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This paper presents and experiments approaches to solve a new bi-objectiverouting problem called the ring star problem. It consists of locating a simplecycle 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 thelength of the cycle. The second one is the minimization of an assignment costfrom non-visited nodes to visited ones. In spite of its obvious bi-objectiveformulation, this problem has always been investigated in a single-objectiveway. To tackle the bi-objective ring star problem, we first investigatedifferent stand-alone search methods. Then, we propose two cooperativestrategies that combines two multiple objective metaheuristics: an elitistevolutionary algorithm and a population-based local search. We apply this newhybrid approaches to well-known benchmark test instances and demonstrate theireffectiveness in comparison to non-hybrid algorithms and to state-of-the-artmethods.

Metaheuristics and Their Hybridization to Solve the Bi-objective Ring Star Problem: a Comparative Study