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Research Papers

Hierarchical Optimization-Based Approach for Two-Dimensional Rectangular Layout Design Problems

[+] Author and Article Information
Kikuo Fujita

Professor
Design Engineering Laboratory,
Department of Mechanical Engineering,
Graduate School of Engineering,
Osaka University,
2-1 Yamadaoka,
Suita 565-0871, Japan
e-mail: fujita@mech.eng.osaka-u.ac.jp

Shintaro Yamasaki

Associate Professor
Design Engineering Laboratory,
Department of Mechanical Engineering,
Graduate School of Engineering,
Osaka University,
2-1 Yamadaoka,
Suita 565-0871, Japan
e-mail: yamasaki@mech.eng.osaka-u.ac.jp

Masayuki Kawamoto

Design Engineering Laboratory,
Department of Mechanical Engineering,
Graduate School of Engineering,
Osaka University,
2-1 Yamadaoka,
Suita 565-0871, Japan

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING. Manuscript received October 3, 2013; final manuscript received July 12, 2014; published online September 10, 2014. Assoc. Editor: Krishnan Suresh.

J. Comput. Inf. Sci. Eng 14(4), 041006 (Sep 10, 2014) (11 pages) Paper No: JCISE-13-1200; doi: 10.1115/1.4028222 History: Received October 03, 2013; Revised July 12, 2014

In this study, we propose a hierarchical optimization-based approach for two-dimensional rectangular layout design problems. Decomposition-based optimization has been a key approach for complicated design problems in multidisciplinary design optimization (MDO), but the main focus has been design problems where the design variables are continuous. On the other hand, various approaches have been developed for layout design based on evolutionary algorithms, e.g., simulated annealing (SA) and genetic algorithms (GAs) which can handle its combinatorial nature in an effective manner. In the present study, we aim to introduce a new paradigm by combining decomposition-based optimization and evolutionary algorithms for solving complicated layout design problems. In this approach, the original layout problem is decomposed into the top-level layout problem and a set of sublevel layout problems, where the layouts obtained from the sublevel problems are used as components of the top-level problem. Since the preferable shapes of these components are unclear when the sublevel problems are solved, a set of Pareto optima are provided in the sublevel problems and these solutions are used as candidate components in the top-level problem. A computational design algorithm is developed based on this approach, which represents the layout topology with sequence pair and the shape of each subsystem or component with the aspect ratio, and they are optimized using GAs. The Pareto optimality of the sublevels is handled by multi-objective GAs, and a set of Pareto optima is generated simultaneously. The top-level and sublevel layout problems are coordinated via the exchange of preferable ranges for the shapes and layout. This approach was implemented and applied to an example problem to demonstrate its performance and capability.

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Copyright © 2014 by ASME
Topics: Design , Optimization
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Figures

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Fig. 1

Two-level rectangle layout problem

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Fig. 4

Squeezing a sublevel layout via hierarchical coordination

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Fig. 3

Coordination between the top-level and sublevel problems

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Fig. 5

Layout representation using a sequence pair.

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Fig. 6

History of the objectives at the top-level

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Fig. 7

History of the overall layout

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