To solve multi-objective Flexible Job-shop Scheduling Problems (FJSP), a Teaching and Peer-Learning Particle Swarm Optimization with Pareto Non-Dominated Solution Set (PNDSS-TPLPSO) algorithm was proposed. First, the minimum completion time of jobs, the maximum work load of machines and the total work load of all machines were taken as the optimization goals to establish a multi-objective flexible job-shop scheduling model. Then, the proposed algorithm combined multi-objective Pareto method with Teaching and Peer-Learning Particle Swarm Optimization (TPLPSO). A fast Pareto non-dominated sorting operator was applied to generate initial Pareto non-dominated solution set, and extracting Pareto dominance layer program was adopted to update Pareto non-dominated solution set. Furthermore, composite dispatching rule was adopted to generate the initial population, and opening up parabola decreasing inertia weigh strategy was taken to improve the convergence speed. Finally, the proposed algorithm was adopted to solve three Benchmark instances. In the comparison experiments with Multi-Objective Evolutionary Algorithm with Guided Local Search (MOEA-GLS) and Controlled Genetic Algorithm with Approach by Localization (AL-CGA), the proposed algorithm can obtain more and better Pareto non-dominated solutions for the same Benchmark instance. In terms of computing time, the proposed algorithm is less than MOEA-GLS. The simulation results demonstrate that the proposed algorithm can solve multi-objective FJSP effectively.

To deal with the Flexible Job-shop Scheduling Problem (FJSP), an Improved Two-Layer Particle Swarm Optimization (ITLPSO) algorithm was proposed. First, minimization of the maximal completion time of all machines was taken as the optimization objective to establish a flexible job-shop scheduling model. And then the improved two-layer PSO algorithm was presented, in which the stagnation prevention strategy and concave function decreasing strategy were adopted to avoid falling into local optimum and to improve the convergence rate. Finally, the proposed algorithm was adopted to solve the relevant instance and the comparison with existing methods was also performed. The experimental results showed that, compared with the standard PSO algorithm and the Two-Layer Particle Swarm Optimization (TLPSO) algorithm, the optimal value of the maximum completion time was reduced by 11 and 6 respectively, the average maximum completion time was reduced by 15.7 and 4 respectively, and the convergence rate was improved obviously. The performance analysis shows that the proposed algorithm can improve the efficiency of the flexible job-shop scheduling obviously and obtain better scheduling solution.