Multi-Objective Design Problem of Tire Wear and Visualization of Its Pareto Solutions2

2006 ◽  
Vol 34 (3) ◽  
pp. 170-194 ◽  
Author(s):  
M. Koishi ◽  
Z. Shida
Keyword(s):  
Inverse Problems ◽  
Conceptual Design ◽  
Dimensional Space ◽  
Design Stage ◽  
Objective Functions ◽  
Pareto Solutions ◽  
Design Problems ◽  
Multi Objective ◽  
Design Engineers ◽  
Design Variables

Abstract Since tires carry out many functions and many of them have tradeoffs, it is important to find the combination of design variables that satisfy well-balanced performance in conceptual design stage. To find a good design of tires is to solve the multi-objective design problems, i.e., inverse problems. However, due to the lack of suitable solution techniques, such problems are converted into a single-objective optimization problem before being solved. Therefore, it is difficult to find the Pareto solutions of multi-objective design problems of tires. Recently, multi-objective evolutionary algorithms have become popular in many fields to find the Pareto solutions. In this paper, we propose a design procedure to solve multi-objective design problems as the comprehensive solver of inverse problems. At first, a multi-objective genetic algorithm (MOGA) is employed to find the Pareto solutions of tire performance, which are in multi-dimensional space of objective functions. Response surface method is also used to evaluate objective functions in the optimization process and can reduce CPU time dramatically. In addition, a self-organizing map (SOM) proposed by Kohonen is used to map Pareto solutions from high-dimensional objective space onto two-dimensional space. Using SOM, design engineers see easily the Pareto solutions of tire performance and can find suitable design plans. The SOM can be considered as an inverse function that defines the relation between Pareto solutions and design variables. To demonstrate the procedure, tire tread design is conducted. The objective of design is to improve uneven wear and wear life for both the front tire and the rear tire of a passenger car. Wear performance is evaluated by finite element analysis (FEA). Response surface is obtained by the design of experiments and FEA. Using both MOGA and SOM, we obtain a map of Pareto solutions. We can find suitable design plans that satisfy well-balanced performance on the map called “multi-performance map.” It helps tire design engineers to make their decision in conceptual design stage.

Multi-Objective Optimization of Pin-Fin Heatsinks

2009 ◽  
Author(s):  
Keisuke Horiuchi ◽  
Atsuo Nishihara ◽  
Kazuyuki Sugimura
Keyword(s):  
Pressure Drop ◽  
Thermal Resistance ◽  
Approximation Model ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Pareto Solutions ◽  
Multi Objective ◽  
Pin Fin ◽  
Design Variables ◽  
Kriging Approximation

The multi-objective optimization of pin-fin heatsinks using a Kriging approximation model is presented based on systematic experimental results. Thermal resistance and pressure drop are the objective functions in this study. Pareto solutions to the objective functions are illustrated. We derived the design rules for the diameter, height, and pitches for the uniform staggered arrays of pin-fin heatsinks by correlating the objective functions with design variables. We also analyzed the contribution of all design variables to the thermal resistance as well as the pressure drop. We found that both the thermal resistance and the pressure drop are the most sensitive to the ratio of transverse pitch to pin-fin diameter.

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.

Multi-Objective Design Optimization of a Mixed-Flow Pump

2009 ◽  
Author(s):  
Yumiko Takayama ◽  
Hiroyoshi Watanabe
Keyword(s):  
Performance Characteristic ◽  
Performance Characteristics ◽  
Inverse Design ◽  
Surface Model ◽  
Objective Functions ◽  
Mixed Flow ◽  
Multi Objective ◽  
Design Variables ◽  
Flow Head ◽  
Flow Pump

In most cases of high specific speed mixed-flow pump applications, it is necessary to satisfy more than one performance characteristic such as deign point efficiency, shut-off power/head and non-stall characteristic (no positive slope in flow-head curve). However, it is known that these performance characteristics are in relation of trade-offs. As a result, it is difficult to optimize these performance characteristics by conventional way such as trial and error approach by modifying geometrical parameters. This paper presents the results of the multi-objective optimization strategy of mixed-flow pump design by means of three dimensional inverse design approach, Computational Fluid Dynamics (CFD), Design of Experiments (DoE), response surface model (RSM) and Multi Objective Genetic Algorism (MOGA). The parameters to control blade loading distributions and meridional geometries for impeller and diffuser blades in inverse design were chosen as design variables of the optimization process. Pump efficiency, maximum slope in flow-head curve and shut-off power/head were selected as objective functions. Objective functions of pumps, designed by design variables specified in DoE, were evaluated by using CFD. Then, trade-off relations between objective functions were analyzed by using Pareto fronts obtained by MOGA. Some pumps which have specific performance characteristic (non-stall, low shut-off power, high efficiency etc.) designed along the Pareto front were numerically evaluated.

