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Linear Programming with CPLEXDear all,
I want to implement the column generation approach for graph coloring usingILOG CPLEX (as described in the original paper by Mehrotra and Trick 1995).. My code looks as follows: int numSubgraphs = graph->getNumSubgraphs (); bool *maximalIndependentSet = new bool [numSubgraphs]; IloEnv env; IloModel mod (env); IloNumExpr x [numSubgraphs]; IloNumExprArray sum_x (env, numSubgraphs); IloNumExpr sum_x_all (env); int i, j, current; for (i = 0; i < numSubgraphs; i++) { sum_x [i] = IloNumExpr (env); mod.add (sum_x [i] >= 1); } sum_x_all = IloNumExpr (env); mod.add (IloMinimize (env, sum_x_all)); IloCplex cp (mod); generateFirstMaximalIndependentSet (maximalIndependentSet); x [0] = IloNumExpr (env); mod.add (x [0] >= 0); mod.add (x [0] <= 1); sum_x_all += x [0]; for (i = 0; i < numSubgraphs; i++) if (!maximalIndependentSet [i]) sum_x [i] += x [0]; current = 1; x [current] = IloNumExpr (env); mod.add (x [current] >= 0); mod.add (x [current] <= 1); sum_x_all += x [current]; for (i = 0; i < numSubgraphs; i++) if (maximalIndependentSet [i]) sum_x [i] += x [current]; // for testing purposes cp.exportModel("model.lp"); cp.solve (); This is only the part of the code that deals with the primal problem. This code leads to an error message of the following kind: IBM ILOG License Manager: "IBM ILOG Optimization Suite for Academic Initiative" is accessing CPLEX 12 with option(s): "e m b q ". Infeasibility row 'id11': 0 >= 1. The only constraints with >= 1 are the sum_x [i] >= 1 constraints. I would like to know whether this error occurs. After all CPLEX is supposed to find solutions for x [0] and x [1] so that for all i, sum_x [i] >= 1 while minimizing sum_x_all. Why does CPLEX apparently set some x [i] to 0? It does not make sense to me. How can I make the code run? Thank you. Claus |

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