scholarly journals A Multiobjective Genetic Algorithm Based on a Discrete Selection Procedure

2015 ◽  
Vol 2015 ◽  
pp. 1-17 ◽  
Author(s):  
Qiang Long ◽  
Changzhi Wu ◽  
Xiangyu Wang ◽  
Lin Jiang ◽  
Jueyou Li
Keyword(s):  
Genetic Algorithm ◽  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Selection Procedure ◽  
Population Based ◽  
Pareto Solution ◽  
Multiobjective Genetic Algorithm ◽  
Trade Offs ◽  
Multiobjective Optimization Problems ◽  
Optimum Order

Multiobjective genetic algorithm (MOGA) is a direct search method for multiobjective optimization problems. It is based on the process of the genetic algorithm; the population-based property of the genetic algorithm is well applied in MOGAs. Comparing with the traditional multiobjective algorithm whose aim is to find a single Pareto solution, the MOGA intends to identify numbers of Pareto solutions. During the process of solving multiobjective optimization problems using genetic algorithm, one needs to consider the elitism and diversity of solutions. But, normally, there are some trade-offs between the elitism and diversity. For some multiobjective problems, elitism and diversity are conflicting with each other. Therefore, solutions obtained by applying MOGAs have to be balanced with respect to elitism and diversity. In this paper, we propose metrics to numerically measure the elitism and diversity of solutions, and the optimum order method is applied to identify these solutions with better elitism and diversity metrics. We test the proposed method by some well-known benchmarks and compare its numerical performance with other MOGAs; the result shows that the proposed method is efficient and robust.

Approximating the Nondominated Front Using the Pareto Archived Evolution Strategy

2000 ◽  
Vol 8 (2) ◽  
pp. 149-172 ◽  
Author(s):  
Joshua D. Knowles ◽  
David W. Corne
Keyword(s):  
Genetic Algorithm ◽  
Multiobjective Optimization ◽  
Local Search ◽  
Optimization Problems ◽  
Population Based ◽  
Evolution Strategy ◽  
Basic Algorithm ◽  
Pareto Optimal Set ◽  
Candidate Solution ◽  
Multiobjective Optimization Problems

We introduce a simple evolution scheme for multiobjective optimization problems, called the Pareto Archived Evolution Strategy (PAES). We argue that PAES may represent the simplest possible nontrivial algorithm capable of generating diverse solutions in the Pareto optimal set. The algorithm, in its simplest form, is a (1+1) evolution strategy employing local search but using a reference archive of previously found solutions in order to identify the approximate dominance ranking of the current and candidate solution vectors. (1+1)-PAES is intended to be a baseline approach against which more involved methods may be compared. It may also serve well in some real-world applications when local search seems superior to or competitive with population-based methods. We introduce (1+λ) and (μ+λ) variants of PAES as extensions to the basic algorithm. Six variants of PAES are compared to variants of the Niched Pareto Genetic Algorithm and the Nondominated Sorting Genetic Algorithm over a diverse suite of six test functions. Results are analyzed and presented using techniques that reduce the attainment surfaces generated from several optimization runs into a set of univariate distributions. This allows standard statistical analysis to be carried out for comparative purposes. Our results provide strong evidence that PAES performs consistently well on a range of multiobjective optimization tasks.

An improved proximal method with quasi-distance for nonconvex multiobjective optimization problem

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Fouzia Amir ◽  
Ali Farajzadeh ◽  
Jehad Alzabut
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Convergence Result ◽  
Proximal Method ◽  
Pareto Solution ◽  
Multiobjective Optimization Problems ◽  
Locally Lipschitz ◽  
The Cost ◽  
Constrained Multiobjective Optimization

Abstract Multiobjective optimization is the optimization with several conflicting objective functions. However, it is generally tough to find an optimal solution that satisfies all objectives from a mathematical frame of reference. The main objective of this article is to present an improved proximal method involving quasi-distance for constrained multiobjective optimization problems under the locally Lipschitz condition of the cost function. An instigation to study the proximal method with quasi distances is due to its widespread applications of the quasi distances in computer theory. To study the convergence result, Fritz John’s necessary optimality condition for weak Pareto solution is used. The suitable conditions to guarantee that the cluster points of the generated sequences are Pareto–Clarke critical points are provided.

Evaluated Preference Genetic Algorithm and its Engineering Applications

2011 ◽  
Vol 467-469 ◽  
pp. 2129-2136
Author(s):  
Tung Kuan Liu ◽  
Hsin Yuan Chang ◽  
Wen Ping Wu ◽  
Chiu Hung Chen ◽  
Min Rong Ho
Keyword(s):  
Genetic Algorithm ◽  
Pareto Front ◽  
Optimization Problems ◽  
Engineering Optimization ◽  
Computation Complexity ◽  
Genetic Population ◽  
Multiobjective Genetic Algorithm ◽  
Multiobjective Optimization Problems ◽  
Engineering Problems ◽  
Objective Vector

This paper proposes a novel multiobjective genetic algorithm (MOGA), Evaluated Preference Genetic Algorithm (EPGA), for efficiently solving engineering multiobjective optimization problems. EPGA utilizes a preferred objective vector to perform a fast multiobjective ranking schema within a low computation complexity O(MNlogN) where N is the size of genetic population and M is the number of objectives. For verifying the proposed algorithms, this paper studies two engineering problems in which multiple mutual-conflicted objectives should be considered. According to the experimental results, the proposed EPGA can efficiently explore the Pareto front and provide very good solution capabilities for the engineering optimization problems.

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.

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