A continuous variable neighborhood search heuristic for finding the three-dimensional structure of a molecule

We develop a continuous variable neighborhood search heuristic for minimizing the potential energy function of a molecule. Computing the global minimum of this function is very difficult because it has a large number of local minimizers which grows exponentially with molecule size. Experimental evidence shows that in the great majority of cases the global minimum potential energy of a given molecule corresponds to its three-dimensional structure and this structure is important because it dictates most of the properties of the molecule. Computational results for problems with up to 200 degrees of freedom are presented and favourable compared with other two existing methods from the literature.     

Necessary conditions for the neutral problem of Bolza with continuously varying time delay

This note uses Clarke's decoupling technique to obtain necessary conditions for the generalized problem of Bolza with Lipschitz continuously varying delay in both the state and velocity variables.     

A minimization method for the sum of a convex function and a continuously differentiable function

This paper presents a method for finding the minimum for a class of nonconvex and nondifferentiable functions consisting of the sum of a convex function and a continuously differentiable function. The algorithm is a descent method which generates successive search directions by solving successive convex subproblems. The algorithm is shown to converge to a critical point.The authors wish to express their appreciation to the referees for their careful review and helpful comments.     

A competing infection model for the spread of different viewpoints of a divisive idea

We develop a non-network, deterministic, competing infections model for the spread of two competing viewpoints of a divisive idea that incorporates external factors in addition to interpersonal interactions. We consider divisive ideas to have polarizing support, i.e. there are no “shades of grey.” The proposed model for the spread of the competing support and skepticism of such an idea within a population is based on both epidemiological and competing species models. The model is then analyzed qualitatively and quantitatively in a case study of the 2016 Republican primary polls. Parameter fitting to this data shows the proposed model is plausible for the spread of viewpoints of a divisive idea.     

Strategies of node selection in search procedures for solving combinatorial optimization problems: A survey and a general formalization

Currently, most combinatorial optimization problems have to be solved, if the optimum solution is sought, using general techniques to explore the space of feasible solutions and, more specifically, through exploratory enumerative procedures in trees and search graphs. The objective of this work is to propose a survey and a general formalization of the selection strategy of the next node to explore, a feature that is common to all these optimization procedures. This research has been partially supported by TAP98-0494 project     

Numerical analysis of a method for high Peclet number transport in porous media

A variationally consistent eddy viscosity discretization is presented in [W.J. Layton, A connection between subgrid scale eddy viscosity and mixed methods, Appl. Math. Comput. 133 (2002) 147-157] for the stationary convection diffusion problem. This discretization is extended to the evolutionary problem in [N. Heitmann, Subgridscale stabilization of time-dependent convection dominated diffusive transport, J. Math. Anal. Appl. 331 (2007) 38-50] with a near optimal error bound. In the following, we couple this discretization with the porous media problem. We present a comprehensive analysis of stability and error for the velocity field derived from the porous media problem. Next, using a backward Euler approximation for the time derivative we follow the inherited error in velocity through the coupling with the convection diffusion problem. The method is shown to be stable and the error near optimal and independent of the diffusion coefficient, ?.     

Long-term integrated surgery room optimization and recovery ward planning,with a case study in the Brazilian National Institute of Traumatology and Orthopedics (INTO)

This paper proposes an integrated approach for the long-term planning and surgery allocation problem with downstream constraints. It is motivated by a case study in the Brazilian National Institute of Traumatology and Orthopedics, which provides elective high complexity surgeries for patients from the Brazilian public health system. We introduce an optimization problem that designs a periodic surgery allocation schedule as well as a recovery ward utilization plan, with a view at balancing patient arrivals and releases in the long term, in such a way that all surgeries are performed in a timely manner.     

Optimality conditions for the control of a double-membrane complex system by a modal decomposition technique

The optimal of damping out the oscillations of an elastically rectangular double-membrane system by means of point-wise actuators is solved analytically. The membrane is clamped along the boundaries. The motion of the system is initiated by given initial displacement and velocity conditions. The basic control problem is to minimize the deflection and the velocity of displacements at a specified time with the minimum expenditure of actuation energy. A quadratic performance functional is chosen as the cost functional which comprises the functionals of the deflection, velocity and the point-wise actuators. Necessary and sufficient conditions of optimality are investigated. The necessary conditions of optimality are obtained from a variational approach and formulated in the form of degenerate integrals which lead to explicit optimal control laws for the actuators. Numerical results are given for various problem parameters and the efficiency of the control mechanism is investigated.     

