Doctor of Philosophy

dissertationThis dissertation aims to develop an innovative and improved paradigm for real-time large-scale traffic system estimation and mobility optimization. To fully utilize heterogeneous data sources in a complex spatial environment, this dissertation proposes an integrated and unified estimation-optimization framework capable of interpreting different types of traffic measurements into various decision-making processes. With a particular emphasis on the end-to-end travel time prediction problem, this dissertation proposes an information-theoretic sensor location model that aims to maximize information gains from a set of point, point-to-point and probe sensors in a traffic network. After thoroughly examining a number of possible measures of information gain, this dissertation selects a path travel time prediction uncertainty criterion to construct a joint sensor location and travel time estimation/prediction framework. To better measure the quality of service for ransportation systems, this dissertation investigates the path travel time reliability from two perspectives: variability and robustness. Based on calibrated travel disutility functions, the path travel time variability in this research is represented by its standard deviation in addition to the mean travel time. To handle the nonlinear and nonadditive cost functions introduced by the quadratic forms of the standard deviation term, a novel Lagrangian substitution approach is introduced to estimate the lower bound of the most reliable path solution through solving a sequence of standard shortest path problems. To recognize the asymmetrical and heavy-tailed travel time distributions, this dissertation proposes Lagrangian relaxation based iterative search algorithms for finding the absolute and percentile robust shortest paths. Moreover, this research develops a sampling-based method to dynamically construct a proxy objective function in terms of travel time observations from multiple days. Comprehensive numerical experiment results with real-world travel time measurements show that 10-20 iterations of standard shortest path algorithms for the reformulated models can offer a very small relative duality gap of about 2-6%, for both reliability measure models. This broadly-defined research has successfully addressed a number of theoretically challenging and practically important issues for building the next-generation Advanced Traveler Information Systems, and is expected to offer a rich foundation beneficial to the model and algorithmic development of sensor network design, traffic forecasting and personalized navigation

Regret Models and Preprocessing Techniques for Combinatorial Optimization under Uncertainty

Ph.DDOCTOR OF PHILOSOPH

Routing and scheduling optimisation under uncertainty for engineering applications

