A Differential Evolution Algorithm for the Median Cycle Problem

Abstract

This paper extends the applications of differential evolution algorithms to the Median Cycle Problem. The median cycle problem is concerned with constructing a simple cycle composed of a subset of vertices of a mixed graph. The objective is to minimize the cost of the cycle and the cost of assigning vertices not on the cycle to the nearest vertex on the cycle. A unique solution representation is presented for the differential evolution algorithm in order to solve the median cycle problem. To the best of our knowledge this is the first reported application of differential evolution algorithms to the median cycle problem in the literature. No local search is employed in order to see the performance of the pure differential evolution algorithm. The differential evolution algorithm is tested on a set of benchmark instances from the literature. For comparisons a continuous genetic algorithm is also developed. The computational results show that the differential evolution algorithm was superior to the genetic algorithm. In addition the computational results also show that the differential evolution algorithm is very promising in solving the median cycle problem when compared to the best performing algorithms from the literature. Ultimately given the fact that no local search is employed the DE algorithm was able to further improve the 5 out of 20 instances.