*Article* **Optimization of Carsharing Fleet Placement in Round-Trip Carsharing Service**

**Boonyarit Changaival 1,†, Kittichai Lavangnananda 2,\*,†, Grégoire Danoy 1,†, Dzmitry Kliazovich 3,†, Frédéric Guinand 4,†, Matthias Brust 5,†, Jedrzej Musial 6,† and Pascal Bouvry 1,†**


† These authors contributed equally to this work.

**Abstract:** In a round-trip carsharing system, stations must be located in such a way that allow for maximum user coverage with the least walking distance as well as offer certain degrees of flexibility for returning. Therefore, a balance must be stricken between these factors. Providing a satisfactory system can be translated into an optimization problem and belongs to an NP-hard class. In this article, a novel optimization model for the round-trip carsharing fleet placement problem, called Fleet Placement Problem (FPP), is proposed. The optimization in this work is multiobjective and its NP-hard nature is proven. Three different optimization algorithms: PolySCIP (exact method), heuristics, and NSGA-II (metaheuristic) are investigated. This work adopts three real instances for the study, instead of their abstracts where they are most commonly used. They are two instance:, in the city of Luxembourg (smaller and larger) and a much larger instance in the city of Munich. Results from each algorithm are validated and compared with solution from human experts. Superiority of the proposed FPP model over the traditional methods is also demonstrated.

**Keywords:** carsharing system; fleet placement; metaheuristic algorithm; multiobjective optimization; NP-hard problem; NSGA-II; optimization; PolySCIP
