Localization of Pareto-Optimal Set in Multi-objective Minimax Problems

2021 ◽  
pp. 260-272
Author(s):  
Dmitry Balandin ◽  
Ruslan Biryukov ◽  
Mark Kogan
Keyword(s):  
Minimax Problems ◽  
Pareto Optimal ◽  
Multi Objective ◽  
Pareto Optimal Set ◽  
Optimal Set

scholarly journals Multi-Objective Optimization of Impedance Parameters in a Prosthesis Test Robot

2015 ◽  
Author(s):  
Poya Khalaf ◽  
Hanz Richter ◽  
Antonie J. van den Bogert ◽  
Dan Simon
Keyword(s):  
Control System ◽  
Motion Tracking ◽  
Optimization Problem ◽  
Peak Load ◽  
Pareto Optimal ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Pareto Optimal Set ◽  
Rms Error ◽  
Optimal Set

We design a control system for a prosthesis test robot that was previously developed for transfemoral prosthesis design and test. The robot’s control system aims to mimic human walking in the sagittal plane. It has been seen in previous work that trajectory control alone fails to produce human-like forces. Therefore, we utilize an impedance controller to achieve reasonable tracking of motion and force simultaneously. However, these objectives conflict. Impedance control design can therefore be viewed as a multi-objective optimization problem. We use an evolutionary multi-objective strategy called Multi-Objective Invasive Weed Optimization (MOIWO) to design the impedance controller. The multi-objective optimization problem admits a set of equally valid alternative solutions known as the Pareto optimal set. We use a pseudo weight vector approach to select a single solution from the Pareto optimal set. Simulation results show that a solution that is selected for pure motion tracking performs very accurate motion tracking (RMS error of 0.06 cm) but fails to produce the desired forces (RMS error of 70% peak load). On the other hand, a solution that is selected for pure force tracking successfully tracks the desired force (RMS error of 12.7% peak load) at the expense of motion trajectory errors (RMS error of 4.5 cm).

Pareto Front Estimation for Decision Making

2014 ◽  
Vol 22 (4) ◽  
pp. 651-678 ◽  
Author(s):  
Ioannis Giagkiozis ◽  
Peter J. Fleming
Keyword(s):  
Pareto Front ◽  
Computational Cost ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Number Of Solutions ◽  
Multi Objective ◽  
Pareto Optimal Set ◽  
Problem Instances ◽  
Optimal Set ◽  
Optimisation Algorithms

The set of available multi-objective optimisation algorithms continues to grow. This fact can be partially attributed to their widespread use and applicability. However, this increase also suggests several issues remain to be addressed satisfactorily. One such issue is the diversity and the number of solutions available to the decision maker (DM). Even for algorithms very well suited for a particular problem, it is difficult—mainly due to the computational cost—to use a population large enough to ensure the likelihood of obtaining a solution close to the DM's preferences. In this paper we present a novel methodology that produces additional Pareto optimal solutions from a Pareto optimal set obtained at the end run of any multi-objective optimisation algorithm for two-objective and three-objective problem instances.

Multi-objective optimization of a welding process by the estimation of the Pareto optimal set

2011 ◽  
Vol 38 (7) ◽  
pp. 8045-8053 ◽  
Author(s):  
Luis M. Torres-Treviño ◽  
Felipe A. Reyes-Valdes ◽  
Victor López ◽  
Rolando Praga-Alejo
Keyword(s):  
Welding Process ◽  
Pareto Optimal ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Pareto Optimal Set ◽  
Optimal Set

scholarly journals Multi-Objective Constructal Optimization for Marine Condensers

Energies ◽  
2021 ◽  
Vol 14 (17) ◽  
pp. 5545
Author(s):  
Huijun Feng ◽  
Wei Tang ◽  
Lingen Chen ◽  
Junchao Shi ◽  
Zhixiang Wu
Keyword(s):  
Heat Transfer ◽  
Entropy Generation Rate ◽  
Working Fluid ◽  
Pareto Optimal ◽  
Pumping Power ◽  
Multi Objective ◽  
Pareto Optimal Set ◽  
Deviation Index ◽  
Optimal Set ◽  
Single Objective

A marine condenser with exhausted steam as the working fluid is researched in this paper. Constructal designs of the condenser are numerically conducted based on single and multi-objective optimizations, respectively. In the single objective optimization, there is an optimal dimensionless tube diameter leading to the minimum total pumping power required by the condenser. After constructal optimization, the total pumping power is decreased by 42.3%. In addition, with the increase in mass flow rate of the steam and heat transfer area and the decrease in total heat transfer rate, the minimum total pumping power required by the condenser decreases. In the multi-objective optimization, the Pareto optimal set of the entropy generation rate and total pumping power is gained. The optimal results gained by three decision methods in the Pareto optimal set and single objective optimizations are compared by the deviation index. The optimal construct gained by the TOPSIS decision method corresponding to the smallest deviation index is recommended in the optimal design of the condenser. These research ideas can also be used to design other heat transfer devices.

PCA-assisted reproduction for continuous multi-objective optimization with complicated Pareto optimal set

2021 ◽  
Vol 60 ◽  
pp. 100795
Author(s):  
Rui Wang ◽  
Nan-Jiang Dong ◽  
Dun-Wei Gong ◽  
Zhong-Bao Zhou ◽  
Shi Cheng ◽  
...  
Keyword(s):  
Assisted Reproduction ◽  
Pareto Optimal ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Pareto Optimal Set ◽  
Optimal Set

On the Pareto Optimality of Ashby's Selection Method for Beams Under Bending

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Giorgio Previati ◽  
Gianpiero Mastinu ◽  
Massimiliano Gobbi
Keyword(s):  
Cross Section ◽  
Pareto Optimality ◽  
Elastic Stability ◽  
Selection Method ◽  
Structural Safety ◽  
Pareto Optimal ◽  
Multi Objective ◽  
Pareto Optimal Set ◽  
Mass Minimization ◽  
Optimal Set

The paper deals with the problem of choosing the material and the cross section of a beam subjected to bending under structural safety, elastic stability, and available room constraints. An extension of the theory proposed by Ashby is presented. The Pareto-optimal set for the multi-objective problem of stiffness maximization and mass minimization under elastic stability, structural safety, and available room constraints for a beam under bending is derived analytically. The Pareto-optimal set is compared with the solution of the Ashby's selection method.

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