scholarly journals A Step Forward in Studying the Compact Genetic Algorithm

2006 ◽  
Vol 14 (3) ◽  
pp. 277-289 ◽  
Author(s):  
Reza Rastegar ◽  
Arash Hariri
Keyword(s):  
Differential Equation ◽  
Genetic Algorithm ◽  
Ordinary Differential Equation ◽  
Point Of View ◽  
Parent Population ◽  
Local Optima ◽  
Mutation Operators ◽  
Compact Genetic Algorithm ◽  
Convergence Point ◽  
Estimation Of Distribution

The compact Genetic Algorithm (cGA) is an Estimation of Distribution Algorithm that generates offspring population according to the estimated probabilistic model of the parent population instead of using traditional recombination and mutation operators. The cGA only needs a small amount of memory; therefore, it may be quite useful in memory-constrained applications. This paper introduces a theoretical framework for studying the cGA from the convergence point of view in which, we model the cGA by a Markov process and approximate its behavior using an Ordinary Differential Equation (ODE). Then, we prove that the corresponding ODE converges to local optima and stays there. Consequently, we conclude that the cGA will converge to the local optima of the function to be optimized.

scholarly journals A GPU-Enabled Compact Genetic Algorithm for Very Large-Scale Optimization Problems

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 758
Author(s):  
Andrea Ferigo ◽  
Giovanni Iacca
Keyword(s):  
Genetic Algorithm ◽  
Large Scale ◽  
Optimization Problems ◽  
Search Space ◽  
Large Scale Problems ◽  
Processing Power ◽  
Compact Genetic Algorithm ◽  
Estimation Of Distribution ◽  
Feasible Solutions ◽  
Compact Optimization

The ever-increasing complexity of industrial and engineering problems poses nowadays a number of optimization problems characterized by thousands, if not millions, of variables. For instance, very large-scale problems can be found in chemical and material engineering, networked systems, logistics and scheduling. Recently, Deb and Myburgh proposed an evolutionary algorithm capable of handling a scheduling optimization problem with a staggering number of variables: one billion. However, one important limitation of this algorithm is its memory consumption, which is in the order of 120 GB. Here, we follow up on this research by applying to the same problem a GPU-enabled “compact” Genetic Algorithm, i.e., an Estimation of Distribution Algorithm that instead of using an actual population of candidate solutions only requires and adapts a probabilistic model of their distribution in the search space. We also introduce a smart initialization technique and custom operators to guide the search towards feasible solutions. Leveraging the compact optimization concept, we show how such an algorithm can optimize efficiently very large-scale problems with millions of variables, with limited memory and processing power. To complete our analysis, we report the results of the algorithm on very large-scale instances of the OneMax problem.

Travelling Wave Solutions for the Unsteady Flow of a Third Grade Fluid Induced Due to Impulsive Motion of Flat Porous Plate Embedded in a Porous Medium

2014 ◽  
Vol 30 (5) ◽  
pp. 527-535 ◽  
Author(s):  
T. Aziz ◽  
F. M. Mahomed ◽  
A. Shahzad ◽  
R. Ali
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Nonlinear Partial Differential Equation ◽  
Porous Plate ◽  
Travelling Wave ◽  
Point Of View ◽  
Third Grade ◽  
Third Grade Fluid ◽  
Physical Point ◽  
Grade Fluid

AbstractThis work describes the time-dependent flow of an incompressible third grade fluid filling the porous half space over an infinite porous plate. The flow is induced due to the motion of the porous plate in its own plane with an arbitrary velocityV(t). Translational type symmetries are employed to perform the travelling wave reduction into an ordinary differential equation of the governing nonlinear partial differential equation which arises from the laws of mass and momentum. The reduced ordinary differential equation is solved exactly, for a particular case, as well as by using the homotopy analysis method (HAM). The better solution from the physical point of view is argued to be the HAM solution. The essentials features of the various emerging parameters of the flow problem are presented and discussed.

scholarly journals Uniform approximation of the Cox-Ingersoll-Ross process

2015 ◽  
Vol 47 (4) ◽  
pp. 1132-1156 ◽  
Author(s):  
Grigori N. Milstein ◽  
John Schoenmakers
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Wiener Process ◽  
Point Of View ◽  
First Passage ◽  
Cir Process ◽  
Quality Of Approximation ◽  
Time Grid ◽  
Passage Times

The Doss-Sussmann (DS) approach is used for uniform simulation of the Cox-Ingersoll-Ross (CIR) process. The DS formalism allows us to express trajectories of the CIR process through solutions of some ordinary differential equation (ODE) depending on realizations of a Wiener process involved. By simulating the first-passage times of the increments of the Wiener process to the boundary of an interval and solving the ODE, we uniformly approximate the trajectories of the CIR process. In this respect special attention is payed to simulation of trajectories near 0. From a conceptual point of view the proposed method gives a better quality of approximation (from a pathwise point of view) than standard, even exact, simulation of the stochastic differential equation at some deterministic time grid.