The thesis aims to develop a viable computational approach suitable for solving large vehicle routing and scheduling optimisation problems affected by uncertainty. The modelling framework is built upon recent advances in Stochastic Optimisation, Robust Optimisation and Distributionally Robust Optimization. The utility of the methodology is presented on two classes of discrete optimisation problems: scheduling satellite communication, which is a variant of Machine Scheduling, and the Vehicle Routing Problem with Time Windows and Synchronised Visits. For each problem class, a practical engineering application is formulated using data coming from the real world. The significant size of the problem instances reinforced the need to apply a different computational approach for each problem class. Satellite communication is scheduled using a Mixed-Integer Programming solver. In contrast, the vehicle routing problem with synchronised visits is solved using a hybrid method that combines Iterated Local Search, Constraint Programming and the Guided Local Search metaheuristic. The featured application of scheduling satellite communication is the Satellite Quantum Key Distribution for a system that consists of one spacecraft placed in the Lower Earth Orbit and a network of optical ground stations located in the United Kingdom. The satellite generates cryptographic keys and transmits them to individual ground stations. Each ground station should receive the number of keys in proportion to the importance of the ground station in the network. As clouds containing water attenuate the signal, reliable scheduling needs to account for cloud cover predictions, which are naturally affected by uncertainty. A new uncertainty sets tailored for modelling uncertainty in predictions of atmospheric phenomena is the main contribution to the methodology. The uncertainty set models the evolution of uncertain parameters using a Multivariate Vector Auto-Regressive Time Series, which preserves correlations over time and space. The problem formulation employing the new uncertainty set compares favourably to a suite of alternative models adapted from the literature considering both the computational time and the cost-effectiveness of the schedule evaluated in the cloud cover conditions observed in the real world. The other contribution of the thesis in the satellite scheduling domain is the formulation of the Satellite Quantum Key Distribution problem. The proof of computational complexity and thorough performance analysis of an example Satellite Quantum Key Distribution system accompany the formulation. The Home Care Scheduling and Routing Problem, which instances are solved for the largest provider of such services in Scotland, is the application of the Vehicle Routing Problem with Time Windows and Synchronised Visits. The problem instances contain over 500 visits. Around 20% of them require two carers simultaneously. Such problem instances are well beyond the scalability limitations of the exact method and considerably larger than instances of similar problems considered in the literature. The optimisation approach proposed in the thesis found effective solutions in attractive computational time (i.e., less than 30 minutes) and the solutions reduced the total travel time threefold compared to alternative schedules computed by human planners. The Essential Riskiness Index Optimisation was incorporated into the Constraint Programming model to address uncertainty in visits' duration. Besides solving large problem instances from the real world, the solution method reproduced the majority of the best results reported in the literature and strictly improved the solutions for several instances of a well-known benchmark for the Vehicle Routing Problem with Time Windows and Synchronised Visits.The thesis aims to develop a viable computational approach suitable for solving large vehicle routing and scheduling optimisation problems affected by uncertainty. The modelling framework is built upon recent advances in Stochastic Optimisation, Robust Optimisation and Distributionally Robust Optimization. The utility of the methodology is presented on two classes of discrete optimisation problems: scheduling satellite communication, which is a variant of Machine Scheduling, and the Vehicle Routing Problem with Time Windows and Synchronised Visits. For each problem class, a practical engineering application is formulated using data coming from the real world. The significant size of the problem instances reinforced the need to apply a different computational approach for each problem class. Satellite communication is scheduled using a Mixed-Integer Programming solver. In contrast, the vehicle routing problem with synchronised visits is solved using a hybrid method that combines Iterated Local Search, Constraint Programming and the Guided Local Search metaheuristic. The featured application of scheduling satellite communication is the Satellite Quantum Key Distribution for a system that consists of one spacecraft placed in the Lower Earth Orbit and a network of optical ground stations located in the United Kingdom. The satellite generates cryptographic keys and transmits them to individual ground stations. Each ground station should receive the number of keys in proportion to the importance of the ground station in the network. As clouds containing water attenuate the signal, reliable scheduling needs to account for cloud cover predictions, which are naturally affected by uncertainty. A new uncertainty sets tailored for modelling uncertainty in predictions of atmospheric phenomena is the main contribution to the methodology. The uncertainty set models the evolution of uncertain parameters using a Multivariate Vector Auto-Regressive Time Series, which preserves correlations over time and space. The problem formulation employing the new uncertainty set compares favourably to a suite of alternative models adapted from the literature considering both the computational time and the cost-effectiveness of the schedule evaluated in the cloud cover conditions observed in the real world. The other contribution of the thesis in the satellite scheduling domain is the formulation of the Satellite Quantum Key Distribution problem. The proof of computational complexity and thorough performance analysis of an example Satellite Quantum Key Distribution system accompany the formulation. The Home Care Scheduling and Routing Problem, which instances are solved for the largest provider of such services in Scotland, is the application of the Vehicle Routing Problem with Time Windows and Synchronised Visits. The problem instances contain over 500 visits. Around 20% of them require two carers simultaneously. Such problem instances are well beyond the scalability limitations of the exact method and considerably larger than instances of similar problems considered in the literature. The optimisation approach proposed in the thesis found effective solutions in attractive computational time (i.e., less than 30 minutes) and the solutions reduced the total travel time threefold compared to alternative schedules computed by human planners. The Essential Riskiness Index Optimisation was incorporated into the Constraint Programming model to address uncertainty in visits' duration. Besides solving large problem instances from the real world, the solution method reproduced the majority of the best results reported in the literature and strictly improved the solutions for several instances of a well-known benchmark for the Vehicle Routing Problem with Time Windows and Synchronised Visits

