对多目标的柔性作业车间调度问题求解，往往不存在唯一的全局最优解，而是求

To solve the multi-objective flexible job shop scheduling problem, there is often no unique global optimal solution, but a set of non-dominant pareto optimal solutions. The traditional solution method is to use a linear weighting strategy to transform a multi-objective problem into a single-objective problem [4], for example, Gonzalez MA [5], Ceylan Z [6] use linear weighting methods to minimize production costs and carbon emissions in the scheduling process. Minimum goal. However, the rationality of the weight coefficients of each target needs to be improved, which limits the effective treatment of some multi-target problems with this method. In addition, with the continuous expansion of the scale of multi-objective optimization problems, accurate solution methods such as branch and bound method, integer programming method, enumeration method, etc. are often incapable or time-consuming. With the development of artificial intelligence technology, it is currently common to learn from the behavior of social groups and widely use swarm intelligence optimization solutions, such as genetic algorithm, bee colony algorithm, ant colony algorithm, immune algorithm, particle swarm algorithm [9,10], etc. Gong [11] and others used a hybrid artificial bee colony algorithm to solve the problem of flexible workshop scheduling considering artificial factors, and Shen [12] and others used genetic algorithm, simulated annealing and ant colony optimization to solve the problem of minimum total production time. The performance was compared and analyzed; Ding [13] et al. solved the problem of minimum completion time in flexible workshop scheduling through an improved particle swarm optimization algorithm.

For solving the multi-objective flexible job shop scheduling problem, there is often no unique global optimal solution, but a set of non dominated Pareto optimal solutions. The traditional solution method is to use the linear weighting strategy to transform the multi-objective problem into a single objective problem [4]. For example, Gonzalez Ma [5], Ceylan Z [6] uses the linear weighting method to achieve the objectives of minimizing production cost and carbon emission in the scheduling process. However, the rationality of the weight coefficient of each objective needs to be improved, which limits the effective treatment of some multi-objective problems by this method. In addition, with the continuous expansion of the scale of multi-objective optimization problems, branch definition method, integer programming method, enumeration method and other [7,8] accurate solution methods are often powerless or quite time-consuming. With the development of artificial intelligence technology, at present, swarm intelligence optimization methods are widely used based on social group behavior, such as genetic algorithm, bee colony algorithm, ant colony algorithm, immune algorithm, particle swarm optimization algorithm [9,10]. Gong [11] et al. Used hybrid artificial bee colony algorithm to solve the flexible job shop scheduling problem considering human factors, and Shen [12] et al. Compared and analyzed the performance of genetic algorithm, simulated annealing and ant colony optimization to solve the problem of minimum total production time respectively; Ding [13] et al. Solved the problem of minimizing the maximum completion time in flexible job shop scheduling through an improved particle swarm optimization algorithm.<br>

When solving the multi-objective flexible job shop scheduling problem, there is usually no unique global optimal solution, but a set of pareto optimal solutions which are not dominated by each other. Traditional solution method is to use linear weighting strategy to transform multi-objective problem into single-objective problem [4]. For example, Gonzalez M A[5] and Ceylan Z[6] use linear weighting method to achieve the goals of minimum production cost and minimum carbon emission in the scheduling process. However, the rationality of the weight coefficient of each objective needs to be improved, which limits the effectiveness of this method in dealing with some multi-objective problems. In addition, with the expanding scale of multi-objective optimization problems, accurate solutions such as branch definition method, integer programming method and enumeration method [7,8] are often powerless or time consuming. With the development of artificial intelligence technology, swarm intelligence optimization methods, such as genetic algorithm, bee colony algorithm, ant colony algorithm, immune algorithm, particle swarm algorithm [9,10], are widely used. Gong[11] et al. used the hybrid artificial bee colony algorithm to solve the flexible job shop scheduling problem considering artificial factors, and Shen[12] et al. compared and analyzed the performance of genetic algorithm, simulated annealing and ant colony optimization respectively to solve the problem of minimum total production time. Ding[13] et al. solved the problem of minimum maximum completion time in flexible job shop scheduling by improved particle swarm optimization algorithm.