Article: Floating-point to integer mapping schemes in differential evolution for permutation flow shop scheduling Journal: International Journal of Bio-Inspired Computation (IJBIC) 2010 Vol.2 No.3/4 pp.183 - 204 Abstract: For over 50 years now, the famous problem of permutation flow shop scheduling has been attracting the attention of researchers in operations research, engineering and computer science. Over the past several years, there has been a spurt of interest in computational intelligence heuristics and metaheuristics for solving this problem – ranging from genetic algorithms to tabu search to complex hybrid techniques. Most recently, differential evolution, one of the newest members of the evolutionary algorithm family, has emerged as a popular technique for application to this problem. The main problem in applying differential evolution to the permutation flow shop is that differential evolution works on continuous, or real-valued, parameters (it is a continuous optimisation method), whereas the flow shop problem involves finding sequences or schedules of n jobs, expressed as permutations of n distinct objects (integers). A mapping, or encoding, of floating-point numbers to integer permutations is therefore necessary for differential evolution to be applied to this problem. This paper provides a review and evaluation of the best-known encoding schemes in the literature. Inderscience Publishers - linking academia, business and industry through research

Title: Floating-point to integer mapping schemes in differential evolution for permutation flow shop scheduling

Authors: Uday K. Chakraborty, Kenneth P. Turvey

Addresses: Department of Mathematics and Computer Science, University of Missouri – St. Louis, One University Blvd., St. Louis, Missouri 63121, USA. ' Department of Mathematics and Computer Science, University of Missouri – St. Louis, One University Blvd., St. Louis, Missouri 63121, USA

Abstract: For over 50 years now, the famous problem of permutation flow shop scheduling has been attracting the attention of researchers in operations research, engineering and computer science. Over the past several years, there has been a spurt of interest in computational intelligence heuristics and metaheuristics for solving this problem – ranging from genetic algorithms to tabu search to complex hybrid techniques. Most recently, differential evolution, one of the newest members of the evolutionary algorithm family, has emerged as a popular technique for application to this problem. The main problem in applying differential evolution to the permutation flow shop is that differential evolution works on continuous, or real-valued, parameters (it is a continuous optimisation method), whereas the flow shop problem involves finding sequences or schedules of n jobs, expressed as permutations of n distinct objects (integers). A mapping, or encoding, of floating-point numbers to integer permutations is therefore necessary for differential evolution to be applied to this problem. This paper provides a review and evaluation of the best-known encoding schemes in the literature.

Keywords: differential evolution; flow shop scheduling; heuristics; optimisation; permutation problem; floating point numbers; integer mapping; integer permutations; encoding schemes.

DOI: 10.1504/IJBIC.2010.033087

International Journal of Bio-Inspired Computation, 2010 Vol.2 No.3/4, pp.183 - 204

Published online: 07 May 2010 *

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Title: Floating-point to integer mapping schemes in differential evolution for permutation flow shop scheduling

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