INCORPORATING TRAVEL TIME RELIABILITY INTO TRANSPORTATION NETWORK MODELING

Travel time reliability is deemed as one of the most important factors affecting travelers’ route choice decisions. However, existing practices mostly consider average travel time only. This dissertation establishes a methodology framework to overcome such limitation. Semi-standard deviation is first proposed as the measure of reliability to quantify the risk under uncertain conditions on the network. This measure only accounts for travel times that exceed certain pre-specified benchmark, which offers a better behavioral interpretation and theoretical foundation than some currently used measures such as standard deviation and the probability of on-time arrival. Two path finding models are then developed by integrating both average travel time and semi-standard deviation. The single objective model tries to minimize the weighted sum of average travel time and semi-standard deviation, while the multi-objective model treats them as separate objectives and seeks to minimize them simultaneously. The multi-objective formulation is preferred to the single objective model, because it eliminates the need for prior knowledge of reliability ratios. It offers an additional benefit of providing multiple attractive paths for traveler’s further decision making. The sampling based approach using archived travel time data is applied to derive the path semi-standard deviation. The approach provides a nice workaround to the problem that there is no exact solution to analytically derive the measure. Through this process, the correlation structure can be implicitly accounted for while simultaneously avoiding the complicated link travel time distribution fitting and convolution process. Furthermore, the metaheuristic algorithm and stochastic dominance based approach are adapted to solve the proposed models. Both approaches address the issue where classical shortest path algorithms are not applicable due to non-additive semi-standard deviation. However, the stochastic dominance based approach is preferred because it is more computationally efficient and can always find the true optimal paths. In addition to semi-standard deviation, on-time arrival probability and scheduling delay measures are also investigated. Although these three measures share similar mathematical structures, they exhibit different behaviors in response to large deviations from the pre-specified travel time benchmark. Theoretical connections between these measures and the first three stochastic dominance rules are also established. This enables us to incorporate on-time arrival probability and scheduling delay measures into the methodology framework as well

Robust and stochastic approaches to network capacity design under demand uncertainty

This thesis considers the network capacity design problem with demand uncertainty using the stochastic, robust and distributionally robust stochastic optimization approaches (DRSO). Network modeling in itself has found wide areas of application in most fields of human endeavor. The network would normally consist of source (origin) and sink (destination) nodes connected by arcs that allow for flows of an entity from the origin to the destination nodes. In this thesis, a special type of the minimum cost flow problem is addressed, the multi-commodity network flow problem. Commodities are the flow types that are transported on a shared network. Offered demands are, for the most part, unknown or uncertain, hence a model that immune against this uncertainty becomes the focus as well as the practicability of such models in the industry. This problem falls under the two-stage optimization framework where a decision is delayed in time to adjust for the first decision earlier made. The first stage decision is called the "here and now", while the second stage traffic re-adjustment is the "wait and see" decision. In the literature, the decision-maker is often believed to know the shape of the uncertainty, hence we address this by considering a data-driven uncertainty set. The research also addressed the non-linearity of cost function despite the abundance of literature assuming linearity and models proposed for this. This thesis consist of four main chapters excluding the "Introduction" chapter and the "Approaches to Optimization under Uncertainty" chapter where the methodologies are reviewed. The first of these four, Chapter 3, proposes the two models for the Robust Network Capacity Expansion Problem (RNCEP) with cost non-linearity. These two are the RNCEP with fixed-charge cost and RNCEP with piecewise-linear cost. The next chapter, Chapter 4, compares the RNCEP models under two types of uncertainties in order to address the issue of usefulness in a real world setting. The resulting two robust models are also comapared with the stochastic optimization model with distribution mean. Chapter 5 re-examines the earlier problem using machine learning approaches to generate the two uncertainty sets while the last of these chapters, Chapter 6, investigates DRSO model to network capacity planning and proposes an efficient solution technique

Design and implementation of components for renewably-powered base-stations with heterogeneous access channel

