Control and Optimization in Applied Mathematics
Volume:1 Issue: 2, Autumn-Winter 2016

In this paperý, ýa computational approach is adopted for solving a multi-objective optimal control problem (MOOCP) formulation of optimal drug scheduling in human immunodeficiency (HIV) virus infected by individualsý. ýThe MOOCPý, ýwhich uses a mathematical model of HIV infectioný, ýhas some incompatible objectivesý. ýThe objectives are maximizing the survival time of patientsý, ýthe level of D4ý ýT-cells and the level of cytotoxic T-lymphocytes (CTLs)ý, ýand minimizing the viral load and the drug costsý. ýIn this approach the fuzzy goals described by the linear membership functionsý, ýare incorporated for the objectives and the optimal solution is investigated by maximizing the degree of attainment of the aggregated fuzzy goals resulting a fuzzy goal optimal control problem (FGOCP)ý. ýUsing the minimum operator for aggregation of fuzzy goalsý, ýthe FGOCP is converted into a constrained optimal control problem (OCP) in canonical formý. ýThe control parametrization enhancing technique (CPET) is used for approximating the OCP by an optimal parameter selection problemý, ýwith the final goal of implementing continuous and interrupted (structured treatment interruptionsý, ýSTI) combinations of reverse transcriptase inhibitor (RTI) and protease inhibitor (PI) drug efficaciesý. ýEfficiency of the proposed method is confirmed by numerical simulations.

In this paperý, ýthe concept of synchronization control along with robust H∞ control are considered to evaluate the seismic response control on multi-story structuresý. ýTo show the accuracy of the novel algorithmý, ýa five-story structure is evaluated under the EL-Centro earthquake loadý. ýIn order to find the performance of the novel algorithmý, ýrandom and uncertainty processes corresponding to Riccati equation is solved under a specific dynamicý. ýTime history graphs corresponding to maximum displacement and floors force control are presented and evaluatedý. ýDespite the existence of random process and uncertainty in structureý, ýstability and optimal performances are shown.

In this paperý, ýwe suggest a fifth order convergence three-step method for solving system of nonlinear equationsý. ýEach iteration of the method requires two function evaluationsý, ýtwo first Fr'{e}chet derivative evaluations and two matrix inversionsý. ýHenceý, ýthe efficiency index is $5^{1/({2n^{2}\frac{4}{3}n^{3}})}$ý, ýwhich is better than that of other three-step methodsý. ýThe advantages of the method lie in the feature that this technique not only achieves an approximate solution with high accuracyý, ýbut also improves the calculation speedý. ýAlsoý, ýunder several mild conditions the convergence analysis of the proposed method is providedý. ýAn efficient error estimation is presented for the approximate solutioný. ýNumerical examples are included to demonstrate the validity and applicability of the method and the comparisons are made with the existing results.

The field of optimization and machine learning are increasingly interplayed and optimization in different problems leads to the use of machine learning approachesý. ýMachine learning algorithms work in reasonable computational time for specific classes of problems and have important role in extracting knowledge from large amount of dataý. ýIn this paperý, ýa methodology has been employed to optimize the precision of defect detection of concrete slabs depending on their qualitative evaluationý. ýBased on this ideaý, ýsome machine learning algorithms such as C4.5 decision treeý, ýRIPPER rule learning method and Bayesian network have been studied to explore the defect of concrete and to supply a decision system to speed up the defect detection processý. ýThe results from the examinations show that the proposed RIPPER rule learning algorithm in combination with Fourier Transform feature extraction method could get a defect detection rate of 93% as compared to other machine learning algorithms.

Graph theory has an important role in the area of applications of networks and clusteringý. ýIn the case of dealing with uncertain dataý, ýwe must utilize ambiguous data such as fuzzy valueý, ýfuzzy interval value or values of fuzzy numberý. ýIn this studyý, ývalues of fuzzy number were usedý. ýInitiallyý, ýwe utilized the fuzzy number value fuzzy relation and then proposed fuzzy number-value fuzzy graph on nodes and arcsý. ýIn this studyý, ýsome properties of the graph on fuzzy number-value fuzzy graph were examinedý. ýFirstý, ýwe define the Cartesian productý, ýcompositioný, ýunion and join operators on fuzzy number-value fuzzy graphs and then prove some of their properties and and give some examples for every one of definitionsý. ýWe also introduced the notion of homomorphismý, ýweak isomorphism,weak co-isomorphismý, ýisomorphismý, ýcompleteý, ýweak complete and compliment on the fuzzy number fuzzy graphs and prove some of their properties and also present some examples for every one of them.