Visualization on Pareto Solutions in Multi-Objective Optimization

2011 ◽  
Author(s):  
Shin-ichi Ito ◽  
Yasue Mitsukura ◽  
Takafumi Saito ◽  
Katsuya Sato ◽  
Shoichiro Fujisawa
Keyword(s):  
Multi Objective Optimization ◽  
Pareto Solutions ◽  
Multi Objective

scholarly journals Search Acceleration of Evolutionary Multi-Objective Optimization Using an Estimated Convergence Point

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 129 ◽  
Author(s):  
Yan Pei ◽  
Jun Yu ◽  
Hideyuki Takagi
Keyword(s):  
Parameter Space ◽  
Statistical Tests ◽  
Distribution Characteristic ◽  
Multi Objective Optimization ◽  
Pareto Improvement ◽  
Pareto Solutions ◽  
Pareto Solution ◽  
Multi Objective ◽  
Objective Space ◽  
Convergence Point

We propose a method to accelerate evolutionary multi-objective optimization (EMO) search using an estimated convergence point. Pareto improvement from the last generation to the current generation supports information of promising Pareto solution areas in both an objective space and a parameter space. We use this information to construct a set of moving vectors and estimate a non-dominated Pareto point from these moving vectors. In this work, we attempt to use different methods for constructing moving vectors, and use the convergence point estimated by using the moving vectors to accelerate EMO search. From our evaluation results, we found that the landscape of Pareto improvement has a uni-modal distribution characteristic in an objective space, and has a multi-modal distribution characteristic in a parameter space. Our proposed method can enhance EMO search when the landscape of Pareto improvement has a uni-modal distribution characteristic in a parameter space, and by chance also does that when landscape of Pareto improvement has a multi-modal distribution characteristic in a parameter space. The proposed methods can not only obtain more Pareto solutions compared with the conventional non-dominant sorting genetic algorithm (NSGA)-II algorithm, but can also increase the diversity of Pareto solutions. This indicates that our proposed method can enhance the search capability of EMO in both Pareto dominance and solution diversity. We also found that the method of constructing moving vectors is a primary issue for the success of our proposed method. We analyze and discuss this method with several evaluation metrics and statistical tests. The proposed method has potential to enhance EMO embedding deterministic learning methods in stochastic optimization algorithms.

scholarly journals On the use of filters to facilitate the post-optimal analysis of the Pareto solutions in multi-objective optimization

2015 ◽  
Vol 74 ◽  
pp. 48-58 ◽  
Author(s):  
E. Antipova ◽  
C. Pozo ◽  
G. Guillén-Gosálbez ◽  
D. Boer ◽  
L.F. Cabeza ◽  
...  
Keyword(s):  
Multi Objective Optimization ◽  
Pareto Solutions ◽  
Multi Objective ◽  
Optimal Analysis

scholarly journals Walking with EMO

2011 ◽  
pp. 300-332
Author(s):  
Jason Teo ◽  
Lynnie D. Neri ◽  
Minh H. Nguyen ◽  
Hussein A. Abbass
Keyword(s):  
Legged Locomotion ◽  
Operational Performance ◽  
Multi Objective Optimization ◽  
Pareto Solutions ◽  
Uncertain Environments ◽  
Multi Objective ◽  
Limb Dynamics

This chapter will demonstrate the various robotics applications that can be achieved using evolutionary multi-objective optimization (EMO) techniques. The main objective of this chapter is to demonstrate practical ways of generating simple legged locomotion for simulated robots with two, four and six legs using EMO. The operational performance as well as complexities of the resulting evolved Pareto solutions that act as controllers for these robots will then be analyzed. Additionally, the operational dynamics of these evolved Pareto controllers in noisy and uncertain environments, limb dynamics and effects of using a different underlying EMO algorithm will also be discussed.

scholarly journals Solving the Asymmetry Multi-Objective Optimization Problem in PPPs under LPVR Mechanism by Bi-Level Programing

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1667
Author(s):  
Feiran Liu ◽  
Jun Liu ◽  
Xuedong Yan
Keyword(s):  
Optimization Problem ◽  
Optimal Strategies ◽  
Decision Makers ◽  
Multi Objective Optimization ◽  
Pareto Solutions ◽  
Present Value ◽  
Public And Private ◽  
The Public ◽  
Multi Objective ◽  
The Cost

