% MILP
%
%>> Usage: [exitMsg exitFlag netState valueFunction timeDefinition timeOptimization] = ...
% MILP(traff_trafficMatrix, phys, parametersString)
%
%>> Abstract: This function and all its auxiliary functions in the
% directory MILP solve the Virtual Topology Design Problem formulated as
% Mixed-Integer Linear Programming (MILP) Problem. It uses the TOMLAB/CPLEX
% software to solve the mathematical programming problem. The inputs to the
% problem include the traffic matrix, the physical topology and the MILP
% parameters. The objective is to design a virtual topology by optimizing
% a certain cost function subject to a set of constraints. The values of
% the output variables of the MILP formulation will yield the OPTIMAL
% VIRTUAL TOPOLOGY.
%
% Arguments:
% o In:
% traff_trafficMatrix(NxN): Average traffic flow offered between node
% pairs. The Traffic Matrix is a two-dimensional matrix with N (N:
% number of nodes) rows and N columns. An entry(s,d) means the average
% traffic flow from node 's' to node 'd', expressed in Gbps. The main
% diagonal is full of 0s.
%
% . phys: Phys Structure. More information about netState in section
% "Structure of phys variable" from Help.
%
% parametersString: String of parameters defined by the user. The syntax
% of this string consist of:
%
% parameter1Name = parameter1Value (, parameter2Name = parameter2Value, ...)
%
% The number of white spaces is not checked.
%
% The default parameters are defines so:
%
% {['Parameter Name'], ['Default Value'], ['Data type'],['ValidRange']}
%
% {['allowWavelengthConversion'], ['true(1)'], ['boolean'], [];...
% ['allowTrafficLosses'], ['false(1)'], ['boolean'], []; ...
% ['cost_GbpsLoss'], ['100'], ['numeric'], ['(0,inf)']; ...
% ['cost_GbpsElectronicallySwitched'], ['10'], ['numeric'], ['[0,inf)']; ...
% ['cost_opticalTxPlusRx'], ['0'], ['numeric'], ['[0,inf)']; ...
% ['cost_virtualPerUsedWavelength'], ['0'], ['numeric'], ['[0,inf]']; ...
% ['maximumAllowedUtilization'], ['1'], ['numeric'], ['[0,1]']; ...
% ['allowMultiLp'], ['true(1)'], ['boolean'], [];...
% ['applyMaximumDistancePerLp'], ['false(1)'], ['boolean'], [];...
% ['maximumDistancePerLp'], ['800'], ['numeric'], ['(0,inf)'];...
% ['applyMaximumPhysicalHopsPerLp'], ['false(1)'], ['boolean'], [];...
% ['maximumPhysicalHopsPerLp'], ['6'], ['integer'], ['[1,inf)'];
% };
%
%
% o Out:
% . exitMsg: Exit Message.
% - If the virtual topology design was successful:
% exitMsg='OK!!!'(exitFlag == 0);
% - If is not possible to find a feasible solution:
% exitMsg = 'No feasible solution found' (exitFlag == 1)
% - Otherwise, exitMsg indicates other sitiation (exitFlag >= 2).
% Exit Message according to the exit flag from the CPLEX solver.
%
% . exitFlag:
% - 0, if it is possible to find a optimal solution
% - 1, if it is not possible to find a feasible solution
% - 2, otherwise (a subpotimal solution)
%
% . netState: NetState Structure. More information about netState in
% section "Structure of netState variable" from Help.
%
% . valueFunction(1x1): Objective function value at optimum. It is a
% real value.
%
% timeDefinition(1x1): Elapsed time in hours, minutes and seconds for
% the mathematical definition of the MILP problem. It is the time
% needed by MATLAB so as to build the matrices and vectors which
% implement the problem constraints and the objective function.
%
% timeOptimization(1x1): Elapsed time in hours, minutes and seconds for
% the optimization of the MILP problem. It is the time needed by
% TOMLAB/CPLEX so as to solve the MILP problem.
%
function [exitMsg exitFlag netState valueFunction timeDefinition timeOptimization] = ...
