Metaheuristics for Common Due Date Total Earliness and Tardiness Single Machine Scheduling Problem

In this chapter, metaheuristic algorithms, namely, a binary particle swarm optimization, a discrete particle swarm optimization, and a discrete differential evolution algorithm, are presented to solve the common due date total earliness and tardiness single machine scheduling problem. Novel discrete versions of both particle swarm optimization and differential evolution algorithms are developed to be applied to all types of combinatorial optimization problems in the literature. The metaheuristic algorithms presented in this chapter employ a binary solution representation, which is very common in the literature in terms of determining the early and tardy job sets so as to implicitly tackle the problem. In addition, a constructive heuristic algorithm, here we call it MHRM, is developed to solve the problem. Together with the MHRM heuristic, a new binary swap mutation operator, here we call it BSWAP, is employed in the metaheuristic algorithms. Furthermore, metaheuristic algorithms are hybridized with a simple local search based on the BSWAP mutation operator to further improve the solution quality. The proposed metaheuristic algorithms are tested on 280 benchmark instances ranging from 10 to 1000 jobs from the OR Library. The computational results show that the metaheuristic algorithms with a simple local search generated either better or competitive results than those of all the existing approaches in the literature.