Optimal design of a parallel robotic gripper using enhanced multi-objective ant lion optimizer with a sensitivity analysis approach

2020 ◽  
Vol 40 (5) ◽  
pp. 703-721
Author(s):  
Golak Bihari Mahanta ◽  
Deepak BBVL ◽  
Bibhuti B. Biswal ◽  
Amruta Rout
Keyword(s):  
Sensitivity Analysis ◽  
Distribution Function ◽  
Design Parameters ◽  
Objective Functions ◽  
Content Type ◽  
Multi Objective ◽  
The Past ◽  
Design Variables ◽  
Pick And Place ◽  
Ant Lion

Purpose From the past few decades, parallel grippers are used successfully in the automation industries for performing various pick and place jobs due to their simple design, reliable nature and its economic feasibility. So, the purpose of this paperis to design a suitable gripper with appropriate design parameters for better performance in the robotic production systems. Design/methodology/approach In this paper, an enhanced multi-objective ant lion algorithm is introduced to find the optimal geometric and design variables of a parallel gripper. The considered robotic gripper systems are evaluated by considering three objective functions while satisfying eight constraint equations. The beta distribution function is introduced for generating the initial random number at the initialization phase of the proposed algorithm as a replacement of uniform distribution function. A local search algorithm, namely, achievement scalarizing function with multi-criteria decision-making technique and beta distribution are used to enhance the existing optimizer to evaluate the optimal gripper design problem. In this study, the newly proposed enhanced optimizer to obtain the optimum design condition of the design variables is called enhanced multi-objective ant lion optimizer. Findings This study aims to obtain optimal design parameters of the parallel gripper with the help of the developed algorithms. The acquired results are investigated with the past research paper conducted in that field for comparison. It is observed that the suggested method to get the best gripper arrangement and variables of the parallel gripper mechanism outperform its counterparts. The effects of the design variables are needed to be studied for a better design approach concerning the objective functions, which is achieved by sensitivity analysis. Practical implications The developed gripper is feasible to use in the assembly operation, as well as in other pick and place operations in different industries. Originality/value In this study, the problem to find the optimum design parameter (i.e. geometric parameters such as length of the link and parallel gripper joint angles) is addressed as a multi-objective optimization. The obtained results from the execution of the algorithm are evaluated using the performance indicator algorithm and a sensitivity analysis is introduced to validate the effects of the design variables. The obtained optimal parameters are used to develop a gripper prototype, which will be used for the assembly process.

Comprehensive Satisfactory Design Method for Product Designs

2001 ◽  
Author(s):  
Eiji Adachi
Keyword(s):  
Decision Making ◽  
Design Method ◽  
Simultaneous Equations ◽  
Objective Functions ◽  
Identification Methods ◽  
Multi Objective ◽  
Sensitivity Coefficients ◽  
Design Variables ◽  
Computer Aided ◽  
Market Needs

Abstract Actual product designs aim to fulfill all product requirements of market needs and wants, which are technical or non-technical, logical or illogical, objective or subjective, and quantitative or qualitative. The actual product designs are objective-aiming designs and can be supposed to be multi-objective satisfactory designs with heterogeneous objective functions and dimensional design variables. To realize computer-aided product designs which can obtain rational and satisfactory solutions, we classify the objective functions and contrive methods to deal with non-theoretical, non-technical, subjective, or illogical objective functions as well. This paper shows all of our methods, including an expression of heterogeneous objective functions which consists of objective and evaluated values, a satisfactory design method by simultaneous equations which searches solutions sequentially, identification methods of non-theoretical or non-technical objective functions and sensitivity coefficients for the simultaneous equations, a decision-making method of promising solutions to fulfill product requirements, and also numerical applications of these methods to actual product designs.

A Collaborative Rapid Analysis Method for Decision-Making in Assembly Line Design

2004 ◽  
Author(s):  
Masataka Yoshimura ◽  
Satoshi Yoshida ◽  
Yoshinori Konishi ◽  
Kazuhiro Izui ◽  
Shinji Nishiwaki ◽  
...  
Keyword(s):  
Decision Making ◽  
Conceptual Design ◽  
Assembly Line ◽  
Rapid Analysis ◽  
Design Stage ◽  
Analysis Method ◽  
Design Engineers ◽  
Volume Flexibility ◽  
Conceptual Design Stage ◽  
Line Design

Many highly accurate computer simulation tools have been developed for assembly line design, such as for simulation of assembly processes, but these tools require much input information and are generally utilized only in detailed design stages. This paper proposes a rapid analysis method for manual assembly line design, which can be utilized in the conceptual design stage. This method is based on a layout tool where design engineers can construct assembly line models using 2- and 3-D views. This method provides design evaluation techniques for multiple important criteria such as volume flexibility, visibility, and so on, using the layout data. Spatial evaluation and quantitative efficiency analyses can be simultaneously performed, which enhance collaborative decision-making in the conceptual design stage.

