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.

Solving Mono- and Multi-Objective Problems Using Hybrid Evolutionary Algorithms and Nelder-Mead Method

2021 ◽  
Vol 12 (4) ◽  
pp. 98-116
Author(s):  
Noureddine Boukhari ◽  
Fatima Debbat ◽  
Nicolas Monmarché ◽  
Mohamed Slimane
Keyword(s):  
Convergence Rate ◽  
Optimization Problem ◽  
Optimization Problems ◽  
State Of The Art ◽  
Hybrid Approach ◽  
Optimization Methods ◽  
Global Optimum ◽  
Stochastic Methods ◽  
Local Optima ◽  
Portfolio Optimization Problem

Evolution strategies (ES) are a family of strong stochastic methods for global optimization and have proved their capability in avoiding local optima more than other optimization methods. Many researchers have investigated different versions of the original evolution strategy with good results in a variety of optimization problems. However, the convergence rate of the algorithm to the global optimum stays asymptotic. In order to accelerate the convergence rate, a hybrid approach is proposed using the nonlinear simplex method (Nelder-Mead) and an adaptive scheme to control the local search application, and the authors demonstrate that such combination yields significantly better convergence. The new proposed method has been tested on 15 complex benchmark functions and applied to the bi-objective portfolio optimization problem and compared with other state-of-the-art techniques. Experimental results show that the performance is improved by this hybridization in terms of solution eminence and strong convergence.

scholarly journals Towards Enhancement of Performance of K-Means Clustering Using Nature-Inspired Optimization Algorithms

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
Simon Fong ◽  
Suash Deb ◽  
Xin-She Yang ◽  
Yan Zhuang
Keyword(s):  
Clustering Algorithms ◽  
Optimization Algorithms ◽  
Optimization Methods ◽  
Global Optimum ◽  
Local Optima ◽  
Clustering Quality ◽  
Global Optima ◽  
Speed Up ◽  
Pros And Cons ◽  
Swarming Behavior

Traditional K-means clustering algorithms have the drawback of getting stuck at local optima that depend on the random values of initial centroids. Optimization algorithms have their advantages in guiding iterative computation to search for global optima while avoiding local optima. The algorithms help speed up the clustering process by converging into a global optimum early with multiple search agents in action. Inspired by nature, some contemporary optimization algorithms which include Ant, Bat, Cuckoo, Firefly, and Wolf search algorithms mimic the swarming behavior allowing them to cooperatively steer towards an optimal objective within a reasonable time. It is known that these so-called nature-inspired optimization algorithms have their own characteristics as well as pros and cons in different applications. When these algorithms are combined with K-means clustering mechanism for the sake of enhancing its clustering quality by avoiding local optima and finding global optima, the new hybrids are anticipated to produce unprecedented performance. In this paper, we report the results of our evaluation experiments on the integration of nature-inspired optimization methods into K-means algorithms. In addition to the standard evaluation metrics in evaluating clustering quality, the extended K-means algorithms that are empowered by nature-inspired optimization methods are applied on image segmentation as a case study of application scenario.

Genetic Optimization Using Derivatives

1998 ◽  
Vol 7 ◽  
pp. 187-210 ◽  
Author(s):  
Jasjeet S. Sekhon ◽  
Walter R. Mebane
Keyword(s):  
Optimization Problems ◽  
Optimization Methods ◽  
Global Optimum ◽  
Genetic Optimization ◽  
Normal Mixture ◽  
Local Optima ◽  
Monte Carlo Experiments ◽  
Unconstrained Optimization Problems ◽  
Global Optima ◽  
Quasi Newton

We describe a new computer program that combines evolutionary algorithm methods with a derivative-based, quasi-Newton method to solve difficult unconstrained optimization problems. The program, called GENOUD (GENetic Optimization Using Derivatives), effectively solves problems that are nonlinear or perhaps even discontinuous in the parameters of the function to be optimized. When a statistical model's estimating function (for example, a log-likelihood) is nonlinear in the model's parameters, the function to be optimized will usually not be globally concave and may contain irregularities such as saddlepoints or discontinuous jumps. Optimization methods that rely on derivatives of the objective function may be unable to find any optimum at all. Or multiple local optima may exist, so that there is no guarantee that a derivative-based method will converge to the global optimum. We discuss the theoretical basis for expecting GENOUD to have a high probability of finding global optima. We conduct Monte Carlo experiments using scalar Normal mixture densities to illustrate this capability. We also use a system of four simultaneous nonlinear equations that has many parameters and multiple local optima to compare the performance of GENOUD to that of the Gauss-Newton algorithm in SAS's PROC 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.

