A Lévy flight embedded particle swarm optimization for multi-objective parallel-machine scheduling with learning and adapting considerations

•Adaptable parallel processors which have never been considered before are addressed for the first time.•This paper pioneers in treating the adapting ratios as imprecise parameters.•A highly-modified meta-heuristic called LFEPSO is designed to implement an efficient search procedure.•The proposed parallel-machine scheduling problem is formulated into a bi-objective mathematical model.

The study at hand is devoted to schedule jobs on uniform parallel processors which are capable of adapting as well as learning. The problem is formulated into a bi-objective mixed integer mathematical model in which several parameters are supposed to follow triangular possibility distributions. Converting the aforementioned model, an auxiliary equivalent mixed integer crisp one is constructed through an interactive possiblistic programming approach. Due to the NP-hardness of the problem, swarm intelligence is hired by applying a highly modified Particle Swarm Optimization (PSO) method. In the proposed evolutionary method, called Lévy Flight Embedded Particle Swarm Optimization (LFEPSO), uniformly distributed walks are replaced by Lévy flights. In order to check the validity of the model and the performance of the proposed LFEPSO, twenty-six data sets are generated on a random basis. As the numerical results indicate, embedding Lévy flights made a tremendous improvement towards solving the local optima problem of the traditional PSO. Compared to the exact solution method, LFEPSO has shown an outstanding performance in scheduling 8–500 jobs on 3–50 parallel processors. In addition, numerical results reveal the significant role of considering the adapting ability in accurately modeling real-world and huge-sized problems.

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