AN EXTENDED SUBSTRUCTURING TECHNIQUE FOR EFFICIENT EVALUATION OF NONLINEAR LOAD-BEARING STRUCTURES IN THE CONCEPTUAL DESIGN STAGE

2014 ◽  
Vol 11 (06) ◽  
pp. 1350086 ◽  
Author(s):  
MLADENKO KAJTAZ ◽  
ALEKSANDAR SUBIC ◽  
MONIR TAKLA
Keyword(s):  
Conceptual Design ◽  
Design Stage ◽  
Element Analysis ◽  
Nonlinear Load ◽  
Design Problems ◽  
Design Concepts ◽  
Structural Problems ◽  
Conceptual Design Stage ◽  
Nonlinear Structural ◽  
The Finite Element Analysis

The research presented in this paper has extended the substructuring technique into the nonlinear domain in order to apply the finite element analysis (FEA) method to complex nonlinear structural design problems in the conceptual design stage. As conventional FE models based on substructures allow only linear analysis, it was necessary in this research to introduce a new algorithm capable of linearizing nonlinear structural problems with sufficient accuracy in order to enable evaluation of engineering design concepts in a more objective and rigorous manner in the early stages of design. The developed method was implemented within a commercial FE solver, and validated using a select number of case studies. The results obtained for the two sample solutions indicate that the new method has achieved an improvement in accuracy of 90% and 98% respectively compared to the conventional FE-based approach applied to the same class of design problems.

An application of Taguchi method on the high-speed motorized spindle system design

2011 ◽  
Vol 225 (9) ◽  
pp. 2198-2205 ◽  
Author(s):  
C-W Lin
Keyword(s):  
Optimal Design ◽  
Taguchi Method ◽  
Machine Tool ◽  
High Speed ◽  
Signal To Noise Ratio ◽  
Design Stage ◽  
Original Design ◽  
Spindle System ◽  
Design Engineers ◽  
Design Variables

As spindle speeds increase, the variations caused by high-speed effects become more significant. Therefore, in the initial design stage, it is necessary for machine tool design engineers to construct a robust high-speed machine tool that possesses high first-mode natural frequencies (FMNFs) and is insensitive to high operating speeds. In this article, Taguchi method is used to identify the optimal values of design variables (DVs) for a robust high-speed spindle system with respect to the signal-to-noise ratio (SNR) of system FMNF. The L18 orthogonal array covers seven main DVs at three levels each, one main DV at two levels, and the noise factor spindle speeds at six levels. The results show that the new optimal design has improved the SNR of the FMNF by 2.06 dB from the original design; this implies that the quality loss has been reduced to 62 per cent of its original value. The optimal design has been verified by a confirmation numerical experiment.

An Approach for the Fast Calculation Method of Pareto Solutions of a Two-objective Network

2015 ◽  
Vol 22 (01) ◽  
pp. 1550005 ◽  
Author(s):  
Natsumi Takahashi ◽  
Tomoaki Akiba ◽  
Shuhei Nomura ◽  
Hisashi Yamamoto
Keyword(s):  
Shortest Path ◽  
Optimization Problem ◽  
Computing Time ◽  
Search Space ◽  
Shortest Path Problem ◽  
Objective Functions ◽  
Pareto Solutions ◽  
Fast Calculation ◽  
Multi Objective ◽  
Other Information

The shortest path problem is a kind of optimization problem and its aim is to find the shortest path connecting two specific nodes in a network, where each edge has its distance. When considering not only the distances between the nodes but also some other information, the problem is formulated as a multi-objective shortest path problem that involves multiple conflicting objective functions. The multi-objective shortest path problem is a kind of optimization problem of multi-objective network. In the general cases, multi-objectives are rarely optimized by a solution. So, to solve the multi-objective shortest path problem leads to obtaining Pareto solutions. An algorithm for this problem has been proposed by using the extended Dijkstra's algorithm. However, this algorithm for obtaining Pareto solutions has many useless searches for paths. In this study, we consider two-objective shortest path problem and propose efficient algorithms for obtaining the Pareto solutions. Our proposed algorithm can reduce more search space than existing algorithms, by solving a single-objective shortest path problem. The results of the numerical experiments suggest that our proposed algorithms reduce the computing time and the memory size for obtaining the Pareto solutions.

Robustness Against Large Variations in Multi-Objective Optimization Problems

2013 ◽  
Author(s):  
Weijun Wang ◽  
Stéphane Caro ◽  
Fouad Bennis
Keyword(s):  
Optimization Problems ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Design Environment ◽  
Multi Objective ◽  
Uncertainty Sources ◽  
Design Variables ◽  
Robustness Index ◽  
Environment Parameters

In the presence of multiple optimal solutions in multi-modal optimization problems and in multi-objective optimization problems, the designer may be interested in the robustness of those solutions to make a decision. Here, the robustness is related to the sensitivity of the performance functions to uncertainties. The uncertainty sources include the uncertainties in the design variables, in the design environment parameters, in the model of objective functions and in the designer’s preference. There exist many robustness indices in the literature that deal with small variations in the design variables and design environment parameters, but few robustness indices consider large variations. In this paper, a new robustness index is introduced to deal with large variations in the design environment parameters. The proposed index is bounded between zero and one, and measures the probability of a solution to be optimal with respect to the values of the design environment parameters. The larger the robustness index, the more robust the solution with regard to large variations in the design environment parameters. Finally, two illustrative examples are given to highlight the contributions of this paper.

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