Reduced Order Design Optimization of Liquid Cooled Heat Sinks

2021 ◽  
Vol 143 (4) ◽  
Author(s):  
Aniket Ajay Lad ◽  
Kai A. James ◽  
William P. King ◽  
Nenad Miljkovic
Keyword(s):  
Design Optimization ◽  
Power Density ◽  
Building Blocks ◽  
Optimization Methods ◽  
Population Based ◽  
Global Optimum ◽  
Heat Sinks ◽  
Geometrical Parameters ◽  
Power Module ◽  
Reduced Order

Abstract The recent growth in electronics power density has created a significant need for effective thermal management solutions. Liquid-cooled heat sinks or cold plates are typically used to achieve high volumetric power density cooling. A natural tradeoff exists between the thermal and hydraulic performance of a cold plate, creating an opportunity for design optimization. Current design optimization methods rely on computationally expensive and time consuming computational fluid dynamics (CFD) simulations. Here, we develop a rapid design optimization tool for liquid cooled heat sinks based on reduced-order models for the thermal-hydraulic behavior. Flow layout is expressed as a combination of simple building blocks on a divided coarse grid. The flow layout and geometrical parameters are incorporated to optimize designs that can effectively address heterogeneous cooling requirements within electronics packages. We demonstrate that the use of population-based searches for optimal layout selection, while not ensuring a global optimum solution, can provide optimal or near-optimal results for most of the test cases studied. The approach is shown to generate optimal designs within a timescale of 60–120 s. A case study based on cooling of a commercial silicon carbide (SiC) electronics power module is used to demonstrate the application of the developed tool and is shown to improve the performance as compared to an aggressive state-of-the-art single-phase liquid cooling solution by reducing the SiC junction-to-coolant thermal resistance by 25% for the same pressure drop.

scholarly journals An Adaptive Particle Swarm Optimization Algorithm for Unconstrained Optimization

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Feng Qian ◽  
Mohammad Reza Mahmoudi ◽  
Hamïd Parvïn ◽  
Kim-Hung Pho ◽  
Bui Anh Tuan
Keyword(s):  
Particle Swarm Optimization ◽  
Optimization Algorithm ◽  
Particle Swarm Optimization Algorithm ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Optimization Methods ◽  
Global Optimum ◽  
Initial Population ◽  
Swarm Optimization ◽  
Conventional Optimization

Conventional optimization methods are not efficient enough to solve many of the naturally complicated optimization problems. Thus, inspired by nature, metaheuristic algorithms can be utilized as a new kind of problem solvers in solution to these types of optimization problems. In this paper, an optimization algorithm is proposed which is capable of finding the expected quality of different locations and also tuning its exploration-exploitation dilemma to the location of an individual. A novel particle swarm optimization algorithm is presented which implements the conditioning learning behavior so that the particles are led to perform a natural conditioning behavior on an unconditioned motive. In the problem space, particles are classified into several categories so that if a particle lies within a low diversity category, it would have a tendency to move towards its best personal experience. But, if the particle’s category is with high diversity, it would have the tendency to move towards the global optimum of that category. The idea of the birds’ sensitivity to its flying space is also utilized to increase the particles’ speed in undesired spaces in order to leave those spaces as soon as possible. However, in desirable spaces, the particles’ velocity is reduced to provide a situation in which the particles have more time to explore their environment. In the proposed algorithm, the birds’ instinctive behavior is implemented to construct an initial population randomly or chaotically. Experiments provided to compare the proposed algorithm with the state-of-the-art methods show that our optimization algorithm is one of the most efficient and appropriate ones to solve the static optimization problems.

scholarly journals A Competitive Memory Paradigm for Multimodal Optimization Driven by Clustering and Chaos

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 934
Author(s):  
Jorge Gálvez ◽  
Erik Cuevas ◽  
Krishna Gopal Dhal
Keyword(s):  
Optimization Problems ◽  
Optimization Methods ◽  
Global Optimum ◽  
Point Of View ◽  
The Other ◽  
Memory Mechanism ◽  
Dominant Individual ◽  
Complex Optimization ◽  
Optimal Values ◽  
Evolutionary Operators

