An effective hybrid multi-objective genetic algorithm for bi-criteria scheduling on a single batch processing machine with non-identical job sizes

This paper addresses the problem of scheduling jobs with non-identical sizes on a single batch processing machine. A batch processing machine is one which can process multiple jobs simultaneously as a batch as long as the total size of jobs being processed does not exceed the machine capacity. The batch processing time is equal to the longest processing time among all jobs in the batch. For the simultaneous minimization of the bi-criteria of makespan and maximum tardiness, we propose two different multi-objective genetic algorithms based on different representation schemes. While the first algorithm do search via generating sequences of jobs using genetic operators and then batching jobs keeping their order in the sequence, the second algorithm uses the idea of generating batches of jobs directly using genetic operators and ensures feasibility through using heuristic procedures. The type of representation used in the second algorithm allows introducing heuristics with the ability of biasing the search towards each objective and also allows hybridization with a local search heuristic that gives the ability of finding Pareto-optimal or locally efficient Pareto-solutions. Computational results show that the non-dominated solutions obtained by the latter algorithm are very superior in closeness to the true Pareto-optimal solutions and to keep diversity in the obtained Pareto-set, as the problem size increases.