Quantum optimization for mine planning with flexible capacity: QAOA implementation with slack variables

Abstract

This work presents an exploratory, preliminary study of applying a variational quantum algorithm to solve open-pit mine planning problems with flexible extraction capacity. The main objective is to assess the technical feasibility of the proposed formulation and its resolution using QAOA, rather than to benchmark its performance against classical methods or address a wide range of instances. A Quadratic Unconstrained Binary Optimization (QUBO) formulation is developed that incorporates slack variables to model capacity constraints as “less than or equal to,” allowing operations below maximum capacity without penalties. The methodology employs the Quantum Approximate Optimization Algorithm (QAOA) to optimize block selection by maximizing the economic gain from extraction while respecting geological precedence constraints and flexible operational limits. The proposed approach is validated through a case study involving an 18-block synthetic copper deposit, which is solved using a quantum simulator. The results demonstrate the quantum algorithm’s capacity to address the increased complexity introduced by auxiliary variables. This study establishes a framework for applying quantum computing to mining planning problems that require more prominent operational flexibility.