A hybrid discrete teaching-learning based meta-heuristic for solving no-idle flow shop scheduling problem with total tardiness criterion

This paper proposes a hybrid discrete teaching-learning based meta-heuristic (HDTLM) to solve the no-idle flow shop scheduling problem (NIFSP) with the total tardiness criterion. To imitate the teaching-learning phenomenon in the real world, the HDTLM is composed of three phases, i.e. discrete teaching phase based on probabilistic model, discrete learning phase based on hierarchical structure, and reinforcement learning. In the discrete teaching phase, a probabilistic model based on the elite learners and the best learner is used to generate a series of position sequences, and the concept of consensus permutation is employed to replace the mean individual in the teaching-learning based optimization (TLBO) algorithm. Each job of the consensus permutation is inserted into a new sequence according to the position sequence. In the discrete learning phase, according to different levels of learners, all learners are divided into three layers, i.e. top layer, middle layer, bottom layer, and then the proposed learning phase adopts the order of top-down to spread the knowledge. The reinforcement learning phase is applied to the best learner to further improve the knowledge level of teacher. The parameters of the HDTLM are calibrated by a design of experiments (DOE) on randomly generated testing instances. The computational results on Taillard and Ruiz's benchmark sets and statistical analyses show that the HDTLM is an efficient and effective method for solving the NIFSP.