2023年最新智能优化算法之——IBI逻辑优化算法(IBL)，附MATLAB代码

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今天给大家带来一个有意思的智能优化算法，IBL算法。

先说效果：在CEC2005函数集测试，基本上毫无压力，把把都能预测的很准确，而且速度极快。大家可以自行尝试哈。

为啥说这个算法有意思呢，大家看IBL的英文全称是：Incomprehensible but Intelligible-in-time logics，我在这里给大家直译成中文就是：难以理解但又能及时理解的逻辑。可能我翻译的不太准确啊，但是我又结合他的摘要，大概的理解就是：人类的思维不像计算机那样，人类的思维是可以随着时间、事物的变化而变化的，在之前看起来毫无逻辑的事情，在经过人类学习一段时间后，这个事情就会变得很有逻辑了。不得不说老外这个思维是真的奇特哈，根据这个也能提出一个新算法，而且效果还很不错。大家感兴趣的可以去看看原文。

参考文献：

Mirrashid, M.; Naderpour, H. Incomprehensible but Intelligible-in-time logics: Theory and optimization algorithm. Knowl.-Based Syst. 2023, 264, . doi点击链接跳转原文 

废话不多说，依旧是2005函数集的测试，附上2005函数集的理论范围：

 大部分优化函数在F8上的表现是不太好的，也就寻优到-4000多，咱们试一下这个IBL：

WOW，直接就干到-9700多去了，看样子不错呀，回头了我会将2023年最新的算法做一个对比，决一雌雄一下。

再试一个F14的，理论值是1，能找到0.，还阔以

 最后再来一个：

上核心代码！

function [Bests_Results,n_it_phase1,n_it_phase2,n_it_phase3,costs1,costs2,costs3] = ILA (CostFunction,Vmin,Vmax,nV,nNL,nModel,nIt,mIt_Phase1,mIt_Phase2,Bmin,Bmax,nRep,nIt_classification) %% Initialization Empty.NL = []; % Current NL Empty.NLprevious = []; % Previous NL Empty.Cost = inf; Empty1.NL = []; % Current NL Empty1.Average = []; % Previous NL Empty1.Cost = inf; Empty1.Members = []; Experts = repmat (Empty, nNL, 1); % Experts n_it_phase1 = round(nIt*mIt_Phase1); % Number of iterations in phase 1 n_it_phase2 = round(nIt*mIt_Phase2); % Number of iterations in phase 2 n_it_phase3 = nIt-n_it_phase1-n_it_phase2; % Number of iterations in phase 3 costs1 = zeros(n_it_phase1,1); % Costs of the phase 1 costs2 = zeros(n_it_phase2,1); % Costs of the phase 2 costs3 = zeros(n_it_phase3,1); % Costs of the phase 3 n_Groups = zeros(nModel,1); Em.NL = []; Em1.NL = []; Em1.Cost = inf; Expert_IbI = repmat (Em1, 1, 1); % The best solution of the current generation Logic = repmat (Em1, 1, 1); % The best solution before the current generation Expert_new = repmat (Em1, 1, 1); K0 = repmat (Em, nNL, 1); % Knowledge 0 K1 = repmat (Em, nNL, 1); % Knowledge 1 Expert_new.NL = []; Expert_new.Cost = inf; Knowledge_Phase1 = K0; Knowledge_Phase2 = K0; Knowledge_Phase3 = K0; GroupNumber = ones(nNL,1); Em2.NL = []; Em2.Cost = inf; Bests_Results = repmat (Em2, nIt, 1); if length(Vmin) ~= (nV) Vmin=Vmin.*ones(1,nV); Vmax=Vmax.*ones(1,nV); end for i = 1:nNL Experts(i).NL = unifrnd(Vmin,Vmax,1,nV); Experts(i).NLprevious = unifrnd(Vmin,Vmax,1,nV); Experts(i).Cost = CostFunction(Experts(i).NL); end % Extract the Logic (Best NL in the previous solutions) for i = 1:nNL if CostFunction(Experts(i).NLprevious) <= Logic.Cost Logic.Cost = CostFunction(Experts(i).NLprevious); % The best solution of before the current generation