MILP(traff_trafficMatrix, phys, parametersString)
netState = struct ('flowRoutingMatrix' , [] , 'lightpathRoutingMatrix' , [] , 'lightpathTable' , [] , 'flowTable' , [] , 'numberOfOccupiedTWCs' , [],'numberOfOccupiedTxs' , [],'numberOfOccupiedRxs' , []);
%We define the default parameter values
cellOfDefaultParameters = {['allowWavelengthConversion'], ['true(1)'], ['boolean'], [];...
['allowTrafficLosses'], ['false(1)'], ['boolean'], []; ...
['cost_GbpsLoss'], ['100'], ['numeric'], ['(0,inf)']; ...
['cost_GbpsElectronicallySwitched'], ['10'], ['numeric'], ['[0,inf)']; ...
['cost_opticalTxPlusRx'], ['0'], ['numeric'], ['[0,inf)']; ...
['cost_virtualPerUsedWavelength'], ['0'], ['numeric'], ['[0,inf]']; ...
['maximumAllowedUtilization'], ['1'], ['numeric'], ['[0,1]']; ...
['allowMultiLp'], ['true(1)'], ['boolean'], [];...
['applyMaximumDistancePerLp'], ['false(1)'], ['boolean'], [];...
['maximumDistancePerLp'], ['800'], ['numeric'], ['(0,inf)'];...
['applyMaximumPhysicalHopsPerLp'], ['false(1)'], ['boolean'], [];...
['maximumPhysicalHopsPerLp'], ['6'], ['integer'], ['[1,inf)'];
};
%We process the string of the algorithm parameters
[exitFlagOfProcessParam exitMsgOfProcessParam userParam] = ...
processAlgorithmParameters (parametersString, cellOfDefaultParameters);
if (exitFlagOfProcessParam ~= 0), error(['>>> Bad Algorithm Parameters:', exitMsgOfProcessParam]); end
%We Initalize the MILP variables
initializationMILPVariablesScript;
constraintsMatrix = sparse(0,NUMBERVARIABLES);
bVector = zeros (0,0);
fprintf('\n\n-->-->-->-->-->-->-->-->-->-->-->-->-->-->-->-->-->-->');
fprintf('\nDefining the Constraints and the Objective Function %d.');
fprintf('\n');
fprintf('-->-->-->-->-->-->-->-->-->-->-->-->-->-->-->-->-->-->\n\n');
fprintf('\n... ');
tDef0 = clock;
%********************1. We define the PROBLEM CONSTRAINTS *****************
%**************************************************************************
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% CONSTRAINTs 0: NOT ALLOWED VALUES FOR DECISION VARIABLES AND
%%%%% NO LOOPS IN ORIGIN AND DESTINATION NODES FOR LIGHTPATHS AND FLOWS
bValue = 0;
constraintType = 0; % -1 <= ; 0 == ; +1 >=
pijmw_constraintMatrix = zeros (N , N , NUMBERLINKWAVELENGTHS);
fijsd_constraintMatrix = zeros (N , N , N , N); % (i,j,s,d)
for i=1:N
incomingLinks = phys.incomingLinksToNode {i};
for m=incomingLinks
initial_mwPosition = MWINITIALANDENDPOSITIONOFLINK (m,1);
end_mwPosition = MWINITIALANDENDPOSITIONOFLINK (m,2);
pijmw_constraintMatrix (i,:,initial_mwPosition:end_mwPosition) = 1;
end
outgoingLinks = phys.outgoingLinksFromNode {i};
for m=outgoingLinks
initial_mwPosition = MWINITIALANDENDPOSITIONOFLINK (m,1);
end_mwPosition = MWINITIALANDENDPOSITIONOFLINK (m,2);
pijmw_constraintMatrix (:,i,initial_mwPosition:end_mwPosition) = 1;
end
pijmw_constraintMatrix (i,i,:) = 1;
fijsd_constraintMatrix (i,i,:,:) = 1;
fijsd_constraintMatrix (:,:,i,i) = 1;
fijsd_constraintMatrix (:,i,i,:) = 1;
