On Convergence of Multi-objective Pareto Front: Perturbation Method

2007 ◽  
pp. 443-456
Author(s):  
Raziyeh Farmani ◽  
Dragan A. Savic ◽  
Godfrey A. Walters
Keyword(s):  
Perturbation Method ◽  
Pareto Front ◽  
Multi Objective

Applications of Multiple Objective Genetic Algorithms in the Optimization Design of Tracked Self-Moving Power’s Layout

2013 ◽  
Vol 307 ◽  
pp. 161-165
Author(s):  
Hai Jin ◽  
Jin Fa Xie
Keyword(s):  
Optimization Design ◽  
Pareto Front ◽  
Layout Optimization ◽  
Multiple Objective ◽  
Multi Objective Optimization ◽  
Layout Problem ◽  
Basic Principles ◽  
Multi Objective ◽  
Multi Objective Genetic Algorithm ◽  
Set Up

A multi-objective genetic algorithm is applied into the layout optimization of tracked self-moving power. The layout optimization mathematical model was set up. Then introduced the basic principles of NSGA-Ⅱ, which is a Pareto multi-objective optimization algorithm. Finally, NSGA-Ⅱwas presented to solve the layout problem. The algorithm was proved to be effective by some practical examples. The results showed that the algorithm can spread toward the whole Pareto front, and provide many reasonable solutions once for all.

scholarly journals Multi-Objective Optimization Design of an Electrohydrostatic Actuator Based on a Particle Swarm Optimization Algorithm and an Analytic Hierarchy Process

Energies ◽  
2018 ◽  
Vol 11 (9) ◽  
pp. 2426 ◽  
Author(s):  
Bo Yu ◽  
Shuai Wu ◽  
Zongxia Jiao ◽  
Yaoxing Shang
Keyword(s):  
Particle Swarm Optimization ◽  
Power Consumption ◽  
Analytic Hierarchy Process ◽  
Optimization Design ◽  
Pareto Front ◽  
Multi Objective Optimization ◽  
Analytic Hierarchy ◽  
Swarm Optimization ◽  
Multi Objective ◽  
Hierarchy Process

During the last few years, the concept of more-electric aircraft has been pushed ahead by industry and academics. For a more-electric actuation system, the electrohydrostatic actuator (EHA) has shown its potential for better reliability, low maintenance cost and reducing aircraft weight. Designing an EHA for aviation applications is a hard task, which should balance several inconsistent objectives simultaneously, such as weight, stiffness and power consumption. This work presents a method to obtain the optimal EHA, which combines multi-objective optimization with a synthetic decision method, that is, a multi-objective optimization design method, that can combine designers’ preferences and experiences. The evaluation model of an EHA in terms of weight, stiffness and power consumption is studied in the first section. Then, a multi-objective particle swarm optimization (MOPSO) algorithm is introduced to obtain the Pareto front, and an analytic hierarchy process (AHP) is applied to help find the optimal design in the Pareto front. A demo of an EHA design illustrates the feasibility of the proposed method.

scholarly journals The dilemma between eliminating dominance-resistant solutions and preserving boundary solutions of extremely convex Pareto fronts

2021 ◽  
Author(s):  
Zhenkun Wang ◽  
Qingyan Li ◽  
Qite Yang ◽  
Hisao Ishibuchi
Keyword(s):  
Evolutionary Algorithms ◽  
Coping Strategies ◽  
Test Problem ◽  
Pareto Front ◽  
Optimization Problems ◽  
Feasible Region ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Pareto Fronts ◽  
Boundary Solutions

AbstractIt has been acknowledged that dominance-resistant solutions (DRSs) extensively exist in the feasible region of multi-objective optimization problems. Recent studies show that DRSs can cause serious performance degradation of many multi-objective evolutionary algorithms (MOEAs). Thereafter, various strategies (e.g., the $$\epsilon $$ ϵ -dominance and the modified objective calculation) to eliminate DRSs have been proposed. However, these strategies may in turn cause algorithm inefficiency in other aspects. We argue that these coping strategies prevent the algorithm from obtaining some boundary solutions of an extremely convex Pareto front (ECPF). That is, there is a dilemma between eliminating DRSs and preserving boundary solutions of the ECPF. To illustrate such a dilemma, we propose a new multi-objective optimization test problem with the ECPF as well as DRSs. Using this test problem, we investigate the performance of six representative MOEAs in terms of boundary solutions preservation and DRS elimination. The results reveal that it is quite challenging to distinguish between DRSs and boundary solutions of the ECPF.

scholarly journals A New Framework of Evolutionary Multi-Objective Algorithms with an Unbounded External Archive

2020 ◽  
Author(s):  
Hisao Ishibuchi ◽  
Lie Meng Pang ◽  
Ke Shang
Keyword(s):  
Pareto Front ◽  
Algorithm Design ◽  
Future Research ◽  
Multi Objective ◽  
Final Population ◽  
External Archive ◽  
Processing Procedure ◽  
Distributed Solutions ◽  
New Framework ◽  
Main Characteristic Feature

This paper proposes a new framework for the design of evolutionary multi-objective optimization (EMO) algorithms. The main characteristic feature of the proposed framework is that the optimization result of an EMO algorithm is not the final population but a subset of the examined solutions during its execution. As a post-processing procedure, a pre-specified number of solutions are selected from an unbounded external archive where all the examined solutions are stored. In the proposed framework, the final population does not have to be a good solution set. The point of the algorithm design is to examine a wide variety of solutions over the entire Pareto front and to select well-distributed solutions from the archive. In this paper, first we explain difficulties in the design of EMO algorithms in the existing two frameworks: non-elitist and elitist. Next, we propose the new framework of EMO algorithms. Then we demonstrate advantages of the proposed framework over the existing ones through computational experiments. Finally we suggest some interesting and promising future research topics.

