Wafaa Mansoor

Multi-objective scheduling problems are inherently complex due to the need to balance competing objectives, such as minimizing the total weighted completion time, reducing the number of delayed jobs, and minimizing the maximum weighted delay. To address these challenges, this article introduces the meerkat clan algorithm (MCA), inspired by the dynamic, cooperative, and adaptive behaviors of meerkats, which enhances the exploration and exploitation of solution spaces. The MCA is further integrated with the traditional branch-and-bound (BAB) method, utilizing it as an upper bound to significantly improve the accuracy and efficiency of the solutions. Comprehensive computational experiments were conducted to evaluate the MCA’s performance against state-of-the-art algorithms, including the bald eagle search optimization algorithm (BESOA) and the standalone BAB method. The MCA demonstrated superior scalability and efficiency, effectively solving problems involving up to n = 30,000 jobs, whereas the BESOA was limited to handling instances with n = 1,000 jobs. Additionally, the integration of MCA with the BAB method achieved exceptional precision and efficiency for smaller problem instances, handling up to n = 13 jobs effectively. The results underscore the MCA algorithm’s potential as a robust solution for multi-objective scheduling problems, combining speed and accuracy to outperform traditional methods. Moreover, the hybrid approach of integrating MCA with BAB provides a flexible and versatile framework capable of addressing a wide range of scheduling scenarios, from small-scale to large-scale applications. These findings position the MCA as a transformative tool for solving complex scheduling problems in both theoretical and practical domains.

The unsteady flow generated by a line source that is located at an arbitrary location beneath the free surface of a fluid of finite depth is considered when there is vertical barrier located nearby. The surface may have surface tension. The barrier is shown to have a significant effect on the wave height generated at the barrier and the outward travelling bore generated by the initiation of the flow. Simulations of free surface flows are very difficult due to the formation of curvature singularities on the surface. The method employed in this work does not appear to have these difficulties and the solutions can be computed almost up until the moment the wave breaks, including in some cases a significant spill at the front. A linearized solution and a fully nonlinear solution are presented and the results compared and discussed.

The human retina is supported by two distinct vascular systems: the highly vascular choroid located behind the retina, and the retinal vascular system, which is designed to minimally disrupt the light path. The avascular retinal layer, situated between these two layers, relies on the diffusion of metabolites through the tissue as it has no circulation. Diseases affecting the microvasculature, such as diabetes and hyper-tension can threaten oxygen supply to these layers, potentially leading to loss of sight. Accurately modeling retinal blood flow is crucial for understanding retinal oxygen supply and the complications arising from systemic vascular diseases. In this paper, we consider a model of just the choroid and avascular layer assuming axisymmetric flow and diffusion, identifying the dispersion pattern from the central region outward. This model captures several significant features of the exchange process and highlights the effects that must be considered in developing more sophisticated models and interpreting experimental results.

The unsteady flow generated when a line sink is located at an arbitrary location beneath the free surface of a fluid of finite depth is considered. Interest is in the evolution to a steady state flow, splashing flows and the drawdown of the surface. The location of the sink away from, but near to, a vertical barrier leads to some interesting new surface flows due to interactions and reflection, some of which have a profound impact on the nature of the critical drawdown flow parameters. Interesting new solutions with a delayed drawdown that are initiated by a reflected wave are presented. A linearized solution and a fully nonlinear solution are presented and the results discussed. Regions of steady, unsteady and supercritical flow are identified.

Machine scheduling problems have become increasingly complex and dynamic. In industrial contexts, managers often evaluate several objectives simultaneously and attempt to identify the optimal solution that satisfies all concerns. This study proposes two heuristic methods based on SPT and dominated rules (DR) to minimize Total Completion ∑Cj, Total Earliness ∑Ej
, and Maximum Tardiness Time Tmax for multicriteria and multi-objective functions (1//(∑Cj,ΣEj,Tmax) and (∑Cj+∑Ej+Tmax)) based on single machine scheduling problems. in addition, two exact methods Branch and Bound (BAB with and without DR) and a complete enumeration method are applied to solve the multi- criteria and multi-objective functions. According to the calculation results, the CEM is able to solve problems up to n=11 jobs, while BAB without DR and BAB with DR able to resolve problems from n=19 to n=50 jobs, respectively, within a reasonable time. However, heuristic methods can solve up to n=5000 jobs. in addition, the experimental results for a subproblem show that the heuristic methods can solve up to n=4000 jobs. Practical experiments demonstrate the proposed heuristic methods are the most effective of all approaches. All methods used in this work were coded with MATLAB 2019a.

The two-dimensional, steady flow of an inviscid fluid induced by a line sink located near a vertical wall in a region of infinite depth is computed. The effects of surface tension are investigated. The solution in the limit of small Froude number is obtained analytically, and numerically for the nonlinear problem. The asymptotic solution is found to have a property that if the horizontal location of the sink, \(x_\mathrm{{s}} < 1\), there is only one stagnation point on the surface, at the wall. However, if the horizontal location \(x_{\mathrm{s}} > 1\), a second stagnation point forms on the free surface. Numerical solution for the nonlinear problem confirms these properties. The effect of moving the sink horizontally has also been considered. The maximum Froude numbers at which steady solutions exist are computed and compared with the previous work.

