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In this paper, we present an improved particle swarm optimization (PSO) algorithm for the hybrid flowshop scheduling (HFS) problem to minimize total weighted completion time. This problem has a strong practical background in process industry. For example, the integrated production process of steelmaking, continuous-casting, and hot rolling in the iron and steel industry, and the short-term scheduling problem of multistage multiproduct batch plants in the chemical industry can be reduced to a HFS problem. To make PSO applicable in the HFS problem, we use a job permutation that is the processing order of jobs in the first stage to represent a solution, and construct a greedy method to transform this job permutation into a complete HFS schedule. In addition, a hybrid variable neighborhood search (VNS) incorporating variable depth search, a hybrid simulated annealing incorporating stochastic local search, and a three-level population update method are incorporated to improve the search intensification and diversification of the proposed PSO algorithm. Computational experiments on practical production data and randomly generated instances show that the proposed PSO algorithm can obtain good solutions compared to the lower bounds and other metaheuristics.