scholarly journals Application of data mining in multiobjective optimization problems

2014 ◽  
Vol 5 ◽  
pp. A15 ◽  
Author(s):  
Amir Mosavi
Keyword(s):  
Data Mining ◽  
Multiobjective Optimization ◽  
Optimization Design ◽  
Optimization Problems ◽  
Objective Functions ◽  
Design Variables ◽  
Modeling Techniques ◽  
Practical Engineering ◽  
Meta Modeling ◽  
Classification Tool

In the most engineering optimization design problems, the value of objective functions is not clearly defined in terms of design variables. Instead it is obtained by some numerical analysis such as FE structural analysis, fluid mechanic analysis, and thermodynamic analysis, etc. Usually, these analyses are considerably time consuming to obtain a value of objective functions. In order to make the number of analyses as few as possible a methodology is presented as a supporting tool for the meta-modeling techniques. Researches in meta-modeling for multiobjective optimization are relatively young and there is still much to do. It is shown that visualizing the problem on the basis of the randomly sampled geometrical data of CAD and CAE simulation results, in addition to utilizing classification tool of data mining could be effective as a supporting system to the available meta-modeling techniques. To evaluate the effectiveness of the proposed method a study case in 3D wing design is given. Along with this example, it is discussed how effective the proposed methodology could be in the practical engineering problems.

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.

Multiobjective optimization design of hybrid composite laminates for vibration using sequential permutation table method

2021 ◽  
pp. 095440622110504
Author(s):  
Zhao Jing ◽  
Qin Sun ◽  
Yongjie Zhang ◽  
Ke Liang
Keyword(s):  
Multiobjective Optimization ◽  
Fundamental Frequency ◽  
Hybrid Composite ◽  
Composite Laminates ◽  
Optimization Design ◽  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Design Flexibility ◽  
The Cost ◽  
Ply Orientation

Due to the large variable design space in optimization problems of composite laminates, it remains one of the challenging tasks to develop efficient optimization design methods to improve the design flexibility and efficiency. This work presents a sequential permutation table (SPT) method for the multiobjective optimization design of two-material hybrid composite laminates with simply supported boundary conditions, which maximizes the fundamental frequency and minimizes the cost/weight. Based on the vibration analysis of hybrid composite laminates, the approximate linear regularity of the square of fundamental frequency is derived, and two best ply orientations for the two materials are identified, respectively. By assigning one best ply orientation with maximum fundamental frequency at respective stacking positions, and using another best ply orientation to replace plies in the stacking sequence from the mid-plane to the outermost can lead to the optimum. Two multiobjective optimization problems are employed to verify the SPT method, results are compared with those obtained by heuristic algorithms. The obtained better solutions demonstrate the effectiveness and efficiency of the SPT method and its potentials for optimal design of hybrid composite laminates.

scholarly journals An Efficient Hybrid Algorithm for Multiobjective Optimization Problems with Upper and Lower Bounds in Engineering

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Guang Yang ◽  
Tao Xu ◽  
Xiang Li ◽  
Haohua Xiu ◽  
Tianshuang Xu
Keyword(s):  
Multiobjective Optimization ◽  
Lower Bounds ◽  
Hybrid Algorithm ◽  
High Efficiency ◽  
Optimization Problems ◽  
Simultaneous Optimization ◽  
Upper And Lower Bounds ◽  
Optimization Models ◽  
Engineering Problems ◽  
Practical Engineering

Generally, the inconvenience of establishing the mathematical optimization models directly and the conflicts of preventing simultaneous optimization among several objectives lead to the difficulty of obtaining the optimal solution of a practical engineering problem with several objectives. So in this paper, a generate-first-choose-later method is proposed to solve the multiobjective engineering optimization problems, which can set the number of Pareto solutions and optimize repeatedly until the satisfactory results are obtained. Based on Frisch’s method, Newton method, and weighed sum method, an efficient hybrid algorithm for multiobjective optimization models with upper and lower bounds and inequality constraints has been proposed, which is especially suitable for the practical engineering problems based on surrogate models. The generate-first-choose-later method with this hybrid algorithm can calculate the Pareto optimal set, show the Pareto front, and provide multiple designs for multiobjective engineering problems fast and accurately. Numerical examples demonstrate the effectiveness and high efficiency of the hybrid algorithm. In order to prove that the generate-first-choose-later method is rapid and suitable for solving practical engineering problems, an optimization problem for crash box of vehicle has been handled well.

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.

Multiobjective Optimization of a Microchannel Heat Sink Using Evolutionary Algorithm

2008 ◽  
Vol 130 (11) ◽  
Author(s):  
Afzal Husain ◽  
Kwang-Yong Kim
Keyword(s):  
Multiobjective Optimization ◽  
Evolutionary Algorithm ◽  
Performance Optimization ◽  
Heat Sink ◽  
Algorithm Design ◽  
Pareto Optimal ◽  
Microchannel Heat Sink ◽  
Objective Functions ◽  
Design Variables ◽  
Polynomial Response Surface

A multiobjective performance optimization of microchannel heat sink is carried out numerically applying surrogate analysis and evolutionary algorithm. Design variables related to microchannel width, depth, and fin width are selected, and two objective functions, thermal resistance and pumping power, are employed. With the help of finite volume solver, Navier–Stokes analyses are performed at the design sites obtained from full factorial design of sampling methods. Using the numerically evaluated objective function values, polynomial response surface is constructed for each objective functions, and multiobjective optimization is performed to obtain global Pareto optimal solutions. Analysis of optimum solutions is simplified by carrying out trade-off with design variables and objective functions. Objective functions exhibit changing sensitivity to design variables along the Pareto optimal front.