Evolutionary Computation Methods (ECMs) are proposed as stochastic search methods to solve complex optimization problems where classical optimization methods are not suitable. Most of the proposed ECMs aim to find the global optimum for a given function. However, from a practical point of view, in engineering, finding the global optimum may not always be useful, since it may represent solutions that are not physically, mechanically or even structurally realizable. Commonly, the evolutionary operators of ECMs are not designed to efficiently register multiple optima by executing them a single run. Under such circumstances, there is a need to incorporate certain mechanisms to allow ECMs to maintain and register multiple optima at each generation executed in a single run. On the other hand, the concept of dominance found in animal behavior indicates the level of social interaction among two animals in terms of aggressiveness. Such aggressiveness keeps two or more individuals as distant as possible from one another, where the most dominant individual prevails as the other withdraws. In this paper, the concept of dominance is computationally abstracted in terms of a data structure called “competitive memory” to incorporate multimodal capabilities into the evolutionary operators of the recently proposed Cluster-Chaotic-Optimization (CCO). Under CCO, the competitive memory is implemented as a memory mechanism to efficiently register and maintain all possible optimal values within a single execution of the algorithm. The performance of the proposed method is numerically compared against several multimodal schemes over a set of benchmark functions. The experimental study suggests that the proposed approach outperforms its competitors in terms of robustness, quality, and precision.

scholarly journals A Novel Parent Centric Crossover with the Log-Logistic Probabilistic Approach Using Multimodal Test Problems for Real-Coded Genetic Algorithms

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Ehtasham ul Haq ◽  
Ishfaq Ahmad ◽  
Ibrahim M. Almanjahie
Keyword(s):  
Optimization Problems ◽  
Probabilistic Approach ◽  
Population Diversity ◽  
Test Problems ◽  
Crossover Operator ◽  
Local Optima ◽  
Mutation Operators ◽  
Multiple Comparison Test ◽  
Power Mutation ◽  
Real Coded Genetic Algorithms

In this paper, a comprehensive empirical study is conducted to evaluate the performance of a new real-coded crossover operator called Fisk crossover (FX) operator. The basic aim of the proposed study is to preserve population diversity as well as to avoid local optima. In this context, a new crossover operator is designed and developed which is linked with Log-logistic probability distribution. For its global performance, a realistic comparison is made between FX versus double Pareto crossover (DPX), Laplace crossover (LX), and simulated binary crossover (SBX) operators. Moreover, these crossover operators are also used in conjunction with three mutation operators called power mutation (PM), Makinen, Periaux, and Toivanen mutation (MPTM), and nonuniform mutation (NUM) for inclusive evaluation. The performance of probabilistic-based algorithms is tested on a set of twenty-one well-known nonlinear optimization benchmark functions with diverse features. The empirical results show a substantial dominance of FX over other crossover operators with authentication of performance index (PI). Moreover, we also examined the significance of the proposed crossover scheme by administrating ANOVA and Gabriel pairwise multiple comparison test. Finally, the statistically significant results of the proposed crossover scheme have a definite edge over the other schemes, and it is also expected that FX has a great potential to solve complex optimization problems.

scholarly journals A Novel Approach to Improve the Performance of Evolutionary Methods for Nonlinear Constrained Optimization

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Alireza Rowhanimanesh ◽  
Sohrab Efati
Keyword(s):  
Constrained Optimization ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Search Space ◽  
Global Optimum ◽  
Constrained Optimization Problems ◽  
Nonlinear Constrained Optimization ◽  
Evolutionary Methods ◽  
Space Reduction ◽  
Reduced Space

Evolutionary methods are well-known techniques for solving nonlinear constrained optimization problems. Due to the exploration power of evolution-based optimizers, population usually converges to a region around global optimum after several generations. Although this convergence can be efficiently used to reduce search space, in most of the existing optimization methods, search is still continued over original space and considerable time is wasted for searching ineffective regions. This paper proposes a simple and general approach based on search space reduction to improve the exploitation power of the existing evolutionary methods without adding any significant computational complexity. After a number of generations when enough exploration is performed, search space is reduced to a small subspace around the best individual, and then search is continued over this reduced space. If the space reduction parameters (red_gen and red_factor) are adjusted properly, reduced space will include global optimum. The proposed scheme can help the existing evolutionary methods to find better near-optimal solutions in a shorter time. To demonstrate the power of the new approach, it is applied to a set of benchmark constrained optimization problems and the results are compared with a previous work in the literature.

Sign in / Sign up

Export Citation Format

Share Document