In this thesis, we look at how the Cross-Entropy (CE) method can be used to solve various optimisation and estimation problems in telecommunication systems and network planning, especially in the presence of noise. In Chapter 2, we mention what comprises optimisation problems. Various optimisation problems, such as constrained optimization and convex optimisation, are discussed. We also address noisy optimisation and how dealing effectively with noise plays a crucial role in locating a global optimal solution. A brief overview of three algorithms that have successfully been applied to noisy optimisation problems is also given. Chapter 3 explores a short overview of the methodology behind the CE method. We discuss how the CE method requires two simple iterative stages to locate an optimal "degenerate" sampling distribution, and hence an optimal solution to the optimisation problem. We also show how a simple modification of the algorithm can tackle noisy optimisation problems. Numerical experiments for solving both non-noisy and noisy multi-extremal continuous optimisation problems are conducted. Three test functions are used to investigate the performance of the CE algorithm on both non-noisy and noisy cases. The results suggest that the proposed algorithm can locate a global optimal solution accurately. Also, we show that the performance of the CE algorithm can be improved using the injection method. Chapter 4 and Chapter 5 discuss two types of the Network Planning Problem (NPP): single-type NPP and multi-type NPP. The aim is to determine which links in the system should be purchased in order to provide the highest possible service to the consumers, subject to a constraint on the total budget. We introduce various CE-based algorithms to tackle such non-linear combinatorial optimisation problem. Numerical experiments suggest that the proposed algorithms perform effectively and reliably in all test cases. Chapter 6 is concerned with estimating the blocking probabilities in circuit switched networks. We look at how Importance Sampling and Sequential Importance Sampling can be used to estimate the blocking probabilities. Here, the CE method is used to find optimal sampling parameters to be used in Importance Sampling and Sequential Importance Sampling. Numerical experiments suggest that Sequential Importance Sampling achieves a variance reduction over Importance Sampling in almost all cases at a cost of increased simulation time. Using CE further increases the efficiency of both.
| Identifer | oai:union.ndltd.org:ADTP/285931 |
| Creators | Sho Nariai |
| Source Sets | Australiasian Digital Theses Program |
| Detected Language | English |
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