Handling Interference in Integrated HAPS-Terrestrial Networks through Radio Resource Management

Vertical heterogeneous networks (vHetNets) are promising architectures to bring significant advantages for 6G and beyond mobile communications. High altitude platform station (HAPS), one of the nodes in the vHetNets, can be considered as a complementary platform for terrestrial networks to meet the ever-increasing dynamic capacity demand and provide sustainable wireless networks for future. However, the problem of interference is the bottleneck for the optimal operation of such an integrated network. Thus, designing efficient interference management techniques is inevitable. In this work, we aim to design a joint power-subcarrier allocation scheme in order to achieve fairness for all users. We formulate the max-min fairness (MMF) optimization problem and develop a rapid converging iterative algorithm to solve it. Numerical results validate the superiority of the proposed algorithm and show better performance over other conventional network scenarios.Comment: 7 pages, 3 figures, Accepted by IEEE Wireless Communications Letter

The Machine-Part Cell Formation Problem with Non-Binary Values: A MILP Model and a Case of Study in the Accounting Profession

The traditional machine-part cell formation problem simultaneously clusters machines and parts in different production cells from a zero–one incidence matrix that describes the existing interactions between the elements. This manuscript explores a novel alternative for the well-known machine-part cell formation problem in which the incidence matrix is composed of non-binary values. The model is presented as multiple-ratio fractional programming with binary variables in quadratic terms. A simple reformulation is also implemented in the manuscript to express the model as a mixed-integer linear programming optimization problem. The performance of the proposed model is shown through two types of empirical experiments. In the first group of experiments, the model is tested with a set of randomized matrices, and its performance is compared to the one obtained with a standard greedy algorithm. These experiments showed that the proposed model achieves higher fitness values in all matrices considered than the greedy algorithm. In the second type of experiment, the optimization model is evaluated with a real-world problem belonging to Human Resource Management. The results obtained were in line with previous findings described in the literature about the case study

Quadratic Binary Programming Models in Computational Biology

In this paper we formulate four problems in computational molecular biology as 0-1 quadratic programs. These problems are all NP-hard and the current solution methods used in practice consist of heuristics or approximation algorithms tailored to each problem. Using test problems from scientific databases, we address the question, “Can a general-purpose solver obtain good answers in reasonable time?” In addition, we use the latest heuristics as incumbent solutions to address the question, “Can a general-purpose solver confirm optimality or find an improved solution in reasonable time?” Our computational experiments compare four different reformulation methods: three forms of linearization and one form of quadratic convexification

Mixed Integer Linear Programming Formulation Techniques

A wide range of problems can be modeled as Mixed Integer Linear Programming (MIP) problems using standard formulation techniques. However, in some cases the resulting MIP can be either too weak or too large to be effectively solved by state of the art solvers. In this survey we review advanced MIP formulation techniques that result in stronger and/or smaller formulations for a wide class of problems

Tight Polyhedral Representations of Discrete Sets Using Projections, Simplices, and Base-2 Expansions

This research effort focuses on the acquisition of polyhedral outer-approximations to the convex hull of feasible solutions for mixed-integer linear and mixed-integer nonlinear programs. The goal is to produce desirable formulations that have superior size and/or relaxation strength. These two qualities often have great influence on the success of underlying solution strategies, and so it is with these qualities in mind that the work of this dissertation presents three distinct contributions. The first studies a family of relatively unknown polytopes that enable the linearization of polynomial expressions involving two discrete variables. Projections of higher-dimensional convex hulls are employed to reduce the dimensionality of the requisite linearizing polyhedra. For certain lower dimensions, a complete characterization of the convex hull is obtained; for others, a family of facets is acquired. Furthermore, a novel linearization for the product of a bounded continuous variable and a general discrete variable is obtained. The second contribution investigates the use of simplicial facets in the formation of novel convex hull representations for a class of mixed-discrete problems having a subset of their variables taking on discrete, affinely independent realizations. These simplicial facets provide new theoretical machinery necessary to extend the reformulation-linearization technique (RLT) for mixed-binary and mixed-discrete programs. In doing so, new insight is provided which allows for the subsumation of previous mixed-binary and mixed-discrete RLT results. The third contribution presents a novel approach for representing functions of discrete variables and their products using logarithmic numbers of 0-1 variables in order to economize on the number of these binary variables. Here, base-2 expansions are used within linear restrictions to enforce the appropriate behavior of functions of discrete variables. Products amongst functions are handled by scaling these linear restrictions. This approach provides insight into, improves upon, and subsumes recent related linearization methods from the literature

