Multi-Objective Optimization in Injection Molding Simulation: A Preference-Driven Approach with an Adaptive Experimental Design to Investigate the Optimal Solution Region

This contribution presents a simulation-based approach for optimizing injection molding processes using digital twins. It combines surrogate modeling via response surface methodology (RSM) with the evolutionary algorithm NSGA-II to efficiently capture complex relationships between process parameters and objectives. A key element is the adaptive enhancement of the training dataset within the decision-relevant region of interest (ADEROI) by a modified greedy max–min algorithm. This strategy closes data gaps, improves model accuracy in the potentially optimal region, and directs additional simulations to informative areas. Leave-one-out (LOO) and hold-out (HO) cross-validations show strong root mean square error (RMSE) and R2 values for deformation, shrinkage, cycle time, and mass. NSGA-II converges after 403 generations and results in 191 Pareto-optimal solutions, which are consolidated into preference-consistent operating points. These points make trade-offs between analyzed objectives’ deformation, shrinkage, and cycle time explicit for process pre-design. Preferred solutions are identified through weighted sums of normalized objectives and inversely mapped process parameters. Their agreement with the physics-based digital twin at the hundredths level supports the plausibility of the selected operating points within the investigated simulation-based workflow. A retrospective benchmark against a scaled single-stage LHS baseline shows that ADEROI achieves ROI-equivalent point density with fewer simulation runs for the investigated case, reducing the estimated runtime by 39.1% and resulting in a 1.64× speed-up. The quantitative validation is limited to one thin-walled PP keyholder component; further geometries, mold layouts, and polymer materials are required to empirically assess generalizability.

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Publication Details

Journal
Applied Sciences
Published
2026-06-17
DOI
https://doi.org/10.3390/app16126148
Primary Topic
Injection Molding Process and Properties
Type
article
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article

Multi-Objective Optimization in Injection Molding Simulation: A Preference-Driven Approach with an Adaptive Experimental Design to Investigate the Optimal Solution Region

Tamara Reinicke, Denis Anders, Markus Baum
Applied Sciences
Injection Molding Process and Properties
article

Multi-Objective Optimization in Injection Molding Simulation: A Preference-Driven Approach with an Adaptive Experimental Design to Investigate the Optimal Solution Region

Tamara Reinicke, Denis Anders, Markus Baum
article en

Abstract

This contribution presents a simulation-based approach for optimizing injection molding processes using digital twins. It combines surrogate modeling via response surface methodology (RSM) with the evolutionary algorithm NSGA-II to efficiently capture complex relationships between process parameters and objectives. A key element is the adaptive enhancement of the training dataset within the decision-relevant region of interest (ADEROI) by a modified greedy max–min algorithm. This strategy closes data gaps, improves model accuracy in the potentially optimal region, and directs additional simulations to informative areas. Leave-one-out (LOO) and hold-out (HO) cross-validations show strong root mean square error (RMSE) and R2 values for deformation, shrinkage, cycle time, and mass. NSGA-II converges after 403 generations and results in 191 Pareto-optimal solutions, which are consolidated into preference-consistent operating points. These points make trade-offs between analyzed objectives’ deformation, shrinkage, and cycle time explicit for process pre-design. Preferred solutions are identified through weighted sums of normalized objectives and inversely mapped process parameters. Their agreement with the physics-based digital twin at the hundredths level supports the plausibility of the selected operating points within the investigated simulation-based workflow. A retrospective benchmark against a scaled single-stage LHS baseline shows that ADEROI achieves ROI-equivalent point density with fewer simulation runs for the investigated case, reducing the estimated runtime by 39.1% and resulting in a 1.64× speed-up. The quantitative validation is limited to one thin-walled PP keyholder component; further geometries, mold layouts, and polymer materials are required to empirically assess generalizability.

Applied SciencesVol. 16(12)
TH Köln - University of Applied Sciences (DE), University of Siegen (DE)
Peace, Justice and strong institutions
Openalex Percentile: Top 12%
Injection Molding Process and Properties
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