Constrained optimization via the Genetic Algorithm (GA) is often a challenging endeavor, as the GA is most directly suited to unconstrained optimization. Traditionally, external penalty functions have been used to convert a constrained optimization problem into an unconstrained problem for GA-based optimization. This approach requires the somewhat arbitrary selection of penalty draw-down coeffi...

We formulate and investigate a statistical inverse problem of a random tomographic nature, where a probability density function on R is to be recovered from observation of finitely many of its twodimensional projections in random and unobservable directions. Such a problem is distinct from the classic problem of tomography where both the projections and the unit vectors normal to the projection...

The paper addresses a problem of optimal staffing in open shop environment. The problem is to determine the optimal number of operators serving a given number of machines to fulfill the number of independent operations while minimizing staff idle. Using a Gantt chart presentation of the problem it is modeled as twodimensional cutting stock problem. A mixed-integer programming model is used to g...

We introduce and solve the Vehicle Routing Problem with Simultaneous Pick-ups and Deliveries and TwoDimensional Loading Constraints (2L-SPD). The 2L-SPD model covers cases where customers raise delivery and pick-up requests for transporting non-stackable rectangular items. 2L-SPD belongs to the class of composite routing-packing optimization problems. However, it is the first such problem to co...

We consider local minimizers u : R 2 ⊃ Ω → R M of the variational integral Ω H(∇u) dx with density H growing at least quadratically and allowing a very large scale of anisotropy. We discuss higher integrability properties of ∇u as well as the differentiability of u in the classical sense. Moreover, a Liouville-type theorem is established.

Here considered is the mathematical analysis and numerical computation of the electromagnetic wave scattering by multiple cavities embedded in an infinite ground plane. Above the ground plane the space is filled with a homogeneous medium, while the interiors of the cavities are filled with inhomogeneous media characterized by variable permittivities. By introducing a new transparent boundary co...

A simulation of reheating furnace in a steel production line where the billets are heated from room temperature up to 1200 ˚C, is carried out using novel meshless solution procedure. The before continuous hot-rolling process should be employed dissolve alloying elements as much possible and redistribute carbon. In this work, governing equations solved by local radial basis function collocation ...

The noncommutative harmonic oscillator in arbitrary dimension is examined. It is shown that the ⋆-genvalue problem can be decomposed into separate harmonic oscillator equations for each dimension. The noncommutative plane is investigated in greater detail. The constraints for rotationally symmetric solutions and the corresponding twodimensional harmonic oscillator are solved. The angular moment...

In this paper we suggest an approach to a completely automatic contouring the left ventricle (LV). We use the method of signatures to describe the shape of the contour. Analysis of contours performed manually enables us to conclude that the signature of any contour of any patient has the shape of the inverted letter "M". This allows reducing the contouring problem to the problem of signature re...

Researchers in many fields often need to quantify the similarity between images using metrics that measure qualities of interest in a robust quantitative manner. We present here the concept of image dimension reduction through characteristic shape sequences. We formulate the problem as a nonlinear optimization program and demonstrate the solution on a test problem of extracting maximal area ell...