Qualitative properties of nonlinear ordinary differential equations

1977 ◽  
Vol 79 (1-2) ◽  
pp. 79-85 ◽  
Author(s):  
Nelson Onuchic ◽  
Plácido Z. Táboas
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Linear Ordinary Differential Equation ◽  
Point Of View ◽  
Nonlinear Ordinary Differential Equations ◽  
Qualitative Properties ◽  
Image Position

SynopsisThe perturbed linear ordinary differential equationis considered. Adopting the same approach of Massera and Schäffer [6], Corduneanu states in [2] the existence of a set of solutions of (1) contained in a given Banach space. In this paper we investigate some topological aspects of the set and analyze some of the implications from a point of view ofstability theory.

scholarly journals Conservation laws for a Boussinesq equation.

2017 ◽  
Vol 2 (2) ◽  
pp. 465-472 ◽  
Author(s):  
M.L. Gandarias ◽  
M.S. Bruzón
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Conservation Laws ◽  
Boussinesq Equation ◽  
Point Of View ◽  
Multiplier Method ◽  
Third Order ◽  
Order Ordinary Differential Equation ◽  
Generalized Boussinesq Equation ◽  
The Relationship

AbstractIn this work, we study a generalized Boussinesq equation from the point of view of the Lie theory. We determine all the low-order conservation laws by using the multiplier method. Taking into account the relationship between symmetries and conservation laws and applying the multiplier method to a reduced ordinary differential equation, we obtain directly a second order ordinary differential equation and two third order ordinary differential equations.

scholarly journals Uniform approximation of the Cox-Ingersoll-Ross process

2015 ◽  
Vol 47 (04) ◽  
pp. 1132-1156 ◽  
Author(s):  
Grigori N. Milstein ◽  
John Schoenmakers
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Wiener Process ◽  
Point Of View ◽  
First Passage ◽  
Cir Process ◽  
Quality Of Approximation ◽  
Time Grid ◽  
Passage Times

The Doss-Sussmann (DS) approach is used for uniform simulation of the Cox-Ingersoll-Ross (CIR) process. The DS formalism allows us to express trajectories of the CIR process through solutions of some ordinary differential equation (ODE) depending on realizations of a Wiener process involved. By simulating the first-passage times of the increments of the Wiener process to the boundary of an interval and solving the ODE, we uniformly approximate the trajectories of the CIR process. In this respect special attention is payed to simulation of trajectories near 0. From a conceptual point of view the proposed method gives a better quality of approximation (from a pathwise point of view) than standard, even exact, simulation of the stochastic differential equation at some deterministic time grid.

scholarly journals On the Optimal Convergence Probability of Univariate Estimation of Distribution Algorithms

2011 ◽  
Vol 19 (2) ◽  
pp. 225-248 ◽  
Author(s):  
Reza Rastegar
Keyword(s):  
Genetic Algorithm ◽  
Confidence Level ◽  
Incremental Learning ◽  
Optimal Solution ◽  
Population Based ◽  
Sufficient Condition ◽  
Estimation Of Distribution Algorithms ◽  
Compact Genetic Algorithm ◽  
Estimation Of Distribution ◽  
Distribution Algorithms

In this paper we obtain bounds on the probability of convergence to the optimal solution for the compact genetic algorithm (cGA) and the population based incremental learning (PBIL). Moreover, we give a sufficient condition for convergence of these algorithms to the optimal solution and compute a range of possible values for algorithm parameters at which there is convergence to the optimal solution with a predefined confidence level.

scholarly journals The Univariate Marginal Distribution Algorithm Copes Well With Deception and Epistasis

2021 ◽  
pp. 1-22
Author(s):  
Benjamin Doerr ◽  
Martin S. Krejca
Keyword(s):  
Genetic Algorithm ◽  
Evolutionary Algorithms ◽  
Genetic Drift ◽  
High Probability ◽  
Marginal Distribution ◽  
Local Optima ◽  
Negative Finding ◽  
Compact Genetic Algorithm ◽  
Population Sizes ◽  
First Time

