###### Abstract
[13] proposed an intrusive weed-optimal scheduling algorithm for optimizing the NFSP and demonstrated the effectiveness of the algorithm in solving the no-idle flow-shop scheduling problem by comparing 12 cases of different sizes with other algorithms. [PERSON] et al. [14] proposed a discrete firefly optimization algorithm for the no-idle permutation flow-shop scheduling problem, which uses an individual encoding approach based on the workpiece sequences and a position update approach and embeds swapping, insertion, and reverse-order operation strategies to enhance the local search performance of the algorithm. [PERSON] et al. [15] proposed a two-population distribution estimation algorithm for solving the no-idle replacement flow-shop scheduling problem with the total delay quasi-side, and demonstrated the effectiveness of the proposed algorithm through numerical experiments as well as algorithm comparisons. [PERSON] et al. [16] proposed a modal algorithm for edge histograms with mixed nodes, which consisted of a population-based global search and local optimization for individuals, and demonstrated the effectiveness of the algorithm in solving this problem through numerical experiments. [PERSON] et al. [17] proposed a discrete fireworks algorithm with a local search for the no-idle permutation flow-shop scheduling problem by using the encoding of artifact sequences, redefining the explosion operator and the variation operator by combining operations such as flip-swap, and incorporating a local search strategy based on the insertion neighborhood to enhance the local search capability of the fireworks algorithm. [PERSON] et al. [18] studied the distributed no-idle permutation flow-shop scheduling problem, proposed a collaborative optimization algorithm to ensure the diversity and quality of the initial population by two heuristic synergies, improvedthe search operator adaptive reinforcement strategy, and finally, demonstrated the effectiveness of the algorithm in solving the current problem with numerical experiments of different scales. Algorithms represent the core research of the HFSP. In the study of solving the HSFP, heuristic algorithms such as the genetic, simulated annealing, particle swarm, and ant colony algorithms are often chosen because of the NP-hard nature of the problem. Among them, genetic algorithms are the most widely used for the HFSP. For example, several studies in the literature [19; 20; 21; 22; 23] are based on genetic algorithms for the solution. For multi-objective problems, the NSGA-II based on a genetic algorithm and the concept of Pareto optimality is often used, which has the advantages of a fast operation and good convergence of the solution set. [PERSON] et al. [24] considered workpiece transportation and machine tool change, and developed an HFSP model with energy consumption and the makespan as the optimization objectives, which was solved using the NSGA-II. [PERSON] et al. [25] designed the NSGA-II based on two-stage chromosome coding to solve a multi-objective HFSP that minimized the total delay time of the workpiece and the standard deviation of the worker job assignment. [PERSON] et al. [26] improved the NSGA-II for solving a multi-objective HFSP with the makespan and load balancing as the optimization objectives. [PERSON] et al. [27] proposed an improved NSGA-II for solving the HFSP with the optimization objectives of minimizing energy consumption and the makespan. [PERSON] et al. [28] proposed an improved NSGA-II for the HFSP with the makespan and energy consumption as the optimization objectives. In addition, in most of the studies on the HFSP, only the processing time was considered, and some auxiliary time was neglected. In real production, there is some preparation time before the processing equipment, and there is handling time when the workpiece is transported from the current process to the next process.