Optimal averaged Hausdorff archives for bi-objective problems: theoretical and numerical results

Günter Rudolph (), Oliver Schütze (), Christian Grimme (), Christian Domínguez-Medina () and Heike Trautmann ()
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Günter Rudolph: TU Dortmund University
Oliver Schütze: CINVESTAV IPN
Christian Grimme: University of Münster
Christian Domínguez-Medina: National Polytechnic Institute
Heike Trautmann: University of Münster

Computational Optimization and Applications, 2016, vol. 64, issue 2, No 11, 589-618

Abstract: Abstract One main task in evolutionary multiobjective optimization (EMO) is to obtain a suitable finite size approximation of the Pareto front which is the image of the solution set, termed the Pareto set, of a given multiobjective optimization problem. In the technical literature, the characteristic of the desired approximation is commonly expressed by closeness to the Pareto front and a sufficient spread of the solutions obtained. In this paper, we first make an effort to show by theoretical and empirical findings that the recently proposed Averaged Hausdorff (or $$\Delta _p$$ Δ p -) indicator indeed aims at fulfilling both performance criteria for bi-objective optimization problems. In the second part of this paper, standard EMO algorithms combined with a specialized archiver and a postprocessing step based on the $$\Delta _p$$ Δ p indicator are introduced which sufficiently approximate the $$\Delta _p$$ Δ p -optimal archives and generate solutions evenly spread along the Pareto front.

Keywords: Evolutionary computation; $$\Delta _p$$ Δ p indicator; Hausdorff distance; Evolutionary multiobjective optimization (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10589-015-9815-8

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