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The efficiency of interior-point algorithms for linear programming is related to the effort required to factorize the matrix used to solve for the search direction at each iteration. When the linear program is in symmetric form (i.e., the constraints are Ax b, x > 0 ), then there are two mathematically equivalent forms of the search direction, involving different matrices. One form necessitates factoring a matrix whose sparsity pattern has the same form as that of (A AT). The other form necessitates factoring a matrix whose sparsity pattern has the same form as that of (ATA). Depending on the structure of the matrix A, one of these two forms may produce significantly less fill-in than the other. Furthermore, by analyzing the fill-in of both forms prior to starting the iterative phase of the algorithm, the form with the least fill-in can be computed and used throughout the algorithm. Finally, this methodology can be applied to linear programs that are not in symmetric form, that contain both equality and inequality constraints.

The transmission of power across the GB transmission system, as operated by National Grid, results in inevitable loss of electrical power. Operationally these power losses cannot be eliminated, but they can be reduced by adjustment of the system voltage profile. At present the minimisation of active power losses relies upon a lengthy manually based iterative adjustment process. Therefore the system operator requires the development of advanced optimisation tools to cope with the challenges faced over the next decade, such as achieving the stringent greenhouse gas emission targets laid down by the UK government, while continue to provide an economical, secure and efficient service. To meet these challenges the research presented in this thesis has developed optimisation techniques that can assist control centre engineers by automatically setting up voltage studies that are low loss and low cost. The proposed voltage optimisation techniques have been shown to produce solutions that are secured against 800 credible contingency cases. A prototype voltage optimisation tool has been deployed, which required the development of a series of novel approaches to extend the functionality of an existing optimisation program. This research has lead to the development of novel methods for handling multi-objectives, contradictory shunt switching configurations and selecting all credible contingencies. Studies indicate that a theoretical loss saving of 1.9% is achievable, equivalent to an annual emissions saving of approximately 64,000 tonnes of carbon dioxide. A novel security constrained mixed integer non-linear optimisation technique has also been developed. The proposed method has been shown to be superior to several conventional methods on a wide range of IEEE standard network models and also on a range of large-scale GB network models. The proposed method manages to further reduce active power losses and also satisfies all security constraints.

In this dissertation, a finitely convergent disjunctive programming procedure, the Convex Hull Tree (CHT) algorithm, is proposed to obtain the convex hull of a general mixed–integer linear program with bounded integer variables. The CHT algorithm constructs a linear program that has the same optimal solution as the associated mixed-integer linear program. The standard notion of sequential cutting planes is then combined with ideasunderlying the CHT algorithm to help guide the choice of disjunctions to use within a new cutting plane method, the Cutting Plane Tree (CPT) algorithm. We show that the CPT algorithm converges to an integer optimal solution of the general mixed-integer linear program with bounded integer variables in finitely many steps. We also enhance the CPT algorithm with several techniques including a “round-of-cuts” approach and an iterative method for solving the cut generation linear program (CGLP). Two normalization constraints are discussed in detail for solving the CGLP. For moderately sized instances, our study shows that the CPT algorithm provides significant gap closures with a pure cutting plane method.

This research aims to understand the different requirements of civilian multiple autonomous vehicle systems in order to propose an adequate solution for the resource allocation problem. A new classification of unmanned system applications is presented with focus on unmanned aerial vehicles (UAVs). The main resource allocation systems requirements in each category are presented and discussed. A novel dynamic resource allocation model is introduced for efficient sharing of services provided by ad hoc assemblies of heterogeneous autonomous vehicles. A key contribution is the provision of capability to dynamically select sensors and platforms within constraints imposed by time dependencies, refuelling, and transportation services. The resource allocation problem is modelled as a connected network of nodes and formulated as an Integer Linear Program (ILP). Solution fitness is prioritized over computation time. Simulation results of an illustrative scenario are used to demonstrate the ability of the model to plan for sensor selection, refuelling, collaboration and cooperation between heterogeneous resources. Prioritization of operational cost leads to missions that use cheaper resources but take longer to complete. Prioritization of completion time leads to shorter missions at the expense of increased overall resource cost. Missions can be successfully re-planned through dynamic reallocation of new requests during a mission. Monte Carlo studies on systems of increasing complexity show that good solutions can be obtained using low time resolutions, with small time windows at a relatively low computational cost. In comparison with other approaches, the developed ILP model provides provably optimal solutions at the expense of longer computation time. Flight test procedures were developed for performing low cost experiments on a small scale, using commercial off the shelf equipment, with ability to infer conclusions on the large-scale implementation. Flight test experiments were developed and performed that assessed the performance of the developed ILP model and successfully demonstrated its main capabilities.

