Optimization the Problem of Packing Rectangular Shapes by using Imperialist Competitive Algorithm

Packing is one of the well-known problems in operation research, especially in production planning. The main objective of studying the packing problem is to reduce the wastes of cutting through optimization of packing of pieces. Packing is a kind of NP-hard problem that the precise methods are not able to solve it. In this paper, in order to achieve an optimal packing of Non-guillotine cutting problems, the meta-heuristic emerging Imperialist Competitive Algorithm was used and the results were compared with the output of the genetic algorithm, which is the typical algorithm in solving packing problems. To achieve better solutions, the parameters of all meta-heuristics were calibrated with Taguchi experiment method. The efficacy of the proposed approach was tested on a set of instances, taken from the literature, and the results of the proposed algorithm were tested statistically by ANOVA. The results of this study showed that the meta-heuristic emerging Imperialist Competitive algorithm is more efficient and faster in solving packing problems.