Differential evolution with multi-constraint consensus methods for constrained optimization

Constrained optimization is an important research topic that assists in quality planning and decision making. To solve such problems, one of the important aspects is to improve upon any constraint violation, and thus bring infeasible individuals to the feasible region. To achieve this goal, different constraint consensus methods have been introduced, but no single method performs well for all types of problems. Hence, in this research, for solving constrained optimization problems, we introduce different variants of the Differential Evolution algorithm, with multiple constraint consensus methods. The proposed algorithms are tested and analyzed by solving a set of well-known bench mark problems. For further improvements, a local search is applied to the best variant. We have compared our algorithms among themselves, as well as with other state of the art algorithms. Those comparisons show similar, if not better performance, while also using significantly lower computational time.     

Real time disruption management for a two-stage batch production–inventory system with reliability considerations

In this research, a two-stage batch production–inventory system is introduced. In this system, the production may be disrupted, for a given period of time, either at one or both stages. In this paper, firstly, a mathematical model has been developed to suggest a recovery plan for a single occurrence of disruption at either stage. Secondly, multiple disruptions have been considered, for which a new disruption may or may not affect the recovery plan of earlier disruptions. We propose a new approach that deals with a series of disruptions over a period of time, which can be implemented for disruption recovery on a real time basis. In this approach, the model formulated for single disruption has been integrated to generate initial solutions for individual disruptions and the solutions have been revised for multiple dependent disruptions with changed parameters. With the proposed approach, an optimal recovery plan can be obtained in real time, whenever the production system experiences either a sudden disruption or a series of disruptions, at different points in time. Some numerical examples and a real-world case study are presented to explain the benefits of our proposed approach.     

Segal-Bargmann transforms associated with finite Coxeter groups

Using a polarization of a suitable restriction map, and heat-kernel analysis, we construct a generalized Segal-Bargmann transform associated with every finite Coxeter group G on ? ^N . We find the integral representation of this transform, and we prove its unitarity. To define the Segal-Bargmann transform, we introduce a Hilbert space of holomorphic functions on with reproducing kernel equal to the Dunkl-kernel. The definition and properties of extend naturally those of the well-known classical Fock space. The generalized Segal-Bargmann transform allows to exhibit some relationships between the Dunkl theory in the Schrödinger model and in the Fock model. Further, we prove a branching decomposition of as a unitary -module and a general version of Hecke's formula for the Dunkl transform.     

Partial difference equation method for lattice path problems

Many problems concerning lattice paths, especially on the square lattice have been exactly solved. For a single path, many methods exist that allow exact calculation regardless of whether the path inhabits a strip, a semi-infinite space or infinite space, or perhaps interacts with the walls. It has been shown that a transfer matrix method using the Bethe Ansatz allows for the calculation of the partition function for many non-intersecting paths interacting with a wall. This problem can also be considered using the Gessel-Viennot methodology. In a concurrent development, two non-intersecting paths interacting with a wall have been examined in semi-infinite space using a set of partial difference equations.Here, we review thispartial difference equation method for the case of one path in a half plane. We then demonstrate that the answer for arbitrary numbers of non-intersecting paths interacting with a wall can be obtained using this method. One reason for doing this is its pedagogical value in showing its ease of use compared to the transfer matrix method. The solution is expressed in a new form as a constant term formula, which is readily evaluated. More importantly, it is the natural method that generalizes easily to many intersecting paths where there is inter-path interactions (e.g., osculating lattice paths). We discuss the relationship of the partial difference equation method to the transfer matrix method and their solution via a Bethe Ansatz.     

Fractional order boundary value problem with integral boundary conditions involving Pettis integral

In this article, we investigate the existence of Pseudo solutions for some fractional order boundary value problem with integral boundary conditions in the Banach space of continuous function equipped with its weak topology. The class of such problems constitute a very interesting and important class of problems. They include two, three, multi-point and nonlocal boundary-value problems as special cases. In our investigation, the right hand side of the above problem is assumed to be Pettis integrable function. To encompass the full scope of this article, we give an example illustrating the main result.     

The family of D-weights for a two-rooted graph

Let Π(G) be the set of paths of a particular class Π from the initial to the terminal root of a two-rooted (possibly directed) graph G. We consider the family of $\text{D}$-weights defined by

where Π_x(G) is the family of subsets of Π(G) which cover x(G), the vertex set or the edge (arc) set of G.A number of the common properties and interrelations of these weights are discussed. Some of the weights have been considered previously, [1, 2], in the context of percolation theory but here only combinatorial arguments are used.     

Effects of variable properties on MHD heat and mass transfer flow near a stagnation point towards a stretching sheet in a porous medium with thermal radiation

The effect of variable viscosity and thermal conductivity on steady magnetohydrodynamic(MHD) heat and mass transfer flow of viscous and incompressible fluid near a stagnation point towards a permeable stretching sheet embedded in a porous medium are presented,taking into account thermal radiation and internal heat genberation/absorbtion.The stretching velocity and the ambient fluid velocity are assumed to vary linearly with the distance from the stagnation point.The Rosseland approximation is used to describe the radiative heat flux in the energy equation.The governing fundamental equations are first transformed into a system of ordinary differential equations using a scaling group of transformations and are solved numerically by using the fourth-order Rung-Kutta method with the shooting technique.A comparison with previously published work has been carried out and the results are found to be in good agreement.The results are analyzed for the effect of different physical parameters,such as the variable viscosity and thermal conductivity,the ratio of free stream velocity to stretching velocity,the magnetic field,the porosity,the radiation and suction/injection on the flow,and the heat and mass transfer characteristics.The results indicate that the inclusion of variable viscosity and thermal conductivity into the fluids of light and medium molecular weight is able to change the boundary-layer behavior for all values of the velocity ratio parameter λ except for λ = 1.In addition,the imposition of fluid suction increases both the rate of heat and mass transfer,whereas fluid injection shows the opposite effect.