Variable neighbourhood decomposition search for 0–1 mixed integer programs

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.

Hybrid metaheuristics in combinatorial optimization: A survey

“…Examples of effective variable fixing strategies are the core concepts for knapsack problems [43,44]. Another example where variable fixing is essential is the variable neighborhood decomposition approach proposed in [45]. Problem kernelization, which is a systematic approach based on tools from the field of parameterized complexity, is also related to multilevel strategies and variable fixing.…”

A hybrid heuristic for the 0–1 Knapsack Sharing Problem

“…Finally, Lazić , Hanafi, Mladenović , and Urošević (2010) proposed an approach which exploits the underlying principles of the methods presented in Fischetti and Lodi (2003), Danna et al (2005) and the Variable Neighborhood Decomposition Search (VNDS) developed in Hansen, Mladenovic, and Pérez-Brito (2001) in order to produce optimal and near-optimal solutions for the 0-1 MIP. More precisely, VNDS is used to define a variable fixation scheme for generating a sequence of smaller sub-problems, which are normally easier to solve than the original problem.…”

Survey of Metaheuristic Algorithms for Combinatorial Optimization

“…Another work proposed by Hanafi et al is a Variable neighborhood decomposition approach (2010) which hybridizes VNS with general purpose CPLEX MIP solver. The hybridization was done to solve 0-1 mixed integer program [58]. Glover and Laguna proposed a concept based on the tabu search for improving metaheuristic that is called as a proximate optimality principle (POP).…”