Providing high-speed broadband services in remote areas can be a challenging task, especially because of the lack of network infrastructure. As typical broadband technologies are often expensive to deploy, they require large investment from the local authorities. Previous studies have shown that a viable alternative is to use wireless base stations with high-throughput point to point (PTP) backhaul links. With base stations comes the problem of powering their systems, it is tackled in this thesis by relying on renewable energy harvesting, such as solar panels or wind turbines. This thesis, in the context of the sustainable cellular network harvesting ambient energy (SCAVENGE) project, aims to contribute to a reliable and energy efficient solution to this problem, by adjusting the design of an existing multi-radio energy harvesting base station. In Western Europe, 49 channels of 8 MHz were used for analogue TV transmissions, ranging from 470 MHz (Channel 21) to 862 MHz (Channel 69); this spectrum, now partially unused due to the digital television (DTV) switch-over, has been opened to alternative uses by the regulatory authorities. Using this newly freed ultra high frequency (UHF) range, also known as TV white space (TVWS), can offer reliable low-cost broadband access to housings and businesses in low-density areas. While UHF transmitters allow long range links, the overcrowding of the TV spectrum limits the achievable throughput; to increase the capacity of such TVWS rural broadband base station the UHF radio has previously been combined with a lower-range higher throughput GHz radio like Wireless Fidelity (WiFi). From the regulatory constraints of TVWS applications arises the need for frequency agile transceivers that observe strict spectral mask requirements, this guided previous works towards discrete Fourier transform (DFT) modulated filter-bank multicarrier (FBMC) systems. These systems are numerically efficient, as they permit the up-and-down conversion of the 40 TV channels at the cost of a single channel transceiver and the modulating transform. Typical implementations rely on power-of two fast Fourier transforms (FFTs); however the smallest transform covering the full 40 channels of the TVWS spectrum is a 64 points wide, thus involving 24 unused channels. In order to attain a more numerically-efficient implemented design, we introduce the use of mixed-radix FFTs modulating transform. Testing various sizes and architectures, this approach provides up to 6.7% of energy saving compared to previous designs. Different from orthogonal frequency-division multiplexing (OFDM), FBMC systems are generally expected to be more robust to synchronisation errors, as oversampled FBMC systems can include a guard band, and even in a doubly-dispersive channel, inter-carrier interference (ICI) can be considered negligible. Even though sub-channels can be treated independently—i.e. without the use of cross-terms—they still require equalisation. We introduce a per-band equalisation, amongst different options, a robust and fast blind approach based on a concurrent constant modulus (CM)/decision directed (DD) fractionally-space equaliser (FSE) is selected. The selected approach is capable of equalising a frequency-selective channel. Furthermore the proposed architecture is advantageous in terms of power consumption and implementation cost. After focussing on the design of the radio for TVWS transmission, we address a multi-radio user assignment problem. Using various power consumption and harvesting models for the base station, we formulate two optimisation problems, the first focuses on the base station power consumption, while the second concentrates on load balancing. We employ a dynamic programming approach to optimise the user assignment. The use of such algorithms could allow a downsizing of the power supply systems (harvesters and batteries), thus reducing the cost of the base station. Furthermore the algorithms provide a better balance between the number of users assigned to each network, resulting in a higher quality of service (QoS) and energy efficiency.Providing high-speed broadband services in remote areas can be a challenging task, especially because of the lack of network infrastructure. As typical broadband technologies are often expensive to deploy, they require large investment from the local authorities. Previous studies have shown that a viable alternative is to use wireless base stations with high-throughput point to point (PTP) backhaul links. With base stations comes the problem of powering their systems, it is tackled in this thesis by relying on renewable energy harvesting, such as solar panels or wind turbines. This thesis, in the context of the sustainable cellular network harvesting ambient energy (SCAVENGE) project, aims to contribute to a reliable and energy efficient solution to this problem, by adjusting the design of an existing multi-radio energy harvesting base station. In Western Europe, 49 channels of 8 MHz were used for analogue TV transmissions, ranging from 470 MHz (Channel 21) to 862 MHz (Channel 69); this spectrum, now partially unused due to the digital television (DTV) switch-over, has been opened to alternative uses by the regulatory authorities. Using this newly freed ultra high frequency (UHF) range, also known as TV white space (TVWS), can offer reliable low-cost broadband access to housings and businesses in low-density areas. While UHF transmitters allow long range links, the overcrowding of the TV spectrum limits the achievable throughput; to increase the capacity of such TVWS rural broadband base station the UHF radio has previously been combined with a lower-range higher throughput GHz radio like Wireless Fidelity (WiFi). From the regulatory constraints of TVWS applications arises the need for frequency agile transceivers that observe strict spectral mask requirements, this guided previous works towards discrete Fourier transform (DFT) modulated filter-bank multicarrier (FBMC) systems. These systems are numerically efficient, as they permit the up-and-down conversion of the 40 TV channels at the cost of a single channel transceiver and the modulating transform. Typical implementations rely on power-of two fast Fourier transforms (FFTs); however the smallest transform covering the full 40 channels of the TVWS spectrum is a 64 points wide, thus involving 24 unused channels. In order to attain a more numerically-efficient implemented design, we introduce the use of mixed-radix FFTs modulating transform. Testing various sizes and architectures, this approach provides up to 6.7% of energy saving compared to previous designs. Different from orthogonal frequency-division multiplexing (OFDM), FBMC systems are generally expected to be more robust to synchronisation errors, as oversampled FBMC systems can include a guard band, and even in a doubly-dispersive channel, inter-carrier interference (ICI) can be considered negligible. Even though sub-channels can be treated independently—i.e. without the use of cross-terms—they still require equalisation. We introduce a per-band equalisation, amongst different options, a robust and fast blind approach based on a concurrent constant modulus (CM)/decision directed (DD) fractionally-space equaliser (FSE) is selected. The selected approach is capable of equalising a frequency-selective channel. Furthermore the proposed architecture is advantageous in terms of power consumption and implementation cost. After focussing on the design of the radio for TVWS transmission, we address a multi-radio user assignment problem. Using various power consumption and harvesting models for the base station, we formulate two optimisation problems, the first focuses on the base station power consumption, while the second concentrates on load balancing. We employ a dynamic programming approach to optimise the user assignment. The use of such algorithms could allow a downsizing of the power supply systems (harvesters and batteries), thus reducing the cost of the base station. Furthermore the algorithms provide a better balance between the number of users assigned to each network, resulting in a higher quality of service (QoS) and energy efficiency

