A study on PGEP to evolve heuristic rules for FJSSP considering the total cost of energy consumption and weighted tardiness

Performance indicators such as makespan, flow time and tardiness are considered to be optimisation objectives in the traditional flexible job shop scheduling problem (FJSSP). However, the cost of energy consumption or environmental problems should not be ignored. This paper addresses the FJSSP by minimising the sum of the cost of energy consumption and the weighted tardiness. First, a mathematical model of the problem and a heuristic algorithm for the problem are presented. Second, a parallel gene expression programming (PGEP) method with a migration scheme is put forward to evolve rules for the proposed heuristic algorithm to solve the problem. To speed up the system learning process, a parallel and distributed computing framework is also designed. Finally, the performance of the proposed PGEP approach is evaluated through extensive simulations. The time-of-use electricity pricing, due date tightness and tardiness penalty weight are considered when evaluating the effect of the heuristic rules. Experimental results show that the proposed PGEP approach can significantly improve the quality of the heuristic rules, and the PGEP-evolved rules can fast and effectively solve FJSSP.