Orthology and paralogy distinguish whether a pair of genes originated by a speciation or a gene duplication event, whereas xenology refers to horizontal gene transfer. These concepts play a key role in phylogenomics and species tree inference is one of its prevalent tasks. Commonly, species tree inference is performed using sequence-based phylogenetic methods which heavily rely on the initial data sets to be solely composed of 1:1 orthologs. Such approaches are strongly restricted to a small set of genes that provide information about the species tree. In this work, it is shown that the restriction to 1:1 orthologs is not necessary to reconstruct a reliable hypothesis on the evolutionary history of species. Besides orthology, knowledge on all three major driving forces of gene evolution can be considered: speciation, gene duplication, and horizontal gene transfer. The corresponding concepts of orthology, paralogy, and xenology imply binary relations on pairs of genes. These relations, in turn, convey meaningful phylogenetic information and allow the inference of plausible phylogenetic species trees. To this end, it is shown that orthology, paralogy, and xenology have to fulfill certain mathematical properties. In particular, they have to be representable as a tree – the so-called gene tree. This work investigates the theoretical concepts of tree representable sets of binary relations to unfold the underlying mathematical structure. Various novel characterizations for those relations are given and the close connection between tree representable sets of binary relations and cographs, symbolic ultrametrics, and so-called unp 2-structures is revealed. Based on the novel characterizations, polynomial-time recognition algorithms for tree representable sets of relations are presented. In the case, a set of relations is tree representable, the corresponding tree representation can be found in polynomial time as well. Moreover, for the NP-complete problems of editing a given set of relations to its closest tree representable set, exact algorithms are developed by means of formulations as integer linear program. Finally, all algorithms have been implemented in the software ParaPhylo, a species tree inference method based on orthology and paralogy data. It is demonstrated on simulated data sets, as well as real-life data sets, that non-trivial phylogenies can indeed be reconstructed from tree-free orthology estimates alone.