fijsd_constraintMatrix (i,:,:,i) = 1;
end
[constraintsMatrix , bVector] = addConstraint (constraintsMatrix , bVector , pijmw_constraintMatrix , fijsd_constraintMatrix , bValue , constraintType , NUMBERVARIABLES_PIJMW , NUMBERVARIABLES_FIJSD);
fprintf('\nConstraints Type 0 Defined\n');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%% LIGHTPATH ROUTING AND WAVELENGTH CONSTRAINTS %%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% CONSTRAINTs 1: VIRTUAL INDEGREE
for node = 1:N
pijmw_constraintMatrix = zeros (N , N , NUMBERLINKWAVELENGTHS);
bValue = phys.numberRxPerNode (node);
constraintType = -1; % -1 <= ; 0 == ; +1 >=
incomingLinks=phys.incomingLinksToNode {node}; % row vector of incoming links to the node
for m=incomingLinks
initial_mwPosition = MWINITIALANDENDPOSITIONOFLINK (m,1);
end_mwPosition = MWINITIALANDENDPOSITIONOFLINK (m,2);
pijmw_constraintMatrix(:, node , initial_mwPosition:end_mwPosition) = 1;
end
[constraintsMatrix , bVector] = addConstraint (constraintsMatrix , bVector , pijmw_constraintMatrix , [] , bValue , constraintType , NUMBERVARIABLES_PIJMW , NUMBERVARIABLES_FIJSD);
end
fprintf('Constraints Type 1 Defined\n');
%%%%% CONSTRAINTs 2: VIRTUAL OUTDEGREE
for node = 1:N
pijmw_constraintMatrix = zeros (N , N , NUMBERLINKWAVELENGTHS);
bValue = phys.numberTxPerNode (node);
constraintType = -1; % -1 <= ; 0 == ; +1 >=
outgoingLinks = phys.outgoingLinksFromNode {node};
for m=outgoingLinks
initial_mwPosition = MWINITIALANDENDPOSITIONOFLINK (m,1);
end_mwPosition = MWINITIALANDENDPOSITIONOFLINK (m,2);
pijmw_constraintMatrix (node , : , initial_mwPosition:end_mwPosition) = 1;
end
[constraintsMatrix , bVector] = addConstraint (constraintsMatrix , bVector , pijmw_constraintMatrix , [] , bValue , constraintType , NUMBERVARIABLES_PIJMW , NUMBERVARIABLES_FIJSD);
end
fprintf('Constraints Type 2 Defined\n');
%%%%% CONSTRAINTs 3: NO WAVELENGTH IN A LINK CARRIES MORE THAN ONE LP
for mw=1:NUMBERLINKWAVELENGTHS
pijmw_constraintMatrix = zeros (N , N , NUMBERLINKWAVELENGTHS);
bValue = 1;
constraintType = -1; % -1 <= ; 0 == ; +1 >=
pijmw_constraintMatrix (:,:,mw) = 1;
[constraintsMatrix , bVector] = addConstraint (constraintsMatrix , bVector , pijmw_constraintMatrix , [] , bValue , constraintType , NUMBERVARIABLES_PIJMW , NUMBERVARIABLES_FIJSD);
end
fprintf('Constraints Type 3 Defined\n');
%%%%% CONSTRAINTs 4: CONSTRAINT OF MAX 1 LIGHPTATH BETWEEN EACH I,J PAIR
if not(userParam.allowMultiLp),
for i = 1:N,
outgoingLinks = phys.outgoingLinksFromNode {i};
for j = 1:N,
if (i == j)
continue;
end
pijmw_constraintMatrix = zeros (N , N , NUMBERLINKWAVELENGTHS);
bValue = 1;
constraintType = -1; % -1 <= ; 0 == ; +1 >=
for m = outgoingLinks
initial_mwPosition = MWINITIALANDENDPOSITIONOFLINK (m,1);
end_mwPosition = MWINITIALANDENDPOSITIONOFLINK (m,2);
pijmw_constraintMatrix (i , j , initial_mwPosition:end_mwPosition) = 1;
end