Logic.NL = Experts(i).NLprevious; end if Experts(i).Cost <= Expert_IbI.Cost Expert_IbI.Cost = Experts(i).Cost; % The best solution of the current generation Expert_IbI.NL = Experts(i).NL; end end n_t = zeros(nModel,1); nt = round((n_it_phase1)/nModel); for m = 1:nModel n_t(m,1) = nt; end n_t(nModel,1) = (n_it_phase1)-(nModel-1)*nt; for m = 1:nModel n_Groups(m,1) = randi(round(nNL/2)); % Number of workgropus in each model end %% Phase 0: Grouping (Clustering) for m = 1:nModel % Clustering MAT = zeros(nNL,nV); for i = 1:nNL MAT(i,:) = Experts(i).NL; end opts = statset('MaxIter',nIt_classification); lastwarn('Success'); GroupNumber0 = GroupNumber; GroupNumber = kmeans(MAT,n_Groups(m,1),'Distance','sqeuclidean','Replicates',nRep,'Options',opts); [warningMessage, warningMessageID] = lastwarn; if contains(warningMessage, 'Failed to converge') warnStruct = warning('off'); GroupNumber = GroupNumber0; if m ==1 n_Groups(m,1) = 1; else n_Groups(m,1) = n_Groups(m-1,1); end end Experts_Groups = repmat (Empty1, n_Groups(m,1),1); n_members = zeros(n_Groups(m,1),1); for c = 1:n_Groups(m,1) nn=0; for i = 1:nNL if GroupNumber(i,1) == c nn = nn+1; end end n_members(c,1) = nn; Experts_Groups(c).Members = repmat (Em, n_members(c,1), 1); end %% Phase 1: Workgropus for it_phase1 = 1:n_t(m,1) for c = 1:n_Groups(m,1) SUM = 0; num = 0; for i = 1:nNL if GroupNumber(i,1) == c num = num+1; SUM = Experts(i).NL + SUM; Experts_Groups(c).Members(num).NL = Experts(i).NL; if Experts(i).Cost <= Experts_Groups(c).Cost Experts_Groups(c).NL = Experts(i).NL; Experts_Groups(c).Cost = Experts(i).Cost; end end end Experts_Groups(c).Average = SUM./n_members(c,1); end % Calculate the ratios D = zeros(nNL,1); P = zeros(nNL,1); C = zeros(nNL,1); for i = 1:nNL C(i,1) = sqrt(sum((Experts(i).NL-Logic.NL).^2)); D(i,1) = sqrt(sum((Experts(i).NL-Experts(i).NLprevious).^2)); P(i,1) = sqrt(sum((Experts(i).NL-Experts_Groups(GroupNumber(i,1)).NL).^2)); end min_D = min(D); max_D = max(D); min_P = min(P); max_P = max(P); min_C = min(C); max_C = max(C); Rc = (C-min_C)./(max_C-min_C); Rp = (P-min_P)./(max_P-min_P); RD = (D-min_D)./(max_D-min_D); Bc = Bmin + (Bmax-Bmin)*rand(); Bp = Bmin + (Bmax-Bmin)*rand(); BD = Bmin + (Bmax-Bmin)*rand(); for i = 1:nNL B = Bmin + (Bmax-Bmin)*rand(); if (Rc(i,1) <= Bc) && (Rp(i,1) <= Bp) random_member = randi (n_members(GroupNumber(i,1),1)); K0(i).NL = Rp(i,1).*(Experts(i).NL + Experts_Groups(GroupNumber(i,1)).Members(random_member).NL)./2; elseif (Rc(i,1) <= Bc) && (Rp(i,1) > Bp) K0(i).NL = Rp(i,1).*(Experts(i).NL + Experts_Groups(GroupNumber(i,1)).Average)./2; elseif (Rc(i,1) > Bc) && (Rp(i,1) <= Bp) random_member = randi (n_members(GroupNumber(i,1),1)); K0(i).NL = Rp(i,1).