Solving the bi-objective Robust Vehicle Routing Problem with uncertain costs and demands^∗

¹ Escuela de Ciencias Económicas y Administrativas, Universidad de La Sabana, Km. 7, Autopista Norte, Chía ( Cundinamarca), Colombia.
erlyn.solano@unisabana.edu.co
² ICD-LOSI, UMR CNRS 6281, Université de Technologie de Troyes, 12 rue Marie Curie, CS 42060, 10004 Troyes cedex, France.
christian.prins@utt.fr; andrea.duhamel@utt.fr

Received: 22 May 2015
Accepted: 5 July 2016

Abstract

In this paper, a bi-objective Vehicle Routing Problem (bi-RVRP) with uncertainty in both demands and travel times is studied by means of robust optimization. Uncertain demands per customer are modeled by a discrete set of scenarios representing the deviations from an expected demand, while uncertain travel times are independent from customer demands. Then, traffic records are considered to get discrete scenarios to each arc of the transportation network. Here, the bi-RVRP aims at minimizing the worst total cost of traversed arcs and minimizing the maximum total unmet demand over all scenarios. As far as we know, this is the first study for the bi-RVRP which finds practical applications in urban transportation, e.g., serving small retail stores. To solve the problem, different variations of solution approaches, coupled with a local search procedure are proposed: the Multiobjective Evolutionary Algorithm (MOEA) and the Non-dominated Sorting Genetic Algorithm (NSGAII). Different metrics are used to measure the algorithmic performance, the convergence, as well as the diversity of solutions for the different methods.