Flexible Job-shop Scheduling Problem (FJSP) is a widely applied combinatorial optimization problem. Aiming at the problems of multi-objective FJSP that the solution process is complex and the algorithm is easy to fall into the local optimum, a Hybrid Particle Swarm Optimization algorithm with Multi-Region Sampling strategy (HPSO-MRS) was proposed to optimize both the makespan and total machine delay time. The multi-region sampling strategy was able to reorganize the positions of the Pareto frontiers that the particles belonging to, and guide the corresponding moving directions for the particles in multiple regions of the Pareto frontiers after sampling. Thus, the convergence ability of particles in multiple directions was adjusted, and the ability of uniform distribution was improved to a certain extent. In addition, in the encoding and decoding aspect, the decoding strategy with interpolation mechanism was used to eliminate the potential local left shift; in the particle updating aspect, the particle update method of traditional Particle Swarm Optimization (PSO) algorithm was combined with the crossover and mutation operators of Genetic Algorithm (GA), which improved the diversity of search process and avoid the algorithm from falling into the local optimum. The proposed algorithm was tested on benchmark problems Mk01-Mk10 and compared with Hybrid Particle Swarm Optimization algorithm (HPSO), Non-dominated Sorting Genetic Algorithm Ⅱ (NSGA-Ⅱ), Strength Pareto Evolutionary Algorithm 2 (SPEA2) and Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) on algorithm effectiveness and operation efficiency. Experimental results of significance analysis showed that, HPSO-MRS was significantly better than the comparison algorithms on the convergence evaluation indexes Hyper Volume (HV) and Inverted Generational Distance (IGD) in 85% and 77.5% of the control groups, respectively. In 35% of the control groups, the distribution index Spacing of the algorithm was significantly better than those of the comparison algorithms. And there was no situation that the proposed algorithm was significantly worse than the comparison algorithms on the three indexes. It can be seen that, compared with the others, the proposed algorithm has better convergence and distribution performance.

A fast multi-objective hybrid evolutionary algorithm was proposed for solving bi-criteria Flow shop Scheduling Problem (FSP) with the objectives of minimizing makespan and total flow time. The sampling strategy of the Vector Evaluated Genetic Algorithm (VEGA) and a new sampling strategy according to the Pareto dominating and dominated relationship-based fitness function were integrated with the proposed algorithm. The new sampling strategy made up the shortage of the sampling strategy of VEGA. VEGA was good at searching the edge region of the Pareto front, but it neglected the central area of the Pareto front, while the new sampling strategy preferred the center region of the Pareto front. The fusion of these two mechanisms ensured that the hybrid algorithm can converge to the Pareto front quickly and smoothly. Moreover, the algorithm efficiency was improved greatly without calculating the distance. Simulation experiments on Taillard benchmark sets show that, compared with Non-dominated Sorting Genetic Algorithm-Ⅱ (NSGA-Ⅱ) and Strength Pareto Evolutionary Algorithm 2 (SPEA2), the fast multi-objective hybrid evolutionary algorithm is improved in the performance of convergence and distribution, and the efficiency of the algorithm has been improved. The proposed algorithm can be better at solving the bi-criteria flow shop scheduling problem.