scholarly journals An Efficient Pareto Set Identification Approach for Multiobjective Optimization on Black-Box Functions

2004 ◽  
Vol 127 (5) ◽  
pp. 866-874 ◽  
Author(s):  
Songqing Shan ◽  
G. Gary Wang
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Black Box ◽  
Pareto Set ◽  
Design Problems ◽  
Engineering Design Problems ◽  
Multiobjective Optimization Problems ◽  
Identification Approach ◽  
Practical Tool ◽  
Set Identification

Both multiple objectives and computation-intensive black-box functions often exist simultaneously in engineering design problems. Few of existing multiobjective optimization approaches addresses problems with expensive black-box functions. In this paper, a new method called the Pareto set pursuing (PSP) method is developed. By developing sampling guidance functions based on approximation models, this approach progressively provides a designer with a rich and evenly distributed set of Pareto optimal points. This work describes PSP procedures in detail. From testing and design application, PSP demonstrates considerable promises in efficiency, accuracy, and robustness. Properties of PSP and differences between PSP and other approximation-based methods are also discussed. It is believed that PSP has a great potential to be a practical tool for multiobjective optimization problems.

scholarly journals An Efficient Pareto Set Identification Approach for Multi-Objective Optimization on Black-Box Functions

2004 ◽  
Author(s):  
G. Gary Wang ◽  
Songqing Shan
Keyword(s):  
Optimization Problems ◽  
Black Box ◽  
Pareto Set ◽  
Multi Objective Optimization ◽  
Design Problems ◽  
Multi Objective ◽  
Engineering Design Problems ◽  
Identification Approach ◽  
Practical Tool ◽  
Set Identification

Both multiple objectives and computation-intensive black-box functions often exist simultaneously in engineering design problems. Few of existing multi-objective optimization approaches addresses problems with expensive black-box functions. In this paper, a new method called the Pareto set pursing (PSP) method is developed. By developing sampling guidance functions, this approach progressively provides a designer with a rich and evenly distributed Pareto optimal points. This work describes PSP in detail with analysis of its properties. From testing and design application, PSP demonstrates considerable efficiency, accuracy, and robustness. Theoretical proof of convergence of PSP is also given. It is believed that PSP has a great potential to be a practical tool for multi-objective optimization problems.

scholarly journals New multiobjective optimization algorithm using NBI-SASP approaches for mechanical structural problems

2022 ◽  
Vol 13 ◽  
pp. 4
Author(s):  
Samira El Moumen ◽  
Siham Ouhimmou
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Pareto Frontier ◽  
Optimization Method ◽  
Multi Objective Optimization ◽  
Design Problems ◽  
Multi Objective ◽  
Structural Problems ◽  
Engineering Design Problems ◽  
Set Of Points

Various engineering design problems are formulated as constrained multi-objective optimization problems. One of the relevant and popular methods that deals with these problems is the weighted method. However, the major inconvenience with its application is that it does not yield a well distributed set. In this study, the use of the Normal Boundary Intersection approach (NBI) is proposed, which is effective in obtaining an evenly distributed set of points in the Pareto set. Given an evenly distributed set of weights, it can be strictly shown that this approach is absolutely independent of the relative scales of the functions. Moreover, in order to ensure the convergence to the Global Pareto frontier, NBI approach has to be aligned with a global optimization method. Thus, the following paper suggests NBI-Simulated Annealing Simultaneous Perturbation method (NBI-SASP) as a new method for multiobjective optimization problems. The study shall test also the applicability of the NBI-SASP approach using different engineering multi-objective optimization problems and the findings shall be compared to a method of reference (NSGA). Results clearly demonstrate that the suggested method is more efficient when it comes to search ability and it provides a well distributed global Pareto Front.