A numerical approach for solving initial-boundary value problem describing the process of cooling of a semi-infinite body by radiation

In this article, we have introduced a Taylor collocation method, which is based on collocation method for solving initial-boundary value problem describing the process of cooling of a semi-infinite body by radiation. This method is based on first taking the truncated Taylor expansions of the solution function in the fractional differential equation and then substituting their matrix forms into the equation. Using collocation points, we have the system of nonlinear algebraic equation. Then, we solve the system of nonlinear algebraic equation using Maple 13 and we have the coefficients of Taylor expansion. In addition, numerical results are presented to demonstrate the effectiveness of the proposed method.     

Using the tabu search method for the distribution of supplies in a hospital

Two supply delivery systems in a hospital are compared. In order to evaluate the number of carriers required by the new system, an operational research model has been developed and solved by the tabu search method. The results indicate that the new system is better except on weekend days.This work has been achieved while the second author was visiting the Université de Montréal.     

Conjugate duality in the optimization of the search for a target with generalized conditionally deterministic motion

A target moves in Euclideann-spaceR ⁿ according to the generalized conditionally deterministic law. The search density that accumulates on the target during its route determines the probability of detection. A necessary and sufficient condition for the search density (x, t) to be optimal is first represented, when there are two types of constraints for the search density: pointwise constraints and total-amount constraints. The second part consists of formulation of the dual problem with the aid of sensitivity parameters for the constraints. By using the dual functional, we obtain the maximal error from the minimum value of the primal objective functional for an arbitrary feasible . Finally, we study the discretized case, which is necessary for numerical calculations.     

Extended use of the cards procedure as a simple elicitation technique for MAVT. Application to public procurement in Switzerland

The cards procedure was designed in the early 90 as a simple way to elicit weights for multiple criteria decision analysis outranking methods. It is based on the elicitation of the difference of importance between successive pairs of criteria. We propose to extend its use in two directions:     

Application of artificial neural networks for the prediction of roll force and roll torque in hot strip rolling process

This paper introduces an artificial neural network (ANN) application to a hot strip mill to improve the model’s prediction ability for rolling force and rolling torque, as a function of various process parameters. To obtain a data basis for training and validation of the neural network, numerous three dimensional finite element simulations were carried out for different sets of process variables. Experimental data were compared with the finite element predictions to verify the model accuracy. The input variables are selected to be rolling speed, percentage of thickness reduction, initial temperature of the strip and friction coefficient in the contact area. A comprehensive analysis of the prediction errors of roll force and roll torque made by the ANN is presented. Model responses analysis is also conducted to enhance the understanding of the behavior of the NN model. The resulted ANN model is feasible for on-line control and rolling schedule optimization, and can be easily extended to cover different aluminum grades and strip sizes in a straight-forward way by generating the corresponding training data from a FE model.     

Application of transparent boundary conditions to high-order finite-difference schemes for the wave equation in waveguides

We propose a method for generating finite-difference approximations of transparent boundary conditions (TBCs) with the fourth and sixth order in space. It is based on the wave equation solution continuation extra two or three layers of grid points outside the computational domain to use them in central-difference operators on approaching the boundary. We present the theoretical background of the method, give estimates of computational resources, and discuss accuracy and stability results of numerical tests in 1D and 2D cases.     

Necessary optimality conditions for a singular surface in the form of synthesis

For a linear control problem using the traditional open-loop approach, a new representation for the singular control and generalized, invariant conditions for optimality are found. The phase portrait of a nonlinear control problem is considered in the neighborhood of singular trajectories. The singular paths form a hypersurface, approached by regular paths from both sides. The Bellman function for this problem is a classical (smooth) solution to a first-order PDE with nonsmooth Hamiltonian over two smooth (regular) branches, related to the halfneighborhoods of the surface. These solutions are at least twice differentiable and have first discontinuous derivatives of odd order. The invariant form for these necessary conditions is found in terms of Jacobi (Poisson) brackets, consisting of several equalities and inequalities. The latter relations guarantee the validity of the Kelley condition as well as the geometrical constraints for the singular control variables. Thus, the Kelley condition appears to be just a certain property of a smooth solution to a first-order PDE with nonsmooth Hamiltonian. All the relations, including the Hamiltonian equations of singular motion, do not use singular controls; they are based on regular Hamiltonians depending only upon the state vector and the gradient of the Bellman function (adjoint vector).This work was suported by Grant No. 93-013-16285 of the Russian Fund for Fundamental Research.     

