Dependency structure matrix, genetic algorithms, and effective recombination

Authors:
Tian-Li Yu;David E. Goldberg;Kumara Sastry;Claudio F. Lima;Martin Pelikan
Affiliations:
Department of Electrical Engineering, National Taiwan University, Taipei 106, Taiwan. tianliyu@cc.ee.ntu.edu.tw;Department of Industrial & Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, Illinois 61801. deg@uiuc.edu;Department of Industrial & Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, Illinois 61801. kumara@kumarasastry.com;Department of Electronics and Computer Science Engineering, University of Algarve Campus de Gambelas, 8000-117 Faro, Portugal. clima@ualg.pt;Department of Math and Computer Science, University of Missouri at St. Louis, Missouri 63121. pelikan@cs.umsl.edu
Venue:
Evolutionary Computation
Year:
2009

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Abstract

In many different fields, researchers are often confronted by problems arising from complex systems. Simple heuristics or even enumeration works quite well on small and easy problems; however, to efficiently solve large and difficult problems, proper decomposition is the key. In this paper, investigating and analyzing interactions between components of complex systems shed some light on problem decomposition. By recognizing three bare-bones interactions---modularity, hierarchy, and overlap, facet-wise models are developed to dissect and inspect problem decomposition in the context of genetic algorithms. The proposed genetic algorithm design utilizes a matrix representation of an interaction graph to analyze and explicitly decompose the problem. The results from this paper should benefit research both technically and scientifically. Technically, this paper develops an automated dependency structure matrix clustering technique and utilizes it to design a model-building genetic algorithm that learns and delivers the problem structure. Scientifically, the explicit interaction model describes the problem structure very well and helps researchers gain important insights through the explicitness of the procedure.