scholarly journals Multi-objective dynamic programming with limited precision

2021 ◽  
Author(s):  
L. Mandow ◽  
J. L. Perez-de-la-Cruz ◽  
N. Pozas
Keyword(s):  
Dynamic Programming ◽  
Pareto Front ◽  
Dynamic Programming Algorithm ◽  
Programming Algorithm ◽  
Value Iteration ◽  
Multi Objective ◽  
All Solutions ◽  
Markov Decision ◽  
Objective Value ◽  
Limited Precision

AbstractThis paper addresses the problem of approximating the set of all solutions for Multi-objective Markov Decision Processes. We show that in the vast majority of interesting cases, the number of solutions is exponential or even infinite. In order to overcome this difficulty we propose to approximate the set of all solutions by means of a limited precision approach based on White’s multi-objective value-iteration dynamic programming algorithm. We prove that the number of calculated solutions is tractable and show experimentally that the solutions obtained are a good approximation of the true Pareto front.

scholarly journals Integration of Operability Framework and Pareto Optimal Front to Calculate Optimal Condition of Ethane Cracking Process

2020 ◽  
pp. 105-113
Author(s):  
M. Farsi
Keyword(s):  
Pareto Front ◽  
Optimal Solution ◽  
Optimization Procedure ◽  
Operating Conditions ◽  
Base Case ◽  
Pareto Optimal ◽  
Multi Objective Optimization ◽  
Pareto Optimal Front ◽  
Multi Objective ◽  
Cracking Process

The main aim of this research is to present an optimization procedure based on the integration of operability framework and multi-objective optimization concepts to find the single optimal solution of processes. In this regard, the Desired Pareto Index is defined as the ratio of desired Pareto front to the Pareto optimal front as a quantitative criterion to analyze the performance of chemical processes. The Desired Pareto Front is defined as a part of the Pareto front that all outputs are improved compared to the conventional operating condition. To prove the efficiency of proposed optimization method, the operating conditions of ethane cracking process is optimized as a base case. The ethylene and methane production rates are selected as the objectives in the formulated multi-objective optimization problem. Based on the simulation results, applying the obtained operating conditions by the proposed optimization procedure on the ethane cracking process improve ethylene production by about 3% compared to the conventional condition.  

Toward the Use of Pareto Performance Solutions and Pareto Robustness Solutions for Multi-Objective Robust Optimization Problems

2012 ◽  
Author(s):  
Weijun Wang ◽  
Stéphane Caro ◽  
Fouad Bennis ◽  
Oscar Brito Augusto
Keyword(s):  
Robust Optimization ◽  
Pareto Front ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Multi Objective Optimization ◽  
Robust Solutions ◽  
Multi Objective ◽  
Robust Optimization Problem ◽  
Design Solutions ◽  
Further Development

For Multi-Objective Robust Optimization Problem (MOROP), it is important to obtain design solutions that are both optimal and robust. To find these solutions, usually, the designer need to set a threshold of the variation of Performance Functions (PFs) before optimization, or add the effects of uncertainties on the original PFs to generate a new Pareto robust front. In this paper, we divide a MOROP into two Multi-Objective Optimization Problems (MOOPs). One is the original MOOP, another one is that we take the Robustness Functions (RFs), robust counterparts of the original PFs, as optimization objectives. After solving these two MOOPs separately, two sets of solutions come out, namely the Pareto Performance Solutions (PP) and the Pareto Robustness Solutions (PR). Make a further development on these two sets, we can get two types of solutions, namely the Pareto Robustness Solutions among the Pareto Performance Solutions (PR(PP)), and the Pareto Performance Solutions among the Pareto Robustness Solutions (PP(PR)). Further more, the intersection of PR(PP) and PP(PR) can represent the intersection of PR and PP well. Then the designer can choose good solutions by comparing the results of PR(PP) and PP(PR). Thanks to this method, we can find out the optimal and robust solutions without setting the threshold of the variation of PFs nor losing the initial Pareto front. Finally, an illustrative example highlights the contributions of the paper.

scholarly journals Direct Tracking of the Pareto Front of a Multi-Objective Optimization Problem

2020 ◽  
Vol 8 (9) ◽  
pp. 699
Author(s):  
Daniele Peri
Keyword(s):  
Pareto Front ◽  
Optimization Problem ◽  
Ship Design ◽  
Multi Objective Optimization ◽  
Design Problems ◽  
Multi Objective ◽  
Regular Sampling ◽  
Normal Boundary ◽  
Direct Tracking ◽  
Local Sampling

In this paper, some methodologies aimed at the identification of the Pareto front of a multi-objective optimization problem are presented and applied. Three different approaches are presented: local sampling, Pareto front resampling and Normal Boundary Intersection (NBI). A first approximation of the Pareto front is obtained by a regular sampling of the design space, and then the Pareto front is improved and enriched using the other two above mentioned techniques. A detailed Pareto front is obtained for an optimization problem where algebraic objective functions are applied, also in comparison with standard techniques. Encouraging results are also obtained for two different ship design problems. The use of the algebraic functions allows for a comparison with the real Pareto front, correctly detected. The variety of the ship design problems allows for a generalization of the applicability of the methodology.

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