CalcDominationMatrix.m

function domMat = CalcDominationMatrix(numCons, sumCons, cost, consImp,gwCons)
%************************ calcDominationMatrix ********************************
%% Function: calcDominationMatrix()
% 
%% Description: 
%   Calculate the domination maxtrix which specified the domination
%   releation between two individual using constrained-domination.
%% Syntax:  : 
%   domMat = calcDominationMatrix(nViol, violSum, obj)
%% Parameters: 
%   Inputs: 
%       numCons:    the number of constrain violations
%       sumCons:    sum of abs(constrain violation)
%       cost:       objective values of grey wolves
%       consImp:    constriant methods
%       gwCons:     constraint values of grey wolves
%   Outputs:
%       domMat:     dominated relationship between two grey wolf
%
%% ----------------------------  Copyright  -------------------------------- 
%% Cited from NSPM and PlatEMO All rights reserved.
%%              NSPM
%           LSSSSWC, NWPU
%    Revision: 1.1  Date: 2011-07-25
%
%
%% Modified by Zhang, T.
%                
%   Revision: 1.0.0  Date: 2021-04-01
%************************************************************************

    % Obtain parameters
    numGwo  = size(cost, 1);    % the number of grey wolves
    numObj  = size(cost, 2);    % the number of objective functions
    domMat  = zeros(numGwo, numGwo); 
    gwConsViol = -gwCons;       % constriant violations
    
    % constrian implementation method selection
    if strcmp(consImp,'NPGM')
        domMat = calcDMNPGM(numCons, sumCons, numGwo, numObj,cost,domMat);
    elseif strcmp(consImp,'PlatEMO')
        domMat = calcDMPlatEMO(numGwo,cost,domMat,gwConsViol);
    end
end



% NPGM 
function domMat = calcDMNPGM(numConVoil, sumCons, numGwo, numObj, cost, domMat)

    for p = 1:numGwo-1
        for q = p+1:numGwo
            %*************************************************************************
            % 1. p and q are both feasible  (weak domination)
            %*************************************************************************
            if(numConVoil(p) == 0 && numConVoil(q)==0) 
                pdomq = false;
                qdomp = false;
                for i = 1:numObj
                    if( cost(p, i) < cost(q, i) )         % objective function is minimization!
                        pdomq = true; % 
                    elseif(cost(p, i) > cost(q, i))
                        qdomp = true;
                    end
                end
                if( pdomq && ~qdomp)
                    domMat(p, q) = 1; %
                elseif(~pdomq && qdomp )
                    domMat(p, q) = -1; %
                end
            %*************************************************************************
            % 2. p is feasible, and q is infeasible
            %*************************************************************************
            elseif(numConVoil(p) == 0 && numConVoil(q)~=0)
                domMat(p, q) = 1;
            %*************************************************************************
            % 3. q is feasible, and p is infeasible
            %*************************************************************************
            elseif(numConVoil(p) ~= 0 && numConVoil(q)==0)
                domMat(p, q) = -1;
            %*************************************************************************
            % 4. p and q are both infeasible (the less constraint voilation)
            %*************************************************************************
            else
                if(sumCons(p) < sumCons(q))
                    domMat(p, q) = 1;
                elseif(sumCons(p) > sumCons(q))
                    domMat(p, q) = -1;
                end
            end
        end
    end
end


% PlatEMO
function domMat = calcDMPlatEMO(varargin)
    
    % Obtain parameters
    numGwo  = varargin{1};
    cost    = varargin{2};
    domMat   = varargin{3};
    [~,numObj]  = size(cost);
    if nargin == 4
        gwCV = varargin{4};
    end
    
    Infeasible            = any(gwCV>0,2);
    cost(Infeasible,:) = repmat(max(cost,[],1),sum(Infeasible),1) + repmat(sum(max(0,gwCV(Infeasible,:)),2),1,numObj);
    
    % only comparing p and q based on costSum
    for p_Gwo = 1:numGwo-1
        for q_Gwo = p_Gwo+1:numGwo
            if ( any(cost(p_Gwo,:) < cost(q_Gwo,:)) && all(cost(p_Gwo,:) <= cost(q_Gwo,:)))
                domMat(p_Gwo,q_Gwo) = 1;
            elseif (any(cost(q_Gwo,:) < cost(p_Gwo,:)) && all(cost(q_Gwo,:) <= cost(p_Gwo,:)))
                domMat(p_Gwo,q_Gwo) = -1;
            end
        end
    end
    
end