Formulation of Multicriterion Design Optimization Problems for Solution With Scalar Numerical Optimization Methods

2004 ◽  
Vol 48 (01) ◽  
pp. 61-76 ◽  
Author(s):  
Michael G. Parsons ◽  
Randall L. Scott
Keyword(s):  
Design Optimization ◽  
Numerical Optimization ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Pareto Optimum ◽  
Compromise Solution ◽  
Design Problems ◽  
Common Definition ◽  
Bulk Carriers ◽  
Definition Of

Most marine design problems involve multiple conflicting criteria, objectives, or goals. The most common definition of the multicriterion optimum is the Pareto optimum, which usually results in a set of solutions. Design teams, however, need to arrive at a single answer that provides an acceptable compromise solution within the Pareto set. Methods have been developed to solve multicriterion optimization problems using a number of related definitions of the compromise solution or "optimum" in the presence of multiple conflicting criteria. The most common of these definitions are reviewed and their solutions are formulated in a consistent form utilizing a preference function that will allow their solution using conventional scalar criterion numerical optimization methods. This approach permits the use and comparison of the various definitions of the multicriterion "optimum" with modest additional computation. The design team can use these results to guide its selection of the solution that best reflects their design intent in a particular case. A sixparameter, three-criterion, 14-to 16-constraint conceptual marine design optimization example adapted from the literature is presented to illustrate the use of this approach. The results for the various definitions of the multicriterion optimum for Panamax and post-Panamax bulk carriers are presented for comparison.

Optimization of Machine System Designs Using Hierarchical Decomposition Based on Criteria Influence

2002 ◽  
Author(s):  
Masataka Yoshimura ◽  
Kazuhiro Izui ◽  
Shigeaki Komori
Keyword(s):  
Design Optimization ◽  
Structural Model ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Hierarchical Level ◽  
Hierarchical Optimization ◽  
Pareto Optimum ◽  
Local Optimum ◽  
Optimization Strategy ◽  
Basic Characteristics

Machine product designs routinely have so many mutually related characteristics that common design optimization methods often result in an unsatisfactory local optimum solution. In order to overcome this problem, this paper proposes a design optimization method based on the clarification of the conflicting and cooperative relationships among the characteristics. First of all, each performance characteristic is divided into simpler basic characteristics according to its structure. Next, the relationships among the basic characteristics are systematically identified and clarified. Then, based on this clarification, the optimization problem is expressed using hierarchical constructions of these basic characteristics and design variables related to the most basic characteristics. Finally, an optimization strategy and detailed hierarchical optimization procedures are constructed, after clarifying the influence levels of each basic characteristic upon the objective functions and setting a core characteristic for the product under consideration. Here, optimizations are sequentially repeated starting with the basic optimal unit group at the bottom hierarchical level and proceeding to higher levels by the hierarchical genetic algorithms. Then, the Pareto optimum solutions at the top hierarchical level are obtained. With the proposed optimization methods, optimization can be more easily applied after the optimization problems have been simplified by decomposition. In doing so, the volume of design spaces for each optimization is reduced, while useful and unique rules and laws may be uncovered. The optimization strategy expressed by the hierarchical structures can be used for the optimization of similar product designs, which realize these breakthroughs, yielding improved product performances. The proposed method is applied to a machine-tool structural model.

scholarly journals Recent Design Optimization Methods for Energy-Efficient Electric Motors and Derived Requirements for a New Improved Method—Part 1

Proceedings ◽  
2018 ◽  
Vol 2 (22) ◽  
pp. 1400
Author(s):  
Johannes Schmelcher ◽  
Max Kleine Büning ◽  
Kai Kreisköther ◽  
Dieter Gerling ◽  
Achim Kampker
Keyword(s):  
Rare Earth ◽  
Design Optimization ◽  
Energy Efficient ◽  
Degrees Of Freedom ◽  
High Efficiency ◽  
Optimization Problems ◽  
Computing Time ◽  
Optimization Methods ◽  
Electric Motors ◽  
Electric Cars

Energy-efficient electric motors are gathering an increased attention since they are used in electric cars or to reduce operational costs, for instance. Due to their high efficiency, permanent-magnet synchronous motors are used progressively more. However, the need to use rare-earth magnets for such high-efficiency motors is problematic not only in regard to the cost but also in socio-political and environmental aspects. Therefore, an increasing effort has to be put in finding the best design possible. The goals to achieve are, among others, to reduce the amount of rare-earth magnet material but also to increase the efficiency. In the first part of this multipart paper, characteristics of optimization problems in engineering and general methods to solve them are presented. In part two, different approaches to the design optimization problem of electric motors are highlighted. The last part will evaluate the different categories of optimization methods with respect to the criteria: degrees of freedom, computing time and the required user experience. As will be seen, there is a conflict of objectives regarding the criteria mentioned above. Requirements, which a new optimization method has to fulfil in order to solve the conflict of objectives will be presented in this last paper.

