這篇論文中我們提出了一個變動長度基因演算法的方式來解決多重限制異質性無線傳輸設備佈建的問題，這是一個NP-hard 的問題。現實中有許多因素會影響到無線傳輸設備佈建的問題，而這篇論文考量了四個主要的佈建需求，分別是:無線傳輸設備涵蓋範圍、總成本、資料傳輸速率的需求以及無線傳輸設備間訊號的重疊。在提出的變動長度多目標基因演算法中，我們解決了現有方法對無線傳輸設備個數的上限的限制以及更佳的達成無線傳輸設備位置佈建，同時對位置及需求做考量。

在實驗部分，我們使用了自由空間傳播模型、考慮遮蔽效應的大尺度傳遞模型及延伸的哈他模型在真實的室內以及室外的地圖上的平面以及立體的無線傳輸設備的佈建。實驗結果顯示提出的演算法對所有測試都能夠找出許多可用的解答。

In this thesis we have proposed a variable-length multiobjective genetic algorithm to solve heterogeneous wireless transmitter placement with multiple constraints. Among many factors that may affect the result of placement, we focus on four major requirements, coverage, cost, data rate demand, and overlap. In the proposed algorithm we release the need for the upper bound number of transmitters that is a major constraint in the existing methods and achieve better wireless transmitter placement while considering the transmitter position and design requirement simultaneously.
In experiments, we use the free space propagation model, the large scale propagation model which considers the shadowing effect, and the extended Hata-Okumura model to predict the path loss in a real two dimensional indoor environment, and an outdoor environment and even a real three dimensional outdoor environment. Experimental results show that the proposed algorithm can find many feasible solutions for all test cases under four objectives.

1 INTRODUCTION……………………………………………......1
2 RELATED WORK.……………………………………………5
2.1 Variable-length multi-objective genetic algorithm.……………………………………………5
2.2 Heterogeneous.……………………………………………6
2.3 Propagation model.……………………………………………6
3 THE PROPOSED ALGORITHM.……………………………………………9
3.1 Problem definition.……………………………………………9
3.1.1 Planning model.……………………………………………9
3.1.1.1 Map M.……………………………………………9
3.1.1.2 Receiver set R……………………………………………10
3.1.1.3 Transmitter set T.……………………………………………10
3.2 Path loss propagation model.……………………………………………11
3.2.1 Path loss model.……………………………………………11
3.2.2 ECC-33 model.……………………………………………13
3.3 Objectives.……………………………………………14
3.3.1 Coverage.……………………………………………14
3.3.2 Cost.……………………………………………16
3.3.3 Data rate demand.……………………………………………16
3.3.4 Overlap.……………………………………………16
3.3.5 Objective function.……………………………………………17
3.4 The proposed variable-length multi-objective genetic algorithm.………18
3.4.1 Individual representation.……………………………………………19
3.4.2 Initialization.……………………………………………20
3.4.3 Examination of the individual placement.……………………………………………21
3.4.4 Ranking and crowding distance.……………………………………………21
3.4.5 Selection.……………………………………………22
3.4.6 Crossover .……………………………………………23
3.4.6.1 Overall crossover.……………………………………………23
3.4.6.2 Uniform crossover.……………………………………………24
3.4.6.3 The variable-length one -point crossover.……………………………………………25
3.4.7 Mutation .……………………………………………26
4 SIMULATION AND RESULTS.……………………………………………27
4.1 Indoor free space model.……………………………………………28
4.2 Indoor path loss model .……………………………………………32
4.3 Outdoor path loss model.……………………………………………35
4.4 Outdoor three dimensional path loss model.……………………………………………42
4.5 Upper bound.……………………………………………52
4.6 Heterogeneous.……………………………………………55
4.7 Discussion.……………………………………………60
5 CONCLUSION.……………………………………………61
REFERENCES.……………………………………………62

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