Enhanced Genetic Algorithm-Based Fuzzy Multiobjective Strategy to Multiproduct Batch Plant Design

This paper addresses the problem of the optimal design of batch plants with imprecise demands in product amounts. The design of such plants necessary involves how equipment may be utilized, which means that plant scheduling and production must constitute a basic part of the design problem. Rather than resorting to a traditional probabilistic approach for modeling the imprecision on product demands, this work proposes an alternative treatment by using fuzzy concepts. The design problem is tackled by introducing a new approach based on a multiobjective genetic algorithm, combined wit the fuzzy set theory for computing the objectives as fuzzy quantities. The problem takes into account simultaneous maximization of the fuzzy net present value NP̃V and of two other performance criteria, i.e. the production delay/advance and a flexibility index. The delay/advance objective is computed by comparing the fuzzy production time for the products to a given fuzzy time horizon, and the flexibility index represents the additional fuzzy production that the plant would be able to produce. The multiobjective optimization provides the Pareto’s front which is a set of scenarios that are helpful for guiding the decision’s maker in its final choices. About the solution procedure, a genetic algorithm was implemented since it is particularly well-suited to take into account the arithmetic of fuzzy numbers. Furthermore because a genetic algorithm is working on populations of potential solutions, this type of procedure is well adapted for multiobjective optimization. * Corresponding author. Tel.: +33 5 34 61 52 52. E-mail addresses: [email protected] (A.A. Aguilar-Lasserre), [email protected] (L. Pibouleau), [email protected] (C. Azzaro-Pantel), [email protected] (S. Domenech). doi:10.1016/j.asoc.2009.05.005 (the net present value), the respect of due dates (advances/delays) and a flexibility criterion. The innovative approach presented in this paper combines a multiobjective genetic algorithmwith fuzzy arithmetic for computing the three objective functions above mentioned. The fuzzy net present value NP̃V is calculated from fuzzy revenue Ṽp and fuzzy depreciation D̃ p, the advance/delay criterion is given by the common surface between the time horizon H̃ represented by a rectangular fuzzy number and the fuzzy trapezoidal production time H̃i for product i, and the flexibility, in the case of an advance (respectively a delay), represents the additional production (the demand not satisfied) that the batch plant is able to produce. The article is organized as follows. Section 2 presents the literature analysis; Section 3 is devoted to process description and problem formulation. Section 4 presents a brief overview of fuzzy set theory; the multiobjective genetic algorithm is briefly described in the following part. The paper is then illustrated by some typical results presented in Section 6. Finally, the general conclusions on this work are drawn in the last part. 2. Previous works