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.

Enhanced Multi-Objective Optimization of a Microchannel Heat Sink Using Multiple Surrogates Modeling

2009 ◽  
Author(s):  
Afzal Husain ◽  
Kwang-Yong Kim
Keyword(s):  
Heat Sink ◽  
Design Space ◽  
Surrogate Models ◽  
Pareto Optimal ◽  
Microchannel Heat Sink ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Pareto Optimal Front ◽  
Multi Objective ◽  
Design Variables

A liquid flow microchannel heat sink has been studied and optimized with the help of three-dimensional numerical analysis and multiple surrogate methods. Two objective functions, thermal resistance and pumping power have been selected to assess the performance of the microchannel heat sink. The design variables related to the microchannel top and bottom widths, depth and fin width, which contribute to objective functions, have been identified and design space has been explored through some preliminary calculations. Design of experiments was performed and a three-level full factorial design was selected to exploit the design space. The numerical solutions obtained at these design points were utilized to construct surrogate models namely Response Surface Approximations and Kriging. A hybrid multi-objective evolutionary algorithm coupled with surrogate models and a gradient-based search algorithm is applied to find global Pareto-optimal solutions. Since, the surrogate models are highly problem-dependent, the accuracy of the two surrogate models has been discussed in view of their predictions at on- and off-Pareto-optimal front. The trade-off analysis was performed in view of the two competing objectives. The Pareto-optimal sensitivity (change in value along the Pareto-optimal front) of the design variables has been found out to economically compromise with the design variables contributing relatively less to the objective functions. The application of the multiple surrogate methods not only improves quality of multi-objective optimization but also gives the feedback of the fidelity of the model near the optimum region.

Shape Optimization of Microchannels Using Surrogate Modelling

2018 ◽  
Author(s):  
Muhammad Ansab Ali ◽  
Tariq S. Khan ◽  
Saqib Salam ◽  
Ebrahim Al Hajri
Keyword(s):  
Shape Optimization ◽  
Heat Sink ◽  
Pareto Front ◽  
Sampling Method ◽  
Design Space ◽  
Latin Hypercube Sampling ◽  
Optimum Shape ◽  
Microchannel Heat Sink ◽  
Objective Functions ◽  
Computational Resources

To minimize the computational and optimization time, a numerical simulation of 3D microchannel heat sink was performed using surrogate model to achieve the optimum shape. Latin hypercube sampling method was used to explore the design space and to construct the model. The accuracy of the model was evaluated using statistical methods like coefficient of multiple determinations and root mean square error. Thermal resistance and pressure drop being conflicting objective functions were selected to optimize the geometric parameters of the microchannel. Multi objective shape optimization of design was conducted using genetic algorithm and the optimum design solutions are presented in the Pareto front. The application of the surrogate methods has predicted the performance of the heat sink with the sufficient accuracy employing significantly lower computational resources.

scholarly journals The Impact of Surrogate Models on the Multi-Objective Optimization of Pump-As-Turbine (PAT)

Energies ◽  
2020 ◽  
Vol 13 (9) ◽  
pp. 2271 ◽  
Author(s):  
Stephen Ntiri Asomani ◽  
Jianping Yuan ◽  
Longyan Wang ◽  
Desmond Appiah ◽  
Kofi Asamoah Adu-Poku
Keyword(s):  
Neural Network ◽  
Objective Function ◽  
Surrogate Model ◽  
Surrogate Models ◽  
Operating Conditions ◽  
Pareto Optimal ◽  
Objective Functions ◽  
Operating Range ◽  
Design Variables ◽  
Pareto Optimal Points

