combineCost

COMBINECOST Calculate the cost of combining two maximal cliques.
   [COST] = COMBINECOST(MAXCLIQUES,MAXCLIQUEIDX)

   Calculate the cost of combining two maximal cliques in terms of the 
   number of scalar variables and linking constraints that will be 
   required after combining the maximal cliques specified in
   maxcliquesidx. This is the clique combination heuristic described in
   [1]. Negative costs indicate that the heuristic predicts
   decreased computational costs after combining the specified maximal
   cliques.

   Inputs:
       MAXCLIQUES : Cell array containing the buses contained in each
           maximal clique.
       MAXCLIQUESIDX : Vector of length two with elements corresponding to
           the candidate maximal cliques.

   Outputs:
       COST : Scalar indicating the cost, as defined by the heuristic in
       [1] of combining the specified maximal cliques.

   [1] D.K. Molzahn, J.T. Holzer, B.C. Lesieutre, and C.L. DeMarco,
       "Implementation of a Large-Scale Optimal Power Flow Solver Based on
       Semidefinite Programming," IEEE Transactions on Power Systems,
       vol. 28, no. 4, pp. 3987-3998, November 2013.

0001 function [cost] = combineCost(maxcliques,maxcliquesidx)
0002 %COMBINECOST Calculate the cost of combining two maximal cliques.
0003 %   [COST] = COMBINECOST(MAXCLIQUES,MAXCLIQUEIDX)
0004 %
0005 %   Calculate the cost of combining two maximal cliques in terms of the
0006 %   number of scalar variables and linking constraints that will be
0007 %   required after combining the maximal cliques specified in
0008 %   maxcliquesidx. This is the clique combination heuristic described in
0009 %   [1]. Negative costs indicate that the heuristic predicts
0010 %   decreased computational costs after combining the specified maximal
0011 %   cliques.
0012 %
0013 %   Inputs:
0014 %       MAXCLIQUES : Cell array containing the buses contained in each
0015 %           maximal clique.
0016 %       MAXCLIQUESIDX : Vector of length two with elements corresponding to
0017 %           the candidate maximal cliques.
0018 %
0019 %   Outputs:
0020 %       COST : Scalar indicating the cost, as defined by the heuristic in
0021 %       [1] of combining the specified maximal cliques.
0022 %
0023 %   [1] D.K. Molzahn, J.T. Holzer, B.C. Lesieutre, and C.L. DeMarco,
0024 %       "Implementation of a Large-Scale Optimal Power Flow Solver Based on
0025 %       Semidefinite Programming," IEEE Transactions on Power Systems,
0026 %       vol. 28, no. 4, pp. 3987-3998, November 2013.
0027 
0028 %   MATPOWER
0029 %   Copyright (c) 2013-2019, Power Systems Engineering Research Center (PSERC)
0030 %   by Daniel Molzahn, PSERC U of Wisc, Madison
0031 %
0032 %   This file is part of MATPOWER/mx-sdp_pf.
0033 %   Covered by the 3-clause BSD License (see LICENSE file for details).
0034 %   See https://github.com/MATPOWER/mx-sdp_pf/ for more info.
0035 
0036 %% define undocumented MATLAB function ismembc() if not available (e.g. Octave)
0037 if exist('ismembc')
0038     ismembc_ = @ismembc;
0039 else
0040     ismembc_ = @ismembc_octave;
0041 end
0042 
0043 maxcliques1 = maxcliques{maxcliquesidx(1)};
0044 maxcliques2 = maxcliques{maxcliquesidx(2)};
0045 nintersect = sum(ismembc_(maxcliques1, maxcliques2));
0046 
0047 elimmaxcliques(1) = length(maxcliques1);
0048 elimmaxcliques(2) = length(maxcliques2);
0049 lnewmaxcliques = sum(elimmaxcliques) - nintersect;
0050 
0051 nvarafter = (lnewmaxcliques)*(2*lnewmaxcliques+1) - sum((elimmaxcliques).*(2*elimmaxcliques+1));
0052 
0053 ocostbefore = (nintersect)*(2*nintersect+1);
0054 
0055 cost = nvarafter - ocostbefore;