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A Genetic Algorithm Enhanced by Dominance Properties for Single Machine Scheduling Problems with Setup costs

This paper considers a single machine scheduling problem in which n jobs are to be processed and a machine setup time is required when the machine switches jobs from one to the other. All jobs have a common due date that has been predetermined using the median of the set of sequenced jobs. The objective is to find an optimal sequence of the set of n jobs to minimize the sum of the job’s setups and the cost of tardy or early jobs related to the common due date. In this research, dominance properties are developed by swapping the neighborhood jobs. The time complexity of the dominance properties is in O(n) and it is very efficient when combined with the GA. To prevent earlier convergence of a Simple Genetic Algorithm (SGA), these dominance properties are further embedded in SGA to improve the efficiency and effectiveness of the global searching procedure. Analytical results in benchmark problems are presented and the computational algorithms are developed.