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A Method for Generating a Well-Distributed Pareto Set in Nonlinear Multiobjective Optimization
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In this article, the Physical Programming Method is modified to make its realization easier and more efficient, the main focus being the even generation of the complete Pareto set for different test cases.Abstract:
In multidisciplinary optimization the designer needs to find solution to optimization problems which include a number of usually contradicting criteria. Such a problem is mathematically related to the field of nonlinear vector optimization where there are many numerical methods capable of providing a solution. However, only a few of those are suitable for real multidisciplinary design in industry because an iteration design circle usually is very time-consuming. This is due to the time scales and computational resources associated with each iterative design cycle. The recently suggested Physical Programming Method appears to match many requirements raised in industrial applications. The method is modified to make its realization easier and more efficient, the main focus being the even generation of the complete Pareto set. The method is used to find the Pareto surface for different test cases.read more
Citations
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Journal ArticleDOI
Normal Constraint Method with Guarantee of Even Representation of Complete Pareto Frontier
TL;DR: The normal constraint method is offered, which is a simple approach for generating Pareto solutions that are evenly distributed in the design space of an arbitrary number of objectives, and its critical distinction is defined, namely, the ability to generate a set of evenly distributed PareTo solutions over the complete Pare to frontier.
Journal ArticleDOI
Directed search domain: a method for even generation of the Pareto frontier in multiobjective optimization
Tohid Erfani,Sergei Utyuzhnikov +1 more
TL;DR: The main objective of this article is to develop and give detailed description of an algorithm that is able to generate an evenly distributed Pareto set in a general formulation and to demonstrate the effectiveness of the algorithm by a number of challenging test cases.
Journal ArticleDOI
A normal boundary intersection approach to multiresponse robust optimization of the surface roughness in end milling process with combined arrays
Tarcisio Gonçalves Brito,Anderson Paulo de Paiva,João Roberto Ferreira,José Henrique de Freitas Gomes,Pedro Paulo Balestrassi +4 more
TL;DR: In this paper, the use of normal boundary intersection (NBI) method coupled with mean-squared error (MSE) functions is proposed to generate equispaced Pareto frontiers for a bi-objective robust design model.
Journal ArticleDOI
Pareto Tracer: a predictor–corrector method for multi-objective optimization problems
Adanay Martín,Oliver Schütze +1 more
TL;DR: A novel predictor–corrector (PC) method for the numerical treatment of multi-objective optimization problems (MOPs) that is capable of performing a continuation along the set of (local) solutions of a given MOP with k objectives, and can cope with equality and box constraints.
Book ChapterDOI
Continuous Multiobjective Programming
TL;DR: In this article, the authors present a view of the state of the art in continuous multiobjective programming and discuss the most important solution concepts for continuous MOPs and present a perspective on future research directions.
References
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Book
Principles of mathematical analysis
TL;DR: The real and complex number system as discussed by the authors is a real number system where the real number is defined by a real function and the complex number is represented by a complex field of functions.
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Nonlinear Multiobjective Optimization
TL;DR: This paper is concerned with the development of methods for dealing with the role of symbols in the interpretation of semantics.
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Multicriteria Optimization
TL;DR: This paper presents a meta-modelling framework for estimating the modeled solutions for various types of optimization problems in the multicriteria setting.
Journal ArticleDOI
Normal-Boundary Intersection: A New Method for Generating the Pareto Surface in Nonlinear Multicriteria Optimization Problems
Indraneel Das,John E. Dennis +1 more
TL;DR: In this paper, an alternate method for finding several Pareto optimal points for a general nonlinear multicriteria optimization problem is proposed, which can handle more than two objectives while retaining the computational efficiency of continuation-type algorithms.
Journal ArticleDOI
A closer look at drawbacks of minimizing weighted sums of objectives for Pareto set generation in multicriteria optimization problems
Indraneel Das,John E. Dennis +1 more
TL;DR: In this article, the authors provide a geometrical argument as to why the Pareto curve is convex, and show that this is not the case for all parts of the set.