A low-level hybridization between memetic algorithm and VNS for the max-cut problem

Abstract

The Max-Cut problem consists of finding a partition of the graph nodes into two subsets, such that the sum of the edge weights having endpoints in different subsets is maximized. This NP-hard problem for non planar graphs has different applications in areas such as VLSI and ASIC design. This paper proposes an evolutionary hybrid algorithm based on low-level hybridization between Memetic Algorithms and Variable Neighborhood Search. This algorithm is tested and compared with the results, found in the bibliography, obtained by other hybrid metaheuristics for the same problem. Achieved experimental results show the suitability of the approach, and that the proposed hybrid evolutionary algorithm finds near-optimal solutions. Moreover, on a set of standard test problems, new best known solutions were produced for several instances.

Variable neighbourhood search: methods and applications

“…A VNS is proposed for the max-cut problem in a graph and compared with other metaheuristics in Festa et al (2002) and an hybridization between a memetic algorithm and VNS is proposed for the same problem by Duarte et al (2005). Moreno- Pérez et al (2003) propose a VNTS hybrid for the median cycle problem.…”

Multi-objective variable neighborhood search: an application to combinatorial optimization problems

“…See [18,19] for a recent thorough review. VNS has been successfully applied to a wide variety of optimization problems such as Max-Cut [7], Antibandwidth [24], or Cutwidth [30]. However, as far as we know, the adaptation of VNS to multi-objective optimization problems has been mainly ignored by the research community.…”

Variable neighbourhood search: methods and applications

“…A VNS is proposed for the max-cut problem in a graph and compared with other metaheuristics in Festa et al (2002) and an hybridization between a memetic algorithm and VNS is proposed for the same problem by Duarte et al (2005). Moreno- Pérez et al (2003) propose a variable neighbourhood tabu search (VNTS) hybrid for the median cycle problem.…”