Optimizing the cost and benefit allocation among multiple players in a public-private partnership (PPP) project is recognized to be a multi-objective optimization problem (MOP). When the least present value of revenue (LPVR) mechanism is adopted in the competitive procurement of PPPs, the MOP presents asymmetry in objective levels, control variables and action orders. This paper characterizes this asymmetrical MOP in Stackelberg theory and builds a bi-level programing model to solve it in order to support the decision-making activities of both the public and private sectors in negotiation. An intuitive algorithm based on the non-dominated sorting genetic algorithm III (NSGA III) framework is designed to generate Pareto solutions that allow decision-makers to choose optimal strategies from their own criteria. The effectiveness of the model and algorithm is validated via a real case of a highway PPP project. The results reveal that the PPP project will be financially infeasible without the transfer of certain amounts of exterior benefits into supplementary income for the private sector. Besides, the strategy of transferring minimum exterior benefits is more beneficial to the public sector than to users.

scholarly journals A Hybrid Multi-Objective Optimization Method Based on NSGA-II Algorithm and Entropy Weighted TOPSIS for Lightweight Design of Dump Truck Carriage

Machines ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 156
Author(s):  
Rongchao Jiang ◽  
Shukun Ci ◽  
Dawei Liu ◽  
Xiaodong Cheng ◽  
Zhenkuan Pan
Keyword(s):  
Optimal Design ◽  
Lightweight Design ◽  
Dump Truck ◽  
Strength Analysis ◽  
Multi Objective Optimization ◽  
Pareto Solutions ◽  
Entropy Weight ◽  
Nsga Ii ◽  
Multi Objective ◽  
Entropy Weighted

The lightweight design of vehicle components is regarded as a complex optimization problem, which usually needs to achieve two or more optimization objectives. It can be firstly solved by a multi-objective optimization algorithm for generating Pareto solutions, before then seeking the optimal design. However, it is difficult to determine the optimal design for lack of engineering knowledge about ideal and nadir values. Therefore, this paper proposes a multi-objective optimization procedure combined with the NSGA-II algorithm with entropy weighted TOPSIS for the lightweight design of the dump truck carriage. The finite element model of the dump truck carriage was firstly developed for modal analysis under unconstrained free state and strength analysis under the full load and lifting conditions. On this basis, the multi-objective lightweight optimization of the dump truck carriage was carried out based on the Kriging surrogate model and the NSGA-II algorithm. Then, the entropy weight TOPSIS method was employed to select the optimal design of the dump truck from Pareto solutions. The results show that the optimized dump truck carriage achieves a remarkable mass reduction of 81 kg, as much as 3.7%, while its first-order natural frequency and strength performance are slightly improved compared with the original model. Accordingly, the proposed procedure provides an effective way for vehicle lightweight design.

Application of Multi-Objective Optimization Algorithm Based on Physical Programming in Ship Conceptual Design

2014 ◽  
Vol 904 ◽  
pp. 408-413
Author(s):  
Zhai Liu Hao ◽  
Zu Yuan Liu ◽  
Bai Wei Feng
Keyword(s):  
Conceptual Design ◽  
Optimization Algorithm ◽  
Optimization Design ◽  
Uniform Design ◽  
Multi Objective Optimization ◽  
Pareto Solutions ◽  
Physical Programming ◽  
Multi Objective ◽  
Objective Space ◽  
Preference Structures

Ship optimization design is a typical multi-objective problem. The multi-objective optimization algorithm based on physical programming is able to obtain evenly distributed Pareto front. But the number of Pareto solutions and the search positions of pseudo-preference structures still exit some disadvantages that are improved in this paper. Firstly uniform design for mixture experiments is used to arbitrarily set the number of Pareto solutions and evenly distribute the search positions of pseudo-preference structures. Then the objective space is searched by shrinking of search domain and rotation of pseudo-preference structure technology. The optimization quality is able to be improved. Finally, the improved multi-objective optimization algorithm is applied to ship conceptual design optimization and compared with the multi-objective evolutionary algorithm to verify the effectiveness of the improved algorithm.