Available-To-Promise modeling for multi-plant manufacturing characterized by lack of homogeneity in the product: An illustration of a ceramic case

Lack of homogeneity in the product (LHP) appears in some production processes which incorporate raw materials that originate directly from nature and/or production processes with operations that confer heterogeneity to the characteristics of the outputs obtained, even when the inputs used are homogeneous. Poor LHP management may have a very negative impact on the customer service level and on the supply chains’ operation costs, especially when the customer needs to be served with homogeneous units of one same product. One of the key processes for suitable LHP management is the order-promising process. This work presents a mathematical programming order-promising model for make-to-stock environments with LHP. The model considers two objectives placed within a single objective by the weighted sum method. For the purpose of testing the validity of the proposed model and to evaluate the characteristics of the solutions obtained in different scenarios, numerical experiments based on realistic data from a ceramic tile company have been conducted. The results show that better results are obtained for the defined performance measures if multiple objectives are considered when promising orders than the single objective of maximizing profits. Furthermore, the superiority of the results obtained from the proposed model, if compared with current company practice, proves the model’s utility.     

A tabu search algorithm for the integrated scheduling problem of container handling systems in a maritime terminal

The scheduling problem in a container terminal is characterized by the coordination of different types of equipment. In this paper, we present an integrated model to schedule the equipment. The objective is to minimize the makespan, or the time it takes to serve a given set of ships. The problem is formulated as a Hybrid Flow Shop Scheduling problem with precedence and Blocking constraints (HFSS-B). A tabu search algorithm is proposed to solve this problem. Certain mechanisms are developed and introduced into the algorithm to assure its quality and efficiency. The performance of the tabu search algorithm is analyzed from the computational point of view.     

On the value of customer information for an independent supplier in a continuous review inventory system

We consider the inventory control problem of an independent supplier in a continuous review system. The supplier faces demand from a single customer who in turn faces Poisson demand and follows a continuous review (R, Q) policy. If no information about the inventory levels at the customer is available, reviews and ordering are usually carried out by the supplier only at points in time when a customer demand occurs. It is common to apply an installation stock reorder point policy. However, as the demand faced by the supplier is not Markovian, this policy can be improved by allowing placement of orders at any point in time. We develop a time delay policy for the supplier, wherein the supplier waits until time t after occurrence of the customer demand to place his next order. If the next customer demand occurs before this time delay, then the supplier places an order immediately. We develop an algorithm to determine the optimal time delay policy. We then evaluate the value of information about the customer’s inventory level. Our numerical study shows that if the supplier were to use the optimal time delay policy instead of the installation stock policy then the value of the customer’s inventory information is not very significant.     

Convergence of a difference scheme for the heat equation in a long strip by artificial boundary conditions

The numerical solution of the heat equation on a strip in two dimensions is considered. An artificial boundary is introduced to make the computational domain finite. On the artificial boundary, an exact boundary condition is proposed to reduce the original problem to an initial‐boundary value problem in a finite computational domain. A difference scheme is constructed by the method of reduction of order to solve the problem in the finite computational domain. It is proved that the difference scheme is uniquely solvable, unconditionally stable and convergent with the convergence order 2 in space and order 3/2 in time in an energy norm. A numerical example demonstrates the theoretical results.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2007     

Application of a hybrid meshless technique for natural frequencies analysis in functionally graded thick hollow cylinder subjected to suddenly thermal loading

A hybrid meshless technique based on composition of meshless local Petrov–Galerkin method (for spatial variables) and Newmark finite difference method (for time domain) is developed for natural frequencies analysis of thick cylinder made of functionally graded materials (FGMs). The FG cylinder is assumed to be under suddenly thermal loading, axisymmetric and plane strain conditions. The dynamic behaviors and time history of displacements are obtained in time domain using Green–Naghdi (GN) theory of coupled thermo-elasticity (without energy dissipation). Using fast Fourier transform (FFT) technique, the displacements are transferred to frequency domain and all natural frequencies are illustrated for various grading patterns of FGMs. The variations of mechanical properties in FG thick hollow cylinder are considered to be in nonlinear volume fraction law through radial direction. The presented hybrid meshless technique furnishes a ground to analyze the effects of various grading patterns of FGMs on natural frequencies, which are obtained employing GN coupled thermo-elasticity governing equations. Also, the frequency history and natural frequencies are illustrated for various grading patterns at several points across thickness of cylinder.