A Genetic Algorithm Approach for Large-Scale Cutting Stock Problem

Abstract

This work investigates the one-dimensional integer cutting stock problem, which has many applications in Information and Communications Technology for green objectives. The problem consists of cutting a set of available objects in stock to produce smaller items with minimum the wastage of materials. On the basis of the traditional group-based Genetic Algorithm, we solve the large-scale cutting stock problems by adding two new proposals. Firstly, we put two additional steps to the First Fit heuristic to utilize wastage stock rolls when items are added to genes. These steps are applied to initialize the first population and to perform the mutation operation between two parents. Secondly, we propose a new heuristic in the crossover operation to create new individuals. The heuristic increases good genes and decreases bad genes which appeared in the population. We use them to improve traditional Genetic Algorithm in terms of the individual’s quality and the diversity of good genes in the populations. As a result, the wastage of stock rolls decreases. These heuristics are empirically analyzed by solving randomly generated instances and large instances from the literature, then results are compared to other methods. We specify an indicator to show some solutions are optimal. The numerical simulation shows that our approach is effective when it is applied to large-scale data sets, with better result in 40% of instances than the traditional cutting plane algorithm. On the other hand, we show that our approach can reach 289 optimal solutions out of 400 generated instances.