Automating Discovery of Innovative Design Principles through Optimization

In this paper, we propose a methodology for automatically extracting innovative design principles which make a system or process (subject to conflicting objectives) optimal using its Pareto-optimal set data. Such “higher knowledge” would, not only help designers to execute the system better, but also enable them to predict how changes in one variable would effect other variables if the system has to retain its optimal behaviour. This in turn would help solve other similar systems with different parameter settings easily without the need to perform a fresh optimization task. The proposed methodology is capable of discovering hidden functional relationships among the variables, objective and constraint functions and any other function that the designer wishes to include as a “basis function”. For our study, we have considered a number of engineering design problems for which the mathematical structure of these explicit relationships exists and was revealed by a previous manual study. A comparison with the multivariate adaptive regression splines (MARS) approach for a flexible regression task reveals the practicality of our proposed approach due to its ability to find meaningful design principles. The success of our simultaneous clustering and optimization procedure for automated innovization is highly encouraging and indicates a suitability for its further development in tackling more complex design scenarios.

[1]  Kalyanmoy Deb,et al.  Scope of stationary multi-objective evolutionary optimization: a case study on a hydro-thermal power dispatch problem , 2008, J. Glob. Optim..

[2]  Andrzej Osyczka,et al.  Evolutionary Algorithms for Single and Multicriteria Design Optimization , 2001 .

[3]  John S. Gero,et al.  A LEARNING AND INFERENCE MECHANISM FOR DESIGN OPTIMIZATION PROBLEM (RE)- FORMULATION USING SINGULAR VALUE DECOMPOSITION , 2008 .

[4]  Daisuke Sasaki,et al.  Visualization and Data Mining of Pareto Solutions Using Self-Organizing Map , 2003, EMO.

[5]  K. Deb,et al.  An estimation of nadir objective vector using a: hybrid evolutionary-cum-local-search procedure , 2009 .

[6]  Shigeru Obayashi,et al.  Multi-Objective Design Exploration of a Centrifugal Impeller Accompanied With a Vaned Diffuser , 2007 .

[7]  Pavel Berkhin,et al.  A Survey of Clustering Data Mining Techniques , 2006, Grouping Multidimensional Data.

[8]  Aravind Srinivasan,et al.  Innovization: innovating design principles through optimization , 2006, GECCO.

[9]  Amitabha Mukerjee,et al.  THE BIRTH OF SYMBOLS IN DESIGN , 2009 .

[10]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems , 2002, Genetic Algorithms and Evolutionary Computation.

[11]  Yacov Y. Haimes,et al.  Multiobjective Decision Making: Theory and Methodology , 1983 .

[12]  Kalyanmoy Deb,et al.  Simulated Binary Crossover for Continuous Search Space , 1995, Complex Syst..

[13]  E. Lehmann.  Testing Statistical Hypotheses , 1960 .

[14]  Kalyanmoy Deb,et al.  Unveiling innovative design principles by means of multiple conflicting objectives , 2003 .

[15]  Kalyanmoy Deb,et al.  An Investigation of Niche and Species Formation in Genetic Function Optimization , 1989, ICGA.

[16]  J. Freidman,et al.  Multivariate adaptive regression splines , 1991 .

[17]  Shigeru Obayashi,et al.  Kriging-model-based multi-objective robust optimization and trade-off-rule mining using association rule with aspiration vector , 2009, 2009 IEEE Congress on Evolutionary Computation.

[18]  A. Messac,et al.  Normal Constraint Method with Guarantee of Even Representation of Complete Pareto Frontier , 2004 .

[19]  R. K. Ursem.  Multi-objective Optimization using Evolutionary Algorithms , 2009 .

[20]  Kaisa Miettinen,et al.  Nonlinear multiobjective optimization , 1998, International series in operations research and management science.

[21]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[22]  A. Ravindran,et al.  Engineering Optimization: Methods and Applications , 2006 .

[23]  B. Williams,et al.  ACTIVITY ANALYSIS: SIMPLIFYING OPTIMAL DESIGN PROBLEMS THROUGH QUALITATIVE PARTITIONING† , 1996 .

[24]  Kalyanmoy Deb,et al.  Deciphering innovative principles for optimal electric brushless D.C. permanent magnet motor design , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[25]  S. N. Kramer,et al.  An Augmented Lagrange Multiplier Based Method for Mixed Integer Discrete Continuous Optimization and Its Applications to Mechanical Design , 1994 .