A Genetic Algorithm Approach for the Multiple Length Cutting Stock Problem

Abstract

In this paper, we proposes a genetic algorithm approach to solving the one dimensional cutting stock problem with multiple stock lengths. The methods to solve one-dimensional cutting stock problems can be divided into two types: (1) exact algorithm, and (2) approximation algorithm. The execution time of an exact algorithm will increase to an unacceptable degree if the scale of the problem is larger. Since the one-dimensional cutting stock problem is a constrained optimization problem, the methods of genetic algorithm are suitable to solve this problem. The chromosome encodes the index of the stock material that demand pieces will be cut from. Then, the chromosome initialization process combining with random and heuristic scheme was proposed. Since infeasible solution may be generated after crossover and mutation operation were applied on chromosomes. A repair process was proposed to keep the offspring feasible. Experimentation shows that the proposed method actually can obtain an approximation solution in the constraint of acceptable time cost.