[constraintsMatrix , bVector] = addConstraint (constraintsMatrix , bVector , pijmw_constraintMatrix , [] , bValue , constraintType , NUMBERVARIABLES_PIJMW , NUMBERVARIABLES_FIJSD);
end
end
end
fprintf('Constraints Type 4 Defined\n');
%%%%% CONSTRAINT 5: CONSTRAINT OF MAX NUMBER OF PHYSICAL HOPS PER
if not(userParam.allowMultiLp) & (userParam.applyMaximumPhysicalHopsPerLp),
for i = 1:N,
for j = 1:N,
if (i == j)
continue;
end
pijmw_constraintMatrix = zeros (N , N , NUMBERLINKWAVELENGTHS);
bValue = userParam.maximumPhysicalHopsPerLp;
constraintType = -1; % -1 <= ; 0 == ; +1 >=
pijmw_constraintMatrix (i , j , :) = 1;
[constraintsMatrix , bVector] = addConstraint (constraintsMatrix , bVector , pijmw_constraintMatrix , [] , bValue , constraintType , NUMBERVARIABLES_PIJMW , NUMBERVARIABLES_FIJSD);
end
end
end
fprintf('Constraints Type 5 Defined\n');
%%%%% CONSTRAINT 6: CONSTRAINT OF MAX DISTANCE IN KM OF PHYSICAL HOPS
%%%%% OF LP
if not(userParam.allowMultiLp) & (userParam.applyMaximumDistancePerLp),
for i = 1:N,
for j = 1:N,
if (i == j)
continue;
end
pijmw_constraintMatrix = zeros (N , N , NUMBERLINKWAVELENGTHS);
bValue = userParam.maximumDistancePerLp;
constraintType = -1; % -1 <= ; 0 == ; +1 >=
for m = 1:M
initial_mwPosition = MWINITIALANDENDPOSITIONOFLINK (m,1);
end_mwPosition = MWINITIALANDENDPOSITIONOFLINK (m,2);
pijmw_constraintMatrix (i , j , initial_mwPosition:end_mwPosition) = phys.linkLengthInKm (m);
end
[constraintsMatrix , bVector] = addConstraint (constraintsMatrix , bVector , pijmw_constraintMatrix , [] , bValue , constraintType , NUMBERVARIABLES_PIJMW , NUMBERVARIABLES_FIJSD);
end
end
end
fprintf('Constraints Type 6 Defined\n');
%%%%% CONSTRAINT 7: ROUTING OF LIGHTPATHS WITH/WITHOUT WAVELENGTH CONTINUITY
%%%%% CONSTRAINT
bValue = 0;
if (not(userParam.allowWavelengthConversion))
for lpConservationNode = 1:N
incomingLinks = phys.incomingLinksToNode {lpConservationNode};
outgoingLinks = phys.outgoingLinksFromNode {lpConservationNode};
nodeInputOrOutputLinks = union (incomingLinks,outgoingLinks);
Wmax_thisNode = max(phys.numberWavelengthPerFiber (nodeInputOrOutputLinks));
for sourceNodeOfLpAggregate = 1:N
for endNodeOfLpAggregate = 1:N
if (sourceNodeOfLpAggregate == endNodeOfLpAggregate)
continue;
end
if (sourceNodeOfLpAggregate == lpConservationNode)
constraintType = -1;
elseif (endNodeOfLpAggregate == lpConservationNode)
constraintType = +1;
else
constraintType = 0;
end
for w = 1:Wmax_thisNode % the number of wavelengths of the fibre with more number of wavelengths
pijmw_constraintMatrix = zeros (N , N , NUMBERLINKWAVELENGTHS);
pijmw_constraintMatrix (sourceNodeOfLpAggregate , endNodeOfLpAggregate , MWPOSITIONSOFTHENODE_INCOMING{lpConservationNode,w}) = 1;
pijmw_constraintMatrix (sourceNodeOfLpAggregate , endNodeOfLpAggregate , MWPOSITIONSOFTHENODE_OUTGOING{lpConservationNode,w}) = -1;
[constraintsMatrix , bVector] = addConstraint (constraintsMatrix , bVector , pijmw_constraintMatrix , [] , bValue , constraintType , NUMBERVARIABLES_PIJMW , NUMBERVARIABLES_FIJSD);
end
end
end
end
else