Multi Objective Design Optimization of Two Bar Truss Using NSGA II and TOPSIS

2014 ◽  
Vol 984-985 ◽  
pp. 419-424
Author(s):  
P. Sabarinath ◽  
M.R. Thansekhar ◽  
R. Saravanan
Keyword(s):  
Design Optimization ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Nsga Ii ◽  
Multi Objective ◽  
Total Displacement ◽  
Design Variables ◽  
Conflicting Objectives

Arriving optimal solutions is one of the important tasks in engineering design. Many real-world design optimization problems involve multiple conflicting objectives. The design variables are of continuous or discrete in nature. In general, for solving Multi Objective Optimization methods weight method is preferred. In this method, all the objective functions are converted into a single objective function by assigning suitable weights to each objective functions. The main drawback lies in the selection of proper weights. Recently, evolutionary algorithms are used to find the nondominated optimal solutions called as Pareto optimal front in a single run. In recent years, Non-dominated Sorting Genetic Algorithm II (NSGA-II) finds increasing applications in solving multi objective problems comprising of conflicting objectives because of low computational requirements, elitism and parameter-less sharing approach. In this work, we propose a methodology which integrates NSGA-II and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) for solving a two bar truss problem. NSGA-II searches for the Pareto set where two bar truss is evaluated in terms of minimizing the weight of the truss and minimizing the total displacement of the joint under the given load. Subsequently, TOPSIS selects the best compromise solution.

The Complementary Roles of Symbolic Computing and Numerical Optimization in Engineering Design Software

1987 ◽  
Author(s):  
R. Ellsworth ◽  
A. Parkinson ◽  
F. Cain
Keyword(s):  
Expert System ◽  
Engineering Design ◽  
Numerical Optimization ◽  
Optimization Methods ◽  
Design Rule ◽  
Rule Base ◽  
Design Problems ◽  
Symbolic Computing ◽  
Engineering Design Problems ◽  
Trial And Error Method

Abstract In many engineering design problems, the designer converges upon a good design by iteratively evaluating a mathematical model of the design problem. The trial-and-error method used by the designer to converge upon a solution may be complex and difficult to capture in an expert system. It is suggested that in many cases, the design rule base could be made significantly smaller and more maintainable by using numerical optimization methods to identify the best design. The expert system is then used to define the optimization problem and interpret the solution, as well as to apply the true heuristics to the problem. An example of such an expert system is presented for the design of a valve anti-cavitation device. Because of the capabilities provided by the optimization software, the expert system has been able to outperform the expert in the test cases evaluated so far.

Development of a Common Platform for Testing Metamodel Based Design Optimization Methods

2013 ◽  
Author(s):  
Adel A. Younis ◽  
George H. Cheng ◽  
G. Gary Wang ◽  
Zuomin Dong
Keyword(s):  
Design Optimization ◽  
Optimization Problems ◽  
Optimization Algorithms ◽  
Computation Time ◽  
Optimization Methods ◽  
Global Optimum ◽  
Test Problems ◽  
Test Bed ◽  
Test Procedures ◽  
Local Optima

Metamodel based design optimization (MBDO) algorithms have attracted considerable interests in recent years due to their special capability in dealing with complex optimization problems with computationally expensive objective and constraint functions and local optima. Conventional unimodal-based optimization algorithms and stochastic global optimization algorithms either miss the global optimum frequently or require unacceptable computation time. In this work, a generic testbed/platform for evaluating various MBDO algorithms has been introduced. The purpose of the platform is to facilitate quantitative comparison of different MBDO algorithms using standard test problems, test procedures, and test outputs, as well as to improve the efficiency of new algorithm testing and improvement. The platform consists of a comprehensive test function database that contains about 100 benchmark functions and engineering problems. The testbed accepts any optimization algorithm to be tested, and only requires minor modifications to meet the test-bed requirements. The testbed is useful in comparing the performance of competing algorithms through execution of same problems. It allows researchers and practitioners to test and choose the most suitable optimization tool for their specific needs. It also helps to increase confidence and reliability of the newly developed MBDO tools. Many new MBDO algorithms, including Mode Pursuing Sampling (MPS), Pareto Set Pursuing (PSP), and Space Exploration and Unimodal Region Elimination (SEUMRE), were tested in this work to demonstrate its functionality and benefits.

