Evolutionary Algorithms Enhanced with Quadratic Coding and Sensing Search for Global Optimization

Abstract

Enhancing Evolutionary Algorithms (EAs) using mathematical elements significantly contribute to their development and control the randomness they are experiencing. Moreover, the automation of the primary process steps of EAs is still one of the hardest problems. Specifically, EAs still have no robust automatic termination criteria. Moreover, the highly random behavior of some evolutionary operations should be controlled, and the methods should invoke advanced learning process and elements. As follows, this research focuses on the problem of automating and controlling the search process of EAs by using sensing and mathematical mechanisms. These mechanisms can provide the search process with the needed memories and conditions to adapt to the diversification and intensification opportunities. Moreover, a new quadratic coding and quadratic search operator are invoked to increase the local search improving possibilities. The suggested quadratic search operator uses both regression and Radial Basis Function (RBF) neural network models. Two evolutionary-based methods are proposed to evaluate the performance of the suggested enhancing elements using genetic algorithms and evolution strategies. Results show that for both the regression, RBFs and quadratic techniques could help in the approximation of high-dimensional functions with the use of a few adjustable parameters for each type of function. Moreover, the automatic termination criteria could allow the search process to stop appropriately.

Search Graph Magnification in Rapid Mixing of Markov Chains Associated with the Local Search-Based Metaheuristics

“…Metaheuristics are applied successfully to obtain the optimum or near to optimum solution for many optimization problems in the literature [31][32][33][34][35][36][37][38]. To apply metaheuristics for the optimization problem, one should define a search space for the problem.…”

A Novel Non-Isotonic Statistical Bivariate Regression Method—Application to Stratigraphic Data Modeling and Interpolation

“…When a data set is not non-monotonic, it is harder to obtain a model of the data and to infer the value of missing records by interpolation than for a monotonic data set. One solution is to infer a functional relationship between variables using regression analysis as illustrated, to cite a few, in the paper [2] on evolutionary algorithms, in the contribution [3] on autonomous agents, and in the contributions [4][5][6] which cover several practical aspects of regression analysis. Regression is a computation application of paramount importance as testified by the research paper [7] that illustrates an application to drowsiness estimation using electroencephalographic data, by the book [8] on statistical methods for engineers and scientists, by [9] that explores an improved power law for nonlinear least-squares fitting, in the papers [10][11][12] that exploit regression analysis in forecasting and prediction, by the research paper [13] that compares a number of linear and non-linear regression methods, in the paper [14] that uses support vector regression for the modeling and synthesis of antenna arrays, and by the contribution [15] that applies kernel Ridge regression to short-term wind speed forecasting.…”