Algorithms for network design and routing problems

In this thesis we study three combinatorial optimization problems belonging to the classes of Network Design and Vehicle Routing problems that are strongly linked in the context of the design and management of transportation networks: the Non-Bifurcated Capacitated Network Design Problem (NBP), the Period Vehicle Routing Problem (PVRP) and the Pickup and Delivery Problem with Time Windows (PDPTW). These problems are NP-hard and contain as special cases some well known difficult problems such as the Traveling Salesman Problem and the Steiner Tree Problem. Moreover, they model the core structure of many practical problems arising in logistics and telecommunications. The NBP is the problem of designing the optimum network to satisfy a given set of traffic demands. Given a set of nodes, a set of potential links and a set of point-to-point demands called commodities, the objective is to select the links to install and dimension their capacities so that all the demands can be routed between their respective endpoints, and the sum of link fixed costs and commodity routing costs is minimized. The problem is called non- bifurcated because the solution network must allow each demand to follow a single path, i.e., the flow of each demand cannot be splitted. Although this is the case in many real applications, the NBP has received significantly less attention in the literature than other capacitated network design problems that allow bifurcation. We describe an exact algorithm for the NBP that is based on solving by an integer programming solver a formulation of the problem strengthened by simple valid inequalities and four new heuristic algorithms. One of these heuristics is an adaptive memory metaheuristic, based on partial enumeration, that could be applied to a wider class of structured combinatorial optimization problems. In the PVRP a fleet of vehicles of identical capacity must be used to service a set of customers over a planning period of several days. Each customer specifies a service frequency, a set of allowable day-combinations and a quantity of product that the customer must receive every time he is visited. For example, a customer may require to be visited twice during a 5-day period imposing that these visits take place on Monday-Thursday or Monday-Friday or Tuesday-Friday. The problem consists in simultaneously assigning a day- combination to each customer and in designing the vehicle routes for each day so that each customer is visited the required number of times, the number of routes on each day does not exceed the number of vehicles available, and the total cost of the routes over the period is minimized. We also consider a tactical variant of this problem, called Tactical Planning Vehicle Routing Problem, where customers require to be visited on a specific day of the period but a penalty cost, called service cost, can be paid to postpone the visit to a later day than that required. At our knowledge all the algorithms proposed in the literature for the PVRP are heuristics. In this thesis we present for the first time an exact algorithm for the PVRP that is based on different relaxations of a set partitioning-like formulation. The effectiveness of the proposed algorithm is tested on a set of instances from the literature and on a new set of instances. Finally, the PDPTW is to service a set of transportation requests using a fleet of identical vehicles of limited capacity located at a central depot. Each request specifies a pickup location and a delivery location and requires that a given quantity of load is transported from the pickup location to the delivery location. Moreover, each location can be visited only within an associated time window. Each vehicle can perform at most one route and the problem is to satisfy all the requests using the available vehicles so that each request is serviced by a single vehicle, the load on each vehicle does not exceed the capacity, and all locations are visited according to their time window. We formulate the PDPTW as a set partitioning-like problem with additional cuts and we propose an exact algorithm based on different relaxations of the mathematical formulation and a branch-and-cut-and-price algorithm. The new algorithm is tested on two classes of problems from the literature and compared with a recent branch-and-cut-and-price algorithm from the literature.

Decomposition Methods and Network Design Problems

Decomposition based approaches are recalled from primal and dual point of view. The possibility of building partially disaggregated reduced master problems is investigated. This extends the idea of aggregated-versus-disaggregated formulation to a gradual choice of alternative level of aggregation. Partial aggregation is applied to the linear multicommodity minimum cost flow problem. The possibility of having only partially aggregated bundles opens a wide range of alternatives with different trade-offs between the number of iterations and the required computation for solving it. This trade-off is explored for several sets of instances and the results are compared with the ones obtained by directly solving the natural node-arc formulation. An iterative solution process to the route assignment problem is proposed, based on the well-known Frank Wolfe algorithm. In order to provide a first feasible solution to the Frank Wolfe algorithm, a linear multicommodity min-cost flow problem is solved to optimality by using the decomposition techniques mentioned above. Solutions of this problem are useful for network orientation and design, especially in relation with public transportation systems as the Personal Rapid Transit. A single-commodity robust network design problem is addressed. In this, an undirected graph with edge costs is given together with a discrete set of balance matrices, representing different supply/demand scenarios. The goal is to determine the minimum cost installation of capacities on the edges such that the flow exchange is feasible for every scenario. A set of new instances that are computationally hard for the natural flow formulation are solved by means of a new heuristic algorithm. Finally, an efficient decomposition-based heuristic approach for a large scale stochastic unit commitment problem is presented. The addressed real-world stochastic problem employs at its core a deterministic unit commitment planning model developed by the California Independent System Operator (ISO).

