A shuffled complex evolution algorithm with opposition-based learning for a permutation flow shop scheduling problem

The permutation flow shop scheduling problem (PFSP) is a typical non-deterministic polynomial-time hard problem, which has wide engineering applications, and performs an important function in manufacturing fields. In this paper, an improved shuffled complex evolution algorithm with opposition-based learning (SCE-OBL) was proposed to obtain the optimal makespan for permutation flow shop scheduling. The OBL strategy was used to improve the population quality and accelerate the convergence speed. The theoretical analysis demonstrated that the improved algorithm converged to optimum with a probability of 1. Moreover, the largest-order-value mechanism was used in the combinational optimisation problem to change the variables in the continuous domain to discrete variables, and job-based representation was adopted for encoding the solution of the PFSP. Twenty-nine typical instances were then used to test the performance of the SCE-OBL, and the computational results showed that the SCE-OBL algorithm could obtain better solutions for the PFSP than other algorithms.