Methods for Employing Real Options Models to Mitigate Risk in R&D Funding Decisions

Government acquisitions requiring research and development (R&D) efforts are fraught with uncertainty. The risks are often mitigated by employing a multi-stage competition, with multiple projects funded initially until a single successful project is selected. While decision-makers recognize they are using a real options approach, analytical tools are often unavailable to evaluate optimal decisions. The use of these techniques for R&D project selection to reduce the uncertainties has been shown to increase overall project value. This dissertation first presents an efficient stochastic dynamic programming (SDP) approach that managers can use to determine optimal project selection strategies and apply the proposed approach on illustrative numerical examples. While the SDP approach produces optimal solutions for many applications, this approach does not easily accommodate the inclusion of a budget-optimal allocation or side constraints, since its formulation is scenario specific. Thus, we then formulate an integer program (IP), whose solution set is equivalent to the SDP model, but facilitates the incorporation of these features and can be solved using available commercial IP solvers. The one-level IP formulation can solve what is otherwise a nested two-level problem when solved as an SDP. We then compare the performance of both models on differently sized problems. For larger problems, where the IP approach appears to be untenable, we provide heuristics for the two-level SDP formulation to solve problems efficiently. Finally, we apply these methods to carbon capture and storage (CCS) projects in the European Union currently under development that may be subject to public funding. Taking the perspective of a funding agency, we employ the real options models presented in this dissertation for determining optimal funding strategies for CCS project selection. The models demonstrate the improved risk reduction by employing a multi-stage competition and explicitly consider the benefits of knowledge spillover generated by competing projects. We then extend the model to consider two sensitivities: 1) the flexibility to spend the budget among the time periods and 2) optimizing the budget, but specifying each time period's allocation a priori. State size, scenario reduction heuristics and run-times of the models are provided

Bilevel linear programs: generalized models for the lower-level reaction set and related problems

Bilevel programming forms a class of optimization problems that model hierarchical relation between two independent decision-makers, namely, the leader and the follower, in a collaborative or conflicting setting. Decisions in this hierarchical structure are made sequentially where the leader decides first and then the follower responds by solving an optimization problem, which is parameterized by the leader's decisions. The follower's reaction, in return, affects the leader's decision, usually through shaping the leader's objective function. Thus, the leader should take into account the follower's response in the decision-making process. A key assumption in bilevel optimization is that both participants, the leader and the follower, solve their problems optimally. However, this assumption does not hold in many important application areas because: (i) there is no known efficient method to solve the lower-level formulation to optimality; (ii) the follower either is not sufficiently sophisticated or does not have the required computational resources to find an optimal solution to the lower-level problem in a timely manner; or (iii) the follower might be willing to give up a portion of his/her optimal objective function value in order to inflict more damage to the leader. This dissertation mainly focuses on developing approaches to model such situations in which the follower does not necessarily return an optimal solution of the lower-level problem as a response to the leader's action. That is, we assume that the follower's reaction set may include both exact and inexact solutions of the lower-level problem. Therefore, we study a generalized class of the follower's reaction sets. This is arguably the case in many application areas in practice, thus our approach contributes to closing the gap between the theory and practice in the bilevel optimization area. In addition, we develop a method to solve bilevel problems through single-level reformulations under the assumption that the lower-level problem is a linear program. The most common technique for such transformations is to replace the lower-level linear optimization problem by its KKT optimality conditions. We propose an alternative technique for a broad class of bilevel linear integer problems, based on the strong duality property of linear programs and compare its performance against the current methods. Finally, we explore bilevel models in an application setting of the pediatric vaccine pricing problem