Heuristic algorithms for the Capacitated Location-Routing Problem and the Multi-Depot Vehicle Routing Problem

The Capacitated Location-Routing Problem (CLRP) is a NP-hard problem since it generalizes two well known NP-hard problems: the Capacitated Facility Location Problem (CFLP) and the Capacitated Vehicle Routing Problem (CVRP). The Multi-Depot Vehicle Routing Problem (MDVRP) is known to be a NP-hard since it is a generalization of the well known Vehicle Routing Problem (VRP), arising with one depot. This thesis addresses heuristics algorithms based on the well-know granular search idea introduced by Toth and Vigo (2003) to solve the CLRP and the MDVRP. Extensive computational experiments on benchmark instances for both problems have been performed to determine the effectiveness of the proposed algorithms. This work is organized as follows: Chapter 1 describes a detailed overview and a methodological review of the literature for the the Capacitated Location-Routing Problem (CLRP) and the Multi-Depot Vehicle Routing Problem (MDVRP). Chapter 2 describes a two-phase hybrid heuristic algorithm to solve the CLRP. Chapter 3 shows a computational comparison of heuristic algorithms for the CLRP. Chapter 4 presents a hybrid granular tabu search approach for solving the MDVRP.

Many-core Algorithms for Combinatorial Optimization

Combinatorial Optimization is becoming ever more crucial, in these days. From natural sciences to economics, passing through urban centers administration and personnel management, methodologies and algorithms with a strong theoretical background and a consolidated real-word effectiveness is more and more requested, in order to find, quickly, good solutions to complex strategical problems. Resource optimization is, nowadays, a fundamental ground for building the basements of successful projects. From the theoretical point of view, Combinatorial Optimization rests on stable and strong foundations, that allow researchers to face ever more challenging problems. However, from the application point of view, it seems that the rate of theoretical developments cannot cope with that enjoyed by modern hardware technologies, especially with reference to the one of processors industry. In this work we propose new parallel algorithms, designed for exploiting the new parallel architectures available on the market. We found that, exposing the inherent parallelism of some resolution techniques (like Dynamic Programming), the computational benefits are remarkable, lowering the execution times by more than an order of magnitude, and allowing to address instances with dimensions not possible before. We approached four Combinatorial Optimization’s notable problems: Packing Problem, Vehicle Routing Problem, Single Source Shortest Path Problem and a Network Design problem. For each of these problems we propose a collection of effective parallel solution algorithms, either for solving the full problem (Guillotine Cuts and SSSPP) or for enhancing a fundamental part of the solution method (VRP and ND). We endorse our claim by presenting computational results for all problems, either on standard benchmarks from the literature or, when possible, on data from real-world applications, where speed-ups of one order of magnitude are usually attained, not uncommonly scaling up to 40 X factors.

Ottimizzazione delle reti di distribuzione idrica tramite algoritmi genetici multi-obiettivo

Water distribution networks optimization is a challenging problem due to the dimension and the complexity of these systems. Since the last half of the twentieth century this field has been investigated by many authors. Recently, to overcome discrete nature of variables and non linearity of equations, the research has been focused on the development of heuristic algorithms. This algorithms do not require continuity and linearity of the problem functions because they are linked to an external hydraulic simulator that solve equations of mass continuity and of energy conservation of the network. In this work, a NSGA-II (Non-dominating Sorting Genetic Algorithm) has been used. This is a heuristic multi-objective genetic algorithm based on the analogy of evolution in nature. Starting from an initial random set of solutions, called population, it evolves them towards a front of solutions that minimize, separately and contemporaneously, all the objectives. This can be very useful in practical problems where multiple and discordant goals are common. Usually, one of the main drawback of these algorithms is related to time consuming: being a stochastic research, a lot of solutions must be analized before good ones are found. Results of this thesis about the classical optimal design problem shows that is possible to improve results modifying the mathematical definition of objective functions and the survival criterion, inserting good solutions created by a Cellular Automata and using rules created by classifier algorithm (C4.5). This part has been tested using the version of NSGA-II supplied by Centre for Water Systems (University of Exeter, UK) in MATLAB® environment. Even if orientating the research can constrain the algorithm with the risk of not finding the optimal set of solutions, it can greatly improve the results. Subsequently, thanks to CINECA help, a version of NSGA-II has been implemented in C language and parallelized: results about the global parallelization show the speed up, while results about the island parallelization show that communication among islands can improve the optimization. Finally, some tests about the optimization of pump scheduling have been carried out. In this case, good results are found for a small network, while the solutions of a big problem are affected by the lack of constraints on the number of pump switches. Possible future research is about the insertion of further constraints and the evolution guide. In the end, the optimization of water distribution systems is still far from a definitive solution, but the improvement in this field can be very useful in reducing the solutions cost of practical problems, where the high number of variables makes their management very difficult from human point of view.

