Knowledge Extraction from Pareto Solutions in Multi-Objective Engineering Design Problem Based on Geodetic Distance between Objective Space and Design Variable Space

2013 ◽  
Vol 3 (2) ◽  
pp. 70-79
Author(s):  
Fumiya Kudo ◽  
Yoshikawa Tomohiro
Keyword(s):  
Engineering Design ◽  
Design Variable ◽  
Design Problem ◽  
Knowledge Extraction ◽  
Pareto Solutions ◽  
Multi Objective ◽  
Engineering Design Problem ◽  
Objective Space ◽  
Variable Space

Analysis of Pareto Solutions Based on Non-Correspondence in Spread Between Objective Space and Design Variable Space

2015 ◽  
Vol 19 (5) ◽  
pp. 681-687 ◽  
Author(s):  
Toru Yoshida ◽  
◽  
Tomohiro Yoshikawa
Keyword(s):  
Design Variable ◽  
Optimization Problems ◽  
Design Knowledge ◽  
Pareto Solutions ◽  
Three Solutions ◽  
Genetic Search ◽  
Multi Objective ◽  
Engineering Design Problems ◽  
Objective Space ◽  
Variable Space

Recently, many studies have been conducted on Multi-Objective Genetic Algorithm (MOGA), in which Genetic Algorithms are applied to Multi-objective Optimization Problems (MOPs). Among various applications, MOGA is also applied to engineering design problems, which require not only high-performance Pareto solutions to be obtained, but also an analysis of the obtained Pareto solutions and extraction of design knowledge about the problem itself. In order to analyze the Pareto solutions obtained by MOGA, it is necessary to consider the objective space and the design variable space. The aim of this study is to extract and analyze solutions of relevant interest to designers. In this paper, we propose three solutions to analyze and extract design knowledge from MOGA. (1) We define “Non-Correspondence in Spread” between the objective space and the design variable space. (2) We try to extract the Non-Correspondence area in Spread using the index defined in this paper. (3) We apply the defined index to genetic search to obtain Pareto solutions that have different design variables and similar fitness values. This paper applies the above index to the trajectory design optimization problem and extracts Non-Correspondence area in Spread from the obtained Pareto solutions. This paper also shows that robust Pareto solutions can be obtained using genetic search using the defined index.

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 Mapping Assets of Diverse Groups for Chemical Engineering Design Problem Framing Ability

2016 ◽  
Author(s):  
Vanessa Svihla ◽  
Abhaya Datye ◽  
Jamie Gomez ◽  
Victor Law ◽  
Sophia Bowers
Keyword(s):  
Engineering Design ◽  
Design Problem ◽  
Chemical Engineering ◽  
Problem Framing ◽  
Engineering Design Problem ◽  
Diverse Groups

scholarly journals CURRICULUM AS AN ENGINEERING DESIGN PROBLEM

2011 ◽  
Author(s):  
D. W. Ruth ◽  
M. G. Britton
Keyword(s):  
Engineering Design ◽  
Design Process ◽  
Design Problem ◽  
Mechanical Engineering ◽  
Engineering Program ◽  
Arts And Humanities ◽  
Engineering Design Process ◽  
The Arts ◽  
Engineering Design Problem ◽  
Rules Of Thumb

If the teaching of engineering is indeed the practice of engineering, then it stands to reason that the development of engineering curricula can be treated as an engineering design problem. In this paper, the authors apply the engineering design process to develop a list of courses, for a Mechanical Engineering Program, that conforms to the constraints of the Canadian system of engineering accreditation. For the purpose of this exercise, the following steps are used to define the engineering design process: identical and delimit the problem, establish the outline of the solution (and alternatives), break the problem into its constituent parts, analyze the parts, synthesize the parts into a final configuration, and document the solution. The limits and constraints on the solution are based on the criteria specified by the Canadian Engineering Accreditation Board (CEAB), the syllabus specified by the Canadian Engineering Qualifications Board (CEQB), some common rules-of-thumb, and previously published work by the authors. By utilizing the engineering design process, schools of engineering and applied science can ensure that their curricula, at least at the level of the course specification, will conform to the CEAB and CEQB requirements. As a final exercise, variations on the curriculum are studied to analyze the possibility of introducing such additional elements as options and minors, expanded studies in the arts and humanities, and development of skills in additional languages.

APPLICATION OF TAYLOR-NEWTON HOMOTOPY METHOD FOR SOLVING ELECTRICAL ENGINEERING DESIGN PROBLEM

2009 ◽  
Author(s):  
Talib Hashim Hasan ◽  
Mohammed Azram ◽  
Jamal Ibrahim Daoua ◽  
Abdul Halim Hakim ◽  
Pandian Vasant ◽  
...  
Keyword(s):  
Engineering Design ◽  
Design Problem ◽  
Electrical Engineering ◽  
Homotopy Method ◽  
Engineering Design Problem ◽  
Newton Homotopy

scholarly journals Variation Rate to Maintain Diversity in Decision Space within Multi-Objective Evolutionary Algorithms

2019 ◽  
Vol 24 (3) ◽  
pp. 82 ◽  
Author(s):  
Oliver Cuate ◽  
Oliver Schütze
Keyword(s):  
Significant Loss ◽  
Selection Strategy ◽  
Benchmark Problems ◽  
Decision Space ◽  
Multi Objective ◽  
Approximation Quality ◽  
Selection Strategies ◽  
Objective Space ◽  
Variation Rate ◽  
Variable Space

The performance of a multi-objective evolutionary algorithm (MOEA) is in most cases measured in terms of the populations’ approximation quality in objective space. As a consequence, most MOEAs focus on such approximations while neglecting the distribution of the individuals of their populations in decision space. This, however, represents a potential shortcoming in certain applications as in many cases one can obtain the same or very similar qualities (measured in objective space) in several ways (measured in decision space). Hence, a high diversity in decision space may represent valuable information for the decision maker for the realization of a given project. In this paper, we propose the Variation Rate, a heuristic selection strategy that aims to maintain diversity both in decision and objective space. The core of this strategy is the proper combination of the averaged distance applied in variable space together with the diversity mechanism in objective space that is used within a chosen MOEA. To show the applicability of the method, we propose the resulting selection strategies for some of the most representative state-of-the-art MOEAs and show numerical results on several benchmark problems. The results demonstrate that the consideration of the Variation Rate can greatly enhance the diversity in decision space for all considered algorithms and problems without a significant loss in the approximation qualities in objective space.

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