Graph theory has become a hot topic in the past two decades as evidenced by the increasing number of citations in research. Its applications are found in many fields, e.g. database, clustering, routing, etc. In this thesis, two novel graph-based algorithms are presented. The first algorithm finds itself in the thriving carsharing service, while the second algorithm is about large graph discovery to unearth the unknown graph before any analyses can be performed. In the first scenario, the automatisation of the fleet planning process in carsharing is proposed. The proposed work enhances the accuracy of the planning to the next level by taking an advantage of the open data movement such as street networks, building footprints, and demographic data. By using the street network (based on graph), it solves the questionable aspect in many previous works, feasibility as they tended to use rasterisation to simplify the map, but that comes with the price of accuracy and feasibility. A benchmark suite for further research in this problem is also provided. Along with it, two optimisation models with different sets of objectives and contexts are proposed. Through a series of experiment, a novel hybrid metaheuristic algorithm is proposed. The algorithm is called NGAP, which is based on Reference Point based Non-dominated Sorting genetic Algorithm (NSGA-III) and Pareto Local Search (PLS) and a novel problem specific local search operator designed for the fleet placement problem in carsharing called Extensible Neighbourhood Search (ENS). The designed local search operator exploits the graph structure of the street network and utilises the local knowledge to improve the exploration capability. The results show that the proposed hybrid algorithm outperforms the original NSGA-III in convergence under the same execution time. The work in smart mobility is done on city scale graphs which are considered to be medium size. However, the scale of the graphs in other fields in the real-world can be much larger than that which is why the large graph discovery algorithm is proposed as the second algorithm. To elaborate on the definition of large, some examples are required. The internet graph has over 30 billion nodes. Another one is a human brain network contains around 1011 nodes. Apart of the size, there is another aspect in real-world graph and that is the unknown. With the dynamic nature of the real-world graphs, it is almost impossible to have a complete knowledge of the graph to perform an analysis that is why graph traversal is crucial as the preparation process. I propose a novel memoryless chaos-based graph traversal algorithm called Chaotic Traversal (CHAT). CHAT is the first graph traversal algorithm that utilises the chaotic attractor directly. An experiment with two well-known chaotic attractors, Lozi map and Rössler system is conducted. The proposed algorithm is compared against the memoryless state-of-the-art algorithm, Random Walk. The results demonstrate the superior performance in coverage rate over Random Walk on five tested topologies; ring, small world, random, grid and power-law. In summary, the contribution of this research is twofold. Firstly, it contributes to the research society by introducing new study problems and novel approaches to propel the advance of the current state-of-the-art. And Secondly, it demonstrates a strong case for the conversion of research to the industrial sector to solve a real-world problem.
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