A factorial representation of permutations and its application to flow-shop scheduling

Abstract

The first objective of the current research was to incorporate the NEH search method, which is the classical heuristic algorithm for the flow-shop scheduling problem, into a genetic algorithm to improve search performance. To achieve this objective, the author used factorial numbers to represent permutations. Since chromosome representations according to factorial numbers have a one-to-one correspondence with permutations, there is no redundancy. Since no lethal gene is produced by crossover, uniform crossover can also be applied, not just one-point or two-point cross-over. In addition, it was apparent that the NEH concept could be naturally introduced into the genetic algorithm search process by arranging n jobs in ascending order of total work times as the basic permutation that is used when associating permutations and factorial numbers. Factorial numbers can also be used to represent certain types of constraints. The second objective of the current research was to verify the effectiveness of the factorial number representation in order-constrained permutation searches. To accomplish this, the author performed numerical experiments and obtained superior results than were obtained by conventional methods. © 2006 Wiley Periodicals, Inc.