A Genetic Algorithm with Dominance Properties for Single Machine Scheduling Problems

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. Dominance properties are developed according to the sequence swapping of two neighborhood jobs. These dominance properties are further embedded in the simple genetic algorithm to improve the efficiency and effectiveness of the global searching procedure. Analytical results in benchmark problems are presented and computational algorithms are developed