scholarly journals Understanding measure-driven algorithms solving irreversibly ill-conditioned problems

2021 ◽  
Author(s):  
Jakub Sawicki ◽  
Marcin Łoś ◽  
Maciej Smołka ◽  
Robert Schaefer
Keyword(s):  
Global Optimization ◽  
Markov Chain ◽  
Dynamic Systems ◽  
Positive Measure ◽  
Numerical Solutions ◽  
Optimization Problems ◽  
Real Life ◽  
Population Based ◽  
Ergodic Markov Chain ◽  
Markov Chain Models

AbstractThe paper helps to understand the essence of stochastic population-based searches that solve ill-conditioned global optimization problems. This condition manifests itself by presence of lowlands, i.e., connected subsets of minimizers of positive measure, and inability to regularize the problem. We show a convenient way to analyze such search strategies as dynamic systems that transform the sampling measure. We can draw informative conclusions for a class of strategies with a focusing heuristic. For this class we can evaluate the amount of information about the problem that can be gathered and suggest ways to verify stopping conditions. Next, we show the Hierarchic Memetic Strategy coupled with Multi-Winner Evolutionary Algorithm (HMS/MWEA) that follow the ideas from the first part of the paper. We introduce a complex, ergodic Markov chain of their dynamics and prove an asymptotic guarantee of success. Finally, we present numerical solutions to ill-conditioned problems: two benchmarks and a real-life engineering one, which show the strategy in action. The paper recalls and synthesizes some results already published by authors, drawing new qualitative conclusions. The totally new parts are Markov chain models of the HMS structure of demes and of the MWEA component, as well as the theorem of their ergodicity.

scholarly journals Differential Evolution: A Survey and Analysis

2018 ◽  
Vol 8 (10) ◽  
pp. 1945 ◽  
Author(s):  
Tarik Eltaeib ◽  
Ausif Mahmood
Keyword(s):  
Global Optimization ◽  
Differential Evolution ◽  
Optimization Problems ◽  
State Of The Art ◽  
Population Based ◽  
Vital Role ◽  
Fine Tuning ◽  
Control Parameters ◽  
Hybrid Techniques ◽  
Global Optimizer

Differential evolution (DE) has been extensively used in optimization studies since its development in 1995 because of its reputation as an effective global optimizer. DE is a population-based metaheuristic technique that develops numerical vectors to solve optimization problems. DE strategies have a significant impact on DE performance and play a vital role in achieving stochastic global optimization. However, DE is highly dependent on the control parameters involved. In practice, the fine-tuning of these parameters is not always easy. Here, we discuss the improvements and developments that have been made to DE algorithms. In particular, we present a state-of-the-art survey of the literature on DE and its recent advances, such as the development of adaptive, self-adaptive and hybrid techniques.

Nonlinear Control of Dynamic Systems Using Single Multiplicative Neuron Models

2012 ◽  
Author(s):  
Jonathan G. Turner ◽  
Biswanath Samanta
Keyword(s):  
Nonlinear Control ◽  
Dynamic Systems ◽  
Optimization Technique ◽  
Real Life ◽  
Population Based ◽  
Motor Speed ◽  
Neuron Models ◽  
On Line ◽  
On Line Learning ◽  
Better Than

The paper presents an approach to nonlinear control of dynamic systems using artificial neural networks (ANN). A novel form of ANN, namely, single multiplicative neuron (SMN) model is proposed in place of more traditional multi-layer perceptron (MLP). SMN derives its inspiration from the single neuron computation model in neuroscience. SMN model is trained off-line, to estimate the network weights and biases, using a population based stochastic optimization technique, namely, particle swarm optimization (PSO). Both off-line training and on-line learning of SMN have been considered. The development of the control algorithm is illustrated through the hardware-in-the-loop (HIL) implementation of DC motor speed control in LabVIEW environment. The controller based on SMN performs better than MLP. The simple structure and faster computation of SMN have the potential to make it a preferred candidate for implementation of real-life complex control systems.

Hybrid Harmony Search Algorithm for Global Optimization Problems

2014 ◽  
Vol 1065-1069 ◽  
pp. 3438-3441
Author(s):  
Guo Jun Li
Keyword(s):  
Global Optimization ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Harmony Search ◽  
Population Based ◽  
Harmony Search Algorithm ◽  
Search Method ◽  
Local Optima ◽  
Population Based Algorithm ◽  
Better Than

Harmony search (HS) algorithm is a new population based algorithm, which imitates the phenomenon of musical improvisation process. Its own potential and shortage, one shortage is that it easily trapped into local optima. In this paper, a hybrid harmony search algorithm (HHS) is proposed based on the conception of swarm intelligence. HHS employed a local search method to replace the pitch adjusting operation, and designed an elitist preservation strategy to modify the selection operation. Experiment results demonstrated that the proposed method performs much better than the HS and its improved algorithms (IHS, GHS and NGHS).

scholarly journals A bridging method for global optimization

1999 ◽  
Vol 41 (1) ◽  
pp. 41-57 ◽  
Author(s):  
Y. Liu ◽  
K. L. Teo
Keyword(s):  
Global Optimization ◽  
Differentiable Function ◽  
Numerical Solutions ◽  
Finite Interval ◽  
Optimization Problems ◽  
Optimal Solutions ◽  
Numerical Examples ◽  
One Dimensional ◽  
Differentiable Functions ◽  
Global Optimal

AbstractIn this paper a bridging method is introduced for numerical solutions of one-dimensional global optimization problems where a continuously differentiable function is to be minimized over a finite interval which can be given either explicitly or by constraints involving continuously differentiable functions. The concept of a bridged function is introduced. Some properties of the bridged function are given. On this basis, several bridging algorithm are developed for the computation of global optimal solutions. The algorithms are demonstrated by solving several numerical examples.