bValue = 0;
for lpConservationNode = 1:N
incomingLinks = phys.incomingLinksToNode {lpConservationNode};
outgoingLinks = phys.outgoingLinksFromNode {lpConservationNode};
nodeInputOrOutputLinks = union (incomingLinks,outgoingLinks);
for sourceNodeOfLpAggregate = 1:N
for endNodeOfLpAggregate = 1:N
if (sourceNodeOfLpAggregate == endNodeOfLpAggregate)
continue;
end
pijmw_constraintMatrix = zeros (N , N , NUMBERLINKWAVELENGTHS);
if (sourceNodeOfLpAggregate == lpConservationNode)
constraintType = -1;
elseif (endNodeOfLpAggregate == lpConservationNode)
constraintType = +1;
else
constraintType = 0;
end
for m = incomingLinks
initial_mwPosition = MWINITIALANDENDPOSITIONOFLINK (m,1);
end_mwPosition = MWINITIALANDENDPOSITIONOFLINK (m,2);
pijmw_constraintMatrix (sourceNodeOfLpAggregate , endNodeOfLpAggregate , initial_mwPosition:end_mwPosition) = 1;
end
for m = outgoingLinks
initial_mwPosition = MWINITIALANDENDPOSITIONOFLINK (m,1);
end_mwPosition = MWINITIALANDENDPOSITIONOFLINK (m,2);
pijmw_constraintMatrix (sourceNodeOfLpAggregate , endNodeOfLpAggregate , initial_mwPosition:end_mwPosition) = -1;
end
[constraintsMatrix , bVector] = addConstraint (constraintsMatrix , bVector , pijmw_constraintMatrix , [] , bValue , constraintType , NUMBERVARIABLES_PIJMW , NUMBERVARIABLES_FIJSD);
end
end
end
end
fprintf('Constraints Type 7 Defined\n');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%% TRAFFIC FLOW ROUTING CONSTRAINTS %%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% CONSTRAINT 8: LP CAPACITY CONSTRAINTS
for sourceNodeOfLpAggregate = 1:N
for endNodeOfLpAggregate = 1:N
if (sourceNodeOfLpAggregate == endNodeOfLpAggregate)
continue;
end
pijmw_constraintMatrix = zeros (N , N , NUMBERLINKWAVELENGTHS);
fijsd_constraintMatrix = zeros (N , N , N , N); % (i,j,s,d)
bValue = 0;
constraintType = -1; % -1 <= ; 0 == ; +1 >=
fijsd_constraintMatrix (sourceNodeOfLpAggregate,endNodeOfLpAggregate,:,:)= 1;
outgoingLinks = phys.outgoingLinksFromNode{sourceNodeOfLpAggregate};
for m=outgoingLinks
initial_mwPosition = MWINITIALANDENDPOSITIONOFLINK (m,1);
end_mwPosition = MWINITIALANDENDPOSITIONOFLINK (m,2);
pijmw_constraintMatrix (sourceNodeOfLpAggregate , endNodeOfLpAggregate , initial_mwPosition:end_mwPosition) = -userParam.maximumAllowedUtilization*phys.lightpathCapacity;
end
[constraintsMatrix , bVector] = addConstraint (constraintsMatrix , bVector , pijmw_constraintMatrix , fijsd_constraintMatrix , bValue , constraintType , NUMBERVARIABLES_PIJMW , NUMBERVARIABLES_FIJSD);
end
end
fprintf('Constraints Type 8 Defined\n');
%%%%% CONSTRAINT 9: CONSERVATION FLOW CONSTRAINTS
for conservationFlowNode = 1:N
for ingressNodeOfFlow = 1:N
for egressNodeOfFlow = 1:N
if (ingressNodeOfFlow == egressNodeOfFlow)
continue;
end
fijsd_constraintMatrix = zeros (N , N , N , N); % (i,j,s,d)
if (ingressNodeOfFlow == conservationFlowNode)
if (userParam.allowTrafficLosses)
constraintType = -1;
else
constraintType = 0;
end
bValue = traff_trafficMatrix (ingressNodeOfFlow,egressNodeOfFlow);
