Unequal individual genetic algorithm with intelligent diversification for the lot-scheduling problem in integrated mills using multiple-paper machines

This paper addresses the lot-sizing and scheduling problem of pulp and paper mills involving multiple paper machines. The underlying multi-stage integrated production process considers the following critical units: continuous digester, intermediate stocks of pulp and liquor, multiple paper machines and a recovery line to treat by-products. This work presents a mixed integer programming (MIP) model to represent the problem, as well as a solution approach based on a customized genetic algorithm (GA) with an embedded residual linear programming model. Some GA tools are explored, including literature and new operators, a novel diversification process and other features. In particular, the diversification process uses a new allele frequency measure to change between diversification and intensification procedures. Computational results show the effectiveness of the method to solve relatively large instances of the single paper machine problem when compared to other single paper machine solution methods found in the literature. For multiple paper machine settings, in most runs the GA solutions are better than those obtained for the MIP model using an optimization software.