## AI帮你理解科学

## AI 精读

AI抽取本论文的概要总结

微博一下：

# The normalized normal constraint method for generating the Pareto frontier

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

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

代码：

数据：

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

- Table1: Effectiveness of methods to generate Pareto solutions

基金

- This research was supported by NSF award number DMI-0196243

引用论文

- Belegundu, A.; Chandrupatla, T. 1999: Optimization concepts and applications in engineering. New Jersey: Prentice Hall
- Chen, W.; Wiecek, M.M.; Zhang, J. 1999: Quality utility – a compromise programming approach to robust design. J. Mech. Des. 121, 179–187
- Cheng, F.; Li, D. 1998: Genetic algorithm development for multiobjective optimization of structures. AIAA J. 36, 1105–1112
- Das, I.; Dennis, J.E. 1997: A closer look at drawbacks of minimizing weighted sums of objectives for Pareto set generation in multicriteria optimization problems. Struct. Optim. 14, 63–69
- Das, I.; Dennis, J.E. 1998: Normal-boundary intersection: a new method for generating the Pareto surface in nonlinear multicriteria optimization problems. SIAM J. Optim. 8, 631–657
- Grandhi, R.V.; Bharatram, G. 1993: Multiobjective optimization of large-scale structures. AIAA J. 31, 1329–1337
- Holland, J.H. 1975: Adaptation in natural and artificial systems. Ann Arbor, MI: The University of Michigan Press
- Ismail-Yahaya, A.; Messac, A. 2002: Effective generation of the Pareto frontier using the normal constraint method. 40th Aerospace Sciences Meeting and Exhibit (held in Reno, Nevada), Paper No. AIAA 2002-0178
- Koski, J. 1985: Defectiveness of weighting methods in multicriterion optimization of structures. Commun. Appl. Numer. Methods 1, 333–337
- Messac, A. 1996: Physical programming: effective optimization for computational design. AIAA J. 34, 149–158
- Messac, A.; Mattson, C.A. 2002: Generating Well-Distributed Sets of Pareto Points for Engineering Design using Physical Programming. Optim. Eng. 3, 431–450
- Messac, A.; Ismail-Yahaya, A. 2001: Required relationship between objective function and Pareto frontier orders: practical implications. AIAA J. 11, 2168–2174
- Miettinen, K. 1999: Nonlinear multiobjective optimization. Massachusetts: Kluwer Academic Publishers
- Osyczka, A.; Kundu, S. 1995: New method to solve generalized multicriteria optimization problems using the simple genetic algorithm. Struct. Optim. 10, 94–99
- Pareto, V. 1964: Cour d’economie politique, Librarie DrozGeneve (the first edition in 1896)
- Pareto, V. 1971: Manuale di economica politica, societa editrice libraria. Milano, Italy: MacMillan Press (the first edition in 1906), (translated into English by A. S. Schwier as Manual of Political Economy)
- Srinivasan, D.; Tettamanzi, A. 1996: Heuristic-guided evolutionary approach to multiobjective generation scheduling. IEE Proc. Generation, Transmission and Distribution 143, 553–559
- Steuer, R. 1986: Multiple criteria optimization: theory, computation, and applications. New York: John Wiley & Sons

标签

评论