elseif (egressNodeOfFlow == conservationFlowNode)
if (userParam.allowTrafficLosses)
constraintType = +1;
else
constraintType = 0;
end
bValue = - traff_trafficMatrix (ingressNodeOfFlow,egressNodeOfFlow);
else
constraintType = 0;
bValue = 0;
end
fijsd_constraintMatrix (conservationFlowNode,:,ingressNodeOfFlow,egressNodeOfFlow)= 1;
fijsd_constraintMatrix (:,conservationFlowNode,ingressNodeOfFlow,egressNodeOfFlow)= -1;
fijsd_constraintMatrix (conservationFlowNode,conservationFlowNode,ingressNodeOfFlow,egressNodeOfFlow)= 0;
[constraintsMatrix , bVector] = addConstraint (constraintsMatrix , bVector , [] , fijsd_constraintMatrix , bValue , constraintType , NUMBERVARIABLES_PIJMW , NUMBERVARIABLES_FIJSD);
end
end
end
fprintf('Constraints Type 9 Defined\n');
%*****************2. We define the OBJECTIVE FUNCTION**********************
%**************************************************************************
%% first, the contribution of electronic costs
fijsd_objectiveMatrix = userParam.cost_GbpsElectronicallySwitched * ones (N , N , N , N);
%% now, the contribution of virtual costs
pijmw_objectiveMatrix = userParam.cost_virtualPerUsedWavelength * ones (N , N , NUMBERLINKWAVELENGTHS);
%% now, the contribution of optical costs
for i=1:N
for m=phys.outgoingLinksFromNode {i}
initial_mwPosition = MWINITIALANDENDPOSITIONOFLINK (m,1);
end_mwPosition = MWINITIALANDENDPOSITIONOFLINK (m,2);
pijmw_objectiveMatrix (i,:,initial_mwPosition:end_mwPosition) = ...
pijmw_objectiveMatrix (i,:,initial_mwPosition:end_mwPosition) + userParam.cost_opticalTxPlusRx;
end
end
%% now the contribution of the cost of loosing traffic
if (userParam.allowTrafficLosses)
totalTrafficOffered = sum (sum (traff_trafficMatrix));
routedTraffic = 0;
for i_s=1:N
fijsd_objectiveMatrix (i_s,:,i_s,:) = fijsd_objectiveMatrix (i_s,:,i_s,:) - userParam.cost_GbpsLoss;
end
end
functionToOptimize = [array2vect(pijmw_objectiveMatrix) array2vect(fijsd_objectiveMatrix)];
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
tDef1 = clock;
timeDefinition=etime(tDef1,tDef0);
[hDef, minDef, secDef]=sec2time(timeDefinition);
fprintf(' Definition Ready');
fprintf(['\n\n Elapsed time to define the problem: ',num2str(hDef),' hours ',num2str(minDef),' minutes ',num2str(secDef),' seconds \n']);
%-----------------------------********************3. TOMLAB CPLEX OPTMIZATION ***********************---------------------------------------------------------------
%----------------------------------------------------------------------------------------------------------------------------------------------------
fprintf('\n\n-->-->-->-->-->-->-->-->-->-->-->-->-->-->-->-->-->-->-->');
fprintf('\nTOMLAB / Cplex solving Problem %d.');
fprintf('\n');
fprintf('-->-->-->-->-->-->-->-->-->-->-->-->-->-->-->-->-->-->-->\n\n');
fprintf('\n... ');
[exitMsg exitFlag x, slack, v, rc, valueFunction, ninf, sinf, basis, lpiter, ...
glnodes, confstat, iconfstat, sa] = ...
