Effectiveness of an evolutionary algorithm for the multi‐objective rectangular packing problem

This paper considers the rectangular packing problem and investigates the effectiveness of the neighborhood cultivation genetic algorithm (NCGA). NCGA, which we proposed, is a new algorithm in which the unique mechanism of neighborhood crossover is combined with effective mechanisms for search in multi-objective GA proposed in the past. The effectiveness of the proposed method in typical test problems has already been investigated with satisfactory results in past studies. The rectangular packing problem, on the other hand, is applied to floor planning, such as chip area minimization in large-scale integrated circuits. It is a kind of discrete combinatorial problem in which it is known that the search is difficult and a very long time is required until the solution is obtained. This paper formulates the rectangular packing problem as a multi-objective problem with the vertical and horizontal lengths of the placement configuration as the objectives. The sequence-pair is used as the block placement representation, and PPEX is used as the crossover procedure. Using these processes, the effectiveness of NCGA is investigated. For comparison, three other methods—NSGA-II, SPEA2, and non-NCGA (NCGA without neighborhood crossover)—are investigated. © 2007 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 90(12): 111–120, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjb.20427