The work presented in this thesis concerns the problem of dynamic vehicle routing. The motivation for this is the increasing demands on transportation services to deliver fast, efficient and reliable service. Systems are now needed for dispatching transportation requests that arrive dynamically throughout the scheduling horizon. Therefore the focus of this research is the dynamic pickup and delivery problem with time windows, where requests are not completely known in advance but become available during the scheduling horizon. All requests have to be satisfied by a given fleet of vehicles and each request has a pickup and delivery location, along with a time window at which services can take place. To solve the DPDPTW, our algorithm is embedded in a rolling horizon framework, thus allowing the problem to be viewed as a series of static sub-problems. This research begins by considering the static variant of the problem. Both heuristic and metaheuristic methods are applied and an analysis is performed across a range of well-known instances. Results competitive with the state of the art are obtained. For the dynamic problem, investigations are performed to identify how requests arriving dynamically should be incorporated into the solution. Varying degrees of urgency and proportions of dynamic requests have been examined. Further investigations look at improving the solutions over time and identifying appropriate improvement heuristics. Again competitive results are achieved across a range of instances from the literature. This continually increasing area of research covers many real-life problems such as a health courier service. Here, the problem consists of the pickup and delivery of mail, specimens and equipment between hospitals, GP surgeries and health centres. Final research applies our findings to a real-life example of this problem, both for static schedules and a real-time 24/7 service.

The principal aim of this PhD program is the development of an optimisation and risk based methodology for reliability and robustness predictions of packaged electronic components. Reliability based design optimisation involves the integration of reduced order modelling, risk analysis and optimisation. The increasing cost of physical prototyping and extensive qualification testing for reliability assessment is making virtual qualification a very attractive alternative for the electronics industry. Given the availability of low cost processing technology and advanced numerical techniques such as finite element analysis, design engineers can now undertake detailed calculations of physical phenomena in electronic packages such as temperature, electromagnetics, and stress. Physics of failure analysis can also be performed using the results from these detailed calculations to predict modes of failure and estimated lifetime of an electronic component. At present the majority of calculations performed using finite element techniques assume that the input parameters are single valued without any variation. Obviously this is not the case as variation in design variables (such as dimensions of the package, operating conditions, etc) can have statistical distributions. The research undertaken in this PhD resulted in the development of software libraries and a toolset which can be used in parallel with finite element analysis to assess the impact of design variable variations on the package reliability and robustness. This resulted in the development of the ROMARA software which now contains a number of best in class reduced order modelling techniques, optimisation algorithms, and stochastic risk assessment procedures. The software has been developed using the C# language and demonstrated for a number of case studies. The case study detailed in this thesis is related to a power electronics IGBT structure and demonstrates the technology for predicting the reliability and robustness of a wirebond interconnect structure that is subjected to electro-thermo-mechanical loads. The design variables investigated in this study included wire-loop ratio, current in the wire, and thickness of the silicon die each represented as input variables with normal distribution. In terms of reliability the damage variable under investigation was the plastic strain at the wire/aluminium pad interface. Using ANSYS for predicting the physics in the package we have demonstrated the ability of the ROMARA code to optimise the design of wirebond, in terms of minimising the induced damage. Other real cases have been investigated using the developed ROMARA software and these are reported in the public domain and briefly detailed in this thesis.

Hospitals in the UK are increasingly having to cancel a large proportion of elective operations due to the unavailability of beds on hospital wards for post-operative recovery. The availability of post-operative beds is therefore critical to the scheduling of surgical procedures and the throughput of patients in a hospital. The focus of this research is to investigate, via data-driven modelling, systematic reasons for the unavailability of beds and to demonstrate how the Master Surgery Schedule (MSS) can be constructed using Operational Research techniques to minimise the number of cancellations of elective operations. Statistical analysis of data provided by the University Hospital of Wales, Cardiff was performed, providing information on patient demand and length of stay distributions. A two-stage modelling process was developed to construct and simulate an MSS that minimises the number of cancellations. The first stage involves a novel set partitioning based optimisation model that incorporates operating room and bed constraints. The second stage simulates the resulting optimal schedule to provide measures on how well the schedule would perform if implemented. The results from this two-stage model provide insights into when best to schedule surgical specialties and how best the beds are distributed between wards. Two optimisation under uncertainty techniques are then employed to incorporate the uncertainty associated with the bed requirements into the optimisation process. A robust optimisation (RO) approach that uses protection functions in each bed constraint is developed. Investigations into varying levels of protection are performed in order to gain insight into the so called `price of robustness'. Results show that MSSs that are constructed from protecting more of the uncertainty result in fewer cancellations and a smaller probability of requiring more beds than are available. The deterministic optimisation model is then extended to become a scenario-based optimisation model in which more scenarios of bed requirement are incorporated into a single optimisation model. Results show that as more scenarios are included, a more robust schedule is generated and fewer cancellations are expected. Results from the different approaches are compared to assess the benefits of using RO techniques. Future research directions following from this work are discussed, including the construction of the MSS based on sub-specialties and investigation of different working practices within the case study hospital.

