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 %   $Id: combineCost.m 2280 2014-01-17 23:28:37Z ray $
0030 %   by Daniel Molzahn, PSERC U of Wisc, Madison
0031 %   Copyright (c) 2013-2014 by Power System Engineering Research Center (PSERC)
0032 %
0033 %   This file is part of MATPOWER.
0034 %   See http://www.pserc.cornell.edu/matpower/ for more info.
0035 %
0036 %   MATPOWER is free software: you can redistribute it and/or modify
0037 %   it under the terms of the GNU General Public License as published
0038 %   by the Free Software Foundation, either version 3 of the License,
0039 %   or (at your option) any later version.
0040 %
0041 %   MATPOWER is distributed in the hope that it will be useful,
0042 %   but WITHOUT ANY WARRANTY; without even the implied warranty of
0043 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
0044 %   GNU General Public License for more details.
0045 %
0046 %   You should have received a copy of the GNU General Public License
0047 %   along with MATPOWER. If not, see <http://www.gnu.org/licenses/>.
0048 %
0049 %   Additional permission under GNU GPL version 3 section 7
0050 %
0051 %   If you modify MATPOWER, or any covered work, to interface with
0052 %   other modules (such as MATLAB code and MEX-files) available in a
0053 %   MATLAB(R) or comparable environment containing parts covered
0054 %   under other licensing terms, the licensors of MATPOWER grant
0055 %   you additional permission to convey the resulting work.
0056 
0057 maxcliques1 = maxcliques{maxcliquesidx(1)};
0058 maxcliques2 = maxcliques{maxcliquesidx(2)};
0059 nintersect = sum(ismembc(maxcliques1, maxcliques2));
0060 
0061 elimmaxcliques(1) = length(maxcliques1);
0062 elimmaxcliques(2) = length(maxcliques2);
0063 lnewmaxcliques = sum(elimmaxcliques) - nintersect;
0064 
0065 nvarafter = (lnewmaxcliques)*(2*lnewmaxcliques+1) - sum((elimmaxcliques).*(2*elimmaxcliques+1));
0066 
0067 ocostbefore = (nintersect)*(2*nintersect+1);
0068 
0069 cost = nvarafter - ocostbefore;