scholarly journals Parametric Control to Second-Order Quasi-Linear Systems Based on Dynamic Compensator and Multi-Objective Optimization

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 67287-67304 ◽  
Author(s):  
Yin-Dong Liu ◽  
Da-Wei Zhang ◽  
Li-Mei Wang ◽  
Da-Ke Gu
Keyword(s):  
Linear Systems ◽  
Second Order ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Parametric Control ◽  
Dynamic Compensator

scholarly journals Improved NSGA-III with Second-Order Difference Random Strategy for Dynamic Multi-Objective Optimization

Processes ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 911
Author(s):  
Haijuan Zhang ◽  
Gai-Ge Wang ◽  
Junyu Dong ◽  
Amir H. Gandomi
Keyword(s):  
State Of The Art ◽  
Second Order ◽  
Test Functions ◽  
Multi Objective Optimization ◽  
Order Difference ◽  
Good Convergence ◽  
Multi Objective ◽  
Random Strategy ◽  
Single Strategy ◽  
Real World Problems

Most real-world problems that have two or three objectives are dynamic, and the environment of the problems may change as time goes on. For the purpose of solving dynamic multi-objective problems better, two proposed strategies (second-order difference strategy and random strategy) were incorporated with NSGA-III, namely SDNSGA-III. When the environment changes in SDNSGA-III, the second-order difference strategy and random strategy are first used to improve the individuals in the next generation population, then NSGA-III is employed to optimize the individuals to obtain optimal solutions. Our experiments were conducted with two primary objectives. The first was to test the values of the metrics mean inverted generational distance (MIGD), mean generational distance (MGD), and mean hyper volume (MHV) on the test functions (Fun1 to Fun6) via the proposed algorithm and the four state-of-the-art algorithms. The second aim was to compare the metrics’ value of NSGA-III with single strategy and SDNSGA-III, proving the efficiency of the two strategies in SDNSGA-III. The comparative data obtained from the experiments demonstrate that SDNSGA-III has good convergence and diversity compared with four other evolutionary algorithms. What is more, the efficiency of second-order difference strategy and random strategy was also analyzed in this paper.

Second-Order Composed Radial Derivatives of the Benson Proper Perturbation Map for Parametric Multi-Objective Optimization Problems

2020 ◽  
Vol 37 (04) ◽  
pp. 2040011
Author(s):  
Qilin Wang ◽  
Xiaoyan Zhang
Keyword(s):  
Lipschitz Continuity ◽  
Optimization Problems ◽  
Second Order ◽  
Proper Efficiency ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Benson Proper Efficiency ◽  
Perturbation Map ◽  
Derivatives Of ◽  
Cone Convexity

In this paper, we introduce second-order composed radial derivatives of set-valued maps and establish some of its properties. By applying this second-order derivative, we obtain second-order sensitivity results for parametric multi-objective optimization problems under the Benson proper efficiency without assumptions of cone-convexity and Lipschitz continuity. Some of our results improve and derive the recent corresponding ones in the literature.

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