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This paper proposes an effective harmony search (HS) based heuristics method for the no-wait flow-shop scheduling optimization. The purpose of this paper is to minimize the total flow time. Firstly, the basic HS optimization mechanism, FSSP is presented and the total flow time is calculated by a novel method. Secondly, a largest-order-value rule is used to transform harmony in harmony memory from real vectors to job sequence so that the harmony search can be applied for FSSP. Improvising rule of new harmony is expatiated and high effective algorithm parameters are set for optimization object. Thirdly, HS and Insert-and interchange-based neighbor search, is proposed to solve the FSSP. At last, simulations and comparisons demonstrate the efficiency, effectiveness and robustness of harmony search algorithm for no-wait FSSP.

Quantum approximate optimization algorithm (QAOA) is a promising variational quantum algorithm for combinatorial optimization problems. However, the implementation of QAOA is limited due to the requirement that the problems be mapped to Ising Hamiltonians and the nonconvex optimization landscapes. Although the Ising Hamiltonians for many NP hard problems have been obtained, a general method to obtain the Ising Hamiltonians for constrained combinatorial optimization problems (CCOPs) has not yet been investigated. In this paper, a general method is introduced to obtain the Ising Hamiltonians for CCOPs and the Metropolis‐Hastings warm‐starting algorithm for QAOA is presented which can provably converge to the global optimal solutions. The effectiveness of this method is demonstrated by tackling the minimum weight vertex cover (MWVC) problem, the minimum vertex cover (MVC) problem, and the maximal independent set problem as examples. The Ising Hamiltonian for the MWVC problem is obtained first time by using this method. The advantages of the Metropolis‐Hastings warm‐starting algorithm presented here is numerically analyzed through solving 30 randomly generated MVC cases with 1‐depth QAOA.