Reasoning with imprecise trade-offs in decision making under certainty and uncertainty

In many real world situations, we make decisions in the presence of multiple, often conflicting and non-commensurate objectives. The process of optimizing systematically and simultaneously over a set of objective functions is known as multi-objective optimization. In multi-objective optimization, we have a (possibly exponentially large) set of decisions and each decision has a set of alternatives. Each alternative depends on the state of the world, and is evaluated with respect to a number of criteria. In this thesis, we consider the decision making problems in two scenarios. In the first scenario, the current state of the world, under which the decisions are to be made, is known in advance. In the second scenario, the current state of the world is unknown at the time of making decisions. For decision making under certainty, we consider the framework of multiobjective constraint optimization and focus on extending the algorithms to solve these models to the case where there are additional trade-offs. We focus especially on branch-and-bound algorithms that use a mini-buckets algorithm for generating the upper bound at each node of the search tree (in the context of maximizing values of objectives). Since the size of the guiding upper bound sets can become very large during the search, we introduce efficient methods for reducing these sets, yet still maintaining the upper bound property. We define a formalism for imprecise trade-offs, which allows the decision maker during the elicitation stage, to specify a preference for one multi-objective utility vector over another, and use such preferences to infer other preferences. The induced preference relation then is used to eliminate the dominated utility vectors during the computation. For testing the dominance between multi-objective utility vectors, we present three different approaches. The first is based on a linear programming approach, the second is by use of distance-based algorithm (which uses a measure of the distance between a point and a convex cone); the third approach makes use of a matrix multiplication, which results in much faster dominance checks with respect to the preference relation induced by the trade-offs. Furthermore, we show that our trade-offs approach, which is based on a preference inference technique, can also be given an alternative semantics based on the well known Multi-Attribute Utility Theory. Our comprehensive experimental results on common multi-objective constraint optimization benchmarks demonstrate that the proposed enhancements allow the algorithms to scale up to much larger problems than before. For decision making problems under uncertainty, we describe multi-objective influence diagrams, based on a set of p objectives, where utility values are vectors in Rp, and are typically only partially ordered. These can be solved by a variable elimination algorithm, leading to a set of maximal values of expected utility. If the Pareto ordering is used this set can often be prohibitively large. We consider approximate representations of the Pareto set based on ϵ-coverings, allowing much larger problems to be solved. In addition, we define a method for incorporating user trade-offs, which also greatly improves the efficiency.

Quaternary geology of the German North Sea and Western Irish Sea Mud Belt: revised stratigraphies, geotechnical properties, sedimentology and anthropogenic impacts

The climatic development of the Mid to Late Quaternary (last 400,000 years) is characterised by fluctuation between glacial and interglacial periods leading to the present interglacial, the Holocene. In comparison to preceding periods it was believed the Holocene represented a time of relative climatic stability. However, recent work has shown that the Holocene can be divided into cooler periods such as the Little Ice Age alternating with time intervals where climatic conditions ameliorated i.e. Medieval Warm Period, Holocene Thermal Optimum and the present Modern Optimum. In addition, the Holocene is recognised as a period with increasing anthropogenic influence on the environment. Onshore records recording glacial/interglacial cycles as well as anthropogenic effects are limited. However, sites of sediment accumulation on the shallow continental shelf offer the potential to reconstruct these events. Such sites include tunnel valleys and low energy, depositional settings. In this study we interrogated the sediment stratigraphy at such sites in the North Sea and Irish Sea using traditional techniques, as well as novel applications of geotechnical data, to reconstruct the palaeoenvironmental record. Within the German North Sea sector a combination of core, seismic and in-situ Cone Penetration Testing (CPT) data was used to identify sedimentary units, place them within a morphological context, relate them to glacial or interglacial periods stratigraphically, and correlate them across the German North Sea. Subsequently, we were able to revise the Mid to Late Quaternary stratigraphy for the North Sea using this new and novel data. Similarly, Holocene environmental changes were investigated within the Irish Sea at a depositional site with active anthropogenic influence. The methods used included analyses on grain-size distribution, foraminifera, gamma spectrometry, AMS 14C and physical core logging. The investigation revealed a strong fluctuating climatic signal early in the areas history before anthropogenic influence affects the record through trawling.