通过求解数学模型来选择编码节点的最佳数量和位置（Matlab代码实现）

%% Failure constraint
failureIsDest=zeros(length(FailureScenarios)*numberOfNodes,numberOfLinks);
failureIsSrc=zeros(length(FailureScenarios)*numberOfNodes,numberOfLinks);
e=0;
esrc=0;
% Failure sources
for f=1:length(FailureScenarios)
    for k=1:failedLinksInScen(f)
        workingLinks=get_workingLinks_in_failureScen(f,failedLinksInScen,links,FailureScenarios);
        for i=1:numberOfNodes
            for j=1:length(workingLinks)
                bool=isAgateway(workingLinks(j),1,gateways,network);
                if networkF(workingLinks(j),1)==i  && bool==false
                    failureIsSrc(i+e,workingLinks(j)+esrc)=1;
                else
                    failureIsSrc(i+e,workingLinks(j)+esrc)=0;
                end
            end
        end
        e=e+numberOfNodes;
    end
end
%% failure destination
e=0;
edest=0;
for f=1:length(FailureScenarios)
    for k=1:failedLinksInScen(f)
        workingLinks=get_workingLinks_in_failureScen(f,failedLinksInScen,links,FailureScenarios);
        for i=1:numberOfNodes
            for j=1:length(workingLinks)
                bool=isAgateway(workingLinks(j),1,gateways,network);
                if networkF(workingLinks(j),2)==i && bool==false
                    failureIsDest(i+e,workingLinks(j)+edest)=-1;
                else
                    failureIsDest(i+e,workingLinks(j)+edest)=0;
                end
            end
        end
        e=e+numberOfNodes;
    end
end
% adjFailure Matrix
adjFailure=failureIsSrc(:,:)+failureIsDest(:,:);
% store all the sources of failed links in sourcesF matrix
sourcesF=cell(1,numberOfFailScens);
for f=1:numberOfFailScens
    for l=1:failedLinksInScen(f)
        for n=1:numberOfNodes
            for j=1:numberOfLinks
                if networkF(j,1)==n && networkF(j,3)==FailureScenarios{f}(1,l)
                    sourcesF{f}(1,l)=networkF(j,1);  
                end
            end
        end
    end
end
%% Failure scenario:indicate the failed links in each failure scenario
e=0;
fCol=numberOfNodes+1;
fColEnd=fCol-1+numberOfLinks;
gmmaCol=numberOfNodes+numberOfLinks+1;
etaCol=numberOfLinks + numberOfNodes+failure_scen_var_length*numberOfLinks;
GRow=0;
for f=1:numberOfFailScens
    for i=1: failedLinksInScen(f)
        workingLinks=get_workingLinks_in_failureScen(f,failedLinksInScen,links,FailureScenarios);
        for j= 1:numberOfNodes
            Aeq(GRow+j+e,fCol:fColEnd)=adjFailure(j+e,1:numberOfLinks);
            if isSource(j,FailureScenarios{f}(1,i))==1
                sum_lPrime=sum_Working_Links(j,gammaTree,workingLinks,network);
                beq(GRow+j+e)=1-sum_lPrime;
            else
                Aeq(GRow+j+e,etaCol+j+e)=1;
                beq(GRow+j+e)=0;
            end
        end
        fCol=fColEnd+1;
        fColEnd=fColEnd+numberOfLinks;
        e=e+numberOfNodes;
    end
end