Pump-as-turbine (PAT) technology permits two operating states—as a pump or turbine, depending on the demand. Nevertheless, designing the geometrical components to suit these operating states has been an unending design issue, because of the multi-conditions for the PAT technology that must be attained to enhance the hydraulic performance. Also, PAT has been known to have a narrow operating range and operates poorly at off-design conditions, due to the lack of flow control device and poor geometrical designs. Therefore, for the PAT to have a wider operating range and operate effectively at off-design conditions, the geometric parameters need to be optimized. Since it is practically impossible to optimize more than one objective function at the same time, a suitable surrogate model is needed to mimic the objective functions for it to be solvable. In this study, the Latin hypercube sampling method was used to obtain the objective function values, the Adaptive Neuro-Fuzzy Inference System (ANFIS), Artificial Neural Network (ANN) and Generalized Regression Neural Network (GRNN) were used as surrogate models to approximate the objective functions in the design space. Then, a suitable surrogate model was chosen for the optimization. The Pareto-optimal solutions were obtained by using the Pareto-based genetic algorithm (PBGA). To evaluate the results of the optimization, three representative Pareto-optimal points were selected and analyzed. Compared to the baseline model, the Pareto-optimal points showed a great improvement in the objective functions. After optimization, the geometry of the impeller was redesigned to suit the operating conditions of PAT. The findings show that the efficiencies of the optimized design variables of PAT were enhanced by 23.7%, 11.5%, and 10.4% at part load, design point, and under overload flow conditions, respectively. Moreover, the results also indicated that the chosen design variables (b2, β2, β1, and z) had a substantial impact on the objective functions, justifying the feasibility of the optimization method employed in this study.

Thermal Optimization of a Microchannel Heat Sink With Trapezoidal Cross Section

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
Afzal Husain ◽  
Kwang-Yong Kim
Keyword(s):  
Shape Optimization ◽  
Thermal Resistance ◽  
Objective Function ◽  
Response Surface ◽  
Heat Sink ◽  
Fractional Factorial ◽  
Surface Model ◽  
Microchannel Heat Sink ◽  
Reference Shape ◽  
Design Variables

A microchannel heat sink shape optimization has been performed using response surface approximation. Three design variables related to microchannel width, depth, and fin width are selected for optimization, and thermal resistance has been taken as objective function. Design points are chosen through a three-level fractional factorial design of sampling methods. Navier–Stokes and energy equations for steady, incompressible, and laminar flow and conjugate heat transfer are solved at these design points using a finite volume solver. Solutions are carefully validated with the analytical and experimental results and the values of objective function are calculated at the specified design points. Using the numerically evaluated objective-function values, a polynomial response surface model is constructed and the optimum point is searched by sequential quadratic programming. The process of shape optimization greatly improves the thermal performance of the microchannel heat sink by decreasing thermal resistance of about 12% of the reference shape. Sensitivity of objective function to design variables has been studied to utilize the substrate material efficiently.

Global WASF-GA: An Evolutionary Algorithm in Multiobjective Optimization to Approximate the Whole Pareto Optimal Front

2017 ◽  
Vol 25 (2) ◽  
pp. 309-349 ◽  
Author(s):  
Rubén Saborido ◽  
Ana B. Ruiz ◽  
Mariano Luque
Keyword(s):  
Multiobjective Optimization ◽  
Evolutionary Algorithm ◽  
Fitness Function ◽  
Weight Vector ◽  
Reference Points ◽  
Pareto Optimal ◽  
Computational Results ◽  
Nsga Ii ◽  
Nondominated Solutions ◽  
Pareto Optimal Front

In this article, we propose a new evolutionary algorithm for multiobjective optimization called Global WASF-GA ( global weighting achievement scalarizing function genetic algorithm), which falls within the aggregation-based evolutionary algorithms. The main purpose of Global WASF-GA is to approximate the whole Pareto optimal front. Its fitness function is defined by an achievement scalarizing function (ASF) based on the Tchebychev distance, in which two reference points are considered (both utopian and nadir objective vectors) and the weight vector used is taken from a set of weight vectors whose inverses are well-distributed. At each iteration, all individuals are classified into different fronts. Each front is formed by the solutions with the lowest values of the ASF for the different weight vectors in the set, using the utopian vector and the nadir vector as reference points simultaneously. Varying the weight vector in the ASF while considering the utopian and the nadir vectors at the same time enables the algorithm to obtain a final set of nondominated solutions that approximate the whole Pareto optimal front. We compared Global WASF-GA to MOEA/D (different versions) and NSGA-II in two-, three-, and five-objective problems. The computational results obtained permit us to conclude that Global WASF-GA gets better performance, regarding the hypervolume metric and the epsilon indicator, than the other two algorithms in many cases, especially in three- and five-objective problems.

