Unbiased approximation in multicriteria optimization

Klamroth, Kathrin; Tind, Jørgen; Wiecek, Margaret M.

doi:10.1007/s001860200217

Cited by 63 publications

(51 citation statements)

References 19 publications

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“…However, if the problem is computationally costly, it is better to generate the representative set before involving the DM. Instead of approximation algorithms of the MCDM field (Klamroth et al 2002;Lotov et al 2004;Ruzika and Wiecek 2005) we can also use evolutionary approaches (see, e.g., Deb 2001). The advantage of using an approximation algorithm as in Klamroth et al (2002) is that it also produces an upper bound for the approximation error.…”

Section: Discussionmentioning

confidence: 99%

“…To begin with, we apply an approximation method in the initialization phase and as a result we get a list of actual Pareto optimal solutions (see Table 1) to be used to produce a polyhedral approximation. We use the adaptive approximation method Klamroth et al (2002). Here we have selected to use seven solutions.…”

Section: Using Pareto Navigatormentioning

confidence: 99%

“…Possible methods that can be used are given, for example, in Deb (2001), Klamroth et al (2002), Lotov et al (2004), Ruzika and Wiecek (2005). However, we emphasize that the representative set can be generated off-line before involving the DM.…”

Section: Introductionmentioning

confidence: 99%

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Pareto navigator for interactive nonlinear multiobjective optimization

Eskelinen¹,

Miettinen

Klamroth

et al. 2008

OR Spectrum

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We describe a new interactive learning-oriented method called Pareto navigator for nonlinear multiobjective optimization. In the method, first a polyhedral approximation of the Pareto optimal set is formed in the objective function space using a relatively small set of Pareto optimal solutions representing the Pareto optimal set. Then the decision maker can navigate around the polyhedral approximation and direct the search for promising regions where the most preferred solution could be located. In this way, the decision maker can learn about the interdependencies between the conflicting objectives and possibly adjust one's preferences. Once an interesting region has been identified, the polyhedral approximation can be made more accurate in that region or the decision maker can ask for the closest counterpart in the actual Pareto optimal set. If desired, (s)he can continue with another interactive method from the solution obtained. Pareto navigator can be seen as a nonlinear extension of the linear Pareto race method. After the representative set of Pareto optimal solutions has been generated, Pareto navigator is computationally efficient because the computations are performed in the polyhedral approximation and for that reason function evaluations of the actual objective functions are not needed. Thus, the method is well suited especially for problems with computationally costly functions. Furthermore, thanks to the visualization technique used, the method is applicable also for problems with three or more objective functions, and in fact it is best suited for such problems. After introducing the method in more detail, we illustrate it and the underlying ideas with an example.

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Section: Discussionmentioning

confidence: 99%

Section: Using Pareto Navigatormentioning

confidence: 99%

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Pareto navigator for interactive nonlinear multiobjective optimization

Eskelinen¹,

Miettinen

Klamroth

et al. 2008

OR Spectrum

Self Cite

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“…Another hybrid is described in Klamroth and Miettinen (2007), where an adaptive approximation method (Klamroth et al, 2002) approximating the Pareto optimal set is hybridized with reference point ideas. This means that the approximation is made more accurate only in those parts of the Pareto optimal set that the DM is interested in.…”

Section: Some Other Interactive Methodsmentioning

confidence: 99%

Why Use Interactive Multi-Objective Optimization in Chemical Process Design?

Miettinen

Hakanen

2008

Multi-Objective Optimization

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“…A detailed explanation of this algorithm can be found in [1,16,17]. It enables the calculation of Pareto sets with a well-defined approximation quality and with the corresponding lowest possible number of Pareto points, and hence, with a minimum of computing time.…”

Section: Introductionmentioning

confidence: 99%

Multi‐criteria Optimization of an Industrial World‐Scale Process

Kurnatowski

Bortz

Scherrer

et al. 2017

Chemie Ingenieur Technik

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Commercially available flow sheet simulators cannot perform optimization runs with more than one criterion. To overcome this problem, the flow sheet simulator CHEMCAD is combined with an external optimization solver, and the Excel VBA client is used to arrange inter-process communications. The resulting tool for multi-criteria optimization in chemical process engineering is applied to two separation problems. First, a dividing-wall column is used as a theoretical example to test different starting points and different scalarization techniques. Second, a significant decrease in energy demand is achieved for a real continuous world-scale facility.

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Unbiased approximation in multicriteria optimization

Cited by 63 publications

References 19 publications

Pareto navigator for interactive nonlinear multiobjective optimization

Pareto navigator for interactive nonlinear multiobjective optimization

Why Use Interactive Multi-Objective Optimization in Chemical Process Design?

Multi‐criteria Optimization of an Industrial World‐Scale Process

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