Application-oriented Mixed Integer Non-Linear Programming

In the most recent years there is a renovate interest for Mixed Integer Non-Linear Programming (MINLP) problems. This can be explained for different reasons: (i) the performance of solvers handling non-linear constraints was largely improved; (ii) the awareness that most of the applications from the real-world can be modeled as an MINLP problem; (iii) the challenging nature of this very general class of problems. It is well-known that MINLP problems are NP-hard because they are the generalization of MILP problems, which are NP-hard themselves. However, MINLPs are, in general, also hard to solve in practice. We address to non-convex MINLPs, i.e. having non-convex continuous relaxations: the presence of non-convexities in the model makes these problems usually even harder to solve. The aim of this Ph.D. thesis is to give a flavor of different possible approaches that one can study to attack MINLP problems with non-convexities, with a special attention to real-world problems. In Part 1 of the thesis we introduce the problem and present three special cases of general MINLPs and the most common methods used to solve them. These techniques play a fundamental role in the resolution of general MINLP problems. Then we describe algorithms addressing general MINLPs. Parts 2 and 3 contain the main contributions of the Ph.D. thesis. In particular, in Part 2 four different methods aimed at solving different classes of MINLP problems are presented. Part 3 of the thesis is devoted to real-world applications: two different problems and approaches to MINLPs are presented, namely Scheduling and Unit Commitment for Hydro-Plants and Water Network Design problems. The results show that each of these different methods has advantages and disadvantages. Thus, typically the method to be adopted to solve a real-world problem should be tailored on the characteristics, structure and size of the problem. Part 4 of the thesis consists of a brief review on tools commonly used for general MINLP problems, constituted an integral part of the development of this Ph.D. thesis (especially the use and development of open-source software). We present the main characteristics of solvers for each special case of MINLP.

Networks, Uncertainty, Applications and a Crusade for Optimality

In this thesis we address a collection of Network Design problems which are strongly motivated by applications from Telecommunications, Logistics and Bioinformatics. In most cases we justify the need of taking into account uncertainty in some of the problem parameters, and different Robust optimization models are used to hedge against it. Mixed integer linear programming formulations along with sophisticated algorithmic frameworks are designed, implemented and rigorously assessed for the majority of the studied problems. The obtained results yield the following observations: (i) relevant real problems can be effectively represented as (discrete) optimization problems within the framework of network design; (ii) uncertainty can be appropriately incorporated into the decision process if a suitable robust optimization model is considered; (iii) optimal, or nearly optimal, solutions can be obtained for large instances if a tailored algorithm, that exploits the structure of the problem, is designed; (iv) a systematic and rigorous experimental analysis allows to understand both, the characteristics of the obtained (robust) solutions and the behavior of the proposed algorithm.

