A MILP formulation and an Iterated Local Search-based algorithm for the grinding ball replacement planning problem

This study introduces the grinding ball replacement planning problem. This problem arises in the grinding process of ore mining industries. The aim is to optimize the replacement of the grinding balls to maintain the specific energy consumption and percentage of the final product particle size of the grinding process for the subsequent beneficiation stage of the plant within the recommended values during daily operation. We propose a fuzzy controller to determine the recommended power for the mills and a predictive model to estimate their power from operational data. We also introduce a mixed-integer linear programming formulation and design an Enhanced Iterated Local Search-based (E-ILS) algorithm specialized in deciding the instant and bulk weight of the grinding balls to be replaced into each mill throughout a work shift. We have embedded the E-ILS algorithm into a decision system with a two-level architecture. The higher level proposes the grinding ball replacement through the E-ILS, and the lower level executes this solution through an industrial programmable logic controller. We tested the solution methods using 30 instances representing production data from 15 days in 12-h daily work shifts of the grinding process at Usina Cauê of Vale S.A., Brazil. Compared with Gurobi, the E-ILS achieved the optimal solutions in all instances, with an average variability of 1%. Compared with the current solution method, the E-ILS results showed savings of up to 40% in costs with grinding media replacement.