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Statistical Models Based Algorithms

In: Non-Convex Multi-Objective Optimization

Author

Listed:
  • Panos M. Pardalos

    (University of Florida
    Research University Higher School of Economics)

  • Antanas Žilinskas

    (Vilnius University)

  • Julius Žilinskas

    (Vilnius University)

Abstract

Multi-objective optimization problems with expensive objective functions expensive function are typical in engineering design, where time-consuming computations are involved for modeling technological processes. Frequently, the available software implements an algorithm to compute the values of objective functions, but neither details of implementation nor analytical properties of the objective functions are known. Nevertheless, the continuity of the objective functions can be normally assumed. The complexity of the computational model implies not only the expensiveness of the objective function but also the uncertainty in its properties, so that other analytical properties of f(x), besides the continuity, cannot be substantiated. Such unfavorable, from the optimization point of view, properties of f(x) as non-differentiability, non-convexity, and multimodality cannot be excluded. Difficulties of the black-box black-box global optimization of expensive functions are well known from the experience gained in the single-objective case.

Suggested Citation

  • Panos M. Pardalos & Antanas Žilinskas & Julius Žilinskas, 2017. "Statistical Models Based Algorithms," Springer Optimization and Its Applications, in: Non-Convex Multi-Objective Optimization, chapter 0, pages 97-120, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-61007-8_7
    DOI: 10.1007/978-3-319-61007-8_7
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