Mathematical Optimization Applied to Thermal and Electrical Energy Systems

This Thesis aims at building and discussing mathematical models applications focused on Energy problems, both on the thermal and electrical side. The objective is to show how mathematical programming techniques developed within Operational Research can give useful answers in the Energy Sector, how they can provide tools to support decision making processes of Companies operating in the Energy production and distribution and how they can be successfully used to make simulations and sensitivity analyses to better understand the state of the art and convenience of a particular technology by comparing it with the available alternatives. The first part discusses the fundamental mathematical background followed by a comprehensive literature review about mathematical modelling in the Energy Sector. The second part presents mathematical models for the District Heating strategic network design and incremental network design. The objective is the selection of an optimal set of new users to be connected to an existing thermal network, maximizing revenues, minimizing infrastructure and operational costs and taking into account the main technical requirements of the real world application. Results on real and randomly generated benchmark networks are discussed with particular attention to instances characterized by big networks dimensions. The third part is devoted to the development of linear programming models for optimal battery operation in off-grid solar power schemes, with consideration of battery degradation. The key contribution of this work is the inclusion of battery degradation costs in the optimisation models. As available data on relating degradation costs to the nature of charge/discharge cycles are limited, we concentrate on investigating the sensitivity of operational patterns to the degradation cost structure. The objective is to investigate the combination of battery costs and performance at which such systems become economic. We also investigate how the system design should change when battery degradation is taken into account.

Design and Performance Evaluation of Network-on-Chip Communication Protocols and Architectures

The scale down of transistor technology allows microelectronics manufacturers such as Intel and IBM to build always more sophisticated systems on a single microchip. The classical interconnection solutions based on shared buses or direct connections between the modules of the chip are becoming obsolete as they struggle to sustain the increasing tight bandwidth and latency constraints that these systems demand. The most promising solution for the future chip interconnects are the Networks on Chip (NoC). NoCs are network composed by routers and channels used to inter- connect the different components installed on the single microchip. Examples of advanced processors based on NoC interconnects are the IBM Cell processor, composed by eight CPUs that is installed on the Sony Playstation III and the Intel Teraflops pro ject composed by 80 independent (simple) microprocessors. On chip integration is becoming popular not only in the Chip Multi Processor (CMP) research area but also in the wider and more heterogeneous world of Systems on Chip (SoC). SoC comprehend all the electronic devices that surround us such as cell-phones, smart-phones, house embedded systems, automotive systems, set-top boxes etc... SoC manufacturers such as ST Microelectronics , Samsung, Philips and also Universities such as Bologna University, M.I.T., Berkeley and more are all proposing proprietary frameworks based on NoC interconnects. These frameworks help engineers in the switch of design methodology and speed up the development of new NoC-based systems on chip. In this Thesis we propose an introduction of CMP and SoC interconnection networks. Then focusing on SoC systems we propose: • a detailed analysis based on simulation of the Spidergon NoC, a ST Microelectronics solution for SoC interconnects. The Spidergon NoC differs from many classical solutions inherited from the parallel computing world. Here we propose a detailed analysis of this NoC topology and routing algorithms. Furthermore we propose aEqualized a new routing algorithm designed to optimize the use of the resources of the network while also increasing its performance; • a methodology flow based on modified publicly available tools that combined can be used to design, model and analyze any kind of System on Chip; • a detailed analysis of a ST Microelectronics-proprietary transport-level protocol that the author of this Thesis helped developing; • a simulation-based comprehensive comparison of different network interface designs proposed by the author and the researchers at AST lab, in order to integrate shared-memory and message-passing based components on a single System on Chip; • a powerful and flexible solution to address the time closure exception issue in the design of synchronous Networks on Chip. Our solution is based on relay stations repeaters and allows to reduce the power and area demands of NoC interconnects while also reducing its buffer needs; • a solution to simplify the design of the NoC by also increasing their performance and reducing their power and area consumption. We propose to replace complex and slow virtual channel-based routers with multiple and flexible small Multi Plane ones. This solution allows us to reduce the area and power dissipation of any NoC while also increasing its performance especially when the resources are reduced. This Thesis has been written in collaboration with the Advanced System Technology laboratory in Grenoble France, and the Computer Science Department at Columbia University in the city of New York.