A Newton method for capturing Pareto optimal solutions of fuzzy multiobjective optimization problems

2019 ◽  
Vol 53 (3) ◽  
pp. 867-886
Author(s):  
Mehrdad Ghaznavi ◽  
Narges Hoseinpoor ◽  
Fatemeh Soleimani
Keyword(s):  
Multiobjective Optimization ◽  
Newton Method ◽  
Optimization Problems ◽  
Order Relation ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Multiobjective Optimization Problems ◽  
Generalized Hukuhara Differentiability

In this study, a Newton method is developed to obtain (weak) Pareto optimal solutions of an unconstrained multiobjective optimization problem (MOP) with fuzzy objective functions. For this purpose, the generalized Hukuhara differentiability of fuzzy vector functions and fuzzy max-order relation on the set of fuzzy vectors are employed. It is assumed that the objective functions of the fuzzy MOP are twice continuously generalized Hukuhara differentiable. Under this assumption, the relationship between weakly Pareto optimal solutions of a fuzzy MOP and critical points of the related crisp problem is discussed. Numerical examples are provided to demonstrate the efficiency of the proposed methodology. Finally, the convergence analysis of the method under investigation is discussed.

Multi-Objective Robust Optimization Design of a Fixed-Speed Horizontal Axis Wind Turbine

2013 ◽  
Author(s):  
Weijun Wang ◽  
Stéphane Caro ◽  
Fouad Bennis
Keyword(s):  
Wind Turbine ◽  
Optimization Design ◽  
Optimization Problems ◽  
Horizontal Axis ◽  
Design Environment ◽  
Horizontal Axis Wind Turbine ◽  
Multi Objective ◽  
Design Variables ◽  
Robust Optimization Design ◽  
Environment Parameters

The produced power and the thrust force exerted on the wind turbine are two conflicting objectives in the design of a floating horizontal axis wind turbine. Meanwhile, the variations in design variables and design environment parameters are unavoidable. The variations include the small variations in the design variables due to manufacturing errors, and the large variations in the wind speed. Therefore, two robustness indices are introduced in this paper. The first one characterizes the robustness of multi-objective optimization problems against small variations in the design variables and the design environment parameters. The second robustness index characterizes the robustness of multi-objective optimization problems against large variations in the design environment parameters. The robustness of the solutions based on the two robustness indices is treated as a vector defined in the robustness function space. As a result, the designer can compare the robustness of all Pareto optimal solutions and make a decision. Finally, the multi-objective robust optimization design of a fixed-speed horizontal axis wind turbine illustrates the proposed methodology.

Particle Swarm Methodologies for Engineering Design Optimization

2009 ◽  
Author(s):  
Singiresu S. Rao ◽  
Kiran K. Annamdas
Keyword(s):  
Particle Swarm Optimization ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Multiple Objective ◽  
Optimization Approach ◽  
Objective Functions ◽  
Mixed Design ◽  
Swarm Optimization ◽  
Design Variables ◽  
Mixed Design Variables

Particle swarm methodologies are presented for the solution of constrained mechanical and structural system optimization problems involving single or multiple objective functions with continuous or mixed design variables. The particle swarm optimization presented is a modified particle swarm optimization approach, with better computational efficiency and solution accuracy, is based on the use of dynamic maximum velocity function and bounce method. The constraints of the optimization problem are handled using a dynamic penalty function approach. To handle the discrete design variables, the closest discrete approach is used. Multiple objective functions are handled using a modified cooperative game theory approach. The applicability and computational efficiency of the proposed particle swarm optimization approach are demonstrated through illustrate examples involving single and multiple objectives as well as continuous and mixed design variables. The present methodology is expected to be useful for the solution of a variety of practical engineering design optimization problems.

Vibration Isolator Design for Space Application Based on Multiobjective Optimization Method

2013 ◽  
Vol 365-366 ◽  
pp. 77-81
Author(s):  
Zhi Wei Feng ◽  
Qian Gang Tang ◽  
Qing Bin Zhang
Keyword(s):  
Multiobjective Optimization ◽  
High Frequency ◽  
Optimization Problems ◽  
Optimization Method ◽  
Resonant Peak ◽  
Space Application ◽  
Vibration Isolator ◽  
Peak Reduction ◽  
Space Applications ◽  
Design Variables

A multiobjective optimization based vibration isolator design for space application is described. It is common to use passive isolator and isolate the platform noise in space applications. The design of a passive isolator involves a trade-off between the resonant peak reduction and the high frequency attenuation. The equation of motion and transfer function model for single-stage and two-stage connector model is derived by using basic principle. The multiobjective optimization model is proposed, where the design variables are the damping coefficients and stiffness coefficients, the objective functions are the resonant peak reduction and the high frequency attenuation, and the constraints are the natural frequency of the connector. The multiobjective optimization problems for the design of the passive isolator are solved by using the multiobjective evolutionary algorithm based on decomposition (MOEA/D). The Pareto front obtained can provide multiple candidate solutions for the designer. The method is effective for the design process of the passive isolator.

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