P3GA: An Algorithm for Technology Characterization

It is important for engineers to understand the capabilities and limitations of the technologies they consider for use in their systems. However, communicating this information can be a challenge. Mathematical characterizations of technical capabilities are of interest as a means to reduce ambiguity in communication and to increase opportunities to utilize design automation methods. The parameterized Pareto frontier (PPF) was introduced in prior work as a mathematical basis for modeling technical capabilities. One advantage of PPFs is that, in many cases, engineers can model a system by composing frontiers of its components. This allows for rapid technology evaluation and design space exploration. However, finding the PPF can be difficult. The contribution of this article is a new algorithm for approximating the PPF, called predictive parameterized Pareto genetic algorithm (P3GA). The proposed algorithm uses concepts and methods from multi-objective genetic optimization and machine learning to generate a discrete approximation of the PPF. If needed, designers can generate a continuous approximation of the frontier by generalizing beyond these data. The algorithm is explained, its performance is analyzed on numerical test problems, and its use is demonstrated on an engineering example. The results of the investigation indicate that P3GA may be effective in practice. [DOI: 10.1115/1.4028101]

[1]  Robert R. Parker,et al.  An Improved Support Vector Domain Description Method for Modeling Valid Search Domains in Engineering Design Problems , 2011, DAC 2011.

[2]  David E. Goldberg,et al.  A niched Pareto genetic algorithm for multiobjective optimization , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[3]  John E. Dennis,et al.  Normal-Boundary Intersection: A New Method for Generating the Pareto Surface in Nonlinear Multicriteria Optimization Problems , 1998, SIAM J. Optim..

[4]  A. Wayne Wymore,et al.  Model-based systems engineering : an introduction to the mathematical theory of discrete systems and to the tricotyledon theory of system design , 1993 .

[5]  Karl T. Ulrich,et al.  ESTIMATING THE TECHNOLOGY FRONTIER FOR PERSONAL ELECTRIC VEHICLES , 2005 .

[6]  Robert P. W. Duin,et al.  Support vector domain description , 1999, Pattern Recognit. Lett..

[7]  Scott Ferguson,et al.  A study of convergence and mapping in preliminary vehicle design , 2005 .

[8]  Lothar Thiele,et al.  Comparison of Multiobjective Evolutionary Algorithms: Empirical Results , 2000, Evolutionary Computation.

[9]  Kalyanmoy Deb,et al.  Multi-objective optimization using evolutionary algorithms , 2001, Wiley-Interscience series in systems and optimization.

[10]  Dietmar P. F. Möller.  Introduction to Systems , 2016 .

[11]  Kalyanmoy Deb,et al.  Dynamic multiobjective optimization problems: test cases, approximations, and applications , 2004, IEEE Transactions on Evolutionary Computation.

[12]  Andrew P. Sage,et al.  Introduction to systems engineering , 2000 .

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

[14]  S. Baskar,et al.  Application of NSGA-II Algorithm to Generation Expansion Planning , 2009, IEEE Transactions on Power Systems.

[15]  Christiaan J. J. Paredis,et al.  Compositional Modelling of Fluid Power Systems using Predictive Tradeoff Models , 2008 .

[16]  Lothar Thiele,et al.  Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach , 1999, IEEE Trans. Evol. Comput..

[17]  Marco Laumanns,et al.  Combining Convergence and Diversity in Evolutionary Multiobjective Optimization , 2002, Evolutionary Computation.

[18]  Marco Laumanns,et al.  Scalable multi-objective optimization test problems , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[19]  Kalyanmoy Deb,et al.  Multi-objective Genetic Algorithms: Problem Difficulties and Construction of Test Problems , 1999, Evolutionary Computation.

[20]  Jasbir S. Arora,et al.  Survey of multi-objective optimization methods for engineering , 2004 .

[21]  Qingfu Zhang,et al.  Multiobjective Optimization Problems With Complicated Pareto Sets, MOEA/D and NSGA-II , 2009, IEEE Transactions on Evolutionary Computation.

[22]  Ashwin P. Gurnani,et al.  A constraint-based approach to feasibility assessment in preliminary design , 2006, Artificial Intelligence for Engineering Design, Analysis and Manufacturing.

[23]  Dennis M. Buede,et al.  The Engineering Design of Systems , 2009 .

[24]  Serpil Sayin,et al.  Measuring the quality of discrete representations of efficient sets in multiple objective mathematical programming , 2000, Math. Program..

[25]  J.A.M. Kuipers,et al.  Gas Dispersion and Bubble-to-Emulsion Phase Mass Exchange in a Gas-Solid Bubbling Fluidized Bed: A Computational and Experimental Study , 2003 .

[26]  Johannes Bader,et al.  Hypervolume-based search for multiobjective optimization: Theory and methods , 2010 .

[27]  Paolo Cignoni,et al.  Metro: Measuring Error on Simplified Surfaces , 1998, Comput. Graph. Forum.

[28]  S. Sinha.  A Duality Theorem for Nonlinear Programming , 1966 .

