Hybrid genetic algorithm for cutting stock and packaging problems

Abstract

The paper deals with one of the most important optimization problem — the cutting stock and packaging (C&P) problem. This problem contains two sub problem, such as two-dimensional packaging problem and minimization of the tool head way, which belong to the class of NP-hard and complex problems. The formulation and restrictions of the C&P problem are considered in the paper. Authors offer a hybrid approach with the use of a multilevel evolution, which partially allows avoiding a preliminary convergence of algorithms. For packaging and minimization of tool head way there are developed modified genetic algorithms (MGA), which can obtain sets of quasi-optimal solutions in polynomial time. To carry out computational experiments on test examples (benchmarks) authors created software on the basis of hybrid approach for the C&P problem. Conducted tests and experiments allow clarifying theoretical estimations of the algorithm time complexity. In the best case the time complexity of developed algorithms are represented as O (n2), in the worst case — O (n3).