Variable neighbourhood decomposition search for 0-1 mixed integer programs

Authors:
Jasmina Lazić;Saïd Hanafi;Nenad Mladenović;Dragan Urošević
Affiliations:
Brunel University, West London UB8 3PH, UK;LAMIH - Universite de Valenciennes, ISTV 2 Le Mont Houy, 59313 Valenciennes Cedex 9, France;Brunel University, West London UB8 3PH, UK;Mathematical Institute, Serbian Academy of Sciences and Arts, Kneza Mihaila 36, 11000 Belgrade, Serbia
Venue:
Computers and Operations Research
Year:
2010

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Abstract

In this paper we propose a new hybrid heuristic for solving 0-1 mixed integer programs based on the principle of variable neighbourhood decomposition search. It combines variable neighbourhood search with a general-purpose CPLEX MIP solver. We perform systematic hard variable fixing (or diving) following the variable neighbourhood search rules. The variables to be fixed are chosen according to their distance from the corresponding linear relaxation solution values. If there is an improvement, variable neighbourhood descent branching is performed as the local search in the whole solution space. Numerical experiments have proven that exploiting boundary effects in this way considerably improves solution quality. With our approach, we have managed to improve the best known published results for 8 out of 29 instances from a well-known class of very difficult MIP problems. Moreover, computational results show that our method outperforms the CPLEX MIP solver, as well as three other recent most successful MIP solution methods.