A direct barter model for course add/drop process

Even though course timetabling and student scheduling problems have been studied extensively, not much has been done for the optimization of student add/drop requests after the initial registration period. Add/drop registrations are usually processed with a first come first served policy. This, however, can introduce inefficiencies and dead-locks resulting in add/drop requests that are not satisfied even though they can, in fact, be satisfied. We model the course add/drop process as a direct bartering problem in which add/drop requests appear as bids. We formulate the resulting problem as an integer linear program. We show that our problem can be solved polynomially as a minimum cost flow network problem. In our model, we also introduce a two-level weighting system that enables students to express priorities among their requests. We demonstrate improvement in the satisfaction of students over the currently used model and also the fast performance of our algorithms on various test cases based on real-life registration data of our university.     

Optimal dynamic price selection under attraction choice models

We present a single-resource finite-horizon Markov decision process approach for a firm that seeks to maximize expected revenues by dynamically adjusting the menu of offered products and their prices to be selected from a finite set of alternative values predetermined as a matter of policy. Consumers choose among available products according to an attraction choice model, a special but widely applied class of discrete choice models.     

Analysis of static and dynamic structures in economic models: methodological and practical aspects

The paper puts forward operational methods for exploring the properties of systems and more especially, economic models. The results are exclusively based on the causal structure of the model, which is defined by specifying only the presence or absence of the variables in each relation. The analysis presented provides a better understanding of the functioning of the model, but clearly it does not deal with the observable characteristics of the phenomena we attempt to represent with the model.     

PSO with surrogate models for feature selection: static and dynamic clustering-based methods

Feature selection is an important but often expensive process, especially with a large number of instances. This problem can be addressed by using a small training set, i.e. a surrogate set. In this work, we propose to use a hierarchical clustering method to build various surrogate sets, which allows to analyze the effect of surrogate sets with different qualities and quantities on the feature subsets. Further, a dynamic surrogate model is proposed to automatically adjust surrogate sets for different datasets. Based on this idea, a feature selection system is developed using particle swarm optimization as the search mechanism. The experiments show that the hierarchical clustering method can build better surrogate sets to reduce the computational time, improve the feature selection performance, and alleviate overfitting. The dynamic method can automatically choose suitable surrogate sets to further improve the classification accuracy.     

Optimal placement of stereo sensors

Autonomous wireless devices such as sensor nodes and stereo cameras, due to their low cost of operation coupled with the potential for remote deployment, have found a plethora of applications ranging from monitoring air, soil and water to seismic detection and military surveillance. Typically, such a network spans a region of interest with the individual nodes cooperating to detect events and disseminate information. Given a deployment of sensors and targets over a region, a sensor pairing is desired for each target that optimizes the coverage under certain constraints. This problem can be modeled as an integer programming problem and solved using branch-and-cut. For larger problems, it is necessary to limit the number of variables, and a GRASP routine was developed for this purpose. Valid cutting planes are developed and computational results presented. Research supported in part by NSF grant numbers DMS–0317323 and CMS–0301661.     

A comparison of dynamic hazard models and static models for predicting the special treatment of stocks in China with comprehensive variables

The stock exchanges in China give a stock special treatment in order to indicate its risk warning if the corresponding listed company cannot meet some requirements on financial performance. To correctly predict the special treatment of stocks is very important for the investors. The performance of the prediction models is mainly affected by the selection of explanatory variables and modelling methods. This paper makes a comparison between the multi-period hazard models and five widely used single-period static models by investigating a comprehensive category of variables including accounting variables, market variables, characteristic variables and macroeconomic variables. The empirical result shows that the performance of the models is sensitive to the choice of explanatory variables but the performance between the multi-period hazard models and the single-period static models has no significant difference.     

Unified form for static displacement,dynamic response and natural frequency analysis based on convex models

Unified form of analysis for the static displacement, the dynamic response and the natural frequency of structures with uncertain-but-bounded parameters based on convex models is presented. The probabilistic model for them is also given, where the uniform distribution is adopted for the uncertain parameters. The mean values and the standard deviations of the uncertain parameters are derived from the ellipsoid so that the relationship between convex models and probabilistic model is established. Numerical examples are used to illustrate the validity of the presented methods.     

