A genetic algorithm for solving the two-dimensional assortment problem

Assortment problems arise in various industries such as the steel, paper, textiles and transportation industries. Two-dimensional assortment problems involve finding the best way of placing a set of rectangles within another rectangle whose area is minimized. Such problems are nonlinear and combinatorial. Current mixed integer programming models give optimal solutions, but the computation times are unacceptable. This study proposes a genetic algorithm that incorporates a novel random packing process and an encoding scheme for solving the assortment problem. Numerical examples indicate that the proposed genetic algorithm is considerably more efficient and effective than a fast integer programming model. Errors with respect to the optimal solutions are low such that numerous practical industrial cutting problems can be solved efficiently using the proposed method.