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A new graphical visualization of n-dimensional Pareto front for decision-making in multiobjective optimization

机译：用于多目标优化决策的n维Pareto前沿的图形化可视化

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摘要

New challenges in engineering design lead to multiobjective (multicriteria) problems. In this context, the Pareto front supplies a set of solutions where the designer (decision-maker) has to look for the best choice according to his preferences. Visualization techniques often play a key role in helping decision-makers, but they have important restrictions for more than two-dimensional Pareto fronts. In this work, a new graphical representation, called Level Diagrams, for n-dimensional Pareto front analysis is proposed. Level Diagrams consists of representing each objective and design parameter on separate diagrams. This new technique is based on two key points: classification of Pareto front points according to their proximity to ideal points measured with a specific norm of normalized objectives (several norms can be used); and synchronization of objective and parameter diagrams. Some of the new possibilities for analyzing Pareto fronts are shown. Additionally, in order to introduce designer preferences, Level Diagrams can be coloured, so establishing a visual representation of preferences that can help the decision-maker. Finally, an example of a robust control design is presented - a benchmark proposed at the American Control Conference. This design is set as a six-dimensional multiobjective problem. (c) 2008 Elsevier Inc. All rights reserved.
机译：工程设计中的新挑战导致了多目标（多标准）问题。在这种情况下，Pareto前端提供了一套解决方案，设计师（决策制定者）​​必须根据自己的喜好寻找最佳选择。可视化技术通常在帮助决策者方面发挥关键作用，但它们对二维以上的帕累托前沿具有重要的限制。在这项工作中，提出了一种新的图形表示形式，称为水平图，用于n维Pareto前沿分析。级别图包括在单独的图中表示每个目标和设计参数。这项新技术基于两个关键点：根据特定目标归一化目标（可以使用多个标准）对帕累托前沿与理想点的接近程度进行分类。目标图和参数图的同步。显示了一些分析帕累托前沿的新可能性。此外，为了介绍设计人员的偏好，可以对“层次图”进行着色，以便建立偏好的可视化表示形式，以帮助决策者。最后，给出了鲁棒控制设计的示例-美国控制会议上提出的基准。此设计被设置为六维多目标问题。 （c）2008 Elsevier Inc.保留所有权利。

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