Traveling Salesman Problem

This book is a collection of current research in the application of evolutionary algorithms and other optimal algorithms to solving the TSP problem. It brings together researchers with applications in Artificial Immune Systems, Genetic Algorithms, Neural Networks and Differential Evolution Algorithm. Hybrid systems, like Fuzzy Maps, Chaotic Maps and Parallelized TSP are also presented. Most importantly, this book presents both theoretical as well as practical applications of TSP, which will be a vital tool for researchers and graduate entry students in the field of applied Mathematics, Computing Science and Engineering

Simulation optimisation to inform economic evaluations of sequential therapies for chronic conditions: a case study in Rheumatoid Arthritis

This thesis investigates the problem of treatment sequencing within health economic evaluations. For some chronic conditions, sequences of treatments can be used. When there are a lot of alternative treatments, then the number of possible sequences becomes very large. When undertaking an economic evaluation, it may not be feasible to estimate the costs and benefits of every alternative treatment sequence. The objective of the thesis is to test the feasibility of simulation optimisation methods to find an optimal or set of near-optimal sequences of disease modifying treatments for rheumatoid arthritis in an economic evaluation framework. A large number of economic evaluations have been undertaken to estimate the costs and benefits associated with different treatments for rheumatoid arthritis. Many of these have not considered the downstream sequence of treatments provided, and no published study has considered identifying the best, or optimal, treatment sequence. The published evidence is therefore of limited applicability if the objective is to maximise patient benefit while constrained by a finite budget. It is plausible that decision-makers have developed sub-optimal guidance for rheumatoid arthritis, and this could extend to other chronic conditions. A simulation model can provide an expectation of the population mean costs and benefits for alternative treatment sequences. These models are routinely used to inform health economic evaluations. However, they can be computationally expensive to run, and therefore the evaluation of potentially millions of treatment sequences is not feasible. However, simulation optimisation methods exist to identify a good solution from a simulation model within a feasible period of time. Using these methods within an economic evaluation of treatment sequences has not previously been investigated. In this thesis I highlight the importance of the treatment sequencing problem, review and assess relevant simulation optimisation methods, and implement a simulated annealing algorithm to explore its feasibility and appropriateness. From the implementation case study within rheumatoid arthritis, simulation optimisation via simulated annealing appears to be a feasible method to identify a set of good treatment sequences. However, the method requires a significant amount of time to implement and execute, which may limit its appropriateness for health resource allocation decision making. Further research is required to investigate the generalisability of the method, and further consideration regarding its use in a decision-making context is important