A new computational approach for stochastic fluid models of multiplexers with heterogeneous sources

In this paper we derive an efficient computational procedure for the system in which fluid is produced byN ₁ on-off sources of type 1,N ₂ on-off sources of type 2 and transferred to a buffer which is serviced by a channel of constant capacity. This is a canonical model for multiservice ATM multiplexing, which is hard to analyze and also of wide interest. This paper's approach to the computation of the buffer overflow probability,G(x) = Pr{buffer content >x}, departs from all prior approaches in that it transforms the computation ofG(x) for a particularx into a recursive construction of an interpolating polynomial. For the particular case of two source types the interpolating polynomial is in two variables. Our main result is the derivation of recursive algorithms for computing the overflow probabilityG(x) and various other performance measures using their respective relations to two-dimensional interpolating polynomials. To make the computational procedure efficient we first derive a new system of equations for the coefficients in the spectral expansion formula forG(x) and then use specific properties of the new system for efficient recursive construction of the polynomials. We also develop an approximate method with low complexity and analyze its accuracy by numerical studies. We computeG(x) for different values ofx, the mean buffer content and the coefficient of the dominant exponential term in the spectral expansion ofG(x). The accuracy of the approximations is reasonable when the buffer utilization characterized by G(0) is more than 10^–2.     

Optimal closed-loop control stability and transient behaviour of a class of linear dynamic economic models

In this paper an attempt is made to apply results from linear systems theory and Liapunov stability theory to analyze a class of linear economic models. For a quadratic performance index, the Riccati equation can be used to derive the optimal control law in closed-loop form. Once the system is synthesized, the second method of Liapunov can be used to study the transient behaviour of the system. The approach is illustrated through two simple economic models.     

Optimal placement of UV-based communications relay nodes

We consider a constrained optimization problem with mixed integer and real variables. It models optimal placement of communications relay nodes in the presence of obstacles. This problem is widely encountered, for instance, in robotics, where it is required to survey some target located in one point and convey the gathered information back to a base station located in another point. One or more unmanned aerial or ground vehicles (UAVs or UGVs) can be used for this purpose as communications relays. The decision variables are the number of unmanned vehicles (UVs) and the UV positions. The objective function is assumed to access the placement quality. We suggest one instance of such a function which is more suitable for accessing UAV placement. The constraints are determined by, firstly, a free line of sight requirement for every consecutive pair in the chain and, secondly, a limited communication range. Because of these requirements, our constrained optimization problem is a difficult multi-extremal problem for any fixed number of UVs. Moreover, the feasible set of real variables is typically disjoint. We present an approach that allows us to efficiently find a practically acceptable approximation to a global minimum in the problem of optimal placement of communications relay nodes. It is based on a spatial discretization with a subsequent reduction to a shortest path problem. The case of a restricted number of available UVs is also considered here. We introduce two label correcting algorithms which are able to take advantage of using some peculiarities of the resulting restricted shortest path problem. The algorithms produce a Pareto solution to the two-objective problem of minimizing the path cost and the number of hops. We justify their correctness. The presented results of numerical 3D experiments show that our algorithms are superior to the conventional Bellman-Ford algorithm tailored to solving this problem.     

A survey of static and dynamic potential games

Potential games are noncooperative games for which there exist auxiliary functions, called potentials, such that the maximizers of the potential are also Nash equilibria of the corresponding game. Some properties of Nash equilibria, such as existence or stability, can be derived from the potential, whenever it exists. We survey different classes of potential games in the static and dynamic cases, with a finite number of players, as well as in population games where a continuum of players is allowed. Likewise, theoretical concepts and applications are discussed by means of illustrative examples.     

Maximum thick paths in static and dynamic environments

We consider the problem of finding a large number of disjoint paths for unit disks moving amidst static or dynamic obstacles. The problem is motivated by the capacity estimation problem in air traffic management, in which one must determine how many aircraft can safely move through a domain while avoiding each other and avoiding “no-fly zones” and predicted weather hazards. For the static case we give efficient exact algorithms, based on adapting the “continuous uppermost path” paradigm. As a by-product, we establish a continuous analogue of Menger's Theorem.Next we study the dynamic problem in which the obstacles may move, appear and disappear, and otherwise change with time in a known manner; in addition, the disks are required to enter/exit the domain during prescribed time intervals. Deciding the existence of just one path, even for a 0-radius disk, moving with bounded speed is NP-hard, as shown by Canny and Reif [J. Canny, J.H. Reif, New lower bound techniques for robot motion planning problems, in: Proc. 28th Annu. IEEE Sympos. Found. Comput. Sci., 1987, pp. 49–60]. Moreover, we observe that determining the existence of a given number of paths is hard even if the obstacles are static, and only the entry/exit time intervals are specified for the disks. This motivates studying “dual” approximations, compromising on the radius of the disks and on the maximum speed of motion.Our main result is a pseudopolynomial-time dual-approximation algorithm. If K unit disks, each moving with speed at most 1, can be routed through an environment, our algorithm finds (at least) K paths for disks of radius somewhat smaller than 1 moving with speed somewhat larger than 1.     

