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Article

Robust Multi-Objective Optimization of Ore-Drawing Process Using the OGOOSE Algorithm Under an ε-Constraint Framework

1
Faculty of Land Resources Engineering, Kunming University of Science and Technology, Kunming 650093, China
2
School of Resources and Environment, Yunnan Tin Vocational and Technical College, Gejiu 661000, China
3
Xinping Ludian Mining Co., Ltd., Yuxi 653401, China
4
Faculty of Public Safety and Emergency Management, Kunming University of Science and Technology, Kunming 650093, China
*
Author to whom correspondence should be addressed.
Symmetry 2026, 18(2), 254; https://doi.org/10.3390/sym18020254
Submission received: 5 November 2025 / Revised: 20 December 2025 / Accepted: 24 December 2025 / Published: 30 January 2026
(This article belongs to the Section A: Computer Science)

Abstract

To address the complex multi-objective optimization problem of “cost–risk–recovery–dilution” in sublevel caving without bottom pillars under uncertainty, this study develops an operational GOOSE-based framework (OGOOSE) integrated with robust ε-constraint modeling. Methodologically, OGOOSE adopts three synergistic mechanisms: Opposition-Based Learning (OBL) for enhanced initial solution quality and spatial coverage symmetry, an Adaptive Inertia Weight (AIW) mechanism to maintain a symmetrical balance between exploration and exploitation, and a Boundary Reflection Mechanism (BRM) to ensure engineering feasibility. For modeling, an “ellipsoid-plane” geometric surrogate is employed, where the ellipsoid’s structural symmetry serves as the ideal baseline, while the Mean-CVaR criterion quantifies the asymmetry of operational risk (negative tail) under uncertainty. Taking robust cost (C) as the primary objective, the four-objective problem is decomposed via the ϵ-constraint method to enforce a balanced Pareto trade-off. Results demonstrate that OGOOSE significantly outperforms GOOSE, WOA, and HHO on CEC2017 benchmarks, achieving the lowest Friedman rank. In the engineering case study, it attains an average dilution rate of 28.95% (the lowest among comparators) without increasing unit cost or compromising recovery, demonstrating stable operational symmetry across economic and quality indicators. Sensitivity analysis of the ε-thresholds identifies an optimal “knee-point” that establishes a manageable balance between risk control (εR) and dilution limits (εP). OGOOSE effectively balances accuracy, stability, and interpretability, providing a robust tool for stabilizing complex mining systems against inherent operational asymmetry.
Keywords: swarm intelligence; robust multi-objective optimization; ε-Constraint Method; Conditional Value at Risk (CVaR); ore drawing optimization; systemic asymmetry; ellipsoid-plane model swarm intelligence; robust multi-objective optimization; ε-Constraint Method; Conditional Value at Risk (CVaR); ore drawing optimization; systemic asymmetry; ellipsoid-plane model

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MDPI and ACS Style

Cai, C.; Chen, J.; Ren, C.; Xiong, C.; Liu, Q.; He, C. Robust Multi-Objective Optimization of Ore-Drawing Process Using the OGOOSE Algorithm Under an ε-Constraint Framework. Symmetry 2026, 18, 254. https://doi.org/10.3390/sym18020254

AMA Style

Cai C, Chen J, Ren C, Xiong C, Liu Q, He C. Robust Multi-Objective Optimization of Ore-Drawing Process Using the OGOOSE Algorithm Under an ε-Constraint Framework. Symmetry. 2026; 18(2):254. https://doi.org/10.3390/sym18020254

Chicago/Turabian Style

Cai, Chuanchuan, Junzhi Chen, Chunfang Ren, Chaolin Xiong, Qiangyi Liu, and Changyao He. 2026. "Robust Multi-Objective Optimization of Ore-Drawing Process Using the OGOOSE Algorithm Under an ε-Constraint Framework" Symmetry 18, no. 2: 254. https://doi.org/10.3390/sym18020254

APA Style

Cai, C., Chen, J., Ren, C., Xiong, C., Liu, Q., & He, C. (2026). Robust Multi-Objective Optimization of Ore-Drawing Process Using the OGOOSE Algorithm Under an ε-Constraint Framework. Symmetry, 18(2), 254. https://doi.org/10.3390/sym18020254

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