A Tutorial on Clique Problems in Communications and Signal Processing

Since its first use by Euler on the problem of the seven bridges of K\"onigsberg, graph theory has shown excellent abilities in solving and unveiling the properties of multiple discrete optimization problems. The study of the structure of some integer programs reveals equivalence with graph theory problems making a large body of the literature readily available for solving and characterizing the complexity of these problems. This tutorial presents a framework for utilizing a particular graph theory problem, known as the clique problem, for solving communications and signal processing problems. In particular, the paper aims to illustrate the structural properties of integer programs that can be formulated as clique problems through multiple examples in communications and signal processing. To that end, the first part of the tutorial provides various optimal and heuristic solutions for the maximum clique, maximum weight clique, and $k$-clique problems. The tutorial, further, illustrates the use of the clique formulation through numerous contemporary examples in communications and signal processing, mainly in maximum access for non-orthogonal multiple access networks, throughput maximization using index and instantly decodable network coding, collision-free radio frequency identification networks, and resource allocation in cloud-radio access networks. Finally, the tutorial sheds light on the recent advances of such applications, and provides technical insights on ways of dealing with mixed discrete-continuous optimization problems

Automated multigravity assist trajectory planning with a modified ant colony algorithm

The paper presents an approach to transcribe a multigravity assist trajectory design problem into an integrated planning and scheduling problem. A modified Ant Colony Optimization (ACO) algorithm is then used to generate optimal plans corresponding to optimal sequences of gravity assists and deep space manoeuvers to reach a given destination. The modified Ant Colony Algorithm is based on a hybridization between standard ACO paradigms and a tabu-based heuristic. The scheduling algorithm is integrated into the trajectory model to provide a fast time-allocation of the events along the trajectory. The approach demonstrated to be very effective on a number of real trajectory design problems

A Hybrid Tabu/Scatter Search Algorithm for Simulation-Based Optimization of Multi-Objective Runway Operations Scheduling

As air traffic continues to increase, air traffic flow management is becoming more challenging to effectively and efficiently utilize airport capacity without compromising safety, environmental and economic requirements. Since runways are often the primary limiting factor in airport capacity, runway operations scheduling emerge as an important problem to be solved to alleviate flight delays and air traffic congestion while reducing unnecessary fuel consumption and negative environmental impacts. However, even a moderately sized real-life runway operations scheduling problem tends to be too complex to be solved by analytical methods, where all mathematical models for this problem belong to the complexity class of NP-Hard in a strong sense due to combinatorial nature of the problem. Therefore, it is only possible to solve practical runway operations scheduling problem by making a large number of simplifications and assumptions in a deterministic context. As a result, most analytical models proposed in the literature suffer from too much abstraction, avoid uncertainties and, in turn, have little applicability in practice. On the other hand, simulation-based methods have the capability to characterize complex and stochastic real-life runway operations in detail, and to cope with several constraints and stakeholders’ preferences, which are commonly considered as important factors in practice. This dissertation proposes a simulation-based optimization (SbO) approach for multi-objective runway operations scheduling problem. The SbO approach utilizes a discrete-event simulation model for accounting for uncertain conditions, and an optimization component for finding the best known Pareto set of solutions. This approach explicitly considers uncertainty to decrease the real operational cost of the runway operations as well as fairness among aircraft as part of the optimization process. Due to the problem’s large, complex and unstructured search space, a hybrid Tabu/Scatter Search algorithm is developed to find solutions by using an elitist strategy to preserve non-dominated solutions, a dynamic update mechanism to produce high-quality solutions and a rebuilding strategy to promote solution diversity. The proposed algorithm is applied to bi-objective (i.e., maximizing runway utilization and fairness) runway operations schedule optimization as the optimization component of the SbO framework, where the developed simulation model acts as an external function evaluator. To the best of our knowledge, this is the first SbO approach that explicitly considers uncertainties in the development of schedules for runway operations as well as considers fairness as a secondary objective. In addition, computational experiments are conducted using real-life datasets for a major US airport to demonstrate that the proposed approach is effective and computationally tractable in a practical sense. In the experimental design, statistical design of experiments method is employed to analyze the impacts of parameters on the simulation as well as on the optimization component’s performance, and to identify the appropriate parameter levels. The results show that the implementation of the proposed SbO approach provides operational benefits when compared to First-Come-First-Served (FCFS) and deterministic approaches without compromising schedule fairness. It is also shown that proposed algorithm is capable of generating a set of solutions that represent the inherent trade-offs between the objectives that are considered. The proposed decision-making algorithm might be used as part of decision support tools to aid air traffic controllers in solving the real-life runway operations scheduling problem

