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

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.