Chance-Constrained Bi-Objective Evolutionary Optimization for the Open-Pit Mining Operational Planning Problem

2026-10-03

AI Summary

This study addresses the resource allocation challenges in open-pit mine planning arising from ore grade uncertainty. It proposes a chance-constrained bi-objective optimization model to simultaneously maximize production and minimize costs. The core innovation lies in analytically reformulating stochastic constraints into deterministic equivalents under normal distribution assumptions, enabling efficient fitness evaluation without Monte Carlo sampling. Multi-objective evolutionary algorithms, including NSGA-II, NSGA-III, and GSEMO, are subsequently employed to solve the model. Experimental results demonstrate that NSGA-II exhibits significant advantages in both feasible solution quality and computational efficiency. Furthermore, this work reveals the critical impact of uncertainty structures on mine planning decisions, offering an efficient new paradigm for robust scheduling in complex environments.

Abstract

Open-pit mining operational planning involves allocating limited resources while satisfying production, equipment, and ore-quality requirements. Existing approaches often assume deterministic ore grades or rely on simulation-based evaluation under uncertainty. In this paper, we propose a chance-constrained bi-objective formulation of the open-pit mining operational planning problem under uncertain ore grades. We aim to maximize ore production and minimize fleet cost while satisfying stochastic quality requirements through chance constraints. We model ore grades as independent normally distributed random variables and derive a deterministic reformulation of the two-sided chance constraints, avoiding sampling or simulation during fitness evaluation. We evaluate four multi-objective evolutionary algorithms on benchmark instances under different levels and structures of uncertainty. Our results show that NSGA-II and NSGA-III generally obtain the best feasible ore-production values, with NSGA-II requiring less computational time. GSEMO has the lowest computational cost but obtains feasible solutions less consistently and generally provides lower solution quality. We also observe that higher confidence and uncertainty levels reduce feasibility, with the effect depending on the uncertainty structure. The results highlight the importance of considering both the magnitude and structure of uncertainty in short-term open-pit operational planning.

Problem

• Open-pit mining operational planning
• Chance-constrained optimization
• Bi-objective optimization
• Ore grade uncertainty

Innovation

• Chance-Constrained Optimization
• Bi-Objective Evolutionary Algorithm
• Open-Pit Mining Planning
• Deterministic Reformulation
• Uncertainty Modeling