A biased genetic algorithm hybridized with VNS for the two-dimensional knapsack packing problem with defects

Abstract

This paper addresses a two-dimensional knapsack packing problem which packing a set of rectangles into a rectangular board to maximize the total value of the rectangles packed. The rectangle has finite types while its quantity is unlimited, and the board has unusable defects. A biased genetic algorithm hybridized with variable neighborhood search (VNS) is proposed to solve the problem as genetic algorithm can effectively solve the combinational optimization problem, has good searching performance, and is easy to implement. We adopt the replacing strategy for increasing the diversity of the population and avoiding converging too early. An improved placement procedure in charge of producing the layout is presented and four neighborhood structures are constructed. We conduct lots of numerical experiments using 5414 benchmark instances taken from the literature for evaluating our approach and comparing it to other excellent approaches. The experimental results show that the proposed algorithm gets many new best solutions in these benchmark instances and is very competitive.