Flow caused by a line sink near a vertical wall in an otherwise stagnant fluid with a free surface is studied. A linear solution for small flow rates is obtained and a numerical method based on fundamental singularities techniques is applied to the full nonlinear problem. The sink is located at an arbitrary location away from all boundaries and the fluid is of finite depth. Steady solutions are presented for various flow rates and sink location. It is shown that the numerical results and linear solutions are in good agreement for small flow rates. The results suggest that steady nonlinear solutions are limited to flow rates below some critical value. Some interesting surface shapes are obtained depending on the location of the sink.

Two simple mathematical models of advection and diffusion of hydrogen within the retina are discussed. The work is motivated by the hydrogen clearance technique, which is used to estimate blood flow in the retina. The first model assumes that the retina consists of three, well-mixed layers with different thickness, and the second is a two-dimensional model consisting of three regions that represent the layers in the retina. Diffusion between the layers and leakage through the outer edges are considered. Solutions to the governing equations are obtained by employing Fourier series and finite difference methods for the two models, respectively. The effect of important parameters on the hydrogen concentration is examined and discussed. The results contribute to understanding the dispersal of hydrogen in the retina and in particular the effect of flow in the vascular retina. It is shown that the predominant features of the process are captured by the simpler model.

This dissertation is divided into two parts. In the first part we investigate the withdrawal of fluid from a region of fluid with the outlet situated at an arbitrary location. A model for the dispersal of hydrogen released into the retina in an attempt to estimate blood flow in the eye is considered in the second part. In the first part, the flow induced by a line sink at an arbitrary location in a fluid of finite depth with a free surface, relevant to flows in reservoirs, lakes and cooling ponds, is examined. A rigid-lid solution for small flow rates is obtained and a numerical method based on fundamental singularities techniques is applied to the full nonlinear problem. Both linear and numerical steady solutions are obtained for the shape of the free surface and show good agreement. The results suggest that steady non-linear solutions are limited to flow rates below some critical value that depends on the sink location, the surface tension and the strength of the flow. A theorem has been proven regarding the behaviour of the fluid surface and some interesting surface shapes are obtained. The two-dimensional steady flow of an inviscid fluid induced by a line sink located at an arbitrary location in a region of infinite depth is computed. The solution in the limit of small Froude number is obtained analytically, and numerically for the nonlinear problem. The asymptotic solution is found to have a property that if the horizontal location of the sink, xs < 1, there is only one stagnation point on the surface, at the wall. However, if the horizontal location xs > 1 a second stagnation point forms on the free surface. This has implications for the design of outlets in dams and reservoirs. Numerical solution for the nonlinear problem confirms these properties. The effect of moving the sink horizontally has also been considered. The maximum Froude numbers at which steady solutions exist are computed and compared with previous work and the effects of surface tension are investigated. Finally in this part, we examine the unsteady flow due to a line sink in a fluid of finite depth with surface tension where the sink is situated at an arbitrary depth and location. Here we focus on critical values of flow rate that lead to steady or drawn down surfaces and the transitions between the different cases. A solution to the un-steady, linear problem is derived using an integral equation technique. The unsteady, nonlinear equation is then solved numerically using a novel fundamental singularities method. The shape of the free surface is computed for a range of parameter values where the effects of surface tension are taken into account. The linear solution is shown to be in a good agreement with the full nonlinear solution until the depth becomes significant, at which point the nonlinearities become apparent and the two solutions begin to differ slightly. We will examine the behaviour of the flow when the fluid is stagnant and the sink is turned on suddenly. Initially, the free surface is pulled down everywhere regardless of Froude number, F , and surface tension, β, firstly, either near the wall, if the sink is close to the wall, or above the sink, in cases where the sink is situated further from the origin. If the Froude number, F , is large enough the initial dip will keep going until drawdown occurs. However, if the Froude number, F , is smaller, the central region rebounds upward and that leads to a more complicated situation where there are several possible outcomes. There are three general states at the breakdown point of the simulations. These are, evolution to a steady state, drawdown of the surface and something in between which may include breaking waves or splashes. In particular, we obtained critical drawdown values of F for a range of values of β, sink location, xs, and different layer depths, H. In the second major part of the thesis, two mathematical models of advection and diffusion of hydrogen within the retina are discussed to assist in interpretation of the “Hydrogen clearance technique” that is used to estimate blood flow. The first model assumes the retina consists of three, well-mixed layers with different thickness, and the second is a two-dimensional model consisting of three regions that represent the layers in the retina. Diffusion between the layers and leakage through the outer edges are considered. Solutions to the governing equations are obtained by employing Fourier series and finite difference methods for the two models, respectively. The effect of important parameters on the hydrogen concentration is examined and discussed, and a formula is derived for the speed of travel of the bolus of hydrogen. The results contribute to understanding the dispersal of hydrogen in the retina and in particular the effect of flow in the vascular retina. It is shown that the predominant features of the process are captured by the simpler model, meaning that the predictions in experiments can be interpreted without detailed simulation.