Global Search for Diverse Competitive Designs

Design optimization is often performed based on approximate models and incomplete knowledge of the constraints and objectives. Settling on a single optimum may be risky, because this optimum may be rendered useless by refinements in the model or the problem formulation. We therefore explore methodology for finding diverse alternative optima. The objective of this paper is to propose algorithms to search for two competitive diverse alternatives to global optima, and compare their effectiveness and efficiency. This paper presents four algorithms to solve this problem. Three test functions (one dimensional, two dimensional and three dimensional examples) are used to compare the algorithms. Effectiveness and efficiency for the four algorithms are explored by comparing their accuracy and convergence speed.

[1]  Timothy W. Simpson,et al.  Metamodels for Computer-based Engineering Design: Survey and recommendations , 2001, Engineering with Computers.

[2]  Raphael T. Haftka,et al.  Analytical-Experimental Correlation for a Stiffened Composite Panel Loaded in Axial Compression , 2001 .

[3]  Zbigniew Michalewicz,et al.  Evolutionary Computation 1 , 2018 .

[4]  Wang,et al.  Shape Optimization of Pressure Vessel Head Based on the Super-ellipse Equation , 2013 .

[5]  Gauthier Picard,et al.  Dynamic Design Space Partitioning for Optimization of an Integrated Thermal Protection System , 2013 .

[6]  Jack P. C. Kleijnen,et al.  State-of-the-Art Review: A User's Guide to the Brave New World of Designing Simulation Experiments , 2005, INFORMS J. Comput..

[7]  Michael N. Vrahatis,et al.  Modification of the Particle Swarm Optimizer for Locating All the Global Minima , 2001 .

[8]  Xiaoping Du,et al.  The use of metamodeling techniques for optimization under uncertainty , 2001 .

[9]  Donald R. Jones,et al.  A Taxonomy of Global Optimization Methods Based on Response Surfaces , 2001, J. Glob. Optim..

[10]  Donald R. Jones,et al.  Efficient Global Optimization of Expensive Black-Box Functions , 1998, J. Glob. Optim..

[11]  Bernard Grossman,et al.  A Comparison of Global Optimization Methods for the Design of a High-speed Civil Transport , 2001, J. Glob. Optim..

[12]  Thomas J. Santner,et al.  The Design and Analysis of Computer Experiments , 2003, Springer Series in Statistics.

[13]  Arthur C. Sanderson,et al.  Multimodal Function Optimization Using Minimal Representation Size Clustering and Its Application to Planning Multipaths , 1997, Evolutionary Computation.

[14]  Raphael T. Haftka,et al.  Structural optimization complexity: what has Moore’s law done for us? , 2004 .

[15]  Changhe Li,et al.  A Clustering Particle Swarm Optimizer for Locating and Tracking Multiple Optima in Dynamic Environments , 2010, IEEE Transactions on Evolutionary Computation.

[16]  Timothy W. Simpson,et al.  Design and Analysis of Computer Experiments in Multidisciplinary Design Optimization: A Review of How Far We Have Come - Or Not , 2008 .

[17]  G. Gary Wang,et al.  Review of Metamodeling Techniques in Support of Engineering Design Optimization , 2007 .

[18]  Raphael T. Haftka,et al.  Surrogate-based Analysis and Optimization , 2005 .

[19]  Rasmus K. Ursem,et al.  Diversity-Guided Evolutionary Algorithms , 2002, PPSN.

[20]  Samir W. Mahfoud.  Crowding and Preselection Revisited , 1992, PPSN.

[21]  Michael N. Vrahatis,et al.  On the computation of all global minimizers through particle swarm optimization , 2004, IEEE Transactions on Evolutionary Computation.

[22]  Ralph R. Martin,et al.  A Sequential Niche Technique for Multimodal Function Optimization , 1993, Evolutionary Computation.

[23]  Layne T. Watson,et al.  Improved Genetic Algorithm for the Design of Stiffened Composite Panels , 1994 .