F06-3 Multiobjective Optimization and Visualization of Pareto Solutions

Pareto solutions in multiobjective optimization are very problematic to measuring the characteristics of solutions for engineering design because of their considerable variety in function space and parameter space. To overcome these situations, a clustering-based interpretation process for Pareto solutions is considered. For better competitive clustering algorithm, we propose an evolutionary clustering algorithm — ECA. The ECA requires less computational effort, and overcomes local optimum of the K-means clustering algorithm and its related algorithms. Effectiveness of the method is examined in detail through the comparison with other algorithms.

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Sufficient conditions for global weak Pareto solutions in multiobjective optimization

Positivity ◽

10.1007/s11117-012-0194-4 ◽

2012 ◽

Vol 16 (3) ◽

pp. 579-602 ◽

Cited By ~ 6

Author(s):

Truong Q. Bao ◽

Boris S. Mordukhovich

Keyword(s):

Multiobjective Optimization ◽

Sufficient Conditions ◽

Pareto Solutions

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Evolving Opposition-Based Pareto Solutions: Multiobjective Optimization Using Competitive Coevolution

Oppositional Concepts in Computational Intelligence - Studies in Computational Intelligence ◽

10.1007/978-3-540-70829-2_9 ◽

2008 ◽

pp. 161-206 ◽

Cited By ~ 2

Author(s):

Tse Guan Tan ◽

Jason Teo

Keyword(s):

Multiobjective Optimization ◽

Pareto Solutions ◽

Competitive Coevolution

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Sensitivity of Pareto Solutions in Multiobjective Optimization

Journal of Optimization Theory and Applications ◽

10.1007/s10957-005-4713-3 ◽

2005 ◽

Vol 126 (2) ◽

pp. 247-264 ◽

Cited By ~ 8

Author(s):

A. Balbás ◽

E. Galperin ◽

P. Jiménez. Guerra

Keyword(s):

Multiobjective Optimization ◽

Pareto Solutions

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RELIABILITY AND REDUNDANCY APPORTIONMENT OPTIMIZATION USING INTERACTIVE PHYSICAL PROGRAMMING

International Journal of Reliability Quality and Safety Engineering ◽

10.1142/s0218539304001476 ◽

2004 ◽

Vol 11 (03) ◽

pp. 213-222 ◽

Cited By ~ 4

Author(s):

HONG-ZHONG HUANG ◽

ZHI-GANG TIAN ◽

YING-KUI GU

Keyword(s):

Multiobjective Optimization ◽

Optimization Problem ◽

Optimization Approach ◽

Reliability Optimization ◽

Pareto Solutions ◽

Physical Programming ◽

Good Convergence ◽

Convergence Performance

In this paper, a new multiobjective optimization approach named interactive physical programming is proposed and used to solve the reliability and redundancy apportionment optimization problem. Interactive physical programming extends physical programming6 to an interactive framework. After the designer specifies which objectives need to be improved and which objectives can be sacrificed, interactive physical programming can obtain the Pareto solutions satisfying such improving preferences. It has good convergence performance, and can obtain satisfactory design in the end. Interactive physical programming has been successfully applied to a reliability and redundancy apportionment optimization problem. It provides a new effective approach for reliability optimization.

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Multiobjective Optimization of Linear Cooperative Spectrum Sensing: Pareto Solutions and Refinement

IEEE Transactions on Cybernetics ◽

10.1109/tcyb.2015.2395412 ◽

2016 ◽

Vol 46 (1) ◽

pp. 96-108 ◽

Cited By ~ 8

Author(s):

Wei Yuan ◽

Xinge You ◽

Jing Xu ◽

Henry Leung ◽

Tianhang Zhang ◽

...

Keyword(s):

Multiobjective Optimization ◽

Spectrum Sensing ◽

Cooperative Spectrum Sensing ◽

Pareto Solutions

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Multi-Objective Design Problem of Tire Wear and Visualization of Its Pareto Solutions2

Tire Science and Technology ◽

10.2346/1.2345640 ◽

2006 ◽

Vol 34 (3) ◽

pp. 170-194 ◽

Cited By ~ 10

Author(s):

M. Koishi ◽

Z. Shida

Keyword(s):

Inverse Problems ◽

Conceptual Design ◽

Dimensional Space ◽

Design Stage ◽

Objective Functions ◽

Pareto Solutions ◽

Design Problems ◽

Multi Objective ◽

Design Engineers ◽

Design Variables

Abstract Since tires carry out many functions and many of them have tradeoffs, it is important to find the combination of design variables that satisfy well-balanced performance in conceptual design stage. To find a good design of tires is to solve the multi-objective design problems, i.e., inverse problems. However, due to the lack of suitable solution techniques, such problems are converted into a single-objective optimization problem before being solved. Therefore, it is difficult to find the Pareto solutions of multi-objective design problems of tires. Recently, multi-objective evolutionary algorithms have become popular in many fields to find the Pareto solutions. In this paper, we propose a design procedure to solve multi-objective design problems as the comprehensive solver of inverse problems. At first, a multi-objective genetic algorithm (MOGA) is employed to find the Pareto solutions of tire performance, which are in multi-dimensional space of objective functions. Response surface method is also used to evaluate objective functions in the optimization process and can reduce CPU time dramatically. In addition, a self-organizing map (SOM) proposed by Kohonen is used to map Pareto solutions from high-dimensional objective space onto two-dimensional space. Using SOM, design engineers see easily the Pareto solutions of tire performance and can find suitable design plans. The SOM can be considered as an inverse function that defines the relation between Pareto solutions and design variables. To demonstrate the procedure, tire tread design is conducted. The objective of design is to improve uneven wear and wear life for both the front tire and the rear tire of a passenger car. Wear performance is evaluated by finite element analysis (FEA). Response surface is obtained by the design of experiments and FEA. Using both MOGA and SOM, we obtain a map of Pareto solutions. We can find suitable design plans that satisfy well-balanced performance on the map called “multi-performance map.” It helps tire design engineers to make their decision in conceptual design stage.

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