Determining the process parameter settings for plastic injection molding greatly affects the quality of the plastic injection-molded product [9]. Unsuitable process parameter settings can cause many production problems (e.g., many product defects, long lead times, large amounts of scrap, high production costs, etc.), reduce the price competitive advantage, and decrease a company’s profitability. The plastic injection molding process includes four phases: plasticization, filling, packing, and cooling [10]. Therefore, several process parameters which include the melt temperature, mold temperature, injection pressure, injection velocity, injection time, packing pressure, packing time, cooling temperature, and cooling time all potentially influence the quality of injection-molded plastic products [11, 12]. In previous plastic injection molding research, different control process parameters have been used. For example, Shi et al. [13] used four process parameters (mold temperature, melt temperature, injection time, and injection pressure) to determine the optimal initial process parameter settings for injection-molded plastic parts with a butter container lid and under single quality characteristic (the maximum shear stress) considerations. Chiang and Chang [14] used four control process parameters (mold temperature, melt temperature, injection pressure, and injection time) to determine the optimal initial process parameter settings for injection-molded plastic parts with a thin shell feature and under multiple quality characteristic considerations. Therefore, before optimizing process parameter settings, engineers need to select feasible and tractable control process parameters which will influence the production results of plastic injection molding.
  Therefore, for multiple-input multiple-output (MIMO) plastic injection molding process, this research proposes an effective process parameter optimization approach to help manufacturers achieve a competitive advantage of product quality and costs. The proposed approach integrates Taguchi’s parameter design method, back-propagation neural network based on particle swarm optimization (PSONN model), particle swarm optimization multi-objective algorithm, and engineering optimization concept and can effectively help engineers determine final optimal process parameter settings.
  The rest of this paper is organized as follows. Section 2 gives a brief description of literature review. Section 3 describes the optimization methodologies including neural networks, particle swarm optimization, and multi-objective particle swarm optimization algorithms used in this study for optimization. Section 4 proposes a process parameter optimization approach for plastic injection molding under multiresponse considerations. In Section 5, multi-objective optimization applications will be presented to illustrate the performance and capabilities of the proposed optimization strategy according to an illustrative case study. In Section 6, an experiment comparison, results, and discussion are presented. Finally, the last section gives the conclusions of this paper.
2 Literature review
  An alternative means of applying artificial neural networks (ANN) has been proposed to improve conventional Taguchi’s parameter design and is capable of effectively treating continuous parameter values [15, 16]. Subsequently, researchers worldwide have applied widely soft computing for optimizing process parameters. Shi et al. [13] presents a hybrid optimal model in combination with ANN and a genetic algorithm (GA) for the plastic injection molding process under the quality requirement of maximum shear stress. Panneerselvam et al. [17] described a hybrid technique of ANN and GA to obtain optimal weld tensile strength. ANN was used to establish the relationship between the input/output parameters of the process and the established ANN was then suitably integrated with GA. However, such single response requirement rarely exists in practical production processes. Usually, there are multiresponse requirements in product production.
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