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A payment is the most fundamental aspect of a trade that involves funds. In recent years, the development of new payment services has accelerated significantly as the world has moved further into the digital era. This transition has led to an increased demand of digital payment solutions that can handle trades across the world. As trades today can be agreed at any time wherever the payer and payee are located, the party that mediates payments must at any time to be available in order to mediate an agreed exchange. This requires the payment service provider to always have funds available in the required countries and currencies in order for trades to always be available. This thesis concerns how a payment service provider can reallocate capital in a cost efficient way in order for trades to always be available. Traditionally, the reallocation of capital is done in a rule-based manner, which discard the cost dimension and thereby only focus on the reallocation itself. This thesis concerns methods to optimally reallocate capital focusing on the cost of transferring capital within the network. Where the concerned methods has the potential of transferring capital in a far more cost efficient way. When mathematically formulating the reallocation decisions as an optimization problem, the cost function is formulated as a linear program with both Boolean and real constraints. This impose non-feasibility of locating the optimal solution using traditional methods for linear programs, why developed traditional and more advanced methods were used. The model was evaluated based on a large number of simulations in comparison with the performance of a rule-based reallocation system. The developed model provides a significant cost reduction compared to the rule-based approach and thereby outperforms the traditional reallocation system. Future work should focus on expanding the model by broadening the available transfer options, by increasing the considered uncertainty via a bayesian treatment and finally by considering all cost aspects of the network. / En betalning är den mest fundamentala aspekten av handel som involverar kapital. De senaste åren har utvecklingen av nya betalmedel ökat drastiskt då världen fortsatt att utvecklas genom digitaliseringen. Utvecklingen har lett till en ökad efterfrågan på digitala betalningslösningar som kan hantera handel över hela världen. Då handel idag kan ske när som helst oberoende av var betalaren och betalningsmottagaren befinner sig, måste systemet som genomför betalningen alltid vara tillgängligt för att kunna förmedla handel mellan olika parter. Detta kräver att betalningssystemet alltid måste ha medel tillgängligt i efterfrågade länder och valutor för att handeln ska kunna genomföras. Den här uppsatsen fokuserar på hur kapital kostnadseffektivt kan omallokeras i ett betalsystem för att säkerställa att handel alltid är tillgängligt. Traditionellt har omallokeringen av kapital gjorts på ett regelbaserat sätt, vilket inte tagit hänsyn till kostnadsdimensionen och därigenom enbart fokuserat på själva omallokeringen. Den här uppsatsen använder metoder för att optimalt omallokera kapital baserat på kostnaderna för omallokeringen. Därigenom skapas en möjlighet att flytta kapital på ett avsevärt mer kostnadseffektivt sätt. När omallokeringsbesluten formuleras matematiskt som ett optimeringsproblem är kostnadsfunktionen formulerad som ett linjärt program med både Booleska och reella begränsningar av variablerna. Detta gör att traditionella lösningsmetoder för linjära program inte är användningsbara för att finna den optimala lösningen, varför vidareutveckling av tradtionella metoder tillsammans med mer avancerade metoder använts. Modellen utvärderades baserat på ett stort antal simuleringar som jämförde dess prestanda med det regelbaserade systemet. Den utvecklade modellen presterar en signfikant kostnadsreduktion i jämförelse med det regelbaserade systemet och överträffar därigenom det traditionellt använda systemet. Framtida arbete bör fokusera på att expandera modellen genom att utöka de potentiella överföringsmöjligheterna, att ta ökad hänsyn till osäkerhet genom en bayesiansk hantering, samt slutligen att integrera samtliga kostnadsaspekter i nätverket.

Embedded system designers face multiple challenges in fulfilling the runtime requirements of programs. Effective scheduling of programs is required to extract as much parallelism as possible. These scheduling algorithms must also improve speedup after instruction-set extensions have occurred. Scheduling of dynamic code at run time is made more difficult when the static components of the program are scheduled inefficiently. This research aims to optimize a program’s static code at compile time. This is achieved with four algorithms designed to schedule code at the task and instruction level. Additionally, the algorithms improve scheduling using instruction set extended code on symmetrical homogeneous multiprocessor systems. Using these algorithms, we achieve speedups up to 3.86X over sequential execution for a 4-issue 2-processor system, and show better performance than recent heuristic techniques for small programs. Finally, the algorithms generate speedup values for a 64-point FFT that are similar to the test runs.

Embedded system designers face multiple challenges in fulfilling the runtime requirements of programs. Effective scheduling of programs is required to extract as much parallelism as possible. These scheduling algorithms must also improve speedup after instruction-set extensions have occurred. Scheduling of dynamic code at run time is made more difficult when the static components of the program are scheduled inefficiently. This research aims to optimize a program’s static code at compile time. This is achieved with four algorithms designed to schedule code at the task and instruction level. Additionally, the algorithms improve scheduling using instruction set extended code on symmetrical homogeneous multiprocessor systems. Using these algorithms, we achieve speedups up to 3.86X over sequential execution for a 4-issue 2-processor system, and show better performance than recent heuristic techniques for small programs. Finally, the algorithms generate speedup values for a 64-point FFT that are similar to the test runs.