Optimizing on a Global Scale with Random Search | Chapter 4 | Mathematics and Computer Science: Contemporary Developments Vol. 6

The challenge of identifying the global optimum in a space containing numerous local optima is a fundamental problem encountered by all systems capable of adapting and learning. GA offers a thorough search process for optimization.

 

Genetic Algorithms (GA) can be used to solve optimization issues, whether they are continuous or discrete in nature. This study uses binary coded GA approaches to function optimization, utilizing a variable length representation scheme and updated genetic operators.

 

Genes and chromosomes constitute the fundamental components of the binary genetic algorithm. The traditional binary genetic algorithm encodes optimization parameters into binary code strings. A gene in GA is represented as a binary digit. To create a population of individuals that represent search space points using the evolution model, the search process iteratively transforms a population of mathematical objects (typically fixed-length binary character strings) with fitness values into a new population of offspring objects. This is accomplished through the application of Darwinian natural selection and operations that are patterned after natural genetic operations such as crossover and mutation. Each individual is evaluated using an objective function for fitness. Consequently, generational evolution is inclined to yield fitter individuals and enhanced solutions within the search space. This process continues until the problem is resolved or no further improvements are observed.

 

Author (s) Details

Halah Ahmad Abd Almeneem Mhamd
Department of Mathematics, Darb University College, Jazan University, Jazan, 45142, Saudi Arabia.

 

Please see the book here:- https://doi.org/10.9734/bpi/mcscd/v6/2573

 

Estimating the Duration of the Sojourn and the Change in Clinical Conditions for HIV Patients Receiving ART Follow-up in Namibia | Chapter 2 | Research and Applications Towards Mathematics and Computer Science Vol. 3

 This episode introduces a Semi-Markov process for judging sojourn time and change between dispassionate states of HIV patients under ART make inquiries.  A Semi-Markov process under HIV disease progress can be delineated based on the distribution of sojourn opportunities. Sojourn time refers in consideration of time a HIV patient spends in each dispassionate state in a single stay before he/she form a transition to another state.  HIV ailment progression maybe broken down into any of intermediate states, established CD4 counts. The four states of the Markov process of HIV are commonly outlined as: S1: CD4 count > 500 cells/microlitre of ancestry; S2: 350 < CD4 count ≤ 500 cells/microlitre of ancestry; S3: 200 < CD4 count ≤ 350 cells/microlitre of ancestry; S4: CD4 count ≤ 200 cells/microliter of ancestry. The main objective of this chapter to estimate sojourn and change between dispassionate states of patients under ART in Namibia utilizing homogenous semi-Markov processes, on dossier obtained from Ministry of Health and Social Services (MoHSS), Namibia. It is owned by state that during the effect period, no dying was recorded and this maybe attributed to exhaustive efforts for one government and differing stakeholders. Namibia is the first African country to have attained and exceeded the UNAIDS 2020 aim, to have at least 73% of HIV positive men viral load restrained. In this chapter, a backward-looking study design was used to obtain dossier on 2422 patients the one were observed 11028 opportunities, during 2008 to 2017 make inquiries period. The four produced semi-Markov model was working to estimate sojourn times and change between dispassionate states. By the end of the chapter, the main results of the study are likely; this includes explanatory statistics on socio-mathematical characteristics of the patients, probabilities of transiting from individual state to another and sojourn times each state. Furthermore, a full dispute of the main results is provided. Conclusion is likely to reflect on the evidence and to report any restraint of the study. Specific actions that maybe taken established the results and conclusion are contained.

Author(s) Details:

Simon Pombili Kashihalwa,
Department of Mathematics, Statistics and Actuarial Science, Namibia University of Science and Technology, Namibia.

Lilian Pazvakawambwa,
Department of Statistics and Population Studies, University of Namibia, Namibia.

Josua Mwanyekange,
Department of Mathematics, Statistics and Actuarial Science, Namibia University of Science and Technology, Namibia.

Please see the link here: https://stm.bookpi.org/RATMCS-V3/article/view/11563

Precise Estimates for the Solution of Stochastic Functional Differential Equations with Discontinuous Initial Data: A Mathematical Approach | Chapter 01 | Novel Research Aspects in Mathematical and Computer Science Vol. 1

 We have established a uniform error bound for the Euler approximation to the solution process of the Stochastic Funtional Differential Equation (S.F.D.E.) (1.11) over the entire time span in this chapter. We discovered the upper bound for the difference between the actual solution process and its Euler approximation by computing the difference between the actual solution process and its Euler approximation. The reliance of this difference on the starting data has also been investigated. We've also shown that the solution process's Euler approximation has a significant convergence order.

Author(S) Details

Tagelsir A. Ahmed
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Khartoum, Sudan.

J. A. van Casteren
Department of Mathematics and Computer Science, University of Antwerp (UA), Middelheimlaan 1, 2020 Antwerp, Belgium.

View Book:- https://stm.bookpi.org/NRAMCS-V1/article/view/6547

Uniform Convergence of Euler Approximation of the Solution of Stochastic Functional Differential Equations with Discontinuous Initial Data | Chapter 03 | Recent Recent Advances in Mathematical Research and Computer Science Vol. 9

 Because model Delay SDEs are often non-linear and do not allow for explicit solutions, numerical approximation approaches for solutions of delay stochastic equations are clearly required. Early explorations in this area were conducted in [1] and [2]. Many physical phenomenon models are stochastic equations. Many of these stochastic differential equations do not have an explicit solution, but we can apply an appropriate approximation approach to obtain an approximate solution for our ordinary SDE. "Stochastic Functional Differential Equations (S.F.D.E's)" in this context refers to "Delay Stochastic Differential Equations." We developed an Euler approximation scheme for the solution process of a Stochastic Functional Differential Equation with possibly discontinuous initial data in this work, and we demonstrated that this Euler scheme (under appropriate conditions) converges to the solution process as the mesh of the partition approaches zero, see also[3] and [4].

The approximation theorem we proposed provides a mechanism for approximating the solution of S.F.D.E's with potentially discontinuous initial data. It's worth noting that we're looking at S.F.D.E. here, which contains both drift and diffusion coefficients. The current approximation study extends the approximation work in [1] to include S.F.D.E's with both drift and diffusion coefficients. Prof. Salah-E. A. Mohammed recommended the work on approximation in [1], which was completed by Tagelsir A. Ahmed under Prof. Salah-E. A. Mohammed's supervision.

Author(S) Details

Tagelsir A. Ahmed
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Khartoum, Sudan.

J. A. Van Casteren
Department of Mathematics and Computer Science, University of Antwerp (UA), Middelheimlaan 1, 2020 Antwerp, Belgium.

View Book:- https://stm.bookpi.org/RAMRCS-V9/article/view/6021