scholarly journals A closer look at drawbacks of minimizing weighted sums of objectives for Pareto set generation in multicriteria optimization problems

1997 ◽  
Vol 14 (1) ◽  
pp. 63-69 ◽  
Author(s):  
I. Das ◽  
J. E. Dennis
Keyword(s):  
Multicriteria Optimization ◽  
Optimization Problems ◽  
Pareto Set ◽  
Weighted Sums

Optimization Problem

2020 ◽  
pp. 276-291
Author(s):  
Albert N. Voronin
Keyword(s):  
Wide Class ◽  
Multicriteria Optimization ◽  
System Approach ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Systemic Approach ◽  
Multicriteria Decision ◽  
Multicriteria Problems ◽  
Linear Scheme ◽  
Non Linear

A systemic approach to solving multicriteria optimization problems is proposed. The system approach allowed uniting the models of individual schemes of compromises into a single integrated structure that adapts to the situation of adopting a multi-criteria solution. The advantage of the concept of non-linear scheme of compromises is the possibility of making a multicriteria decision formally, without the direct participation of a person. The apparatus of the non-linear scheme of compromises, developed as a formalized tool for the study of control systems with conflicting criteria, makes it possible to solve practically multicriteria problems of a wide class.

scholarly journals A New Method for Dynamic Multi-Objective Optimization Based on Segment and Cloud Prediction

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 465 ◽  
Author(s):  
Peng Ni ◽  
Jiale Gao ◽  
Yafei Song ◽  
Wen Quan ◽  
Qinghua Xing
Keyword(s):  
Optimization Problems ◽  
Pareto Set ◽  
Benchmark Problems ◽  
Small Range ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Good Convergence ◽  
Multi Objective ◽  
The Law ◽  
Cloud Theory

In the real world, multi-objective optimization problems always change over time in most projects. Once the environment changes, the distribution of the optimal solutions would also be changed in decision space. Sometimes, such change may obey the law of symmetry, i.e., the minimum of the objective function in such environment is its maximum in another environment. In such cases, the optimal solutions keep unchanged or vibrate in a small range. However, in most cases, they do not obey the law of symmetry. In order to continue the search that maintains previous search advantages in the changed environment, some prediction strategy would be used to predict the operation position of the Pareto set. Because of this, the segment and multi-directional prediction is proposed in this paper, which consists of three mechanisms. First, by segmenting the optimal solutions set, the prediction about the changes in the distribution of the Pareto front can be ensured. Second, by introducing the cloud theory, the distance error of direction prediction can be offset effectively. Third, by using extra angle search, the angle error of prediction caused by the Pareto set nonlinear variation can also be offset effectively. Finally, eight benchmark problems were used to verify the performance of the proposed algorithm and compared algorithms. The results indicate that the algorithm proposed in this paper has good convergence and distribution, as well as a quick response ability to the changed environment.

Definition of the feasible solution set in multicriteria optimization problems with continuous, discrete, and mixed design variables

2009 ◽  
Vol 71 (12) ◽  
pp. e109-e117 ◽  
Author(s):  
Roman Statnikov ◽  
Alex Bordetsky ◽  
Josef Matusov ◽  
Il’ya Sobol’ ◽  
Alexander Statnikov
Keyword(s):  
Multicriteria Optimization ◽  
Feasible Solution ◽  
Optimization Problems ◽  
Solution Set ◽  
Mixed Design ◽  
Design Variables ◽  
Definition Of ◽  
Mixed Design Variables
Sign in / Sign up

Export Citation Format

Share Document