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.

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.

Ultimate and Practical Limits for Counterweight Balancing of Six-Bar Linkages

2006 ◽  
Author(s):  
Bram Demeulenaere ◽  
Jan Swevers ◽  
Joris De Schutter
Keyword(s):  
Optimization Problem ◽  
Optimization Problems ◽  
Global Optimum ◽  
Great Efficiency ◽  
Convex Programs ◽  
Local Optima ◽  
Trade Off ◽  
Convex Constraint ◽  
Main Challenge ◽  
Dynamic Forces

The designer’s main challenge when counterweight balancing a linkage is to determine the counterweights that realize an optimal trade-off between the dynamic forces of interest. This problem is often formulated as an optimization problem that is generally nonlinear and therefore suffers from local optima. It has been shown earlier, however, that, through a proper parametrization of the counterweights, a convex program can be obtained. Convex programs are nonlinear optimization problems of which the global optimum is guaranteed to be found with great efficiency. The present paper extends this previous work in two respects: (i) the methodology is generalized from four-bar to planar N-bar (rigid) linkages and (ii) it is shown that requiring the counterweights to be realizable in practice can be cast as a convex constraint. Numerical results for a Watt six-bar linkage suggest much more balancing potential for six-bar linkages than for four-bar linkages.

scholarly journals Optimal Operational Scheduling of Reconfigurable Microgrids in Presence of Renewable Energy Sources

Energies ◽  
2019 ◽  
Vol 12 (10) ◽  
pp. 1858 ◽  
Author(s):  
Fatma Yaprakdal ◽  
Mustafa Baysal ◽  
Amjad Anvari-Moghaddam
Keyword(s):  
Distribution System ◽  
Distribution Systems ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Renewable Energy Sources ◽  
Hybrid Approach ◽  
Optimization Methods ◽  
System Optimization ◽  
Distribution Networks ◽  
Optimal Dispatch

Passive distribution networks are being converted into active ones by incorporating distributed means of energy generation, consumption, and storage, and the formation of so-called microgrids (MGs). As the next generation of MGs, reconfigurable microgrids (RMGs) are still in early phase studies, and require further research. RMGs facilitate the integration of distributed generators (DGs) into distribution systems and enable a reconfigurable network topology by the help of remote-controlled switches (RCSs). This paper proposes a day-ahead operational scheduling framework for RMGs by simultaneously making an optimal reconfiguration plan and dispatching controllable distributed generation units (DGUs) considering power loss minimization as an objective. A hybrid approach combining conventional particle swarm optimization (PSO) and selective PSO (SPSO) methods (PSO&SPSO) is suggested for solving this combinatorial, non-linear, and NP-hard complex optimization problem. PSO-based methods are primarily considered here for our optimization problem, since they are efficient for power system optimization problems, easy to code, have a faster convergence rate, and have a substructure that is suitable for parallel calculation rather than other optimization methods. In order to evaluate the suggested method’s performance, it is applied to an IEEE 33-bus radial distribution system that is considered as an RMG. One-hour resolution of the simultaneous network reconfiguration (NR) and the optimal dispatch (OD) of distributed DGs are carried out prior to this main study in order to validate the effectiveness and superiority of the proposed approach by comparing relevant recent studies in the literature.

scholarly journals Application of Genetic Algorithm in Common Optimization Problems

2019 ◽  
Vol 8 (1) ◽  
pp. 17-21
Author(s):  
Nika Topuria ◽  
Omar Kikvidze
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Local Optima ◽  
Deterministic Algorithms ◽  
Complex Optimization ◽  
Short Time ◽  
Fitness Parameter

Use of non-deterministic algorithms for solving multi-variable optimization problems is widely used nowadays. Genetic Algorithm belongs to a group of stochastic biomimicry algorithms, it allows us to achieve optimal or near-optimal results in large optimization problems in exceptionally short time (compared to standard optimization methods). Major advantage of Genetic Algorithm is the ability to fuse genes, to mutate and do selection based on fitness parameter. These methods protect us from being trapped in local optima (Most of deterministic algorithms are prone to getting stuck on local optima). In this paper we experimentally show the upper hand of Genetic Algorithms compared to other traditional optimization methods by solving complex optimization problem.

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.