scholarly journals One-exact approximate Pareto sets

2020 ◽  
Author(s):  
Arne Herzel ◽  
Cristina Bazgan ◽  
Stefan Ruzika ◽  
Clemens Thielen ◽  
Daniel Vanderpooten
Keyword(s):  
Multiobjective Optimization ◽  
Polynomial Time ◽  
Optimization Problems ◽  
Auxiliary Problem ◽  
Constant Factor ◽  
Pareto Set ◽  
Multiobjective Optimization Problems ◽  
Annual Ieee Symposium ◽  
Biobjective Optimization ◽  
Approximation Guarantee

AbstractPapadimitriou and Yannakakis (Proceedings of the 41st annual IEEE symposium on the Foundations of Computer Science (FOCS), pp 86–92, 2000) show that the polynomial-time solvability of a certain auxiliary problem determines the class of multiobjective optimization problems that admit a polynomial-time computable $$(1+\varepsilon , \dots , 1+\varepsilon )$$ ( 1 + ε , ⋯ , 1 + ε ) -approximate Pareto set (also called an $$\varepsilon $$ ε -Pareto set). Similarly, in this article, we characterize the class of multiobjective optimization problems having a polynomial-time computable approximate $$\varepsilon $$ ε -Pareto set that is exact in one objective by the efficient solvability of an appropriate auxiliary problem. This class includes important problems such as multiobjective shortest path and spanning tree, and the approximation guarantee we provide is, in general, best possible. Furthermore, for biobjective optimization problems from this class, we provide an algorithm that computes a one-exact $$\varepsilon $$ ε -Pareto set of cardinality at most twice the cardinality of a smallest such set and show that this factor of 2 is best possible. For three or more objective functions, however, we prove that no constant-factor approximation on the cardinality of the set can be obtained efficiently.

scholarly journals Multiobjective Optimization Involving Quadratic Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Oscar Brito Augusto ◽  
Fouad Bennis ◽  
Stephane Caro
Keyword(s):  
Multiobjective Optimization ◽  
Pareto Front ◽  
Optimization Problems ◽  
Dimensional Space ◽  
Pareto Set ◽  
Quadratic Functions ◽  
Pareto Optimum ◽  
Multiobjective Optimization Problems ◽  
Biobjective Optimization ◽  
Engineering Projects

Multiobjective optimization is nowadays a word of order in engineering projects. Although the idea involved is simple, the implementation of any procedure to solve a general problem is not an easy task. Evolutionary algorithms are widespread as a satisfactory technique to find a candidate set for the solution. Usually they supply a discrete picture of the Pareto front even if this front is continuous. In this paper we propose three methods for solving unconstrained multiobjective optimization problems involving quadratic functions. In the first, for biobjective optimization defined in the bidimensional space, a continuous Pareto set is found analytically. In the second, applicable to multiobjective optimization, a condition test is proposed to check if a point in the decision space is Pareto optimum or not and, in the third, with functions defined inn-dimensional space, a direct noniterative algorithm is proposed to find the Pareto set. Simple problems highlight the suitability of the proposed methods.

scholarly journals Duality Theorems for (ρ,ψ,d)-Quasiinvex Multiobjective Optimization Problems with Interval-Valued Components

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 894
Author(s):  
Savin Treanţă
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Integral Functional ◽  
Multiple Integral ◽  
Control Problems ◽  
Duality Theorems ◽  
New Class ◽  
Duality Results ◽  
Multiobjective Optimization Problems ◽  
Interval Valued

The present paper deals with a duality study associated with a new class of multiobjective optimization problems that include the interval-valued components of the ratio vector. More precisely, by using the new notion of (ρ,ψ,d)-quasiinvexity associated with an interval-valued multiple-integral functional, we formulate and prove weak, strong, and converse duality results for the considered class of variational control problems.

scholarly journals Robust neutrosophic programming approach for solving intuitionistic fuzzy multiobjective optimization problems

2021 ◽  
Author(s):  
Firoz Ahmad
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Practical Implication ◽  
Real Life ◽  
Future Research ◽  
Programming Approach ◽  
Solution Approach ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Multiobjective Optimization Problems

