Bi-Objective Evolutionary Optimization for Large-Scale Open Pit Mine Scheduling Problem under Uncertainty with Chance Constraints

2025-11-11

AI Summary

To address the limitation of conventional deterministic approaches for the Open-Pit Mining Scheduling Problem (OPMSP)—namely, their neglect of geological uncertainty, which often yields suboptimal or infeasible schedules—this paper proposes the first bi-objective optimization framework explicitly accounting for geological uncertainty. It jointly optimizes expected Net Present Value (NPV) and scheduling risk without requiring a pre-specified confidence level. Methodologically, we formulate an integer-encoded model integrating chance constraints with stochastic geological simulations, and design a greedy initialization strategy along with a precedence-aware mutation operator. The framework is solved via an ensemble of multi-objective evolutionary algorithms: GSEMO, MOEA/D (mutation-only variant), and NSGA-II. Validated on a real-world deposit comprising over 110,000 blocks, our approach significantly expands the risk–return Pareto-optimal solution set, substantially enhancing schedule robustness and engineering practicality compared to single-objective benchmarks.

Technology Category

• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Web Mining and Content Analysis: Web data generation and simulation
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Social Networks and Social Media: Social mining and social search on the Web

Abstract

The open-pit mine scheduling problem (OPMSP) is a complex, computationally expensive process in long-term mine planning, constrained by operational and geological dependencies. Traditional deterministic approaches often ignore geological uncertainty, leading to suboptimal and potentially infeasible production schedules. Chance constraints allow modeling of stochastic components by ensuring probabilistic constraints are satisfied with high probability. This paper presents a bi-objective formulation of the OPMSP that simultaneously maximizes expected net present value and minimizes scheduling risk, independent of the confidence level required for the constraint. Solutions are represented using integer encoding, inherently satisfying reserve constraints. We introduce a domain-specific greedy randomized initialization and a precedence-aware period-swap mutation operator. We integrate these operators into three multi-objective evolutionary algorithms: the global simple evolutionary multi-objective optimizer (GSEMO), a mutation-only variant of multi-objective evolutionary algorithm based on decomposition (MOEA/D), and non-dominated sorting genetic algorithm II (NSGA-II). We compare our bi-objective formulation against the single-objective approach, which depends on a specific confidence level, by analyzing mine deposits consisting of up to 112 687 blocks. Results demonstrate that the proposed bi-objective formulation yields more robust and balanced trade-offs between economic value and risk compared to single-objective, confidence-dependent approach.

Problem

• Optimizing large-scale open pit mine scheduling under geological uncertainty constraints
• Maximizing net present value while minimizing scheduling risk simultaneously
• Developing robust evolutionary algorithms for complex mine planning trade-offs

Innovation

• Bi-objective optimization for simultaneous value and risk
• Integer encoding with greedy randomized initialization
• Precedence-aware mutation in multi-objective evolutionary algorithms