Fiber Routing Optimization in Data Centers

Locations of server racks in a data center are constrained by space and power limitations. Connecting pairs of racks optimally (e.g., the shortest-path with sufficient diversity) using fibers involves substantial computation, modeling, and path-walking. This disclosure describes techniques to achieve N-fold diversity with the shortest-path between racks in a data center interconnected by fibers (housed within cable trays) such that the multiple diversity paths are optimally short and have few or no overlapping cable-tray segments

Intelligent approaches to VLSI routing

Very Large Scale Integrated-circuit (VLSI) routing involves many large-size and complex problems and most of them have been shown to be NP-hard or NP-complete. As a result, conventional approaches, which have been successfully used to handle relatively small-size routing problems, are not suitable to be used in tackling large-size routing problems because they lead to \u27combinatorial explosion\u27 in search space. Hence, there is a need for exploring more efficient routing approaches to be incorporated into today\u27s VLSI routing system. This thesis strives to use intelligent approaches, including symbolic intelligence and computational intelligence, to solve three VLSI routing problems: Three-Dimensional (3-D) Shortest Path Connection, Switchbox Routing and Constrained Via Minimization. The 3-D shortest path connection is a fundamental problem in VLSI routing. It aims to connect two terminals of a net that are distributed in a 3-D routing space subject to technological constraints and performance requirements. Aiming at increasing computation speed and decreasing storage space requirements, we present a new A* algorithm for the 3-D shortest path connection problem in this thesis. This new A*algorithm uses an economical representation and adopts a novel back- trace technique. It is shown that this algorithm can guarantee to find a path if one exists and the path found is the shortest one. In addition, its computation speed is fast, especially when routed nets are spare. The computational complexities of this A* algorithm at the best case and the worst case are O(Ɩ) and 0(Ɩ3), respectively, where Ɩ is the shortest path length between the two terminals. Most importantly, this A\u27 algorithm is superior to other shortest path connection algorithms as it is economical in terms of storage space requirement, i.e., 1 bit/grid. The switchbox routing problem aims to connect terminals at regular intervals on the four sides of a rectangle routing region. From a computational point of view, the problem is NP-hard. Furthermore, it is extremely complicated and as the consequence no existing algorithm can guarantee to find a solution even if one exists no matter how high the complexity of the algorithm is. Previous approaches to the switch box routing problem can be divided into algorithmic approaches and knowledge-based approaches. The algorithmic approaches are efficient in computational time, but they are unsucessful at achieving high routing completion rate, especially for some dense and complicated switchbox routing problems. On the other hand, the knowledge-based approaches can achieve high routing completion rate, but they are not efficient in computation speed. In this thesis we present a hybrid approach to the switchbox routing problem. This hybrid approach is based on a new knowledge-based routing technique, namely synchronized routing, and combines some efficient algorithmic routing techniques. Experimental results show it can achieve the high routing completion rate of the knowledge-based approaches and the high efficiency of the algorithmic approaches. The constrained via minimization is an important optimization problem in VLSI routing. Its objective is to minimize the number of vias introduced in VLSI routing. From computational perspective, the constrained via minimization is NP-complete. Although for a special case where the number of wire segments splits at a via candidate is not more than three, elegant theoretical results have been obtained. For a general case in which there exist more than three wire segment splits at a via candidate few approaches have been proposed, and those approaches are only suitable for tackling some particular routing styles and are difficult or impossible to adjust to meet practical requirements. In this thesis we propose a new graph-theoretic model, namely switching graph model, for the constrained via minimization problem. The switching graph model can represent both grid-based and grid less routing problems, and allows arbitrary wire segments split at a via candidate. Then on the basis of the model, we present the first genetic algorithm for the constrained via minimization problem. This genetic algorithm can tackle various kinds of routing styles and be configured to meet practical constraints. Experimental results show that the genetic algorithm can find the optimal solutions for most cases in reasonable time

Optimizing and Reoptimizing: tackling static and dynamic combinatorial problems

As suggested by the title, in this thesis both static and dynamic problems of Operations Research will be addressed by either designing new procedures or adapting well-known algorithmic schemes. Specifically, the first part of the thesis is devoted to the discussion of three variants of the widely studied Shortest Path Problem, one of which is defined on dynamic graphs. Namely, first the Reoptimization of Shortest Paths in case of multiple and generic cost changes is dealt with an exact algorithm whose performance is compared with Dijkstra's label setting procedure in order to detect which approach has to be preferred. Secondly, the k-Color Shortest Path Problem is tackled. It is a recent problem, defined on an edge-constrained graph, for which a Dynamic Programming algorithm is proposed here; its performance is compared with the state of the art solution approach, namely a Branch & Bound procedure. Finally, the Resource Constrained Clustered Shortest Path Tree Problem is presented. It is a newly defined problem for which both a mathematical model and a Branch & Price procedure are detailed here. Moreover, the performance of this solution approach is compared with that of CPLEX solver. Furthermore, in the first part of the thesis, also the Path Planning in Urban Air Mobility, is discussed by considering both the definition of the Free-Space Maps and the computation of the trajectories. For the former purpose, three different but correlated discretization methods are described; as for the latter, a two steps resolution, offline and online, of the resulting shortest path problems is performed. In addition, it is checked whether the reoptimization algorithm can be used in the online step. In the second part of this thesis, the recently studied Additive Manufacturing Machine Scheduling Problem with not identical machines is presented. Specifically, a Reinforcement Learning Iterated Local Search meta-heuristic featuring a Q-learning Variable Neighbourhood Search is described to solve this problem and its performance is compared with the one of CPLEX solver. It is worthwhile mentioning that, for each of the proposed approaches, a thorough experimentation is performed and each Chapter is equipped with a detailed analysis of the results in order to appraise the performance of the method and to detect its limits

Impact of Obstacles on the Degree of Mobile Ad Hoc Connection Graphs

What is the impact of obstacles on the graphs of connections between stations in Mobile Ad hoc Networks? In order to answer, at least partially, this question, the first step is to define both an environment with obstacles and a mobility model for the stations in such an environment. The present paper focuses on a new way of considering the mobility within environments with obstacles, while keeping the core ideas of the well-known Random WayPoint mobility model (a.k.a RWP). Based on a mesh-partitioning of the space, we propose a new model called RSP-O-G for which we compute the spatial distribution of stations and analyse how the presence of obstacles impacts this distribution compared to the distribution when no obstacles are present. Coupled with a simple model of radio propagation, and according to the density of stations in the environment, we study the mean degree of the connection graphs corresponding to such mobile ad hoc networks