Metaheuristics for the Bi-objective Ring Star Problem

The bi-objective ring star problem aims to locate a cycle through a subset of nodes of a graph while optimizing two types of cost. The first criterion is to minimize a ring cost, related to the length of the cycle, whereas the second one is to minimize an assignment cost, from non-visited nodes to visited ones. In spite of its natural multi-objective formulation, this problem has never been investigated in such a way. In this paper, three metaheuristics are designed to approximate the whole set of efficient solutions for the problem under consideration. Computational experiments are performed on well-known benchmark test instances, and the proposed methods are rigorously compared to each other using different performance metrics.