# American Institute of Mathematical Sciences

2015, 5(2): 151-168. doi: 10.3934/naco.2015.5.151

## Speeding up a memetic algorithm for the max-bisection problem

 1 Center for Discrete Mathematics and Theoretical Computer Science, Fuzhou University, Fuzhou 350108, China, China 2 Department of Mathematics, Minjiang University, Fuzhou, 350108, China

Received  September 2014 Revised  May 2015 Published  June 2015

Max-bisection of a weighted graph $G = (V, E)$ is to partition the vertex set $V$ into two subsets that have equal cardinality, such that the sum of the weights of the edges connecting vertices in different subsets is maximized. It is an NP-complete problem. Various heuristics have been proposed for solving the max-bisection problem and some of them get very good quality solutions, but are time consuming. In this paper, we propose several techniques to speeding up Lin and Zhu's memetic algorithm for this problem. It consists of a crossover operator with a greedy strategy, a fast modified Kernighan-Lin local search, and a new population updating function. Experiments are performed on 71 well-known G-set benchmark instances. Results show that the memetic algorithm is much faster than Wu and Hao's memetic algorithm, which can get best solutions up to now, on middle-scale and large-scale instances. Specifically, some current best known solutions of the test instances are improved.
Citation: Wenxing Zhu, Yanpo Liu, Geng Lin. Speeding up a memetic algorithm for the max-bisection problem. Numerical Algebra, Control & Optimization, 2015, 5 (2) : 151-168. doi: 10.3934/naco.2015.5.151
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