1,:); %====================================================================== end
🌈3 Matlab代码实现
🎉4 参考文献
部分理论来源于网络，如有侵权请联系删除。
[1]Duman, S., Kahraman, H. T., Kati, M., "Economical operation of modern power grids incorporating uncertainties of renewable energy sources and load demand using the adaptive fitness-distance balance-based stochastic fractal search algorithm", Engineering Applications of Artificial Intelligence, Volume 117, Part A, 2023, 105501,https://doi.org/10.1016/j.engappai.2022.105501.