*(Experts_Groups(GroupNumber(i,1)).NL + Experts_Groups(GroupNumber(i,1)).Members(random_member).NL)./2; elseif (Rc(i,1) > Bc) && (Rp(i,1) > Bp) K0(i).NL = Rp(i,1).*(Experts_Groups(GroupNumber(i,1)).NL + Experts_Groups(GroupNumber(i,1)).Average)./2; end if RD(i,1)<= BD K1(i).NL = (rand()).*(Experts_Groups(GroupNumber(i,1)).Average); else K1(i).NL = (rand()).*(unifrnd(Vmin,Vmax,1,nV)); end Knowledge_Phase1(i).NL = abs(K0(i).NL + K1(i).NL)./2; % Update the NL alpha1 = -1.5+3.*rand(1,nV); Expert_new.NL = Experts(i).NL + alpha1.*(Knowledge_Phase1(i).NL); Expert_new.NL = max(Expert_new.NL, Vmin); Expert_new.NL = min(Expert_new.NL, Vmax); E1 = Experts(i).NL; Expert_new.Cost = CostFunction(Expert_new.NL); COEF = -1.5+3*rand(); K = rand().*Experts_Groups(GroupNumber(i,1)).NL; NEW.NL = COEF.*(Expert_new.NL) + K; NEW.NL = max(NEW.NL, Vmin); NEW.NL = min(NEW.NL, Vmax); NEW.Cost = CostFunction(NEW.NL); if NEW.Cost < Expert_new.Cost Expert_new = NEW; end if Expert_new.Cost < Experts(i).Cost Experts(i).NL = Expert_new.NL; Experts(i).Cost = Expert_new.Cost; end if Experts(i).NL ~= E1 Experts(i).NLprevious = E1; end E1 = Expert_IbI.NL; if Experts(i).Cost < Expert_IbI.Cost Expert_IbI.Cost = Experts(i).Cost; Expert_IbI.NL = Experts(i).NL; end if Expert_IbI.NL ~= E1 Logic.NL = E1; end end costs1((m-1)*(n_t(1,1))+it_phase1,1) = Expert_IbI.Cost; Bests_Results((m-1)*(n_t(1,1))+it_phase1).NL = Expert_IbI.NL; Bests_Results((m-1)*(n_t(1,1))+it_phase1).Cost = Expert_IbI.Cost; end end NUM = n_it_phase1; for it_phase2 = 1:n_it_phase2 NUM = NUM+1; % Calculate the ratios for i = 1:nNL C(i,1) = sqrt(sum((Experts(i).NL-Logic.NL).^2)); D(i,1) = sqrt(sum((Experts(i).NL-Experts(i).NLprevious).^2)); P(i,1) = sqrt(sum((Experts(i).NL-Expert_IbI.NL).^2)); end min_D = min(D); max_D = max(D); min_P = min(P); max_P = max(P); min_C = min(C); max_C = max(C); Rc = (C-min_C)./(max_C-min_C); Rp = (P-min_P)./(max_P-min_P); RD = (D-min_D)./(max_D-min_D); Bc = Bmin + (Bmax-Bmin)*rand(); Bp = Bmin + (Bmax-Bmin)*rand(); BD = Bmin + (Bmax-Bmin)*rand(); for i = 1:nNL B = Bmin + (Bmax-Bmin)*rand(); if (Rc(i,1) <= Bc) && (Rp(i,1) <= Bp) random_member = randi (nNL); K0(i).NL = Rp(i,1).*(Experts(i).NL + Experts(random_member).NL)./2; elseif (Rc(i,1) <= Bc) && (Rp(i,1) > Bp) SUM = 0; for ii = 1:nNL SUM = Experts(ii).NL + SUM; end Average = SUM./nNL; K0(i).NL = Rp(i,1).*(Experts(i).NL + Average)./2; elseif (Rc(i,1) > Bc) && (Rp(i,1) <= Bp) random_member = randi (nNL); K0(i).NL = Rp(i,1).