We are analyzing https://link.springer.com/article/10.1007/bf01197559.

Title:
A closer look at drawbacks of minimizing weighted sums of objectives for Pareto set generation in multicriteria optimization problems | Structural and Multidisciplinary Optimization
Description:
A 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 observation. 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.
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Keywords {🔍}

optimization, pareto, article, set, problems, multicriteria, privacy, cookies, content, points, distribution, access, springer, information, publish, research, search, dennis, weights, method, google, scholar, data, log, journal, structural, weighted, sums, objectives, convex, observation, curves, related, multiobjective, chapter, control, discover, design, york, download, optional, personal, parties, policy, find, track, closer, drawbacks, minimizing, generation,

Topics {✒️}

month download article/chapter standard technique multiple-objective problems objective space frequent observation generating pareto-optimal points multicriteria optimization problems bicriterial optimization problems privacy choices/manage cookies pareto-optimal solutions multicriteria design optimization full article pdf multicriteria truss optimization uneven distributions related subjects distribution control european economic area scope submit manuscript normal-boundary intersection reference point approximation proper equality constraints check access instant access conditions privacy policy evenly distributed set minimizing weighted sums structural optimization 14 pareto set generation accepting optional cookies main content log weight vector set journal finder publish multicriteria optimization article aims convex pareto curves sobieski rights privacy policy personal data article log books a article das weighted sums observation article cite pareto set optional cookies manage preferences distribution pareto curves data protection

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