Abstract In their recent work, Lehre and Nguyen (FOGA 2019) show that the univariate marginal distribution algorithm (UMDA) needs time exponential in the parent populations size to optimize the DeceptiveLeadingBlocks (DLB) problem. They conclude from this result that univariate EDAs have difficulties with deception and epistasis. In this work, we show that this negative finding is caused by the choice of the parameters of the UMDA. When the population sizes are chosen large enough to prevent genetic drift, then the UMDA optimizes the DLB problem with high probability with at most λ(n2+2elnn) fitness evaluations. Since an offspring population size λ of order n log n can prevent genetic drift, the UMDA can solve the DLB problem with O(n2) log n fitness evaluations. In contrast, for classic evolutionary algorithms no better run time guarantee than O(n3) is known (which we prove to be tight for the (1 + 1) EA), so our result rather suggests that the UMDA can cope well with deception and epistatis. From a broader perspective, our result shows that the UMDA can cope better with local optima than many classic evolutionary algorithms; such a result was previously known only for the compact genetic algorithm. Together with the lower bound of Lehre and Nguyen, our result for the first time rigorously proves that running EDAs in the regime with genetic drift can lead to drastic performance losses.

Optimizing Ontology Alignment Through an Interactive Compact Genetic Algorithm

2021 ◽  
Vol 12 (2) ◽  
pp. 1-17
Author(s):  
Xingsi Xue ◽  
Xiaojing Wu ◽  
Junfeng Chen
Keyword(s):  
Genetic Algorithm ◽  
Intelligent Systems ◽  
Ontology Matching ◽  
Ontology Alignment ◽  
Knowledge Modeling ◽  
Matching Problem ◽  
Local Optima ◽  
Argumentation Framework ◽  
Compact Genetic Algorithm ◽  
Matching Technique

Ontology provides a shared vocabulary of a domain by formally representing the meaning of its concepts, the properties they possess, and the relations among them, which is the state-of-the-art knowledge modeling technique. However, the ontologies in the same domain could differ in conceptual modeling and granularity level, which yields the ontology heterogeneity problem. To enable data and knowledge transfer, share, and reuse between two intelligent systems, it is important to bridge the semantic gap between the ontologies through the ontology matching technique. To optimize the ontology alignment’s quality, this article proposes an Interactive Compact Genetic Algorithm (ICGA)-based ontology matching technique, which consists of an automatic ontology matching process based on a Compact Genetic Algorithm (CGA) and a collaborative user validating process based on an argumentation framework. First, CGA is used to automatically match the ontologies, and when it gets stuck in the local optima, the collaborative validation based on the multi-relationship argumentation framework is activated to help CGA jump out of the local optima. In addition, we construct a discrete optimization model to define the ontology matching problem and propose a hybrid similarity measure to calculate two concepts’ similarity value. In the experiment, we test the performance of ICGA with the Ontology Alignment Evaluation Initiative’s interactive track, and the experimental results show that ICGA can effectively determine the ontology alignments with high quality.

scholarly journals Solving Differential Equation by Modified Genetic Algorithms

2018 ◽  
Vol 26 (10) ◽  
pp. 233-241
Author(s):  
Eman Ali Hussain ◽  
Yahya Mourad Abdul – Abbass
Keyword(s):  
Differential Equation ◽  
Genetic Algorithm ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
Mathematical Equation ◽  
Individual Solution ◽  
Result Show ◽  
String Representation ◽  
Derivatives Of ◽  
Physical Quantities

   Differential equation is a mathematical equation which contains the derivatives of a variable, such as the equation which represent physical quantities, In this paper  we introduced modified on the method which proposes a polynomial to solve the ordinary differential equation (ODEs) of second order and by using the evolutionary algorithm to find the coefficients of the propose a polynomial [1] . Our method propose a polynomial to solve the ordinary differential equations (ODEs) of nth  order and partial differential equations(PDEs) of order two  by using the Genetic algorithm to find the coefficients of the propose a polynomial ,since Evolution Strategies (ESs) use  a string representation of the solution to some problem and attempt to evolve a good solution through a series of fitness –based evolutionary steps .unlike (GA)  ,an ES will typically not use a population of solution but instead will make a sequence of mutations of an individual solution ,using fitness as a guide[2] . A numerical example with good result show the accuracy of our method compared with some existing methods .and the best error of method it’s not much larger than the error in best of the numerical method solutions.

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