Self-reinforcement of liquid-crystal polymers at static and dynamic loading

The self-reinforcement effect of a solid uniaxially oriented SVM-K liquid-crystal polyamide and a copolyester of hydroxybenzoic and hydroxynaphthoic acids has been investigated by tensile-strength, stress-relaxation, and dynamic methods. The samples were prepared by spinning from lyotropic solution (SVM-K) and from a thermotropic melt (polyester). The tensile-strength and stress-relaxation tests were performed on complex fibers and the dynamic test on single fibers. The set of stress-strain curves, changing from a convex shape with two linear sections (at room temperature) to a concave shape (at high temperatures) is shown for both materials in Fig. 1. There is a pronounced difference between the deformation mechanisms at low and high strains in the stability of rigidity. At high temperatures the rigidity becomes less than the initial one during deformation and the current modulus at high strains has the same value within large ranges of temperatures and strains (Fig. 2). A low-deformation transition of another physical parameter than the yield-stress has been found. The stress-strain diagram for both investigated polymers has been generalized by using the constant value of the current modulus for the normalization of the stress value (Fig. 3). The stress-relaxation phenomena are shown to be anomalous. At high temperatures the stress-relaxation intensity decreases with increasing deformation, i.e., after deformation the polymer is characterized by a stability of rigidity which is higher than the initial value (Fig. 4). The dynamic modulus appears to increase with increasing deformation rate (Fig. 5). Due to these peculiarities the liquid-crystal polymers must be considered not only as normal high-modulus reinforcements for composite materials but also as materials, self-reinforcing under loading.Translated from Mekhanika Kompozitnykh Materialov, Vol. 30, No. 4, pp. 435–441, July–August, 1994.     

Stabilizing the XFEM for static and dynamic crack simulations

For many crack geometries the standard XFEM may lead to badly conditioned equation systems. Recently a number of remedies to that problem have been published. In this contribution the stabilization technique presented in [1] is extended to dynamic and possibly nonlinear fracture mechanics and additionally combined with the SGFEM / SXFEM [2]. The performance of the different strategies is demonstrated in a linear elastic 3D mode 1 crack problem for which the analytical solution exists. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimal controller placement in modal control of complex systems

Within the framework of modal control of large systems, a simple approach is advanced for the determination of optimal control configuration under an energy constraint, i.e., optimal locations of a limited number of controllers such that the total energy requirement for control is minimized. It is shown that the resulting design criterion is a simple function of projections of the control matrix onto components of eigenvectors associated with the affected eigenvalues. Furthermore, it is applicable to both single-input and multi-input systems. Systems possessing distinct complex eigenvalues are considered but the approach is equally applicable to other types of systems. Examples show that the minimum-energy control configuration also tends to be the most effective in terms of accomplishing control objectives.     

Multipolar routing: where dynamic and static routing meet

Assuming that the traffic matrix belongs to a polytope, we describe a new routing paradigm where each traffic matrix is routed a combination of a number of extreme routings. This combination depends on the current traffic matrix. Multipolar routing can be seen as a generalization of both routing and robust static routing. Moreover, the time complexity of multipolar routing is under control since it depends on the number of poles (i.e. the number of extreme routings) which can be defined by the network planner     

Optimal placement of available sections in structural eigenvalue problems

Basic principles governing the optimum design of a structure of given geometry to resist buckling are restated, expanded, and generalized. The specific case of column buckling is cast in a complementary energy format. This format is used to treat the discrete optimality problem of finding the best location and length of cover plates of given cross-sectional area. Both necessary and sufficient optimality conditions are derived, and an iterative design-analysis sequence is established, whose convergence is proved. A simple numerical example demonstrates the procedure. Although the strict proof of sufficiency is confined to simply supported and cantilever columns, a possible extension to other cases is introduced at the end of the paper.     

Note on static and dynamic instability of a non-uniform beam

The instability of a non-uniform beam analyzed by Lee and Reissner from a static point of view is reanalyzed by a dynamic approach. The beam is loaded by a parallel or tangential compressive force respectively. As expected the load causing static instability, obtained by both approaches, is exactly the same. A peculiar behaviour of the frequency for both cases of loading is revealed by the dynamic method. The tangential load causing dynamic instability is obtained.

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Zusammenfassung Die Instabilität eines Stabes mit konstantem Querschnitt, welche durch Lee und Reissner vom statischen Standpunkt aus untersucht worden ist, wird einer dynamischen Analyse unterzogen. Der Stab steht unter einer axialen bzw. tangentialen Drucklast. Wie erwartet, ist die Belastung, welche statische Instabilität erzeugt, bei beiden Untersuchungsmethoden dieselbe. Ein besonderes Verhalten der Frequenz für beide Lastfälle wird durch die dynamische Methode aufgezeigt, und es wird die tangentiale Last erhalten, welche dynamische Instabilität erzeugt.

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Preparation of this note has been supported by Sherutei Teuffa, Ltd., Haifa, Israel.