Genetic Algorithms for Optimization of Building Envelopes and the Design and Control of HVAC Systems

2003 ◽  
Vol 125 (3) ◽  
pp. 343-351 ◽  
Author(s):  
L. G. Caldas ◽  
L. K. Norford
Keyword(s):  
Genetic Algorithms ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Optimization Method ◽  
Hvac Systems ◽  
Design Problems ◽  
Building Walls ◽  
Building Form ◽  
And Control ◽  
Future Work

Many design problems related to buildings involve minimizing capital and operating costs while providing acceptable service. Genetic algorithms (GAs) are an optimization method that has been applied to these problems. GAs are easily configured, an advantage that often compensates for a sacrifice in performance relative to optimization methods selected specifically for a given problem, and have been shown to give solutions where other methods cannot. This paper reviews the basics of GAs, emphasizing multi-objective optimization problems. It then presents several applications, including determining the size and placement of windows and the composition of building walls, the generation of building form, and the design and operation of HVAC systems. Future work is identified, notably interfaces between a GA and both simulation and CAD programs.

Hybrid and Adaptive Metamodel Based Global Optimization

2009 ◽  
Author(s):  
J. Gu ◽  
G. Y. Li ◽  
Z. Dong
Keyword(s):  
Global Optimization ◽  
Design Optimization ◽  
Optimization Problems ◽  
Optimization Method ◽  
Global Optimum ◽  
Superior Performance ◽  
Automatic Identification ◽  
Design Problems ◽  
Sample Data ◽  
Data Points

Metamodeling techniques are increasingly used in solving computation intensive design optimization problems today. In this work, the issue of automatic identification of appropriate metamodeling techniques in global optimization is addressed. A generic, new hybrid metamodel based global optimization method, particularly suitable for design problems involving computation intensive, black-box analyses and simulations, is introduced. The method employs three representative metamodels concurrently in the search process and selects sample data points adaptively according to the values calculated using the three metamodels to improve the accuracy of modeling. The global optimum is identified when the metamodels become reasonably accurate. The new method is tested using various benchmark global optimization problems and applied to a real industrial design optimization problem involving vehicle crash simulation, to demonstrate the superior performance of the new algorithm over existing search methods. Present limitations of the proposed method are also discussed.

Review of Metamodeling Techniques in Support of Engineering Design Optimization

2006 ◽  
Author(s):  
G. Gary Wang ◽  
S. Shan
Keyword(s):  
Design Optimization ◽  
Engineering Design ◽  
Design Space Exploration ◽  
Optimization Problems ◽  
Problem Formulation ◽  
Model Approximation ◽  
Design Problems ◽  
Computation Efficiency ◽  
Modern Engineering

Computation-intensive design problems are becoming increasingly common in manufacturing industries. The computation burden is often caused by expensive analysis and simulation processes in order to reach a comparable level of accuracy as physical testing data. To address such a challenge, approximation or metamodeling techniques are often used. Metamodeling techniques have been developed from many different disciplines including statistics, mathematics, computer science, and various engineering disciplines. These metamodels are initially developed as “surrogates” of the expensive simulation process in order to improve the overall computation efficiency. They are then found to be a valuable tool to support a wide scope of activities in modern engineering design, especially design optimization. This work reviews the state-of-the-art metamodel-based techniques from a practitioner’s perspective according to the role of metamodeling in supporting design optimization, including model approximation, design space exploration, problem formulation, and solving various types of optimization problems. Challenges and future development of metamodeling in support of engineering design is also analyzed and discussed.

A Comparison of Numerical Optimization Methods for Engineering Design

1974 ◽  
Vol 96 (1) ◽  
pp. 196-200 ◽  
Author(s):  
E. D. Eason ◽  
R. G. Fenton
Keyword(s):  
Engineering Design ◽  
Numerical Optimization ◽  
Optimization Methods ◽  
Test Functions ◽  
Design Problems

Seventeen numerical optimization methods are compared by plotting their convergence characteristics when applied to design problems and test functions. Several ranking schemes are used to determine the most general, efficient, inexpensive, and convenient methods. Conclusions are presented in the form of a selection guide intended for general use.

The Complementary Roles of Knowledge-Based Systems and Numerical Optimization in Engineering Design Software

1989 ◽  
Vol 111 (1) ◽  
pp. 100-103 ◽  
Author(s):  
R. Ellsworth ◽  
A. Parkinson ◽  
F. Cain
Keyword(s):  
Expert System ◽  
Engineering Design ◽  
Numerical Optimization ◽  
Optimization Methods ◽  
Design Rule ◽  
Rule Base ◽  
Design Problems ◽  
Knowledge Based ◽  
Engineering Design Problems ◽  
Trial And Error Method

In many engineering design problems, the designer converges upon a good design by iteratively evaluating a mathematical model of the design problem. The trial-and-error method used by the designer to converge upon a solution may be complex and difficult to capture in an expert system. It is suggested that in many cases, the design rule base could be made significantly smaller and more maintainable by using numerical optimization methods to identify the best design. The expert system is then used to define the optimization problem and interpret the solution, as well as to apply the true heuristics to the problem. An example of such an expert system is presented for the design of a valve anticavitation device. Because of the capabilities provided by the optimization software, the expert system has been able to outperform the expert in the test cases evaluated so far.

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