Stochastic Methods for Practical Global Optimization

  • Authors:

  • Zelda B. Zabinsky

  • Affiliations:

  • Industrial Engineering, University of Washington, Seattle, Washington, USA

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 1998

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Abstract

Engineering design problems often involve global optimization offunctions that are supplied as ’black box‘ functions. These functions may benonconvex, nondifferentiable and even discontinuous. In addition, thedecision variables may be a combination of discrete and continuousvariables. The functions are usually computationally expensive, and mayinvolve finite element methods. An engineering example of this type ofproblem is to minimize the weight of a structure, while limiting strain tobe below a certain threshold. This type of global optimization problem isvery difficult to solve, yet design engineers must find some solution totheir problem – even if it is a suboptimal one. Sometimes the mostdifficult part of the problem is finding any feasible solution. Stochasticmethods, including sequential random search and simulated annealing, arefinding many applications to this type of practical global optimizationproblem. Improving Hit-and-Run (IHR) is a sequential random search methodthat has been successfully used in several engineering design applications,such as the optimal design of composite structures. A motivation to IHR isdiscussed as well as several enhancements. The enhancements include allowingboth continuous and discrete variables in the problem formulation. This hasmany practical advantages, because design variables often involve a mixtureof continuous and discrete values. IHR and several variations have beenapplied to the composites design problem. Some of this practical experience is discussed.