Flow Shop Scheduling Using Enhanced Differential Evolution Algorithm

This paper presents a new approach of differential evolution to scheduling optimization problem. The developed approach is viewed as an enhanced varient of differential evolution, incorporation new child correction schemas and coversion schemas from differential to discrete domain. The heuristic is extensively evaluated with the scheduling problem of flow shop and compared with published results. INTRODUCTION Metaheuristics are the common tool utilized to solve complex manufacturing problems. The advantage of this process is the production of viable results within the given constraints and resources. Flow shop scheduling (FSS) can be considered as one of the common manufacturing problems that is regurarly realized using optimization techniques. The evolution of optimization techniques has been mainly attributed to the increase in complexity of problems encountered. Two branches of heuristics exist: constructive and improvement (Onwubolu and Mutingi 1999). Constructive methods are usually problem dependent (Cambell et al. 1970, Nawaz et al. 1983). Improvement methods are those involving population-based heuristics which usually follow a naturally occurring paradigm. Some of these are genetic algorithms (GA), tabu search (TS), neural networks (NN), simulated annealing (SA) and particle swamp optimization (PSO) among others. Differential evolution (DE) algorithm was introduced by Price and Storn (1999). Since then, due to its effectiveness, a lot of advanced work (see Onwubolu and Babu 2004; Lampinen and Storn 2004 and Lempinen and Zelinka 1999) have been conducted in order to realize the full potential of this viable approach. In its canonical form, DE is designed to solve differential problems, which involve continuous values; that is, there is no discriminating feature in DE between values within a solution. This approach is effective; however a lot of problems involve solutions which are permutative, such as FSS. To achieve the desired heuristic, certain modifications have to be undertaken to change the operational domain of DE from continuous to discrete. Initial work has been done by Onwubolu and Davendra (2006), to transform the operational domain, however to improve the solutions further, enhancements were required. This varient was termed Discrete Differential Evolution (DDE). This paper covers the work done to DDE to enhance it to enhanced differential evolution (EDE) algorithm, and its application to multiple FSS problems, in order to show its effectiveness over a wider range of FSS problems. FLOW SHOP SCHEDULING In many manufacturing and assembly facilities a number of operations have to be done on every job. Often, these operations have to be done on all jobs in the same order, which implies that the jobs have to follow the same route. The machines are assumed to be set up and the environment is referred to as flow shop (Pinedo 1995). The flow shop can be formatted generally by the sequencing on n jobs on m machines under the precedence condition. The general constraints that are assessed for a flow shop system is the time required to finish all jobs or makespan, minimizing of average flow time, and the maximizing the number of tardy jobs. The minimization of completion time for a flow shop schedule is equivalent to minimizing the objective function