Optimizing Integrated Terminal Airspace Operations Under Uncertainty

In the terminal airspace, integrated departures and arrivals have the potential to increase operations efficiency. Recent research has developed geneticalgorithm- based schedulers for integrated arrival and departure operations under uncertainty. This paper presents an alternate method using a machine jobshop scheduling formulation to model the integrated airspace operations. A multistage stochastic programming approach is chosen to formulate the problem and candidate solutions are obtained by solving sample average approximation problems with finite sample size. Because approximate solutions are computed, the proposed algorithm incorporates the computation of statistical bounds to estimate the optimality of the candidate solutions. A proof-ofconcept study is conducted on a baseline implementation of a simple problem considering a fleet mix of 14 aircraft evolving in a model of the Los Angeles terminal airspace. A more thorough statistical analysis is also performed to evaluate the impact of the number of scenarios considered in the sampled problem. To handle extensive sampling computations, a multithreading technique is introduced

Incorporating Memory and Learning Mechanisms Into Meta-RaPS

Due to the rapid increase of dimensions and complexity of real life problems, it has become more difficult to find optimal solutions using only exact mathematical methods. The need to find near-optimal solutions in an acceptable amount of time is a challenge when developing more sophisticated approaches. A proper answer to this challenge can be through the implementation of metaheuristic approaches. However, a more powerful answer might be reached by incorporating intelligence into metaheuristics. Meta-RaPS (Metaheuristic for Randomized Priority Search) is a metaheuristic that creates high quality solutions for discrete optimization problems. It is proposed that incorporating memory and learning mechanisms into Meta-RaPS, which is currently classified as a memoryless metaheuristic, can help the algorithm produce higher quality results. The proposed Meta-RaPS versions were created by taking different perspectives of learning. The first approach taken is Estimation of Distribution Algorithms (EDA), a stochastic learning technique that creates a probability distribution for each decision variable to generate new solutions. The second Meta-RaPS version was developed by utilizing a machine learning algorithm, Q Learning, which has been successfully applied to optimization problems whose output is a sequence of actions. In the third Meta-RaPS version, Path Relinking (PR) was implemented as a post-optimization method in which the new algorithm learns the good attributes by memorizing best solutions, and follows them to reach better solutions. The fourth proposed version of Meta-RaPS presented another form of learning with its ability to adaptively tune parameters. The efficiency of these approaches motivated us to redesign Meta-RaPS by removing the improvement phase and adding a more sophisticated Path Relinking method. The new Meta-RaPS could solve even the largest problems in much less time while keeping up the quality of its solutions. To evaluate their performance, all introduced versions were tested using the 0-1 Multidimensional Knapsack Problem (MKP). After comparing the proposed algorithms, Meta-RaPS PR and Meta-RaPS Q Learning appeared to be the algorithms with the best and worst performance, respectively. On the other hand, they could all show superior performance than other approaches to the 0-1 MKP in the literature

Dagstuhl Reports : Volume 1, Issue 2, February 2011

Online Privacy: Towards Informational Self-Determination on the Internet (Dagstuhl Perspectives Workshop 11061) : Simone Fischer-Hübner, Chris Hoofnagle, Kai Rannenberg, Michael Waidner, Ioannis Krontiris and Michael Marhöfer Self-Repairing Programs (Dagstuhl Seminar 11062) : Mauro Pezzé, Martin C. Rinard, Westley Weimer and Andreas Zeller Theory and Applications of Graph Searching Problems (Dagstuhl Seminar 11071) : Fedor V. Fomin, Pierre Fraigniaud, Stephan Kreutzer and Dimitrios M. Thilikos Combinatorial and Algorithmic Aspects of Sequence Processing (Dagstuhl Seminar 11081) : Maxime Crochemore, Lila Kari, Mehryar Mohri and Dirk Nowotka Packing and Scheduling Algorithms for Information and Communication Services (Dagstuhl Seminar 11091) Klaus Jansen, Claire Mathieu, Hadas Shachnai and Neal E. Youn