2023年最新智能优化算法之——IBI逻辑优化算法(IBL)，附MATLAB代码
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, 110305. 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0.998004，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);
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