Discrete Search in Design Optimization

It is a common feature of many real-life design optimization problems that some design components can only be selected from a finite set of choices. Each choice corresponds to a possibly multidimensional design point representing the specifications of the chosen design component. In this paper we present a method to explore the resulting discrete search space for design optimization. We use the knowledge about the discrete space represented by its minimum spanning tree and find a splitting based on convex relaxation.

[1]  Alfons Schuster.  Robust Intelligent Systems , 2008 .

[2]  Thorsten Koch,et al.  Branching rules revisited , 2005, Oper. Res. Lett..

[3]  Arnold Neumaier,et al.  Global Optimization by Multilevel Coordinate Search , 1999, J. Glob. Optim..

[4]  Dario Izzo,et al.  Robust and Automated Space System Design , 2008 .

[5]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988 .

[6]  C. Floudas.  Nonlinear and Mixed-Integer Optimization: Fundamentals and Applications , 1995 .

[7]  Lamberto Cesari,et al.  Optimization-Theory And Applications , 1983 .

[8]  Tibor Csendes,et al.  Application of clouds for modeling uncertainties in robust space system design , 2007 .

[9]  Victor Eijkhout,et al.  A Standard and Software for Numerical Metadata , 2009, TOMS.

[10]  Arnold Neumaier,et al.  A splitting technique for discrete search based on convex relaxation , 2009 .

[11]  C. D. Perttunen,et al.  Lipschitzian optimization without the Lipschitz constant , 1993 .

[12]  Nikolaos V. Sahinidis,et al.  Global optimization of mixed-integer nonlinear programs: A theoretical and computational study , 2004, Math. Program..

[13]  Ronald L. Rardin,et al.  Discrete optimization , 1988, Computer science and scientific computing.

[14]  Arnold Neumaier,et al.  SNOBFIT -- Stable Noisy Optimization by Branch and Fit , 2008, TOMS.

[15]  Natalia Alexandrov,et al.  Multidisciplinary design optimization : state of the art , 1997 .

[16]  Eric W. Weisstein.  Minimum Spanning Tree , 2000 .

[17]  Sven Leyffer,et al.  Deterministic Methods for Mixed Integer Nonlinear Programming , 1993 .

[18]  Arnold Neumaier,et al.  Autonomous robust design optimisation with potential clouds , 2009 .