DE-PSO: A NEW HYBRID META-HEURISTIC FOR SOLVING GLOBAL OPTIMIZATION PROBLEMS

2011 ◽  
Vol 07 (03) ◽  
pp. 363-381 ◽  
Author(s):  
MILLIE PANT ◽  
RADHA THANGARAJ ◽  
AJITH ABRAHAM
Keyword(s):  
Global Optimization ◽  
Particle Swarm Optimization ◽  
Optimization Algorithm ◽  
Optimization Problems ◽  
Real Life ◽  
Test Functions ◽  
Global Optimization Algorithm ◽  
Two Phase ◽  
Swarm Optimization ◽  
Life Problems

This paper presents a simple, hybrid two phase global optimization algorithm called DE-PSO for solving global optimization problems. DE-PSO consists of alternating phases of Differential Evolution (DE) and Particle Swarm Optimization (PSO). The algorithm is designed so as to preserve the strengths of both the algorithms. Empirical results show that the proposed DE-PSO is quite competent for solving the considered test functions as well as real life problems.

Comparison of Different Bat Initialization Techniques for Global Optimization Problems

2021 ◽  
Vol 12 (1) ◽  
pp. 157-184
Author(s):  
Wasqas Haider Bangyal ◽  
Jamil Ahmad ◽  
Hafiz Tayyab Rauf
Keyword(s):  
Global Optimization ◽  
Optimization Problems ◽  
Bat Algorithm ◽  
Search Space ◽  
Research Problem ◽  
Population Based ◽  
Premature Convergence ◽  
Ongoing Research ◽  
Low Discrepancy Sequences ◽  
Stochastic Search Technique

Bat algorithm (BA) is a population-based stochastic search technique that has been widely used to solve the diverse kind of optimization problems. Population initialization is the current ongoing research problem in evolutionary computing algorithms. Appropriate population initialization assists the algorithm to investigate the swarm search space effectively. BA faces premature convergence problem to find actual global optimization value. Low discrepancy sequences are slightly lesser random number than pseudo-random; however, they are more powerful for computational approaches. In this work, new population initialization approach Halton (BA-HA), Sobol (BA-SO), and Torus (BA-TO) are proposed, which helps bats to avoid from the premature convergence. The proposed approaches are examined on standard benchmark functions, and simulation results are compared with standard BA initialized with uniform distribution. The results depict that substantial enhancement can be attained in the performance of standard BA while varying the random numbers sequences to low discrepancy sequences.

scholarly journals LADE: Learning Automata Based Differential Evolution

2015 ◽  
Vol 24 (06) ◽  
pp. 1550023 ◽  
Author(s):  
Mahshid Mahdaviani ◽  
Javidan Kazemi Kordestani ◽  
Alireza Rezvanian ◽  
Mohammad Reza Meybodi
Keyword(s):  
Differential Evolution ◽  
Optimization Problems ◽  
Learning Automata ◽  
Real Life ◽  
Population Based ◽  
Exact Algorithms ◽  
Function Optimization ◽  
Crossover Probability ◽  
Mutation Strategy ◽  
Mathematical Techniques

Many engineering optimization problems do not standard mathematical techniques, and cannot be solved using exact algorithms. Evolutionary algorithms have been successfully used for solving such optimization problems. Differential evolution is a simple and efficient population-based evolutionary algorithm for global optimization, which has been applied in many real world engineering applications. However, the performance of this algorithm is sensitive to appropriate choice of its parameters as well as its mutation strategy. In this paper, we propose two different underlying classes of learning automata based differential evolution for adaptive selection of crossover probability and mutation strategy in differential evolution. In the first class, genomes of the population use the same mutation strategy and crossover probability. In the second class, each genome of the population adjusts its own mutation strategy and crossover probability parameter separately. The performance of the proposed methods is analyzed on ten benchmark functions from CEC 2005 and one real-life optimization problem. The obtained results show the efficiency of the proposed algorithms for solving real-parameter function optimization problems.

Applying CI in Biology through PSO

2020 ◽  
pp. 502-527
Author(s):  
Rojalina Priyadarshini ◽  
Nilamadhab Dash ◽  
Brojo Kishore Mishra ◽  
Rachita Misra
Keyword(s):  
Optimization Problems ◽  
Real Life ◽  
Population Based ◽  
Computing Methods ◽  
Future Research ◽  
Natural Systems ◽  
Solution Methods ◽  
Working Together ◽  
Future Research Directions ◽  
Population Based Algorithm

Conventional computing methods face challenges dealing with real world problems, which are characterised by noisy or incomplete data. To find solutions for such problems, natural systems have evolved over the years and on analysis it has been found these contain many simple elements when working together to solve real life complex problems. Swarm Intelligence (SI) is one of the techniques which is inspired by nature and is a population based algorithm motivated by the collective behaviour of a group of social insects. Particle swarm optimization (PSO) is one of the techniques belonging to this group, used to solve some optimization problems. This chapter will discuss some of the problems existing in computational biology, their contemporary solution methods followed by the use of PSO to address those problems. Along with this several applications of PSO are discussed in few of the relevant fields are discussed having some future research directions on this field.

A Population-based Approach for Hard Global Optimization Problems based on Dissimilarity Measures

2006 ◽  
Vol 110 (2) ◽  
pp. 373-404 ◽  
Author(s):  
Andrea Grosso ◽  
Marco Locatelli ◽  
Fabio Schoen
Keyword(s):  
Global Optimization ◽  
Optimization Problems ◽  
Population Based ◽  
Dissimilarity Measures
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