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Multi-objective rectangular packing problem and its applications

In this paper, Neighborhood Cultivation GA (NCGA) is applied to the rectangular packing problem. NCGA is one of the multi-objective Genetic Algorithms that includes not only the mechanisms of effective algorithms such as NSGA-II and SPEA2, but also the mechanism of the neighborhood crossover. This model can derive good non-dominated solutions in typical multi-objective optimization test problems. The rectangular packing problem (RP) is a well-known discrete combinatorial optimization problem in many applications such as LSI layout problems, setting of plant facility problems, and so on. The RP is a difficult and time-consuming problem since the number of possible placements of rectangles increase exponentially as the number of rectangles increases. In this paper, the sequent-pair is used for representing the solution of the rectangular packing and PPEX is used as the crossover. The results were compared to the other methods: SPEA2, NSGA-II and non-NCGA (NCGA without neighborhood crossover). Through numerical examples, the effectiveness of NCGA for the RP is demonstrated and it is found that the neighborhood crossover is very effective both when the number of modules is small and large.