Set Of Smaller Subproblems Research Articles

Efficient Spectrum Occupancy Prediction Exploiting Multidimensional Correlations through Composite 2D-LSTM Models.

In cognitive radio systems, identifying spectrum opportunities is fundamental to efficiently use the spectrum. Spectrum occupancy prediction is a convenient way of revealing opportunities based on previous occupancies. Studies have demonstrated that usage of the spectrum has a high correlation over multidimensions, which includes time, frequency, and space. Accordingly, recent literature uses tensor-based methods to exploit the multidimensional spectrum correlation. However, these methods share two main drawbacks. First, they are computationally complex. Second, they need to re-train the overall model when no information is received from any base station for any reason. Different than the existing works, this paper proposes a method for dividing the multidimensional correlation exploitation problem into a set of smaller sub-problems. This division is achieved through composite two-dimensional (2D)-long short-term memory (LSTM) models. Extensive experimental results reveal a high detection performance with more robustness and less complexity attained by the proposed method. The real-world measurements provided by one of the leading mobile network operators in Turkey validate these results.

Explicit/multi-parametric model predictive control (MPC) of linear discrete-time systems by dynamic and multi-parametric programming

This work presents a new algorithm for solving the explicit/multi-parametric model predictive control (or mp-MPC) problem for linear, time-invariant discrete-time systems, based on dynamic programming and multi-parametric programming techniques. The algorithm features two key steps: (i) a dynamic programming step, in which the mp-MPC problem is decomposed into a set of smaller subproblems in which only the current control, state variables, and constraints are considered, and (ii) a multi-parametric programming step, in which each subproblem is solved as a convex multi-parametric programming problem, to derive the control variables as an explicit function of the states. The key feature of the proposed method is that it overcomes potential limitations of previous methods for solving multi-parametric programming problems with dynamic programming, such as the need for global optimization for each subproblem of the dynamic programming step.

On the (co)girth of a connected matroid

This article studies the girth and cogirth problems for a connected matroid. The problem of finding the cogirth of a graphic matroid has been intensively studied, but studies on the equivalent problem for a vector matroid or a general matroid have been rarely reported. Based on the duality and connectivity of a matroid, we prove properties associated with the girth and cogirth of a matroid whose contraction or restriction is disconnected. Then, we devise algorithms that find the cogirth of a matroid M from the matroids associated with the direct sum components of the restriction of M. As a result, the problem of finding the (co)girth of a matroid can be decomposed into a set of smaller sub-problems, which helps alleviate the computation. Finally, we implement and demonstrate the application of our algorithms to vector matroids.

PARALLEL MULTISPLITTINGS FOR CONSTRAINED OPTIMIZATION

The philosophy of multisplitting methods is the replacement of a large-scale linear or nonlinear problem by a set of smaller subproblems, each of which can be solved locally and independently in parallel by taking advantage of well-tested sequential algorithms. Because of this formulation most compute-intensive operations can be calculated independently and the algorithms are highly parallel. In continuation of our earlier work we utilize a new parameter-free formulation of linearly constrained convex minimization problems to obtain a parallel algorithm of multisplitting type. Numerical results both serial and parallel are reported which demonstrate its efficiency and which also show that it compares favorably to our earlier parameter-dependent approach.

On the determination of overall computer network reliability with m-level hierachical routing

In this paper the overall reliability of mch-level hierarchical computer networks is evaluated. This is an extension of an earlier work wherein two level hierarchical clustrering structures were examined [4]. The method presented first enumerates all the minimal cutsets and then very efficiently evaluates the overall network reliability. There are important savings in computation time and available memory, as the main idea behind the hierarchical design is to impose a decomposable structure which will result in a set of smaller subproblems. The developed technique is very useful in the overall reliability evaluation of large computer networks or many interconnected networks.

Optimal Planning for a Thermal Discharge Treatment System

The characteristics and economic implications of thermal pollution are considered within the context of the planning of a treatment system for a series of hypothetical nuclear power plants that are to be located adjacent to a river. It is assumed that these power plants will discharge sufficient heated cooling water to make these treatment facilities necessary. The problem that is being considered is to determine the optimal planning of a treatment system. The objective of the planning procedure is to minimize the total annual cost for the construction and operation of the entire system. The constraint on this minimization process is not to violate a maximum temperature requirement within each reach or section of the river. The problem is solved by considering the effect that a bypass‐piping system has on temperatures within the river. The technique of bypass piping consists of piping waste water downstream to reaches of a river where the regenerative powers of the physical system have reduced the level of pollution to the extent that more waste water may be disposed. By noting that the bypass‐piping system allows the beginning and end temperatures of a section of the river to be controlled, a procedure can be developed for separating the optimization model of the entire system. This model is separated into a set of small subproblems that are solved by simulation and a system problem that is solved by dynamic programing. The results of the implementation of this model showed that the bypass‐piping system significantly reduced the cost of the entire treatment system.