Multiple criteria districting problems

Districting problems are of high importance in many different fields. Multiple criteria models seem a more adequate representation of districting problems in real-world situations. Real-life decision situations are by their very nature multidimensional. This paper deals with the problem of partitioning a territory into “homogeneous” zones. Each zone is composed of a set of elementary territorial units. A district map is formed by partitioning the set of elementary units into connected zones without inclusions. When multiple criteria are considered, the problem of enumerating all the efficient solutions for such a model is known as being NP-hard, which is why we decided to avoid using exact methods to solve large-size instances. In this paper, we propose a new method to approximate the Pareto front based on an evolutionary algorithm with local search. The algorithm presents a new solution representation and the crossover/mutation operators. Its main features are the following: it F. Tavares-Pereira ( ) Departamento de Matemática, Universidade da Beira Interior, Rua Marquês D’Ávila e Bolama, 6201-001 Covilha, Portugal e-mail: [email protected] F. Tavares-Pereira INESC—Coimbra, Rua Antero de Quental, 199, 3000-033 Coimbra, Portugal F. Tavares-Pereira · J.R. Figueira · V. Mousseau · B. Roy LAMSADE, Université Paris-Dauphine, Place du Maréchal De Lattre de Tassigny, 75 775 Paris Cedex 16, France J.R. Figueira e-mail: [email protected] V. Mousseau e-mail: [email protected] B. Roy e-mail: [email protected] F. Tavares-Pereira · J.R. Figueira CEG-IST, Center for Management Studies, Departamento de Engenharia e Gestão, Instituto Superior Técnico, Universidade Técnica de Lisboa, Tagus Park, Av. Prof. Cavaco Silva, 2780-990 Porto Salvo, Portugal 70 Ann Oper Res (2007) 154: 69–92 deals with multiple criteria; it allows to solve large-size instances in a reasonable CPU time and generates high quality solutions. The algorithm was applied to a real-world problem, that of the Paris region public transportation. Results will be used for a discussion about the reform of its current pricing system.