A genetic algorithm approach to multi-objective scheduling problems with earliness and tardiness penalties

This paper deals with identical parallel machine scheduling problems with two kinds of objective functions, i.e., both regular and non-regular objective functions, and proposes a genetic algorithm approach in which (a) the sequence of jobs on each machine as well as the assignment of jobs to machines are determined directly by referring to a string (genotype), and (b) the start time of each job is fixed by solving the linear programming problem and a feasible schedule (phenotype) is obtained. As for (b), we newly introduce a method of representing the problem to determine the start time of each job as a linear programming problem whose objective function is formed as a weighted sum of the original multiple objective functions. This method enables us to obtain a lot of potential schedules. Moreover, through computational experiments by using our genetic algorithm approach, the effectiveness for generating a variety of Pareto-optimal schedules is investigated.