A Quantum-Inspired Immune Algorithm for Hybrid Flow Shop with Makespan Criterion

This paper presents a quantum-inspired immune algorithm (QIA) for Hybrid flow shop problems (HFSP) to minimize makespan. Since HFSP have been proved to be NP-hard in a strong sense when the objective is to minimize the makespan, an effective immune algorithm (IA) is used to solve the problems. IA is a kind of evolutional computation strategies, which is developed on the basis of a real immune mechanism in the human body, and has been employed to tackle complex scheduling problems and produce a reasonable manufacturing schedule. In order to achieve better results, the standard IA is combined with quantum algorithm (QA), which is based on Q-bit and uses quantum rotation gate to update. A real number representation is proposed to convert the Q-bit representation to job permutation for evaluating value of solutions. The proposed QIA can overcome the limitations of IA, quicken up convergence speed and improve the solution. Forty one benchmarks are examined to validate the efficiency of the proposed algorithm. The computational experiments show that the proposed QIA can also obtain both better and more robust results than IA and QA.