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This paper introduced the notion of a Pareto filter, which performs the function of eliminating all but the global Pareto solutions when given a set of candidate solutions

The normalized normal constraint method for generating the Pareto frontier

Structural and Multidisciplinary Optimization, no. 2 (2003): 86-98

被引用648|浏览8
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摘要

The authors recently proposed the normal constraint (NC) method for generating a set of evenly spaced solutions on a Pareto frontier – for multiobjective optimization problems. Since few methods offer this desirable characteristic, the new method can be of significant practical use in the choice of an optimal solution in a multiobjective ...更多

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简介
  • Multiobjective optimization (MO) plays an important role in engineering design, management, and decision making in general.
  • A Pareto solution is one for which any improvement in one objective can only take place if at least one other objective worsens.
  • This class of solutions is central to multiobjective optimization (Pareto 1964, 1971; Steuer 1986, Chapt.
  • These approaches can be considered as belonging to two classes
重点内容
  • Multiobjective optimization (MO) plays an important role in engineering design, management, and decision making in general
  • Within the context of the literature discussed above, this paper presents a significant extension of the normal constraint method
  • This paper presented an important extension of the normal constraint method that redresses numerical scaling deficiencies of the original NC method
  • A mapping is implemented at the level of the design metrics, which results in highly favorable numerical properties and in the ability to generate a well distributed set of Pareto points even in numerically demanding situations
  • This paper introduced the notion of a Pareto filter, which performs the function of eliminating all but the global Pareto solutions when given a set of candidate solutions
  • This filtering approach is significantly simpler than using analytical means
方法
  • design space and the

    Pareto frontier of a generic biobjective problem. Figure 1b represents the normalized Pareto frontier in the normalized design space.
  • By translating the normal line, 3.1 Normal constraint for bi-objective case
结论
  • This paper presented an important extension of the normal constraint method that redresses numerical scaling deficiencies of the original NC method.
  • This paper introduced the notion of a Pareto filter, which performs the function of eliminating all but the global Pareto solutions when given a set of candidate solutions.
  • This filtering approach is significantly simpler than using analytical means
总结
  • Introduction:

    Multiobjective optimization (MO) plays an important role in engineering design, management, and decision making in general.
  • A Pareto solution is one for which any improvement in one objective can only take place if at least one other objective worsens.
  • This class of solutions is central to multiobjective optimization (Pareto 1964, 1971; Steuer 1986, Chapt.
  • These approaches can be considered as belonging to two classes
  • Methods:

    design space and the

    Pareto frontier of a generic biobjective problem. Figure 1b represents the normalized Pareto frontier in the normalized design space.
  • By translating the normal line, 3.1 Normal constraint for bi-objective case
  • Conclusion:

    This paper presented an important extension of the normal constraint method that redresses numerical scaling deficiencies of the original NC method.
  • This paper introduced the notion of a Pareto filter, which performs the function of eliminating all but the global Pareto solutions when given a set of candidate solutions.
  • This filtering approach is significantly simpler than using analytical means
表格
  • Table1: Effectiveness of methods to generate Pareto solutions
Download tables as Excel
基金
  • This research was supported by NSF award number DMI-0196243
引用论文
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