Almost Symmetries and the Unit Commitment Problem

This thesis explores two main topics. The first is almost symmetry detection on graphs. The presence of symmetry in combinatorial optimization problems has long been considered an anathema, but in the past decade considerable progress has been made. Modern integer and constraint programming solvers have automatic symmetry detection built-in to either exploit or avoid symmetric regions of the search space. Automatic symmetry detection generally works by converting the input problem to a graph which is in exact correspondence with the problem formulation. Symmetry can then be detected on this graph using one of the excellent existing algorithms; these are also the symmetries of the problem formulation.The motivation for detecting almost symmetries on graphs is that almost symmetries in an integer program can force the solver to explore nearly symmetric regions of the search space. Because of the known correspondence between integer programming formulations and graphs, this is a first step toward detecting almost symmetries in integer programming formulations. Though we are only able to compute almost symmetries for graphs of modest size, the results indicate that almost symmetry is definitely present in some real-world combinatorial structures, and likely warrants further investigation.The second topic explored in this thesis is integer programming formulations for the unit commitment problem. The unit commitment problem involves scheduling power generators to meet anticipated energy demand while minimizing total system operation cost. Today, practitioners usually formulate and solve unit commitment as a large-scale mixed integer linear program.The original intent of this project was to bring the analysis of almost symmetries to the unit commitment problem. Two power generators are almost symmetric in the unit commitment problem if they have almost identical parameters. Along the way, however, new formulations for power generators were discovered that warranted a thorough investigation of their own. Chapters 4 and 5 are a result of this research.Thus this work makes three contributions to the unit commitment problem: a convex hull description for a power generator accommodating many types of constraints, an improved formulation for time-dependent start-up costs, and an exact symmetry reduction technique via reformulation

Mitigating risk and ambiguity in service systems

Ph.DDOCTOR OF PHILOSOPH