Mode Pursuing Sampling Method for Discrete Variable Optimization on Expensive Black-Box Functions

Based on previously developed Mode Pursuing Sampling (MPS) approach for continuous variables, a variation of MPS for discrete variable global optimization problems on expensive black-box functions is developed in this paper. The proposed method, namely, the discrete variable MPS (D-MPS) method, differs from its continuous variable version not only on sampling in a discrete space, but moreover, on a novel double-sphere strategy. The double-sphere strategy features two hyperspheres whose radii are dynamically enlarged or shrunk in control of, respectively, the degree of “exploration” and “exploitation” in the search of the optimum. Through testing and application to design problems, the proposed D-MPS method demonstrates excellent efficiency and accuracy as compared to the best results in literature on the test problems. The proposed method is believed a promising global optimization strategy for expensive black-box functions with discrete variables. The double-sphere strategy provides an original search control mechanism and has potential to be used in other search algorithms. DOI: 10.1115/1.2803251

[1]  Omprakash K. Gupta,et al.  Branch and Bound Experiments in Convex Nonlinear Integer Programming , 1985 .

[2]  E. Sandgren,et al.  Nonlinear Integer and Discrete Programming in Mechanical Design Optimization , 1990 .

[3]  Jasbir S. Arora,et al.  Introduction to Optimum Design , 1988 .

[4]  R. G. Fenton,et al.  A MIXED INTEGER-DISCRETE-CONTINUOUS PROGRAMMING METHOD AND ITS APPLICATION TO ENGINEERING DESIGN OPTIMIZATION , 1991 .

[5]  Chun Zhang,et al.  Mixed-discrete nonlinear optimization with simulated annealing , 1993 .

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

[7]  Sven Leyffer,et al.  Solving mixed integer nonlinear programs by outer approximation , 1994, Math. Program..

[8]  P. Pardalos,et al.  Handbook of global optimization , 1995 .

[9]  Jasbir S. Arora,et al.  OPTIMAL DESIGN WITH DISCRETE VARIABLES: SOME NUMERICAL EXPERIMENTS , 1997 .

[10]  Zelda B. Zabinsky,et al.  Stochastic Methods for Practical Global Optimization , 1998, J. Glob. Optim..

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

[12]  Feng-Sheng Wang,et al.  A hybrid method of evolutionary algorithms for mixed-integer nonlinear optimization problems , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[13]  Robert L. Smith,et al.  Implementing pure adaptive search for global optimization using Markov chain sampling , 2001, J. Glob. Optim..

[14]  Thomas Jansen,et al.  A New Framework for the Valuation of Algorithms for Black-Box Optimization , 2002, FOGA.

[15]  Liqun Wang,et al.  A Random-Discretization Based Monte Carlo Sampling Method and its Applications , 2002 .

[16]  Li Zhang,et al.  An evaluation of back-propagation neural networks for the optimal design of structural systems: Part II. Numerical evaluation , 2002 .

[17]  Michael R. Bussieck,et al.  MINLPLib - A Collection of Test Models for Mixed-Integer Nonlinear Programming , 2003, INFORMS J. Comput..

[18]  T. Simpson,et al.  Fuzzy Clustering Based Hierarchical Metamodeling For Space Reduction and Design Optimization , 2004 .

[19]  T. Simpson,et al.  Fuzzy clustering based hierarchical metamodeling for design space reduction and optimization , 2004 .

[20]  Helio J. C. Barbosa,et al.  An adaptive penalty scheme for genetic algorithms in structural optimization , 2004 .

[21]  Jasbir S. Arora,et al.  12 – Introduction to Optimum Design with MATLAB , 2004 .

[22]  G. G. Wang,et al.  Mode-pursuing sampling method for global optimization on expensive black-box functions , 2004 .

[23]  Zelda B. Zabinsky,et al.  Comparative Assessment of Algorithms and Software for Global Optimization , 2005, J. Glob. Optim..

[24]  Afonso C. C. Lemonge,et al.  ANT COLONY ALGORITHMS APPLIED TO DISCRETE OPTIMIZATION PROBLEMS , 2005 .

[25]  Mohammad R. Akbarzadeh-Totonchi,et al.  Evolutionary quantum algorithms for structural design , 2005, 2005 IEEE International Conference on Systems, Man and Cybernetics.

[26]  Masao Fukushima,et al.  Derivative-Free Filter Simulated Annealing Method for Constrained Continuous Global Optimization , 2006, J. Glob. Optim..

[27]  G. Gary Wang,et al.  Review of Metamodeling Techniques in Support of Engineering Design Optimization , 2007, DAC 2006.

[28]  Yaroslav D. Sergeyev,et al.  Global Search Based on Efficient Diagonal Partitions and a Set of Lipschitz Constants , 2006, SIAM J. Optim..