*(Expert_IbI.NL + Experts(random_member).NL)./2; elseif (Rc(i,1) > Bc) && (Rp(i,1) > Bp) SUM = 0; for ii = 1:nNL SUM = Experts(ii).NL + SUM; end Average = SUM./nNL; K0(i).NL = Rp(i,1).*(Expert_IbI.NL + Average)./2; end if RD(i,1)<= BD SUM = 0; for ii = 1:nNL SUM = Experts(ii).NL + SUM; end Average = SUM./nNL; K1(i).NL = (rand()).*(Average); else K1(i).NL = (rand()).*(unifrnd(Vmin,Vmax,1,nV)); end % Update the NL Knowledge_Phase2(i).NL = abs(K0(i).NL + K1(i).NL)./2; alpha2 = -0.75+1.5.*rand(1,nV); Expert_new.NL = Experts(i).NL + alpha2.*(Knowledge_Phase2(i).NL); Expert_new.NL = max(Expert_new.NL, Vmin); Expert_new.NL = min(Expert_new.NL, Vmax); E1 = Experts(i).NL; Expert_new.Cost = CostFunction(Expert_new.NL); COEF = -0.75+1.5*rand(); K = rand().*(Expert_IbI.NL); NEW.NL = COEF.*(Expert_new.NL) + K; NEW.NL = max(NEW.NL, Vmin); NEW.NL = min(NEW.NL, Vmax); NEW.Cost = CostFunction(NEW.NL); if NEW.Cost < Expert_new.Cost Expert_new = NEW; end if Expert_new.Cost < Experts(i).Cost Experts(i).NL = Expert_new.NL; Experts(i).Cost = Expert_new.Cost; end if Experts(i).NL ~= E1 Experts(i).NLprevious = E1; end E1 = Expert_IbI.NL; if Experts(i).Cost < Expert_IbI.Cost Expert_IbI.Cost = Experts(i).Cost; Expert_IbI.NL = Experts(i).NL; end if Expert_IbI.NL ~= E1 Logic.NL = E1; end end costs2(it_phase2,1) = Expert_IbI.Cost; Bests_Results(NUM).NL = Expert_IbI.NL; Bests_Results(NUM).Cost = Expert_IbI.Cost; end %% Phase 3: IbI Logic Search for it_phase3 = 1:n_it_phase3 NUM = NUM+1; for i = 1:nNL SUM = 0; for ii = 1:nNL SUM = SUM + Experts(ii).NL; end Average = SUM./nNL; factor = randi(2); if factor == 1 Knowledge_Phase3(i).NL = abs(Average - Experts(randi(nNL)).NL); else Knowledge_Phase3(i).NL = abs(Average - Expert_IbI.NL); end alpha3 = -0.25+0.5.*rand(1,nV); Expert_new.NL = Experts(i).NL + alpha3.*(Knowledge_Phase3(i).NL); Expert_new.NL = max(Expert_new.NL, Vmin); Expert_new.NL = min(Expert_new.NL, Vmax); Expert_new.Cost = CostFunction(Expert_new.NL); COEF = -0.25+0.5*rand(); K = rand().*(Expert_IbI.NL); NEW.NL = COEF.*(Expert_new.NL) + K; NEW.NL = max(NEW.NL, Vmin); NEW.NL = min(NEW.NL, Vmax); NEW.Cost = CostFunction(NEW.NL); if NEW.Cost < Expert_new.Cost Expert_new = NEW; end if Expert_new.Cost < Experts(i).Cost Experts(i).NL = Expert_new.NL; Experts(i).Cost = Expert_new.Cost; end if Experts(i).Cost < Expert_IbI.Cost Expert_IbI.Cost = Experts(i).Cost; Expert_IbI.NL = Experts(i).NL; end end costs3(it_phase3,1) = Expert_IbI.Cost; Bests_Results(NUM).NL = Expert_IbI.NL; Bests_Results(NUM).Cost = Expert_IbI.Cost; end %% Extract the results Expert_IbI.Cost = CostFunction(Expert_IbI.NL); end

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