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Interactive Nonconvex Pareto Navigator for multiobjective optimization

为 multiobjective 优化的交互 Nonconvex Pareto 导航者

作     者:Hartikainen, Markus Miettinen, Kaisa Klamroth, Kathrin 

作者机构:Univ Jyvaskyla Fac Informat Technol POB 35 Agora FI-40014 Jyvaskyla Finland Univ Wuppertal Sch Math & Nat Sci Gaussstr 20 D-42119 Wuppertal Germany 

出 版 物:《EUROPEAN JOURNAL OF OPERATIONAL RESEARCH》 (欧洲运筹学杂志)

年 卷 期:2019年第275卷第1期

页      面:238-251页

核心收录:

学科分类:1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基  金:We thank Mr. V. Ojalehto for implementing the Nonconvex Pareto Navigator method and Mr. K. Sahlstedt for providing the data and preferences for the wastewater treatment problem. We also thank Dr. H. Isomäki and Prof. P. Saariluoma for fruitful discussions on psychology of thinking and neurobiological and behavioral aspects of decision making. We express our thanks to the anonymous reviewer for valuable comments that helped to improve this paper. This research is related to the thematic research area Decision Analytics utilizing Causal Models and Multiobjective Optimization (DEMO) of the University of Jyväskylä 

主  题:Multiple objective programming Interactive multiobjective optimization Navigation Nonconvex problems Pareto optimality 

摘      要:We introduce a new interactive multiobjective optimization method operating in the objective space called Nonconvex Pareto Navigator. It extends the Pareto Navigator method for nonconvex problems. An approximation of the Pareto optimal front in the objective space is first generated with the PAINT method using a relatively small set of Pareto optimal outcomes that is assumed to be given or computed prior to the interaction with the decision maker. The decision maker can then navigate on the approximation and direct the search for interesting regions in the objective space. In this way, the decision maker can conveniently learn about the interdependencies between the conflicting objectives and possibly adjust one s preferences. To facilitate the navigation, we introduce special cones that enable extrapolation beyond the given Pareto optimal outcomes. Besides handling nonconvexity, the new method contains new options for directing the navigation that have been inspired by the classification-based interactive NIMBUS method. The Nonconvex Pareto Navigator method is especially well-suited for computationally expensive problems, because the navigation on the approximation is computationally inexpensive. We demonstrate the method with an example. Besides proposing the new method, we characterize interactive navigation based methods in general and discuss desirable properties of navigation methods overall and in particular with respect to Nonconvex Pareto Navigator. (C) 2018 Elsevier B.V. All rights reserved.

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