Tackling the Industrial Car Sequencing Problem Using GISMOO Algorithm

Abstract

In many industrial sectors, managers are confronted with problems of an ever-growing complexity. The problem could be bus route optimization for a public transporter, production cost minimization, decision-making support, electronic circuit performance enhancement, or computer system process scheduling. In many cases the situation can be expressed as a combinatorial optimization problem. Solving an optimization problem consists of determining the best solution(s) validating a set of user-defined constraints and goals. To determine if one solution is better than another, the problem must include at least one performance evaluation metric that allows solutions to be compared. The best (or optimal) solution, is thus the one with the best evaluation, with respect to the defined goal. When only one goal is specified (e.g. total distance minimization), the optimal solution is clearly defined (the one with the smallest distance). However, in many situations there are several contradictory goals that have to be satisfied simultaneously. In fact, real-world optimization problems rarely have a single goal. This is the case for the Industrial Car Sequencing Problem (ICSP) on an automobile assembly line. The ICSP consists of determining the order in which automobiles should be produced, taking into account the various model options, assembly line constraints, and production environment goals. In this context, the optimal solution is not a single point, but rather a set of compromise solutions called the Pareto-optimal front. We can thus define two main goals in multi-objective optimization: (i) Find a set of compromise solutions whose evaluation is as close as possible to the Pareto-optimal front; and (ii) Find a set of compromise solutions as diverse as possible. Attaining these two goals in realistic time is an important challenge for any multi-objective algorithm. However, in the literature, the ICSP, despite its multi-objective character, has been treated as a problem with a single goal or with several goals lexicographically ordered (Benoist, 2008; Briant et al., 2008; Cordeau et al., 2008; Estellon et al., 2008; Ribeiro et al., 2008). To our knowledge, the only references that treat the ICSP from a purely multi-objective viewpoint are those of Zinflou et al. (2009) and of de Oliveira dos Reis ( 2007); the latter only examines small instances (fewer than 60 automobiles). Most of the algorithms proposed recently for multi-objective problems are Evolutionary Algorithms (EA) (Deb, 2000; Knowles & Corne, 2000a; Knowles & Corne, 2000b; Zitzler et al., 2001). This is so, doubtlessly because EA’s can traverse a large search space to generate