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Probabilistic Bounds in Multi-Objective Optimization

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

Randomization is one of the most important ideas used in the construction of heuristic methods for multi-objective optimization. Mathematically substantiated stochastic methods for non-convex multi-objective optimization attracted interest of researchers quite recently. A natural idea is to generalize single-objective optimization methods to the multi-objective case, and a prospective candidate is the well developed method based on the statistical methods of extremal values. A brief review of this approach, known as a Branch and Probability Bound (BPB) branch and probability bound method is presented in Sect. 4.4. Some statistical procedures which are well known in single-objective optimization can be extended to multi-objective problems using scalarization. In this chapter, a version of multi-objective BPB method is described and discussed; this method is an extension of the BPB method developed for the case of a single-objective function in [237], see also [239], Sect. 2.6.1. The considered extension is based on the Tchebycheff scalarization method Tchebycheff method briefly discussed in Chap. 2

Suggested Citation

  • Panos M. Pardalos & Antanas Žilinskas & Julius Žilinskas, 2017. "Probabilistic Bounds in Multi-Objective Optimization," Springer Optimization and Its Applications, in: Non-Convex Multi-Objective Optimization, chapter 0, pages 121-135, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-61007-8_8
    DOI: 10.1007/978-3-319-61007-8_8
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