# Bi-objective chance-constrained evolutionary optimization for large-scale open-pit mine scheduling under geological uncertainty

arXiv: https://arxiv.org/abs/2511.08275 · HTML: https://mlsanity.com/paper/2511.08275/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 42 references that are in the map.
- First posted on arXiv 11 Nov 2025.

## Builds on (most cited first, 11 of 11)

- [Should we really use post-hoc tests based on mean-ranks?](https://mlsanity.com/paper/1505.02288/) (2015)
- [Recent Trends in the Use of Statistical Tests for Comparing Swarm and Evolutionary Computing Algorithms: Practical Guidelines and a Critical Review](https://mlsanity.com/paper/2002.09227/) (2020)
- [Optimizing Monotone Chance-Constrained Submodular Functions Using Evolutionary Multi-Objective Algorithms](https://mlsanity.com/paper/2006.11444/) (2020)
- [Runtime Analysis of Single- and Multi-Objective Evolutionary Algorithms for Chance Constrained Optimization Problems with Normally Distributed Random Variables](https://mlsanity.com/paper/2109.05799/) (2021)
- [Evolutionary Algorithms for Limiting the Effect of Uncertainty for the Knapsack Problem with Stochastic Profits](https://mlsanity.com/paper/2204.05597/) (2022)
- [3-Objective Pareto Optimization for Problems with Chance Constraints](https://mlsanity.com/paper/2304.08774/) (2023)
- [Heuristic Strategies for Solving Complex Interacting Stockpile Blending Problem with Chance Constraints](https://mlsanity.com/paper/2102.05303/) (2021)
- [Using 3-Objective Evolutionary Algorithms for the Dynamic Chance Constrained Knapsack Problem](https://mlsanity.com/paper/2404.06014/) (2024)
- [A study of the Bienstock-Zuckerberg algorithm, Applications in Mining and Resource Constrained Project Scheduling](https://mlsanity.com/paper/1607.01104/) (2016)
- [Improving Confidence in Evolutionary Mine Scheduling via Uncertainty Discounting](https://mlsanity.com/paper/2305.17957/) (2023)
- [Heuristic Strategies for Solving Complex Interacting Large-Scale Stockpile Blending Problems](https://mlsanity.com/paper/2104.03440/) (2021)

## Built on by (most cited first, 1 of 1)

- [On the use of evolutionary optimization for the dynamic chance constrained open-pit mine scheduling problem](https://mlsanity.com/paper/2604.13385/) (2026)

## Abstract (arXiv)

The open-pit mine scheduling problem (OPMSP) is a complex optimization problem in long-term mine planning that involves numerous operational and geological constraints. Traditional deterministic approaches often ignore geological uncertainty, leading to suboptimal or unreliable production schedules. Chance constraints provide a framework for handling uncertainty by ensuring that probabilistic constraints are satisfied with a predefined confidence level. In this paper, we consider the OPMSP under geological grade uncertainty and propose a bi-objective chance-constrained formulation that simultaneously maximizes the expected discounted net present value and minimizes scheduling risk. Unlike traditional chance-constrained approaches, the proposed formulation does not require a predefined confidence level during optimization. Instead, it generates a set of Pareto-optimal solutions representing different trade-offs between profitability and risk within a single optimization run. To solve the resulting large-scale stochastic optimization problem, we employ multi-objective evolutionary algorithms and compare their performance against a single-objective chance-constrained evolutionary approach and a deterministic MILP benchmark. We further evaluate the contribution of the problem-specific initialization and mutation components through an ablation study. Experimental results on MineLib benchmark instances containing up to 112 687 blocks demonstrate that the proposed formulation effectively captures the trade-off between profitability and risk under geological uncertainty while providing greater flexibility than confidence-level-dependent approaches.