Dynamic Programming on Nominal Graphs

Many optimization problems can be naturally represented as (hyper) graphs, where vertices correspond to variables and edges to tasks, whose cost depends on the values of the adjacent variables. Capitalizing on the structure of the graph, suitable dynamic programming strategies can select certain orders of evaluation of the variables which guarantee to reach both an optimal solution and a minimal size of the tables computed in the optimization process. In this paper we introduce a simple algebraic specification with parallel composition and restriction whose terms up to structural axioms are the graphs mentioned above. In addition, free (unrestricted) vertices are labelled with variables, and the specification includes operations of name permutation with finite support. We show a correspondence between the well-known tree decompositions of graphs and our terms. If an axiom of scope extension is dropped, several (hierarchical) terms actually correspond to the same graph. A suitable graphical structure can be found, corresponding to every hierarchical term. Evaluating such a graphical structure in some target algebra yields a dynamic programming strategy. If the target algebra satisfies the scope extension axiom, then the result does not depend on the particular structure, but only on the original graph. We apply our approach to the parking optimization problem developed in the ASCENS e-mobility case study, in collaboration with Volkswagen. Dynamic programming evaluations are particularly interesting for autonomic systems, where actual behavior often consists of propagating local knowledge to obtain global knowledge and getting it back for local decisions.Comment: In Proceedings GaM 2015, arXiv:1504.0244

Usage Driven Design of Power System and Multi-criteria Route Planning for Eco-Urban Electric Cars

Eco-urban electric cars (EC) are superior to conventional cars in terms of the operation cost and carbon footprint. However, the performance of EC in terms of their maximum speed and power, initial and maintenance cost and reliability in the available power is lower than conventional cars. The reliability in available energy can be viewed as the main concerns when comparing EC to conventional cars. Reliability in available energy is highly dependent upon the efficiency of the power system as well as the type and size of batteries. Type and size of batteries have a significant effect on the maintenance cost as well as the initial cost. This thesis is focused on two aspects of the research in electric cars, namely, (i) selection and size optimisation of components, and (ii) improving the reliability of the available energy. Traditionally, a robust design approach is adopted in design of the power system of cars. This is mainly aimed at providing the user with the luxury of using the car wherever there is a suitable road and whenever they want to use the car. This flexibility, however, comes with the price of heavier and more expensive power systems. By incorporating data on the dominant usage of an EC and adopting a deterministic design and optimisation method more cost-effective power systems, more compatible with the usage can be obtained. In this study, a power system simulation tool is developed. Using the simulation tool, the performance of the power system components can be analysed for different usage scenarios. Case studies are conducted. Each case is based on a dominant usage defined for a two-person EC driven in Kayseri city in Turkey. For each case, the best power system configuration is obtained. Another original contribution of this thesis is in the context of the reliability of the available energy, by providing a decision support system - a route planning advisor - that helps the user to select the most suitable route in terms of a variety of criteria both conventional, such as travelling time and travelling distance, as well as EC-related such as, available power, vicinity to a charging station. The optimiser of the developed multi criteria route planning advisor (MCRPA) tool is based on a robust hybrid Dijkstra - A* - NSGA-II algorithm. MCRPA incorporates information on EC characteristics (such as power system, aerodynamic shape, weight), city characteristics (current traffic flows, road types, speed limits, altitude, whether conditions), and city charging stations characteristics (capacity, charging level, crowding density). Carrying out case studies, the efficiency and performance of the MCRPA is evaluated