Search

In this paper we will revisit the modification of the piecewise constant policy timestepping (PCPT) method for solving Hamilton-Jacobi-Bellman (HJB) equations. This modification is called piecewise predicted policy timestepping (PPPT) method and if properly used, it may be significantly faster. We will quickly recapitulate the algorithms of PCPT, PPPT methods and of the classical implicit method and apply them on a passport option pricing problem with non-standard payoff. We will present modifications needed to solve this problem effectively with the PPPT method and compare the performance with the PCPT method and the classical implicit method. [ABSTRACT FROM AUTHOR]

This paper presents an algorithm that is able to solve optimal control problems in which the modelling of the system contains variable parameters, with the added complication that, in certain cases, these parameters can lead to control problems governed by quasi-linear equations. Combining the techniques of Pontryagin's Maximum Principle and the shooting method, an algorithm has been developed that is not affected by the values of the parameters, being able to solve conventional problems as well as cases in which the optimal solution is shown to be bang-bang with singular arcs. [ABSTRACT FROM AUTHOR]

Integer goal programming problems arise quite naturally in many real-world applications. In this paper, we propose a reference direction approach and interactive algorithm to solve integer goal programming problem. We use analytic hierarchy process (AHP) to get the reference direction. At each iteration, only one integer linear programming problem is solved to get an efficient solution. Through analytic hierarchy process the decision maker has to provide the preference point such that the original problem has been transformed into linear integer programming model. [ABSTRACT FROM AUTHOR]

The paper deals with the development of algorithms for solving nonlinear problems of heat conduction in bodies consisting of layered metal composites. The nonlinearity of the problems is governed by the temperature dependence of the heat conductivity coefficients of the composite layer materials. Mathematical models and solution algorithms based on the boundary element method have been constructed for one-dimensional cases of heat distribution. [ABSTRACT FROM AUTHOR]

In this paper a hybrid algorithm is proposed to find the optimal solution for any instance of the bin packing problem one-dimensional. The hybrid algorithm considers the use of a heuristic method and a mathematical model based on flow arcs technique to find the optimal solution for an instance of 1D-BPP. The hybrid algorithm makes use of the lower bound of an instance as an element that allows it to identify if it have found the optimum or starting from this value it must find the optimal solution. The experiments were performed using the instances of the hard28 set, finding it the optimal solutions for all instances. The results show that the developed algorithm, called AHR, used 75% less time than using the Valerio model. [ABSTRACT FROM AUTHOR]

It is usually difficult for people to solve real-life problems, although nature has had Its own way of looking at and addressing these challenges for millions of years. This is why these days when people fail to strategize in these circumstances, they turn to nature to solve problems. Thus, it is often difficult for algorithms to arrive at the correct solution to a problem through heuristic processes. On the other hand, these strategies are good for getting close to the required time. One of these algorithms is called the Strawberry Algorithm. Here we propose to study the influence of Strawberry Algorithm roots and runners. In this research, we came up with the best solution to find the roots of a linear equation using one of nature's algorithms, and from these algorithms we find the strawberry algorithm through the Visual Studio 2019 platform. It has been observed that the strawberry algorithm succeeded in finding solutions to the linear equation and was very effective in finding any linear equation and he compared the results of the algorithm with the genetic algorithm in terms of measuring efficiency in time and iteration so that the strawberry algorithm was better than the genetic algorithm. [ABSTRACT FROM AUTHOR]

This article discusses the possibilities in the area of modeling of the so called cooling tower plume emergent at operating evaporating cooling systems. As opposed to recent publication, this text focuses on the possibilities of a simplified analytic description of the whole problem where this description shall - in the future - form the base of a calculation algorithms enabling to simulate the efficiency of systems reducing this cooling tower plume. The procedure is based on the application of basic formula for the calculation of the velocity and concentration fields in the area above the cooling tower. These calculation is then used to determine the form and the total volume of the plume. Although this approach does not offer more exact results, it can provide a basic understanding of the impact of individual quantities relating to this problem. [ABSTRACT FROM AUTHOR]

We consider a model problem for the research of Earth's surface state caused by discharge of tectonic stress on the deep cracks in the earth's crust. Using the numerical method of bicharacteristics, algorithm is developed and solution of the problem of non-stationary dynamics of a homogeneous isotropic elastic half-space is built under plane strain when one resets the vertical stress on crack. Diffraction of waves on the surface is studied, pictures of wave fields and stress-strain state of the medium and the surface for different moments of time are built. [ABSTRACT FROM AUTHOR]

In this work we consider stationary periodic solutions of fourth-order semi-linear parabolic equation, arising in population dynamics and spatial patterns formation. First, using variational method, we establish existence of infinitely many solutions. Next we develop a fast numerical algorithm for solving the model problem. Numerical results are proposed and discussed. [ABSTRACT FROM AUTHOR]