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.

Geometric Size Optimization of Annular Step Fin Using Multi-Objective Genetic Algorithm

2017 ◽  
Vol 9 (2) ◽  
Author(s):  
Abhijit Deka ◽  
Dilip Datta
Keyword(s):  
Heat Transfer ◽  
Genetic Algorithm ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Pareto Optimal ◽  
Objective Functions ◽  
Cross Sectional ◽  
Multi Objective ◽  
Multi Objective Genetic Algorithm ◽  
Design Variables

Although an annular stepped fin can produce better cooling effect in comparison to an annular disk fin, it is yet to be studied in detail. In the present work, one-dimensional heat transfer in a two-stepped rectangular cross-sectional annular fin with constant base temperature and variable thermal conductivity is modeled as a multi-objective optimization problem. Taking cross-sectional half-thicknesses and outer radii of the two fin steps as design variables, an attempt is made to obtain the efficient fin geometry primarily by simultaneously maximizing the heat transfer rate and minimizing the fin volume. For further assessment of the fin performance, three more objective functions are studied, which are minimization of the fin surface area and maximization of the fin efficiency and effectiveness. Evaluating the heat transfer rate through the hybrid spline difference method, the well-known multi-objective genetic algorithm, namely, nondominated sorting genetic algorithm II (NSGA-II), is employed for approximating the Pareto-optimal front containing a set of tradeoff solutions in terms of different combinations of the considered five objective functions. The Pareto-optimal sensitivity is also analyzed for studying the influences of the design variables on the objective functions. As an outcome, it can be concluded that the proposed procedure would give an open choice to designers to lead to a practical stepped fin configuration.

scholarly journals An Environmental Selection and Transfer Learning Based Dynamic Multiobjective Optimization Evolutionary Algorithm

2021 ◽  
Author(s):  
Qiang He ◽  
Zheng Xiang ◽  
Peng Ren
Keyword(s):  
Multiobjective Optimization ◽  
Evolutionary Algorithm ◽  
Transfer Learning ◽  
Optimization Problems ◽  
Evolutionary Process ◽  
Pareto Optimal ◽  
Nsga Ii ◽  
Environmental Selection ◽  
Dynamic Multiobjective Optimization ◽  
Prediction Strategy

Abstract In recent years, the dynamic multiobjective optimization problems (DMOPs), whose major strategy is to track the varying PS (Pareto Optimal Solution, PS) and/or PF (Pareto Optimal Frontier), caused a great deal of attention worldwide. As a promising solution, reusing of “experiences” to establish a prediction model is proved to be very useful and widely used in practice. However, most existing methods overlook the importance of environmental selection in the evolutionary processes. In this paper, we propose a dynamic multiobjective optimal evolutionary algorithm which is based on environmental selection and transfer learning (DMOEA-ESTL). This approach makes full use of the environmental selection and transfer learning technique to generate individuals for a new environment by reusing experience to maintain the diversity of the population and speed up the evolutionary process. As experimental validation, we embed this new scheme in the NSGA-II (non-dominated sorting genetic algorithm). We test the proposed algorithm with the help of six benchmark functions as well as compare it with the other two prediction based strategies FPS (Forward-looking Prediction Strategy, FPS) and PPS (Population Prediction Strategy, PPS). The experimental results testify that the proposed strategy can deal with the DMOPs effectively.

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