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The moth-flame optimization algorithm (MFO) is a novel metaheuristic algorithm for simulating the lateral positioning and navigation mechanism of moths in nature, and it has been successfully applied to various optimization problems. This paper segments the flame energy of MFO by introducing the energy factor from the Harris hawks optimization algorithm, and different updating methods are adopted for moths with different flame-detection abilities to enhance the exploration ability of MFO. A new energy-segmented moth-flame optimization algorithm (ESMFO) is proposed and is applied on 21 benchmark functions and an engineering design problem. The experimental results show that the ESMFO yields very promising results due to its enhanced exploration, exploitation, and convergence capabilities, as well as its effective avoidance of local optima, and achieves better performance than other the state-of-the-art metaheuristic algorithms in terms of the performance measures.

Job Shop Scheduling Problem (JSSP) is a well-known NP-hard combinatorial optimization problem. In recent years, many scholars have proposed various metaheuristic algorithms to solve JSSP, playing an important role in solving small-scale JSSP. However, when the size of the problem increases, the algorithms usually take too much time to converge. In this paper, we propose a hybrid algorithm, namely EOSMA, which mixes the update strategy of Equilibrium Optimizer (EO) into Slime Mould Algorithm (SMA), adding Centroid Opposition-based Computation (COBC) in some iterations. The hybridization of EO with SMA makes a better balance between exploration and exploitation. The addition of COBC strengthens the exploration and exploitation, increases the diversity of the population, improves the convergence speed and convergence accuracy, and avoids falling into local optimum. In order to solve discrete problems efficiently, a Sort-Order-Index (SOI)-based coding method is proposed. In order to solve JSSP more efficiently, a neighbor search strategy based on a two-point exchange is added to the iterative process of EOSMA to improve the exploitation capability of EOSMA to solve JSSP. Then, it is utilized to solve 82 JSSP benchmark instances; its performance is evaluated compared to that of EO, Marine Predators Algorithm (MPA), Aquila Optimizer (AO), Bald Eagle Search (BES), and SMA. The experimental results and statistical analysis show that the proposed EOSMA outperforms other competing algorithms.

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