Dyna, year 79, Nro. 172, pp. 101-107. Medellin, april, 2012. ISSN 0012-7353 EVOLUTIONARY MULTI-OBJECTIVE SCHEDULING PROCEDURES IN NON-STANDARDIZED PRODUCTION PROCESSES PROCEDIMIENTOS DE PROGRAMACIÓN EVOLUTIVA MULTI- OBJETIVO EN PROCESOS PRODUCTIVOS NO ESTANDARIZADOS MARIANO FRUTOS Doctor en Ingeniería, Universidad Nacional del Sur y CONICET, Argentina, mfrutos@uns.edu.ar FERNANDO TOHMÉ Doctor en Economía, Universidad Nacional del Sur y CONICET, Argentina, ftohme@criba.edu.ar Received for review December 9 th , 2010, accepted January 24 th , 2012, inal version February, 9 th , 2012 ABSTRACT: Scheduling problems can be seen as multi-objective optimization problems (MOPs), involving the simultaneous satisfaction of several goals related to the optimal design, coordination, and management of tasks. The complexity of the goal functions and of the combinatorial methods used to ind analytical solutions to them is quite high. The search for solutions (Pareto-optima) is better served by the use of genetic algorithms (GAs). In this paper, we analyze the performance of the non-dominated sorting genetic algorithm II (NSGAII), strength Pareto evolutionary algorithm II (SPEAII), and their predecessors, NSGA and SPEA, when these are devoted to scheduling tasks in non-standardized production activities. KEYWORDS: Job-shop scheduling, multi-objective optimization, Pareto frontier, memetic algorithm, local search RESUMEN: En los problemas de programación de la producción que involucran diseñar, coordinar, administrar y controlar todas las operaciones presentes en el proceso productivo, aparecen numerosos problemas de optimización multi-objetivo (MOPs). Los MOPs constan de varias funciones que suelen ser complejas y evaluarlas puede ser muy costoso. La optimización multi-objetivo es la disciplina que trata de encontrar las soluciones, denominadas Pareto óptimas, a este tipo de problemas. La compleja resolución de los MOPs es debida a las dimensiones del problema, al carácter combinatorio de los algoritmos y a la naturaleza de los objetivos los cuales están vinculados a la eiciencia del sistema. En las últimas décadas muchos MOPs vinculados a la producción han sido tratados con éxito con técnicas de resolución basadas en algoritmos genéticos (GAs). En este trabajo se evalúa a NSGAII (Non-dominated Sorting Genetic Algorithm II), SPEAII (Strength Pareto Evolutionary algorithm II) y a sus antecesores, NSGA y SPEA, en el proceso de planiicación de la producción no estandarizada. PALABRAS CLAVE: Programación job-shop, optimización multi-objetivo, frontera de Pareto, algoritmo memético, búsqueda local 1. INTRODUCTION The scheduling of job-shop (i.e., non-standardized) production activities requires for one to assign in the best possible way the resources used in those processes [1–4]. This, in turn, demands eficient procedures to optimize decisions in those contexts [5,6]. This job- shop scheduling problem (JSSP) has been classiied as NP-Hard, meaning that no polynomial algorithm has been found for solving it. Worse yet, the time required to ind a solution grows exponentially with the size of the problem [7,8]. Different alternative presentations of the problem have been advanced, in order to accelerate the search for solutions [9–12]. A common feature of most JSSPs is the presence of at least two conlicting goals that have to be simultaneously optimized [13]. Such multi-objective optimization problems usually have many different solutions. If we assume that, without loss of generality, all the objectives have to be minimized, a multi-objective optimization problem (MOP) requires finding a vector  x x x n T * * * [ ,..., ] = 1 satisfying q inequality constraints g x i q i ( ) , , ...,  ³ = 0 1 and p equality constraints h x i p i ( ) , , ...,  = = 0 1 that minimizes     f x f x f x k T ( ) [ ( ),..., ( )] = 1 , where the vector of decision variables is  x x x n T = [ ,..., ] 1 . The class of values that satisfy the constraints deines a region of feasible solutions, denoted Ω . That is, any