Multi-objective optimization of single machine scheduling with energy consumption constraints

A bi-objective single machine scheduling problem with energy consumption constraints is studied, in which the objective functions are the total weighted completion time and the total weighted tardiness. Given the NP-hard nature of the problem, a multi-objective particle swarm optimization (MOPSO) algorithm is adopted to solve the problem. Since the original version of the MOPSO was designed for continuous optimization problems, it is crucial to decode its results in order to obtain feasible schedules. After the algorithm framework is determined, key parameters of the MOPSO are analyzed. A design of experiments (DOE) approach based on the Taguchi method is used to optimize parameters of the MOPSO algorithm for both small-scale and large-scale problem instances. To assess the algorithm's performance, we compare it to a well-known multi-objective evolutionary algorithm, the NSGA-II. DOE analysis is also carried out for tuning the parameters of the NSGA-II. Comprehensive computational experiments with different performance measures confirm that the modified MOPSO performs well on both small-scale and large-scale instances tested, and its performance is often superior compared to the NSGA-II.