A Novel Sequential Multi-Objective Optimization Using Anchor Points in the Design Space of Global Variables

2016 ◽  
Vol 138 (12) ◽  
Author(s):  
Jianhua Zhou ◽  
Mian Li ◽  
Min Xu
Keyword(s):  
Design Space ◽  
Computational Cost ◽  
Global Solutions ◽  
Multiple Objectives ◽  
Multi Objective Optimization ◽  
Pareto Solutions ◽  
Data Set ◽  
Multi Objective ◽  
Global Variables ◽  
Anchor Points

Multi-objective problems are encountered in many engineering applications and multi-objective optimization (MOO) approaches have been proposed to search for Pareto solutions. Due to the nature of searching for multiple optimal solutions, the computational efforts of MOO can be a serious concern. To improve the computational efficiency, a novel efficient sequential MOO (S-MOO) approach is proposed in this work, in which anchor points in the design space for global variables are fully utilized and a data set for global solutions is generated to guide the search for Pareto solutions. Global variables refer to those shared by more than one objective or constraint, while local variables appear only in one objective and corresponding constraints. As a matter of fact, it is the existence of global variables that leads to couplings among the multiple objectives. The proposed S-MOO breaks the couplings among multiple objectives (and constraints) by distinguishing the global variables, and thus all objectives are optimized in a sequential manner within each iteration while all iterations can be processed in parallel. The computational cost per produced Pareto point is reduced and a well-spread Pareto front is obtained. Six numerical and engineering examples including two three-objective problems are tested to demonstrate the applicability and efficiency of the proposed approach.

A novel multi-objective optimization algorithm for Pareto design of a fuzzy full state feedback linearization controller applied on a ball and wheel system

2021 ◽  
pp. 014233122110561
Author(s):  
Rahmat Abedzadeh Maafi ◽  
Shahram Etemadi Haghighi ◽  
Mohammad Javad Mahmoodabadi
Keyword(s):  
Optimization Algorithm ◽  
Feedback Linearization ◽  
State Feedback ◽  
Standard Test ◽  
Open Loop ◽  
Multi Objective Optimization ◽  
Pareto Solutions ◽  
Multi Objective ◽  
Full State ◽  
Full State Feedback

The control and stabilization of a ball and wheel system around the equilibrium point are challenging tasks because it is an underactuated, nonlinear, and open-loop unstable plant. In this paper, Pareto design of a Fuzzy Full State Feedback Linearization Controller (FFSFLC) for the ball and wheel system based upon a novel multi-objective optimization algorithm is introduced. To this end, at first, a full state feedback linearization approach is employed to stabilize the dynamics of the system. Next, appropriate fuzzy systems are determined to tune the control gains. Then, a new multi-objective optimization algorithm is utilized to promote the proposed control scheme. This optimization algorithm is a combination of Simulated Annealing (SA) and Artificial Bee Colony (ABC) approaches benefiting advantages of the non-dominated Pareto solutions. To evaluate the capabilities of the suggested algorithm, its optimal solutions of several standard test functions are compared with those of five renowned multi-objective optimization algorithms. The results confirm that the proposed hybrid algorithm yields closer non-dominated Pareto solutions to the true optimal Pareto front with shorter runtimes than other algorithms. After selecting proper objective functions, multi-objective optimization of FFSFLC for the ball and wheel system is performed, and the results are compared with previous works. Simulations illustrate that the proposed strategies can accurately converge the system states to the desired conditions and yield superior robustness against disturbance signals in comparison with former studies.

Some Preliminary Results on the Development and Comparison of a New Multi-Objective Genetic Algorithm

2001 ◽  
Author(s):  
A. Farhang-Mehr ◽  
J. Wu ◽  
S. Azarm
Keyword(s):  
Genetic Algorithm ◽  
Optimization Problem ◽  
Quality Metrics ◽  
Initial Population ◽  
Multi Objective Optimization ◽  
Pareto Solutions ◽  
Preliminary Results ◽  
Multi Objective ◽  
Multi Objective Genetic Algorithm ◽  
Speed Reducer

Abstract Some preliminary results for a new multi-objective genetic algorithm (MOGA) are presented. This new algorithm aims at obtaining the fullest possible representation of observed Pareto solutions to a multi-objective optimization problem. The algorithm, hereafter called entropy-based MOGA (or E-MOGA), is based on an application of the concepts from the statistical theory of gases to a MOGA. A few set quality metrics are introduced and used for a comparison of the E-MOGA to a previously published MOGA. Due to the stochastic nature of the MOGA, confidence intervals with a 95% confidence level are calculated for the quality metrics based on the randomness in the initial population. An engineering example, namely the design of a speed reducer is used to demonstrate the performance of E-MOGA when compared to the previous MOGA.

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