Reallocating Multiple Facilities on the Line

We study the multistage $K$-facility reallocation problem on the real line, where we maintain $K$ facility locations over $T$ stages, based on the stage-dependent locations of $n$ agents. Each agent is connected to the nearest facility at each stage, and the facilities may move from one stage to another, to accommodate different agent locations. The objective is to minimize the connection cost of the agents plus the total moving cost of the facilities, over all stages. $K$-facility reallocation was introduced by de Keijzer and Wojtczak, where they mostly focused on the special case of a single facility. Using an LP-based approach, we present a polynomial time algorithm that computes the optimal solution for any number of facilities. We also consider online $K$-facility reallocation, where the algorithm becomes aware of agent locations in a stage-by-stage fashion. By exploiting an interesting connection to the classical $K$-server problem, we present a constant-competitive algorithm for $K = 2$ facilities

Development and applications of localised Numerical Weather Prediction models in building energy management

Information about the past, present and future state of the weather is valuable in building energy management, as it enables the optimisation of the design and operation of a broad range of the system's aspects. Weather inputs may be used in models that predict building heating and cooling requirements and costs, energy efficiency, as well as onsite generation from renewable sources. However, the acquisition and utilisation of accurate localised weather predictions and data is often challenging, due to the lack of the ability to generate onsite predicitions at any site and potential lack of long term climate data.This thesis proposes the inclusion of localised numerical weather predictions in building energy systems. The development of forecasting and analytical models of weather inputs is done in The Air Pollution Model (TAPM) platform. TAPM is a numerical tool, which allows to downscale synoptic weather data to any location at high spatial resolution. Three applications are also proposed, specifically tailored to meet the needs of building energy systems. The first application utilises predictions and historical trends to develop highly accurate, localised short term forecasts for ambient temperature, relative humidity and wind speed. The second application utilises multiple TAPM predictions run in parallel to detect the timing and relative magnitude of peak cooling loads in a building. Finally, the tool proposed in the third application is based on the long term analysis of local weather trends and the evaluation of precooling potential at any location.The models were validated in a case study university building with the help of a range of newly developed algorithms for the control of internal temperature and humidity over the course of a day. The weather inputs were used in a predictive control scenario and compared to the base control (without weather inputs). The simulations showed that annual cooling demand was reduced by 24% and daily peak loads by 21% on average. Meanwhile, the rolling peak annual load was reduced by 10%. The results confirm the importance of weather input inclusion in control and illustrate that localised numerical weather predictions may be easily implemented in building energy systems

Reallocating Multiple Facilities on the Line

We study the multistage K-facility reallocation problem on the real line, where we maintain K facility locations over T stages, based on the stage-dependent locations of n agents. Each agent is connected to the nearest facility at each stage, and the facilities may move from one stage to another, to accommodate different agent locations. The objective is to minimize the connection cost of the agents plus the total moving cost of the facilities, over all stages. K-facility reallocation problem was introduced by (B.D. Kaijzer and D. Wojtczak, IJCAI 2018), where they mostly focused on the special case of a single facility. Using an LP-based approach, we present a polynomial time algorithm that computes the optimal solution for any number of facilities. We also consider online K-facility reallocation, where the algorithm becomes aware of agent locations in a stage-by stage fashion. By exploiting an interesting connection to the classical K-server problem, we present a constant-competitive algorithm for K = 2 facilities