AbstractThis study presents the modeling of the multiobjective optimization problem in an intuitionistic fuzzy environment. The uncertain parameters are depicted as intuitionistic fuzzy numbers, and the crisp version is obtained using the ranking function method. Also, we have developed a novel interactive neutrosophic programming approach to solve multiobjective optimization problems. The proposed method involves neutral thoughts while making decisions. Furthermore, various sorts of membership functions are also depicted for the marginal evaluation of each objective simultaneously. The different numerical examples are presented to show the performances of the proposed solution approach. A case study of the cloud computing pricing problem is also addressed to reveal the real-life applications. The practical implication of the current study is also discussed efficiently. Finally, conclusions and future research scope are suggested based on the proposed work.

scholarly journals Assessing the Performance of Interactive Multiobjective Optimization Methods

2021 ◽  
Vol 54 (4) ◽  
pp. 1-27
Author(s):  
Bekir Afsar ◽  
Kaisa Miettinen ◽  
Francisco Ruiz
Keyword(s):  
Multiobjective Optimization ◽  
Decision Maker ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Interactive Methods ◽  
Value Functions ◽  
Technical Aspects ◽  
Preference Information ◽  
Multiobjective Optimization Problems ◽  
Human Decision

Interactive methods are useful decision-making tools for multiobjective optimization problems, because they allow a decision-maker to provide her/his preference information iteratively in a comfortable way at the same time as (s)he learns about all different aspects of the problem. A wide variety of interactive methods is nowadays available, and they differ from each other in both technical aspects and type of preference information employed. Therefore, assessing the performance of interactive methods can help users to choose the most appropriate one for a given problem. This is a challenging task, which has been tackled from different perspectives in the published literature. We present a bibliographic survey of papers where interactive multiobjective optimization methods have been assessed (either individually or compared to other methods). Besides other features, we collect information about the type of decision-maker involved (utility or value functions, artificial or human decision-maker), the type of preference information provided, and aspects of interactive methods that were somehow measured. Based on the survey and on our own experiences, we identify a series of desirable properties of interactive methods that we believe should be assessed.

scholarly journals A Multimodal Smart Quantum Particle Swarm Optimization for Electromagnetic Design Optimization Problems

Energies ◽  
2021 ◽  
Vol 14 (15) ◽  
pp. 4613
Author(s):  
Shah Fahad ◽  
Shiyou Yang ◽  
Rehan Ali Khan ◽  
Shafiullah Khan ◽  
Shoaib Ahmed Khan
Keyword(s):  
Particle Swarm Optimization ◽  
Optimization Problems ◽  
Quantum Particle ◽  
Particle Swarm ◽  
Continuous Variables ◽  
Design Problems ◽  
Swarm Optimization ◽  
Electromagnetic Design ◽  
Quantum Particle Swarm Optimization ◽  
Engineering Design Problems

Electromagnetic design problems are generally formulated as nonlinear programming problems with multimodal objective functions and continuous variables. These can be solved by either a deterministic or a stochastic optimization algorithm. Recently, many intelligent optimization algorithms, such as particle swarm optimization (PSO), genetic algorithm (GA) and artificial bee colony (ABC), have been proposed and applied to electromagnetic design problems with promising results. However, there is no universal algorithm which can be used to solve engineering design problems. In this paper, a stochastic smart quantum particle swarm optimization (SQPSO) algorithm is introduced. In the proposed SQPSO, to tackle the premature convergence problem in order to improve the global search ability, a smart particle and a memory archive are adopted instead of mutation operations. Moreover, to enhance the exploration searching ability, a new set of random numbers and control parameters are introduced. Experimental results validate that the adopted control policy in this work can achieve a good balance between exploration and exploitation. Finally, the SQPSO has been tested on well-known optimization benchmark functions and implemented on the electromagnetic TEAM workshop problem 22. The simulation result shows an outstanding capability of the proposed algorithm in speeding convergence compared to other algorithms.

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