A hybrid simulated annealing metaheuristic algorithm for the two-dimensional knapsack packing problem

Authors:
Stephen C. H. Leung;Defu Zhang;Changle Zhou;Tao Wu
Affiliations:
Department of Management Sciences, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong;School of Information Science and Technology, Xiamen University, Xiamen 361005, China and Department of Industrial and Systems Engineering, University of Wisconsin-Madison, Madison, WI 53706, USA;School of Information Science and Technology, Xiamen University, Xiamen 361005, China;Department of Industrial and Systems Engineering, University of Wisconsin-Madison, Madison, WI 53706, USA
Venue:
Computers and Operations Research
Year:
2012

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Abstract

The rectangle knapsack packing problem is to pack a number of rectangles into a larger stock sheet such that the total value of packed rectangles is maximized. The paper first presents a fitness strategy, which is used to determine which rectangle is to be first packed into a given position. Based on this fitness strategy, a constructive heuristic algorithm is developed to generate a solution, i.e. a given sequence of rectangles for packing. Then, a greedy strategy is used to search a better solution. At last, a simulated annealing algorithm is introduced to jump out of the local optimal trap of the greedy strategy, to find a further improved solution. Computational results on 221 rectangular packing instances show that the presented algorithm outperforms some previous algorithms on average.