**Simulation-based Optimization using Genetic Algorithms**

for Multi-objective Flexible JSSP

for Multi-objective Flexible JSSP

**Elena Simona NICOARA ^{1}, Florin Gheorghe FILIP^{2,3}, Nicolae PARASCHIV^{1}**

**Petroleum-Gas University,**

^{1 }39, Bucureşti Blvd., Ploieşti, 100520, Romania,

snicoara@upg-ploiesti.ro

**Romanian Academy – INCE and BAR,**

^{2}125 , Calea Victoriei, Bucharest, 010071, Romania

filipf@acad.ro

**I C I Bucharest**

^{3 }(National Institute for R & D in Informatics)

8-10 Averescu Blvd.

011455 Bucharest 1, Romania

**A****bstract**: The fast technological progress, along with growing requirements in the manufacturing systems have led in the last decades to a true revolution regarding the optimization methods for *job shop scheduling problem* (JSSP), which regularly has the greatest impact on the global optimality from the temporal perspective. An extension to the mathematical framework associated to the JSSP for multi-objective flexible JSSP (MOFJSSP) is proposed; here, the *flexibility of type II*, where the routings of the jobs on the resources are not fixed is considered. Also, a short review of the most used simulation-based optimization methods for (MOF)JSSP is made and a genetic algorithm-based control system is proposed. This is then tested on a complex real-world MOFJSS instance and the *ft*10 test-instance.

**Keywords**: Multi-objective Flexible Job Shop Scheduling Problem, Simulation-based Optimization, Genetic Algorithm, GA-based Control, NSGA-II.

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**CITE THIS PAPER AS**:

Elena Simona NICOARA, Florin Gheorghe FILIP, Nicolae PARASCHIV, **Simulation-based Optimization using Genetic Algorithms for Multi-objective Flexible JSSP**, *Studies in Informatics and Control*, ISSN 1220-1766, vol. 20 (4), pp. 333-344, 2011.

**1. Introduction**

Generally speaking, a job shop scheduling problem (JSSP) is a decision-making process for time optimal assignment of some (limited) resources to some heterogeneous jobs consisting in many operations. The resources have to be available and the associated optimization problem is either mono-objective or multi-objective. This kind of scheduling places the problem in the *discrete-event* *systems* (DES) domain, whose optimal control often involves computer simulation, at least in the large-scale real-world manufacturing systems.

As shown in [11] the simulation-based optimization can be utilised in the decision-making process for DES. For the specific JSSP case, there are two main aspects which make the decision difficult, namely: a) the constraints can not be explicitly expressed related to the decision variables, and b) the number of the decision alternatives in the search space is huge.

Besides the trivial case when the number of decision alternatives is small to average, where simulation-based optimization consists in evaluating all alternatives to detect the one that provides the best value for the optimization criterion/criteria, the proper meaning of the simulation-based optimization refers to an ordered simulation sequence, determined by an algorithm, applied to different decision parameters until a (near) optimal solution is found [11].

This paper is concerned with simulation-based optimization appropriate to the *Multi-objective Flexible JSSP* (*MOFJSSP*). It is organised as follows. An extension of the classical formulation of JSSP to MOFJSSP is presented first. Next, the most used simulation-based optimization methods in the scheduling area are reviewed and a control method, based on a genetic algorithm, is proposed and the test results are presented.

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