A hybrid particle swarm optimisation approach for energy-efficient single machine scheduling with cumulative deterioration and multiple maintenances

This paper addresses the problem of energy-efficient single-machine scheduling with cumulative deteriorating effect and multiple maintenance activities. The actual processing time of a job is defined by a general non-decreasing function dependent on the operational time of the machine between a recent maintenance activity and the job. The aim is to determine the sequence of jobs and the number of maintenance activities as well as their positions, in order to minimise energy consumption. The energy consumption here depends on both the machine's operation and maintenance time. To solve this problem, a mixed integer linear programming model is proposed. Since the problem is NP-hard, exact methods are not feasible in terms of time when the problem scale is large. We therefore present a genetic algorithm (GA), a particle swarm optimisation (PSO) algorithm and a hybrid PSO (HPSO) approach that integrates genetic operators into PSO to optimise large-scale problem instances. Comprehensive computational experiments using 72 test instances coupled with statistical analysis confirm that HPSO performs significantly better than the GA and PSO.