A Closer Look at Drawbacks of Minimizing Weighted Sums of Objectives for Pareto Set Generation in Multicriteria Optimization Problems

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dc.contributor.authorDas, Indraneelen_US
dc.contributor.authorDennis, J.E. Jr.en_US
dc.date.accessioned2018-06-18T17:43:00Zen_US
dc.date.available2018-06-18T17:43:00Zen_US
dc.date.issued1996-12en_US
dc.date.noteDecember 1996en_US
dc.description.abstractA standard technique for generating the Pareto set in multicriteria optimization problems is to minimize (convex) weighted sums of the different objectives for various different settings of the weights. However, it is well-known that this method succeeds in getting points from all parts of the Pareto set only when the Pareto curve is convex. This article provides a geometrical argument as to why this is the case. Secondly, it is a frequent observation that even for convex Pareto curves, an evenly distributed set of weights fails to produce an even distribution of points from all parts of the Pareto set. This article aims to identify the mechanism behind this occurrence. Roughly, the weight is related to the slope of the Pareto curve in the objective space in a way such that an even spread of Pareto points actually corresponds to often very uneven distributions of weights. Several examples are provided showing assumed shapes of Pareto curves and the distribution of weights corresponding to an even spread of points on those Pareto curves.en_US
dc.format.extent14 ppen_US
dc.identifier.citationDas, Indraneel and Dennis, J.E. Jr.. "A Closer Look at Drawbacks of Minimizing Weighted Sums of Objectives for Pareto Set Generation in Multicriteria Optimization Problems." (1996) <a href="https://hdl.handle.net/1911/101886">https://hdl.handle.net/1911/101886</a>.en_US
dc.identifier.digitalTR96-36en_US
dc.identifier.urihttps://hdl.handle.net/1911/101886en_US
dc.language.isoengen_US
dc.titleA Closer Look at Drawbacks of Minimizing Weighted Sums of Objectives for Pareto Set Generation in Multicriteria Optimization Problemsen_US
dc.typeTechnical reporten_US
dc.type.dcmiTexten_US
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