Continuous-time formulation and differential evolution algorithm for an integrated batching and scheduling problem in aluminium industry

Abstract

This paper investigates an integrated batching and scheduling problem of electrolysis and caster in aluminium industry. The problem is to determine the assignment and scheduling of orders considering sequence-dependent setup times caused by technological and operational constraints of electrolysis cells, and determine the batching and scheduling of orders in the following casters. A novel unit-specific event-based continuous-time mixed integer linear programming model (MILP) is proposed to describe the problem. In this model, the event point is stage specific, and lower bounds are specified to tighten the model. A hybrid pointer-based differential evolution algorithm with new individual representation scheme is designed to solve the problem of industrial scale. An improved hybrid pointer-based mutation operator and a new point-cross crossover operator are proposed to enhance the performance of the algorithm. Computational experiments show that the proposed algorithm is more efficient when compared with CPLEX for medium and large size instances. Comparisons with the lower bound demonstrate that the algorithm is effective.