Lazy Clause Generation (LCG) Solving is a state-of-the-art technique for solving finite domain problems. The combination of powerful Constraint Programming (CP) propagators and Conflict Driven Clause Learning (CDCL) from the SAT domain enables both powerful inferences and learning from conflicts. Most research has focused on strengthening propagator explanations but has limited itself to remain within the standard LCG protocol, which only uses basic assignment and bound literals.

This thesis will focus on structurally extending this CDCL resolution protocol with new literals. We investigate the addition of two different literals to this protocol: a partial sum inequality literal and a precedence literal specifically for the cumulative constraint.

We verify previous work on the inequality literal, expand the test suite, and take a dive into metrics specifically related to extended resolution. We propose the novel idea of the cumulative literal, assessing its performance. We evaluate these extensions against both a baseline solver without protocol extensions and against each other across a range of hyper-parameters and search strategies.

Our results show that extending the protocol is not a guarantee for performance, the linear inequality extension remains powerful in some scenarios but fails to improve on a series of benchmarks whilst the cumulative literal shows no improvement at all. Moreover, we find that structurally based extended resolution introduces overlap between the literals in a nogood which negatively affects nogood quality.

These findings showcase that the research is far from done. A powerful technique exists but future research should consider additional infrastructure to make sure these techniques flourish at their fullest potential.

The ever-evolving power grid is becoming smarter and smarter. Modern houses come with smart meters and energy conscious consumers will buy additional smart meters to place in their home to help monitor their energy consumption. This new smart technology also opens the door to more accurate power consumption forecasting. In this study we look at utilizing a partial hierarchy, in which one of the appliances in a household is modelled separately from the rest of the house, to help improve household energy consumption forecasting accuracy. This is done in conjunction with Auto Regressive Moving Average (ARMA) based models. Three variants of ARMA based models will be looked at: Auto Regressive Integrated Moving Average (ARIMA), Seasonal Auto Regressive Integrated Moving Average (SARIMA), and Auto Regressive Integrated Moving Average with Exogenous variables (ARIMAX). These methods will then be compared to more baseline approaches such as a persistence method and a seasonal moving average. Our analysis has led us to conclude that the partial hierarchy model offers little to no benefit when applied in the field of household energy consumption forecasting when built upon ARMA based models. ARMA based models in general appeared to be poor performers when it came to household energy consumption forecasting.