### Metaheuristics and cooperative approaches for the Bi-objective Ring Star Problem

Abstract

This paper presents and investigates different approaches to solve a new bi-objective routing problem
called the ring star problem. It consists of locating a simple cycle through a subset of nodes of a
graph while optimizing two kinds of cost. The first objective is the minimization of a ring cost that
is related to the length of the cycle. The second one is the minimization of an assignment cost from
non-visited nodes to visited ones. In spite of its obvious bi-objective formulation, this problem has
always been investigated in a single-objective way. To tackle the bi-objective ring star problem, we
first investigate different stand-alone search methods. Then, we propose two cooperative strategies
that combine two multi-objective metaheuristics: an elitist evolutionary algorithm and a population-
based local search. We apply these new hybrid approaches to well-known benchmark test instances and
demonstrate their effectiveness in comparison to non-hybrid algorithms and to state-of-the-art methods.