A non dominated ranking Multi Objective Genetic Algorithm and electre method for unequal area facility layout problems

摘要

The unequal area facility layout problem (UA-FLP) comprises a class of extremely difficult and widely applicable optimization problems arising in diverse areas and meeting the requirements for real-world applications. Genetic Algorithms (GAs) have recently proven their effectiveness in finding (sub) optimal solutions to many NP-hard problems such as UA-FLP. A main issue in such approach is related to the genetic encoding and to the evolutionary mechanism implemented, which must allow the efficient exploration of a wide solution space, preserving the feasibility of the solutions and ensuring the convergence towards the optimum. In addition, in realistic situations where several design issues must be taken into account, the layout problem falls in the broader framework of multi-objective optimization problems. To date, there are only a few multi-objective FLP approaches, and most of them employ over-simplified optimization techniques which eventually influence the quality of the solutions obtained and the performance of the optimization procedure. In this paper, this difficulty is overcome by approaching the problem in two subsequent steps: in the first step, the Pareto-optimal solutions are determined by employing Multi Objective Genetic Algorithm (MOGA) implementing four separate fitness functions within a Pareto evolutionary procedure, following the general structure of Non-dominated Ranking Genetic Algorithm (NRGA) and the subsequent selection of the optimal solution is carried out by means of the multi-criteria decision-making procedure Electre. This procedure allows the decision maker to express his preferences on the basis of the knowledge of candidate solution set. Quantitative and qualitative objectives are considered referring to the slicing-tree layout representation scheme. The numerical results obtained outperform previous referenced approaches, thus confirming the effectiveness of the procedure proposed.