A hybrid particulate swarm optimization (hybrid) combination of an optimization algorithm of the particle swarm and a variable neighborhood search algorithm is proposed for the multi-objective permutation flow shop scheduling problem (PFSP) with the smallest cumulative completion time and the smallest total flow time. Algorithm for hybrid particulate swarm optimization (HPSO) is applied to maintain a fair combination of centralized search with decentralized search. The Nawaz-Enscore-Ham )NEH) heuristic algorithm in this hybrid algorithm is used to initialize populations in order to improve the efficiency of the initial solution. The method design is based on ascending order (ranked-order-value, ROV), applying the continuous PSO algorithm to the PFSP, introducing the external archive set storage Pareto solution, and using a hybrid strategy that combines strong dominance and aggregation distance to ensure the distribution of the solution set. We adopted the Sigma method and the roulette method, based on the aggregation distance, to select the global optimal solution. A variable neighborhood search algorithm was proposed to further search the Pareto solution in the external set. The suggested hybrid algorithm was used to solve the Taillard test set and equate the test results with the SPEA2 algorithm to check the scheduling algorithm’s efficacy.