Design of optical networks for advanced applications

Nowadays, computing is migrating from traditional high performance and distributed computing to pervasive and utility computing based on heterogeneous networks and clients. The current trend suggests that future IT services will rely on distributed resources and on fast communication of heterogeneous contents. The success of this new range of services is directly linked to the effectiveness of the infrastructure in delivering them. The communication infrastructure will be the aggregation of different technologies even though the current trend suggests the emergence of single IP based transport service. Optical networking is a key technology to answer the increasing requests for dynamic bandwidth allocation and configure multiple topologies over the same physical layer infrastructure, optical networks today are still “far” from accessible from directly configure and offer network services and need to be enriched with more “user oriented” functionalities. However, current Control Plane architectures only facilitate efficient end-to-end connectivity provisioning and certainly cannot meet future network service requirements, e.g. the coordinated control of resources. The overall objective of this work is to provide the network with the improved usability and accessibility of the services provided by the Optical Network. More precisely, the definition of a service-oriented architecture is the enable technology to allow user applications to gain benefit of advanced services over an underlying dynamic optical layer. The definition of a service oriented networking architecture based on advanced optical network technologies facilitates users and applications access to abstracted levels of information regarding offered advanced network services. This thesis faces the problem to define a Service Oriented Architecture and its relevant building blocks, protocols and languages. In particular, this work has been focused on the use of the SIP protocol as a inter-layers signalling protocol which defines the Session Plane in conjunction with the Network Resource Description language. On the other hand, an advantage optical network must accommodate high data bandwidth with different granularities. Currently, two main technologies are emerging promoting the development of the future optical transport network, Optical Burst and Packet Switching. Both technologies respectively promise to provide all optical burst or packet switching instead of the current circuit switching. However, the electronic domain is still present in the scheduler forwarding and routing decision. Because of the high optics transmission frequency the burst or packet scheduler faces a difficult challenge, consequentially, high performance and time focused design of both memory and forwarding logic is need. This open issue has been faced in this thesis proposing an high efficiently implementation of burst and packet scheduler. The main novelty of the proposed implementation is that the scheduling problem has turned into simple calculation of a min/max function and the function complexity is almost independent of on the traffic conditions.

Collaborative Change: Environmental Jolt, Network (Re)Design and Firm Performance

Motivated by the need to understand which are the underlying forces that trigger network evolution, we develop a multilevel theoretical and empirically testable model to examine the relationship between changes in the external environment and network change. We refer to network change as the dissolution or replacement of an interorganizational tie, adding also the case of the formation of new ties with new or preexisting partners. Previous research has paid scant attention to the organizational consequences of quantum change enveloping entire industries in favor of an emphasis on continuous change. To highlight radical change we introduce the concept of environmental jolt. The September 11 terrorist attacks provide us with a natural experiment to test our hypotheses on the antecedents and the consequences of network change. Since network change can be explained at multiple levels, we incorporate firm-level variables as moderators. The empirical setting is the global airline industry, which can be regarded as a constantly changing network of alliances. The study reveals that firms react to environmental jolts by forming homophilous ties and transitive triads as opposed to the non jolt periods. Moreover, we find that, all else being equal, firms that adopt a brokerage posture will have positive returns. However, we find that in the face of an environmental jolt brokerage relates negatively to firm performance. Furthermore, we find that the negative relationship between brokerage and performance during an environmental jolt is more significant for larger firms. Our findings suggest that jolts are an important predictor of network change, that they significantly affect operational returns and should be thus incorporated in studies of network dynamics.

Modelling and Design of Advanced Reliable Circuits and Devices for Energy Efficiency

Reliable electronic systems, namely a set of reliable electronic devices connected to each other and working correctly together for the same functionality, represent an essential ingredient for the large-scale commercial implementation of any technological advancement. Microelectronics technologies and new powerful integrated circuits provide noticeable improvements in performance and cost-effectiveness, and allow introducing electronic systems in increasingly diversified contexts. On the other hand, opening of new fields of application leads to new, unexplored reliability issues. The development of semiconductor device and electrical models (such as the well known SPICE models) able to describe the electrical behavior of devices and circuits, is a useful means to simulate and analyze the functionality of new electronic architectures and new technologies. Moreover, it represents an effective way to point out the reliability issues due to the employment of advanced electronic systems in new application contexts. In this thesis modeling and design of both advanced reliable circuits for general-purpose applications and devices for energy efficiency are considered. More in details, the following activities have been carried out: first, reliability issues in terms of security of standard communication protocols in wireless sensor networks are discussed. A new communication protocol is introduced, allows increasing the network security. Second, a novel scheme for the on-die measurement of either clock jitter or process parameter variations is proposed. The developed scheme can be used for an evaluation of both jitter and process parameter variations at low costs. Then, reliability issues in the field of “energy scavenging systems” have been analyzed. An accurate analysis and modeling of the effects of faults affecting circuit for energy harvesting from mechanical vibrations is performed. Finally, the problem of modeling the electrical and thermal behavior of photovoltaic (PV) cells under hot-spot condition is addressed with the development of an electrical and thermal model.