A Stochastically Perturbed Particle Swarm Optimization for Identical Parallel Machine Scheduling Problems

Abstract

Identical parallel machine scheduling (PMS) problems with the objective of minimizing makespan (Cmax) is one of the well known NP-hard [1] combinatorial optimization problems. It is unlikely to obtain optimal schedule through polynomial time-bounded algorithms. Small size instances of PMS problem can be solved with reasonable computational time by exact algorithms such as branch-and-bound [2, 3], and the cutting plane algorithm [4]. However, as the problem size increases, the computation time of exact methods increases exponentially. On the other hand, heuristic algorithms generally have acceptable time and memory requirements, but do not guarantee optimal solution. That is, a feasible solution is obtained which is likely to be either optimal or near optimal. The well-known longest processing time (LPT) rule of Graham [5] is a sort of so called list scheduling algorithm. It is known that the rule works very well when makespan is taken as the single criterion [6]. Later, Coffman et al. [7] proposed MULTIFIT algorithm that considers the relation between bin-packing and maximum completion time problems. Yue [8] showed that the MULTIFIT heuristic is not guaranteed to perform better than LPT for every problem. Gupta and Ruiz-Torres [9] developed a LISTFIT algorithm that combines the bin packing method of the MULTIFIT heuristic with multiple lists of jobs. Min and Cheng [10] introduced a genetic algorithm (GA) that outperformed simulated annealing (SA) algorithm. Lee et al. [11] proposed a SA algorithm for the PMS problems and compared their results with the LISTFIT algorithm. Tang and Luo [12] developed a new iterated local search (ILS) algorithm that is based on varying number of cyclic exchanges.