MULTI-OBJECTIVE RECTANGULAR PACKING PROBLEM

Abstract

This chapter describes an implementation of a Multi-Objective Genetic Algorithm (MOGA) for the Multi-Objective Rectangular Packing Problem (RP). RP is a well-known discrete combinatorial optimization problem arising in many applications, such as a floor-planning problem in the LSI problem, truck packing problem, etc. Over the last 20 years, Evolutionary Algorithms (EAs), including Genetic Algorithms (GA), have been applied to RP, as EAs are adapted for pattern generation. On the other hand, many cases of RP have become multi-objective optimization problems. For example, floor-planning problems should take care of the minimum layout area, the minimum length of wires, etc. Therefore, RP is a very important problem as an application of MOGA. In this chapter, we describe the application of MOGA to Multi-Objective RP. We treat RP as two objective optimization problems to archive several critical layout patterns, which have different aspect ratios of packing area. We used the Neighborhood Cultivation GA (NCGA) as a MOGA algorithm. NCGA includes not only the mechanisms of effective algorithms, such as NSGA-II and SPEA2, but also the mechanism of neighborhood crossover. The results were compared to those obtained using other methods. Through numerical examples, we found that MOGA is a very effective method for RP. Especially, NCGA can provide the best solutions as compared to other methods.