A Hybrid Genetic Algorithm for the Minimum Linear Arrangement Problem

This paper presents a hybrid genetic algorithm for the minimum linear arrangement problem. The algorithm was tested on a collection of 22 sparse graphs that has been used to test twelve other algorithms for the minimum linear arrangement problem. The graphs have up to 10,240 vertices and up to 49,820 edges. On about 2/3 of the graphs, our algorithm found solutions superior to all other algorithms except for simulated annealing. For one graph, though, our algorithm found a solution better than any of the other algorithms. While our algorithm was generally slower than all other algorithms, for extremely large graphs it was faster than simulated annealing.