This thesis is concerned with a real-world multi-shift drayage problem at a large international port with multiple docks being operated simultaneously. Several important issues in the drayage problem are identified and a set covering model is developed based on a novel route representation. The model adopts an implicit solution representation to reduce the problem size and aims to find a set of vehicle routes with minimum total cost to deliver all commodities within their time windows. As accurate travel time prediction is necessary to construct the vehicle routes, a short-haul travel time prediction model and an algorithm using real-life GPS data are studied. The output of the prediction model can be used as an input for the set covering model. The set covering model for the multi-shift full truckload transportation problem can be directly solved by a commercial solver for small problems, but results in prohibitive computation time for even moderate-sized problems. In order to solve medium- and large-sized instances, we proposed a 3-stage hybrid solution method and applied it to solve real-life instances at a large international port in China. It was shown that the method is able to find solutions that are very close to the lower bounds. In addition, we also proposed a more efficient hybrid branch-and-price approach. Results show the method performed well and is more suited for solving real-life, large-sized drayage operation problems.

The thesis is concerned with novel Nature-Inspired heuristics for the so called NP-hard problems of optimisation. A particular algorithm which has been recently introduced and shown to be effective in continuous optimisation is the Plant Propagation Algorithm or PPA. Here, we intend to extend it to cope with combinatorial optimisation. In order to show that our extension is viable and effective, we consider three types of problems which are good representatives of the whole topic. These are the Travelling Salesman Problem or TSP, the Knapsack Problem or KP and the scheduling problem of Berth Allocation as arises in container ports or BAP. Because PPA is a population-based search heuristic, we devote a chapter to the important issue of generating good and yet computationally relatively light initial populations of solutions to kick start the search process. In the case of the TSP we revisit and extend the Strip Algorithm (SA). We introduce the 2-Part SA and show that it is better than the classical SA. We also introduce new variants such as the Adaptive SA and the Spiral SA which cope with clustered cities and instances with cities concentrated around the center of the unit square, respectively. In the case of KP we adapt the Roulette Wheel selection approach to generate solutions to start with PPA. And in the case of BAP, we introduce a number of simple heuristics which consider a schedule as a flat box with one side being the processing time and the other the position of vessels on the wharf. The heuristics try to generate schedules by avoiding overlap as much as possible. All approaches and algorithms are implemented and tested against well established algorithms. The results are recorded and discussed extensively. The thesis ends with a conclusion and ideas for further research.

The use of optimisation within financial markets is rapidly increasing. There is a growing demand for a class of new and improved methods to accurately price financial options. Semi-infinite optimisation (SIO) has become a vivid research area in mathematical optimisation during the recent two decades. This is due to the fact that there are many new theoretical advances as well as a broad variety of real-life problems where this mathematical model can be applied. This thesis considers particular applications of SIO to finding bounds on the prices of basket options. Original results have been derived for: • Finding a lower bound on European basket call option prices. • Calculating a lower bound on European basket call option prices, incorporating bid-ask prices within the model. • Analysing price bounds on various types of American basket options. • Deriving an upper bound on the price of a discretely sampled arithmetic average Asian basket option. • Finding an upper bound on the price of an Asian basket call option, incorporating bid-ask prices. • Calculating an upper bound on the price of an Altiplano Mountain Range option. The models and results obtained in this thesis can be used in financial markets by investors, investment banks and hedge funds amongst others.

Operational Research and Optimization are fundamental disciplines which, for decades, provided the real-world with tools for solving practical problems. Many such problems arise in container ports. Container terminals are important assets in modern economies. They constitute an important means of distributing goods made overseas to domestic markets in most countries. They are expensive to build and difficult to operate. We describe here some of the main operations which are faced daily by decision makers at those facilities. Decision makers often use Operational Research and Optimization tools to run these operations effectively. In this thesis, we focus on seaside operations which can be divided into three main problems: 1- the Berth Allocation Problem (BAP), 2- the Quay Crane Assignment Problem (QCAP), 3- the Quay Crane Scheduling Problem (QCSP). Each one of the above is a complex optimization problem in its own right. However, solving them individually without the consideration of the others may lead to overall suboptimal solutions. For this reason we will investigate the pairwise combinations of these problems and their total integration In addition, several important factors that affected on the final solution. The main contributions of this study are modelling and solving of the: 1- Robust berth allocation problem (RBAP): a new efficient mathematical model is formulated and a hybrid algorithm based on Branch-and-Cut and the Genetic Algorithm is used to find optimal or near optimal solutions for large scale instances in reasonable time. 2- Quay crane assignment and quay crane scheduling problem (QCASP): a new mathematical model is built to simultaneously solve QCASP and a heuristic based on the Genetic Algorithm is developed to find solutions to realistic instances in reasonable time. 3- Berth allocation, quay crane assignment and quay crane scheduling problem (BACASP): an aggregate model for all three seaside operations is proposed and to solve realistic instances of the problem, an adapted variant of the Genetic Algorithm is implemented.