[29]  P. Wolfe.  A duality theorem for non-linear programming , 1961 .

[30]  Ajay K. Ray,et al.  Applications of the Non-Dominated Sorting Genetic Algorithm (NSGA) in Chemical Reaction Engineering , 2003 .

[31]  Gert Cauwenberghs,et al.  Incremental and Decremental Support Vector Machine Learning , 2000, NIPS.

[32]  R. Lyndon While,et al.  A review of multiobjective test problems and a scalable test problem toolkit , 2006, IEEE Transactions on Evolutionary Computation.

[33]  Richard J. Malak,et al.  A Genetic Algorithm Approach for Technology Characterization , 2012, DAC 2012.

[34]  A. Messac,et al.  Concept Selection Using s-Pareto Frontiers , 2003 .

[35]  Christina Bloebaum,et al.  Multi-objective pareto concurrent subspace optimization for multidisciplinary design , 2007 .

[36]  Peter J. Fleming,et al.  On the Performance Assessment and Comparison of Stochastic Multiobjective Optimizers , 1996, PPSN.

[37]  Richard J. Malak,et al.  Using parameterized efficient sets to model alternatives for systems design decisions , 2008 .

[38]  H. Abbass.  The self-adaptive Pareto differential evolution algorithm , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[39]  D. Sarkar,et al.  Pareto-optimal solutions for multi-objective optimization of fed-batch bioreactors using nondominated sorting genetic algorithm. , 2005 .

[40]  G. Gary Wang,et al.  An Efficient Pareto Set Identification Approach for Multiobjective Optimization on Black-Box Functions , 2005 .

[41]  Kalyanmoy Deb,et al.  Constrained Test Problems for Multi-objective Evolutionary Optimization , 2001, EMO.

[42]  JiGuan G. Lin.  Multiple-objective problems: Pareto-optimal solutions by method of proper equality constraints , 1976 .

[43]  Marco Laumanns,et al.  Performance assessment of multiobjective optimizers: an analysis and review , 2003, IEEE Trans. Evol. Comput..

[44]  DebK.,et al.  A fast and elitist multiobjective genetic algorithm , 2002 .

[45]  Touradj Ebrahimi,et al.  MESH: measuring errors between surfaces using the Hausdorff distance , 2002, Proceedings. IEEE International Conference on Multimedia and Expo.

[46]  Rolf Drechsler,et al.  Multi-objective Optimisation Based on Relation Favour , 2001, EMO.

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

[48]  Marco Laumanns,et al.  Scalable Test Problems for Evolutionary Multiobjective Optimization , 2005, Evolutionary Multiobjective Optimization.

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

[50]  Christiaan J. J. Paredis,et al.  Using Parameterized Pareto Sets to Model Design Concepts , 2010 .

[51]  Ernest S. Kuh,et al.  Design space exploration using the genetic algorithm , 1996, 1996 IEEE International Symposium on Circuits and Systems. Circuits and Systems Connecting the World. ISCAS 96.

[52]  Christiaan J. J. Paredis,et al.  Using Support Vector Machines to Formalize the Valid Input Domain of Predictive Models in Systems Design Problems , 2010 .

[53]  Kalyanmoy Deb,et al.  Multimodal Deceptive Functions , 1993, Complex Syst..

[54]  Raphael T. Haftka,et al.  Response surface approximation of Pareto optimal front in multi-objective optimization , 2007 .

[55]  C. Poloni,et al.  Hybridization of a multi-objective genetic algorithm, a neural network and a classical optimizer for a complex design problem in fluid dynamics , 2000 .

[56]  Lothar Thiele,et al.  Multiobjective Optimization Using Evolutionary Algorithms - A Comparative Case Study , 1998, PPSN.

[57]  Christopher A. Mattson,et al.  Pareto Frontier Based Concept Selection Under Uncertainty, with Visualization , 2005 .

[58]  Bernhard Schölkopf,et al.  Support Vector Method for Novelty Detection , 1999, NIPS.

[59]  H. Kita,et al.  Failure of Pareto-based MOEAs: does non-dominated really mean near to optimal? , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[60]  Joseph Edward Shigley,et al.  Mechanical engineering design , 1972 .

[61]  Lothar Thiele,et al.  A Tutorial on the Performance Assessment of Stochastic Multiobjective Optimizers , 2006 .

[62]  Edgar Galvan.  Using Predictive Modeling Techniques to Solve Multilevel Systems Design Problems , 2010 .

[63]  Robert R. Parker,et al.  Technology Characterization Models and Their Use in Systems Design , 2014 .

[64]  Ajay K. Ray,et al.  Design stage optimization of an industrial low-density polyethylene tubular reactor for multiple objectives using NSGA-II and its jumping gene adaptations , 2007 .

[65]  Carlos A. Coello Coello,et al.  Using the Averaged Hausdorff Distance as a Performance Measure in Evolutionary Multiobjective Optimization , 2012, IEEE Transactions on Evolutionary Computation.