callSolver_CPLEX (functionToOptimize,constraintsMatrix,bVector,N,NUMBERLINKWAVELENGTHS,NUMBERINGRESSEGRESSNODEPAIRS);
tSolve1 = clock;
timeOptimization=etime(tSolve1, tDef1);
[hOpt, minOpt, secOpt]=sec2time(timeOptimization);
fprintf('\n Optimization Ready');
fprintf(['\n\n Elapsed time to solve the problem: ',num2str(hOpt),' hours ',num2str(minOpt),' minutes ',num2str(secOpt),' seconds \n']);
fprintf('\n exitFlag = %d\n exitMsg = %s\n' ,exitFlag,exitMsg);
if exitFlag == 1,
netState.lightpathTable =[];
netState.lightpathRoutingMatrix=[];
netState.flowTable=[];
netState.flowRoutingMatrix=[];
valueFunction =[];
timeDefinition = [];
timeOptimization =[];
return;
end
%-----------------------********************4. We capture the solver CPLEX OUTPUTS****************************-----------------------------------------
%-----------------------------------------------------------------------------------------------------------------------------------------------------
% We capture into a programming variable the information about the
% Lightpath-Wavelength-Link Indicator contained in the solution vector x
% obtained by the solver.
pijmw = x (1:NUMBERLINKWAVELENGTHS * NUMBERINGRESSEGRESSNODEPAIRS);
fijsd = x (NUMBERLINKWAVELENGTHS * NUMBERINGRESSEGRESSNODEPAIRS + 1 : NUMBERVARIABLES);
[pijmw fijsd] = roundSolutionVector (pijmw , fijsd);
if sum(pijmw)==0 | sum(fijsd)==0,
exitFlag = 1;
exitMsg = 'Null optimal integer solution found';
netState.lightpathTable =[];
netState.lightpathRoutingMatrix=[];
netState.flowTable=[];
netState.flowRoutingMatrix=[];
return
end
%We translate the variables which represent the configuration of the
%virtual topology from the format used in the MILP optimization into the
%standard format.
[netState.lightpathTable netState.lightpathRoutingMatrix] = trans_pijmw2LPRoutingMatrix(pijmw, phys);
[netState.flowTable netState.flowRoutingMatrix] = trans_fijsd2flowRoutingMatrix(fijsd, netState.lightpathTable , netState.lightpathRoutingMatrix , phys, traff_trafficMatrix);
netState.flowTable=[netState.flowTable -1*ones(size(netState.flowTable,1),3)];
netState.lightpathTable =[(1:size(netState.lightpathTable,1))' netState.lightpathTable];
numberOfNodes=length(phys.numberTxPerNode);
for nodei=1:numberOfNodes
netState.numberOfOccupiedTxs(nodei) = length(find(netState.lightpathTable(:,2)==nodei));
netState.numberOfOccupiedRxs(nodei) = length(find(netState.lightpathTable(:,3)==nodei));
end
numberOfLightpaths=size(netState.lightpathTable,1);
netState.numberOfOccupiedTWCs=zeros(numberOfNodes,1);
for lpID=1:numberOfLightpaths,
[sequenceOfNodeIDs, sequenceOfFiberIDs, sequenceOfWavelengthIDs] = lightpathPathComputation (lpID, phys, netState);
for i=1:length(sequenceOfFiberIDs)-1,
if sequenceOfWavelengthIDs(i) ~= sequenceOfWavelengthIDs(i+1),
netState.numberOfOccupiedTWCs (sequenceOfNodeIDs(i+1)) = netState.numberOfOccupiedTWCs (sequenceOfNodeIDs(i+1)) + 1;
end
end
end
end
function [pijmw_result fijsd_result] = roundSolutionVector (pijmw , fijsd)
pijmw_result = pijmw;
fijsd_result = fijsd;
roundLimit = (max (fijsd)) / 1E10;
for i=1:length(fijsd),
if (fijsd(i) < roundLimit),
fijsd_result(i) = 0;
end
end
precision = 1E-1;
for i=1:length(pijmw),
if (abs (pijmw(i)-0) < precision),
pijmw_result(i) = 0;
elseif (abs (pijmw(i)-1) < precision),
pijmw_result(i) = 1;
else
disp ('CPLEX precision error in Pijmw variables');
error ('CPLEX precision error in Pijmw variables');
end
end
end
