Tuning as convex optimisation: a polynomial tuner for multi-parametric combinatorial samplers

Combinatorial samplers are algorithmic schemes devised for the approximate- and exact-size generation of large random combinatorial structures, such as context-free words, various tree-like data structures, maps, tilings, RNA molecules. They can be adapted to combinatorial specifications with additional parameters, allowing for a more flexible control over the output profile of parametrised combinatorial patterns. One can control, for instance, the number of leaves, profile of node degrees in trees or the number of certain sub-patterns in generated strings. However, such a flexible control requires an additional and nontrivial tuning procedure. Using techniques of convex optimisation, we present an efficient tuning algorithm for multi-parametric combinatorial specifications. Our algorithm works in polynomial time in the system description length, the number of tuning parameters, the number of combinatorial classes in the specification, and the logarithm of the total target size. We demonstrate the effectiveness of our method on a series of practical examples, including rational, algebraic, and so-called Pólya specifications. We show how our method can be adapted to a broad range of less typical combinatorial constructions, including symmetric polynomials, labelled sets and cycles with cardinality lower bounds, simple increasing trees or substitutions. Finally, we discuss some practical aspects of our prototype tuner implementation and provide its benchmark results.

Convex Optimisation for Communication Systems

<p>In this thesis new robust methods for the efficient sharing of the radio spectrum for underlay cognitive radio (CR) systems are developed. These methods provide robustness against uncertainties in the channel state information (CSI) that is available to the cognitive radios. A stochastic approach is taken and the robust spectrum sharing methods are formulated as convex optimisation problems. Three efficient spectrum sharing methods; power control, cooperative beamforming and conventional beamforming are studied in detail. The CR power control problem is formulated as a sum rate maximisation problem and transformed into a convex optimisation problem. A robust power control method under the assumption of partial CSI is developed and also transformed into a convex optimisation problem. A novel method of detecting and removing infeasible constraints from the power allocation problem is presented that results in considerably improved performance. The performance of the proposed methods in Rayleigh fading channels is analysed by simulations. The concept of cooperative beamforming for spectrum sharing is applied to an underlay CR relay network. Distributed single antenna relay nodes are utilised to form a virtual antenna array that provides increased gains in capacity through cooperative beamforming. It is shown that the cooperative beamforming problems can be transformed into convex optimisation problems. New robust cooperative beamformers under the assumption of partial and imperfect CSI are developed and also transformed into convex optimisation problems. The performance of the proposed methods in Rayleigh fading channels is analysed by simulations. Conventional beamforming to allow efficient spectrum sharing in an underlay CR system is studied. The beamforming problems are formulated and transformed into convex optimisation problems. New robust beamformers under the assumption of partial and imperfect CSI are developed and also transformed into convex optimisation problems. The performance of the proposed methods in Rayleigh fading channels is analysed by simulations.</p>

Convex Optimisation for Communication Systems

<p>In this thesis new robust methods for the efficient sharing of the radio spectrum for underlay cognitive radio (CR) systems are developed. These methods provide robustness against uncertainties in the channel state information (CSI) that is available to the cognitive radios. A stochastic approach is taken and the robust spectrum sharing methods are formulated as convex optimisation problems. Three efficient spectrum sharing methods; power control, cooperative beamforming and conventional beamforming are studied in detail. The CR power control problem is formulated as a sum rate maximisation problem and transformed into a convex optimisation problem. A robust power control method under the assumption of partial CSI is developed and also transformed into a convex optimisation problem. A novel method of detecting and removing infeasible constraints from the power allocation problem is presented that results in considerably improved performance. The performance of the proposed methods in Rayleigh fading channels is analysed by simulations. The concept of cooperative beamforming for spectrum sharing is applied to an underlay CR relay network. Distributed single antenna relay nodes are utilised to form a virtual antenna array that provides increased gains in capacity through cooperative beamforming. It is shown that the cooperative beamforming problems can be transformed into convex optimisation problems. New robust cooperative beamformers under the assumption of partial and imperfect CSI are developed and also transformed into convex optimisation problems. The performance of the proposed methods in Rayleigh fading channels is analysed by simulations. Conventional beamforming to allow efficient spectrum sharing in an underlay CR system is studied. The beamforming problems are formulated and transformed into convex optimisation problems. New robust beamformers under the assumption of partial and imperfect CSI are developed and also transformed into convex optimisation problems. The performance of the proposed methods in Rayleigh fading channels is analysed by simulations.</p>

Convex Optimisation Model for Ship Speed Profile: Optimisation under Fixed Schedule

We present a novel convex optimisation model for ship speed profile optimisation under varying environmental conditions, with a fixed schedule for the journey. To demonstrate the efficacy of the proposed method, a combined speed profile optimisation model was developed that employed an existing dynamic programming approach, along the novel convex optimisation model. The proposed model was tested with 5 different ships for 20 journeys from Houston, Texas to London Gateway, with differing environmental conditions, which were retrieved from actual weather forecasts. As a result, it was shown that the combined model with both dynamic programming and convex optimisation was approximately 22% more effective in developing a fuel saving speed profile compared to dynamic programming alone. Overall, average fuel savings for the studied voyages with speed profile optimisation was approximately 1.1% compared to operation with a fixed speed and 3.5% for voyages where significant variance in environmental conditions was present. Speed profile optimisation was found to be especially beneficial in cases where detrimental environmental conditions could be avoided with minor speed adjustments. Relaxation of the fixed schedule constraint likely leads to larger savings but makes comparison virtually impossible as a lower speed leads to lower propulsion energy needed.