nsgaiii优化算法matlab代码

function [FrontNo,MaxFNo] = NDSort(varargin) %NDSort - Do non-dominated sorting by efficient non-dominated sort. % % FrontNo = NDSort(F,s) does non-dominated sorting on F, where F is the % matrix of objective values of a set of individuals, and s is the number % of individuals to be sorted at least. FrontNo(i) denotes the front % number of the i-th individual. The individuals have not been sorted are % assigned a front number of inf. % % FrontNo = NDSort(F,C,s) does non-dominated sorting based on constrained % domination, where C is the matrix of constraint values of the % individuals. In this case, feasible solutions always dominate % infeasible solutions, and one infeasible solution dominates another % infeasible solution if the former has a smaller overall constraint % violation than the latter. % % In particular, s = 1 indicates finding only the first non-dominated % front, s = size(F,1)/2 indicates sorting only half the population % (which is often used in the algorithm), and s = inf indicates sorting % the whole population. % % [FrontNo,K] = NDSort(...) also returns the maximum front number besides % inf. % % Example: % [FrontNo,MaxFNo] = NDSort(PopObj,1) % [FrontNo,MaxFNo] = NDSort(PopObj,PopCon,inf) %------------------------------- Reference -------------------------------- % [1] X. Zhang, Y. Tian, R. Cheng, and Y. Jin, An efficient approach to % nondominated sorting for evolutionary multiobjective optimization, IEEE % Transactions on Evolutionary Computation, 2015, 19(2): 201-213. % [2] X. Zhang, Y. Tian, R. Cheng, and Y. Jin, A decision variable % clustering based evolutionary algorithm for large-scale many-objective % optimization, IEEE Transactions on Evolutionary Computation, 2018, 22(1): % 97-112. %------------------------------- Copyright -------------------------------- % Copyright (c) 2018-2019 BIMK Group. You are free to use the PlatEMO for % research purposes. All publications which use this platform or any code % in the platform should acknowledge the use of "PlatEMO" and reference "Ye % Tian, Ran Cheng, Xingyi Zhang, and Yaochu Jin, PlatEMO: A MATLAB platform % for evolutionary multi-objective optimization [educational forum], IEEE % Computational Intelligence Magazine, 2017, 12(4): 73-87". %-------------------------------------------------------------------------- PopObj = varargin{1}; [N,M] = size(PopObj); if nargin == 2 nSort = varargin{2}; else PopCon = varargin{2}; nSort = varargin{3}; Infeasible = any(PopCon>0,2); PopObj(Infeasible,:) = repmat(max(PopObj,[],1),sum(Infeasible),1) + repmat(sum(max(0,PopCon(Infeasible,:)),2),1,M); end if M < 5 || N < 500 % Use efficient non-dominated sort with sequential search (ENS-SS) [FrontNo,MaxFNo] = ENS_SS(PopObj,nSort); else % Use tree-based efficient non-dominated sort (T-ENS) [FrontNo,MaxFNo] = T_ENS(PopObj,nSort); end end function [FrontNo,MaxFNo] = ENS_SS(PopObj,nSort) [PopObj,~,Loc] = unique(PopObj,'rows'); Table = hist(Loc,1:max(Loc)); [N,M] = size(PopObj); [PopObj,rank] = sortrows(PopObj); % if ~(all(PopObj(:) == PopObj1(:))) % disp(2) % end FrontNo = inf(1,N); MaxFNo = 0; while sum(Table(FrontNo<inf)) < min(nSort,length(Loc)) MaxFNo = MaxFNo + 1; for i = 1 : N if FrontNo(i) == inf Dominated = false; for j = i-1 : -1 : 1 if FrontNo(j) == MaxFNo m = 2; while m <= M && PopObj(i,m) >= PopObj(j,m) m = m + 1; end Dominated = m > M; if Dominated || M == 2 break; end end end if ~Dominated FrontNo(i) = MaxFNo; end end end end FrontNo(rank) = FrontNo; FrontNo = FrontNo(:,Loc); end function [FrontNo,MaxFNo] = T_ENS(PopObj,nSort) [PopObj,~,Loc] = unique(PopObj,'rows'); Table = hist(Loc,1:max(Loc)); [N,M] = size(PopObj); [PopObj,rank] = sortrows(PopObj); FrontNo = inf(1,N); MaxFNo = 0; Forest = zeros(1,N); Children = zeros(N,M-1); LeftChild = zeros(1,N) + M; Father = zeros(1,N); Brother = zeros(1,N) + M; [~,ORank] = sort(PopObj(:,2:M),2,'descend'); ORank = ORank + 1; while sum(Table(FrontNo<inf)) < min(nSort,length(Loc)) MaxFNo = MaxFNo + 1; root = find(FrontNo==inf,1); Forest(MaxFNo) = root; FrontNo(root) = MaxFNo; for p = 1 : N if FrontNo(p) == inf Pruning = zeros(1,N); q = Forest(MaxFNo); while true m = 1; while m < M && PopObj(p,ORank(q,m)) >= PopObj(q,ORank(q,m)) m = m + 1; end if m == M break; else Pruning(q) = m; if LeftChild(q) <= Pruning(q) q = Children(q,LeftChild(q)); else while Father(q) && Brother(q) > Pruning(Father(q)) q = Father(q); end if Father(q) q = Children(Father(q),Brother(q)); else break; end end end end if m < M FrontNo(p) = MaxFNo; q = Forest(MaxFNo); while Children(q,Pruning(q)) q = Children(q,Pruning(q)); end Children(q,Pruning(q)) = p; Father(p) = q; if LeftChild(q) > Pruning(q) Brother(p) = LeftChild(q); LeftChild(q) = Pruning(q); else bro = Children(q,LeftChild(q)); while Brother(bro) < Pruning(q) bro = Children(q,Brother(bro)); end Brother(p) = Brother(bro); Brother(bro) = Pruning(q); end end end end end FrontNo(rank) = FrontNo; FrontNo = FrontNo(:,Loc); end