Open Access

ARTICLE

Adaptive Multi-Scale Grid Search with Ensemble Integration for ANN Surrogate Optimization: Application to Multi-Objective Design of Slider–Crank Mechanisms with Springs

Hoang Minh Dang¹, Van Thanh Tien Nguyen¹, Van Binh Phung^2,*

1 Faculty of Mechanical Engineering, Industrial University of Ho Chi Minh City, Ho Chi Minh City, Vietnam
2 Faculty of Aerospace Engineering, Le Quy Don Technical University, Hanoi, Vietnam

* Corresponding Author: Van Binh Phung. Email:

(This article belongs to the Special Issue: AI-Enhanced Computational Mechanics and Structural Optimization Methods)

Computer Modeling in Engineering & Sciences 2026, 148(3), 13 https://doi.org/10.32604/cmes.2026.086495

Received 31 May 2026; Accepted 01 September 2026; Issue published 28 September 2026

Abstract

Evaluating objectives and constraints in complex dynamical or multi-physics systems can take minutes to hours per design point, which motivates the use of artificial neural network (ANN) surrogates; in practice, however, their architectures and hyperparameters are still largely chosen by trial and error. This study proposes the Adaptive Multi-scale Grid Search with Ensemble Integration (AMGSE), an automated framework that constructs ANN surrogates from a fixed, previously generated dataset under an explicit training-time budget and without any additional calls to the expensive model. AMGSE couples four explicit decision rules: budget-tiered search scales, dataset-size-triggered complexity scaling, multi-restart training with algorithm-specific restart selection, and a gap-thresholded conditional ensemble rule that withholds ensembling when candidate models are too heterogeneous. Every accepted surrogate must pass an external acceptance test, and every optimization candidate is re-evaluated on the exact model. Under matched search spaces and data partitions over ten independent runs, AMGSE attains mean prediction errors of 0.11%–0.67%, 3.3–10.6 times lower than those of Bayesian optimization, the Tree-structured Parzen Estimator and random search on three of four response functions; Gaussian process regression remains more accurate on three of these smooth, low-dimensional responses, while the AMGSE-selected ANN provides orders-of-magnitude faster batch inference inside the optimization loop. Applied to the multi-objective design of spring-assisted slider-crank mechanisms, the framework enables NSGA-III to return 151 exact-model-verified feasible solutions, of which 150 are mutually non-dominated; these collectively dominate all 19 previously published solutions and improve the hypervolume indicator by 16.1%. Beyond the case study, the same decision protocol was applied without modification to analytic benchmarks with two, six, and eight input dimensions, either certifying a surrogate or declining certification and returning a structured diagnostic. These contrasting outcomes indicate that response multimodality relative to sample density, rather than input dimensionality as such, determined whether the prescribed accuracy could be certified.

---

Graphic Abstract

---

Keywords

---

Supplementary Material

Supplementary Material File

---