Self-adaptively Commensal Learning-based Jaya Algorithm with Multi-populations and its Application

2021 ◽  
Author(s):  
Zuanjia Xie ◽  
Chunliang Zhang ◽  
Haibin Ouyang ◽  
Steven Li ◽  
Liqun Gao
Keyword(s):  
Learning Strategy ◽  
Optimization Problems ◽  
State Of The Art ◽  
Global Optimum ◽  
Benchmark Problems ◽  
Series System ◽  
Jaya Algorithm ◽  
Roulette Wheel Selection ◽  
Roulette Wheel ◽  
Distribution Scheme

Abstract Jaya algorithm is an advanced optimization algorithm, which has been applied to many real-world optimization problems. Jaya algorithm has better performance in some optimization field. However, Jaya algorithm exploration capability is not better. In order to enhance exploration capability of the Jaya algorithm, a self-adaptively commensal learning-based Jaya algorithm with multi-populations (Jaya-SCLMP) is presented in this paper. In Jaya-SCLMP, a commensal learning strategy is used to increase the probability of finding the global optimum, in which the person history best and worst information is used to explore new solution area. Moreover, a multi-populations strategy based on Gaussian distribution scheme and learning dictionary is utilized to enhance the exploration capability, meanwhile every sub-population employed three Gaussian distributions at each generation, roulette wheel selection is employed to choose a scheme based on learning dictionary. The performance of Jaya-SCLMP is evaluated based on 28 CEC 2013 unconstrained benchmark problems. In addition, three reliability problems, i.e. complex (bridge) system, series system and series-parallel system are selected. Compared with several Jaya variants and several state-of-the-art other algorithms, the experimental results reveal that Jaya-SCLMP is effective.

The Genetic Algorithm

2019 ◽  
pp. 154-178
Author(s):  
Burcu Adıguzel Mercangöz ◽  
Ergun Eroglu
Keyword(s):  
Genetic Algorithm ◽  
Mathematical Models ◽  
Portfolio Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Biological Evolution ◽  
Research Field ◽  
Risk Level ◽  
Important Research ◽  
Portfolio Optimization Problem

The portfolio optimization is an important research field of the financial sciences. In portfolio optimization problems, it is aimed to create portfolios by giving the best return at a certain risk level from the asset pool or by selecting assets that give the lowest risk at a certain level of return. The diversity of the portfolio gives opportunity to increase the return by minimizing the risk. As a powerful alternative to the mathematical models, heuristics is used widely to solve the portfolio optimization problems. The genetic algorithm (GA) is a technique that is inspired by the biological evolution. While this book considers the heuristics methods for the portfolio optimization problems, this chapter will give the implementing steps of the GA clearly and apply this method to a portfolio optimization problem in a basic example.

scholarly journals Parameterized Nonlinear Least Squares for Unsupervised Nonlinear Spectral Unmixing

2019 ◽  
Vol 11 (2) ◽  
pp. 148 ◽  
Author(s):  
Risheng Huang ◽  
Xiaorun Li ◽  
Haiqiang Lu ◽  
Jing Li ◽  
Liaoying Zhao
Keyword(s):  
Least Squares ◽  
Optimization Problem ◽  
Nonnegative Matrix Factorization ◽  
Optimization Problems ◽  
State Of The Art ◽  
Synthetic Data ◽  
Nonnegative Matrix ◽  
Nonlinear Least Squares ◽  
Hyperspectral Data ◽  
Spectral Unmixing

This paper presents a new parameterized nonlinear least squares (PNLS) algorithm for unsupervised nonlinear spectral unmixing (UNSU). The PNLS-based algorithms transform the original optimization problem with respect to the endmembers, abundances, and nonlinearity coefficients estimation into separate alternate parameterized nonlinear least squares problems. Owing to the Sigmoid parameterization, the PNLS-based algorithms are able to thoroughly relax the additional nonnegative constraint and the nonnegative constraint in the original optimization problems, which facilitates finding a solution to the optimization problems . Subsequently, we propose to solve the PNLS problems based on the Gauss–Newton method. Compared to the existing nonnegative matrix factorization (NMF)-based algorithms for UNSU, the well-designed PNLS-based algorithms have faster convergence speed and better unmixing accuracy. To verify the performance of the proposed algorithms, the PNLS-based algorithms and other state-of-the-art algorithms are applied to synthetic data generated by the Fan model and the generalized bilinear model (GBM), as well as real hyperspectral data. The results demonstrate the superiority of the PNLS-based algorithms.

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.

COMPLEXITY OF SCENARIO-BASED PORTFOLIO OPTIMIZATION PROBLEM WITH VaR OBJECTIVE

2002 ◽  
Vol 13 (05) ◽  
pp. 671-679 ◽  
Author(s):  
XIAOGUANG YANG ◽  
SHUO TAO ◽  
RONGJUN LIU ◽  
MAOCHENG CAI
Keyword(s):  
Portfolio Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Np Hard ◽  
Portfolio Optimization Problem

In this paper we discuss the VaR-related portfolio optimization problems. We give a scenario-based formulation of the portfolio optimization problem with VaR objective and show that the problem is NP-hard.

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