This thesis focuses on the portfolio optimisation problems, which concern with allocating the limited capital to invest in a number of potential assets (investments) in order to achieve the investors risk appetites and the return objectives. In the 1950s, Harry Markowitz proposed a mean-variance portfolio optimisation model, which is widely regarded as the foundation of the modern portfolio theory. However, the basic Markowitz mean-variance model has limited practical utilities since it omits many constraints existed in real world trading. The problem quickly becomes more complex with the additional real-world trading constraints involved. One main problem of the mean-variance portfolio optimisation framework is that it relies on the perfect information. In practice, the problems faced in portfolio optimisation are more complex since many sources of market uncertainty are involved. Moreover, different risk measures need to be adopted in order to have a better reflection of the asymmetry nature of asset returns. The thesis firstly studies the single-period mean-variance portfolio optimisation model with two practical trading constraints. Hereafter, a two-stage scenario-based stochastic portfolio optimisation model is developed. The two-stage stochastic programming model minimises the excess shortfall of portfolios which are captured by the CVaR risk measure. The two-stage stochastic programming model can capture the market uncertainty in terms of future asset prices and it enables the investors rebalancing the assets in a dynamic setting. A copula-based method is applied to generate scenarios to represent uncertainty in future asset prices in accordance with their historical information. Stability tests are also performed and the results confirm that the scenario generation method is appropriate for the model. Three hybrid algorithms which hybridise metaheuristics and exact methods in an integrated manner are presented to solve the two models. The principle of designing hybrid methods in this thesis can be described as: metaheuristic algorithms are adopted to search for the assets combination heuristically and exact methods are applied to calculate the corresponding assets weights optimally. For the cardinality constrained mean-variance model, a combinatorial algorithm which hybridises a PSO and the mathematical programming method is proposed to address the problem. For the two-stage stochastic programming model, a hybrid algorithm which integrates a GA and a LP solver is presented to address the problem and a hybrid combinatorial approach which integrates a PBIL-based metaheuristic and a LP solver is developed to address the problem with a large number of scenarios. One main advantage of the hybridisation approach is that it can guarantee the optimal weight allocation of the identified asset combinations. Some useful strategies for different metaheuristics are investigated in order to keep a balance between algorithms' exploration and exploitation. Some useful mechanisms are also adopted in order to enhance the search efficiency and achieve a global better performance. The results have shown that such hybridisation strategy can achieve synergetic effects through the integration of multiple components.

A modified version of the Intelligent Water Drops algorithm (MIWD) was developed then used to determine the most stable configurations of Lennard-Jones (LJ), Binary Lennard-Jones (BLJ) and Morse Clusters. The algorithm is unbiased in that it uses no a priori cluster geometry information or cluster seeds. Results for LJ clusters show that the algorithm is effective and efficient in rediscovering all clusters up to size N = 104 with better success rates specially on difficult clusters compared to previous best methodologies reported in literature. Results on more difficult systems, such as the Binary Lennard Jones clusters up to size 50 (with 5 different atomic size ratios) and Morse clusters up to size 60 (with 2 interparticle range potentials), also showed the ability of MIWD to handle more complex systems. MIWD was then applied to predict the most stable structures of Janus clusters up to size 50 and on size 100 using a LJ potential model with a modulated angular term suited for two-patched Janus particles. Results show that MIWD is able to find well-structured geometries of Janus clusters. It is believed that this has been the first time that a nature-inspired stochastic algorithm and a variant of the IWD algorithm has been applied to the configurational optimization of Janus clusters.

It is expected that freight transport in the European Union will grow significantly and road transport will account for a major part of this growth. By 2020 almost 30% of CO2 emissions in the European Union will be caused by transportation. It is obvious that our present patterns of transport growth are unsustainable. One way toward more sustainable transport is to explicitly take greenhouse gas emissions into account in logistics decisions and to get freight traffic to switch from roads to alternative transport modes. This contribution discusses drivers and opportunities for intermodal transport planning. Related literature is surveyed and fields for future research are identified.