Hybrid Differential Evolution – Scatter Search Algorithm for Permutative Optimization

Abstract

Adaptive memory programming approaches have proven effective in finding high quality solutions to many real world intractable problems. Therefore, over the years, researches have attempted to combine the best features from different adaptive memory approaches to derive more powerful hybrid heuristics (Onwubolu, 2002). Combining the best features of different heuristics will give a new heuristic that is superior to the individual systems from which these features are derived. Differential evolution (DE) algorithm (Price, 1999) is an evolutionary approach which does not inhibit any adaptive memory features. It is however a very powerful and robust heuristic for continuous optimization. Continuous optimization is a very important aspect of optimization; however a heuristics application to permutative optimization is imperative if it is to be generic. Permutative optimization encompasses many aspects of engineering. In practical settings, it is common to observe features which are discrete, such as the different discrete nut and bolt sizes, fixed number of machines in a manufacturing plant or discrete number of buses in a fixed route. All these problems are practical and challenging, which utilize discrete values. The purpose of this paper is then to introduce an enhanced different evolution algorithm for discrete optimization which is hybridized by the adaptive memory heuristic of scatter search (SS) (Glover, 1998). SS is a highly effective heuristic which is the superset of tabu search (TS) (Glover, 1998). It has been successfully applied to many permutative optimization problems. The objective of the proposed hybrid optimization approach is then to isolate its highly effective intensification and diversification routines and embed it in the EDE structure. The result is a highly evolved hybrid enhanced differential evolution scatter search (HEDE-SS) heuristic. The hybrid optimization scheme is applied to two difficult permutative optimization problems of quadratic assignment problem (QAP) and the flow shop scheduling problem (FSS). The results generated by the hybrid scheme are then compared with the heuristics of EDE and SS in order to show that the hybrid scheme is an improvement over the original heuristics. Additionally, the results of the hybrid scheme is compared with the optimal results from the operations research (OR) library and with the results obtained by other heuristics for the same problem instances from the literature. O pe n A cc es s D at ab as e w w w .in te ch w eb .o rg