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    ๋ฌด์ธํ•ญ๊ณต๊ธฐ ์šด์˜์„ ์œ„ํ•œ ๋ฎ๊ฐœ ๋ชจ๋ธ ๊ธฐ๋ฐ˜์˜ ๋Œ€๊ทœ๋ชจ ์ตœ์ ํ™” ๊ธฐ๋ฒ•

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    ํ•™์œ„๋…ผ๋ฌธ (๋ฐ•์‚ฌ) -- ์„œ์šธ๋Œ€ํ•™๊ต ๋Œ€ํ•™์› : ๊ณต๊ณผ๋Œ€ํ•™ ์‚ฐ์—…๊ณตํ•™๊ณผ, 2021. 2. ๋ฌธ์ผ๊ฒฝ.There is increasing interest in the unmanned aerial vehicle (UAV) in various fields of the industry, starting from the surveillance to the logistics. After introducing the smart city, there are attempts to utilize UAVs in the public service sector by connecting individual components of the system with both information and physical goods. In this dissertation, the UAV operation problems in the public service sector is modeled in the set covering approach. There is a vast literature on the facility location and set covering problems. However, when operating UAVs in the system, the plan has to make the most of the flexibility of the UAV, but also has to consider its physical limitation. We noticed a gap between the related, existing approaches and the technologies required in the field. That is, the new characteristics of the UAV hinder the existing solution algorithms, or a brand-new approach is required. In this dissertation, two operation problems to construct an emergency wireless network in a disaster situation by UAV and one location-allocation problem of the UAV emergency medical service (EMS) facility are proposed. The reformulation to the extended formulation and the corresponding branch-and-price algorithm can overcome the limitations and improve the continuous or LP relaxation bounds, which are induced by the UAV operation. A brief explanation of the UAV operation on public service, the related literature, and the brief explanation of the large-scale optimization techniques are introduced in Chapter 1, along with the research motivations and contributions, and the outline of the dissertations. In Chapter 2, the UAV set covering problem is defined. Because the UAV can be located without predefined candidate positions, more efficient operation becomes feasible, but the continuous relaxation bound of the standard formulation is weakened. The large-scale optimization techniques, including the Dantzig-Wolfe decomposition and the branch-and-price algorithm, could improve the continuous relaxation bound and reduce the symmetries of the branching tree and solve the realistic-scaled problems within practical computation time. To avoid numerical instability, two approximation models are proposed, and their approximation ratios are analyzed. In Chapter 3, UAV variable radius set covering problem is proposed with an extra decision on the coverage radius. While implementing the branch-and-price algorithm to the problem, a solvable equivalent formulation of the pricing subproblem is proposed. A heuristic based on the USCP is designed, and the proposed algorithm outperformed the benchmark genetic algorithm proposed in the literature. In Chapter 4, the facility location-allocation problem for UAV EMS is defined. The quadratic variable coverage constraint is reformulated to the linear equivalent formulation, and the nonlinear problem induced by the robust optimization approach is linearized. While implementing the large-scale optimization techniques, the structure of the subproblem is analyzed, and two solution approaches for the pricing subproblem are proposed, along with a heuristic. The results of the research can be utilized when implementing in the real applications sharing the similar characteristics of UAVs, but also can be used in its abstract formulation.ํ˜„์žฌ, ์ง€์—ญ ๊ฐ์‹œ์—์„œ ๋ฌผ๋ฅ˜๊นŒ์ง€, ๋ฌด์ธํ•ญ๊ณต๊ธฐ์˜ ๋‹ค์–‘ํ•œ ์‚ฐ์—…์—์˜ ์‘์šฉ์ด ์ฃผ๋ชฉ๋ฐ›๊ณ  ์žˆ๋‹ค. ํŠนํžˆ, ์Šค๋งˆํŠธ ์‹œํ‹ฐ์˜ ๊ฐœ๋…์ด ๋Œ€๋‘๋œ ์ดํ›„, ๋ฌด์ธํ•ญ๊ณต๊ธฐ๋ฅผ ๊ณต๊ณต ์„œ๋น„์Šค ์˜์—ญ์— ํ™œ์šฉํ•˜์—ฌ ๊ฐœ๋ณ„ ์‚ฌํšŒ ์š”์†Œ๋ฅผ ์—ฐ๊ฒฐ, ์ •๋ณด์™€ ๋ฌผ์ž๋ฅผ ๊ตํ™˜ํ•˜๊ณ ์ž ํ•˜๋Š” ์‹œ๋„๊ฐ€ ์ด์–ด์ง€๊ณ  ์žˆ๋‹ค. ๋ณธ ๋…ผ๋ฌธ์—์„œ๋Š” ๊ณต๊ณต ์„œ๋น„์Šค ์˜์—ญ์—์„œ์˜ ๋ฌด์ธํ•ญ๊ณต๊ธฐ ์šด์˜ ๋ฌธ์ œ๋ฅผ ์ง‘ํ•ฉ๋ฎ๊ฐœ๋ฌธ์ œ ๊ด€์ ์—์„œ ๋ชจํ˜•ํ™”ํ•˜์˜€๋‹ค. ์„ค๋น„์œ„์น˜๊ฒฐ์ • ๋ฐ ์ง‘ํ•ฉ๋ฎ๊ฐœ๋ฌธ์ œ ์˜์—ญ์— ๋งŽ์€ ์—ฐ๊ตฌ๊ฐ€ ์ง„ํ–‰๋˜์–ด ์žˆ์œผ๋‚˜, ๋ฌด์ธํ•ญ๊ณต๊ธฐ๋ฅผ ์šด์˜ํ•˜๋Š” ์‹œ์Šคํ…œ์˜ ๊ฒฝ์šฐ ๋ฌด์ธํ•ญ๊ณต๊ธฐ๊ฐ€ ๊ฐ–๋Š” ์ž์œ ๋„๋ฅผ ์ถฉ๋ถ„ํžˆ ํ™œ์šฉํ•˜๋ฉด์„œ๋„ ๋ฌด์ธํ•ญ๊ณต๊ธฐ์˜ ๋ฌผ๋ฆฌ์  ํ•œ๊ณ„๋ฅผ ๊ณ ๋ คํ•œ ์šด์˜ ๊ณ„ํš์„ ํ•„์š”๋กœ ํ•œ๋‹ค. ์šฐ๋ฆฌ๋Š” ๋ณธ ๋ฌธ์ œ์™€ ๊ด€๋ จ๋œ ๊ธฐ์กด ์—ฐ๊ตฌ์™€ ํ˜„์žฅ์ด ํ•„์š”๋กœ ํ•˜๋Š” ๊ธฐ์ˆ ์˜ ๊ดด๋ฆฌ๋ฅผ ์ธ์‹ํ•˜์˜€๋‹ค. ์ด๋Š” ๋‹ค์‹œ ๋งํ•ด, ๋ฌด์ธํ•ญ๊ณต๊ธฐ๊ฐ€ ๊ฐ€์ง€๋Š” ์ƒˆ๋กœ์šด ํŠน์„ฑ์„ ๊ณ ๋ คํ•˜๋ฉด ๊ธฐ์กด์˜ ๋ฌธ์ œ ํ•ด๊ฒฐ ๋ฐฉ๋ฒ•์„ ํ†ตํ•ด ํ’€๊ธฐ ์–ด๋ ต๊ฑฐ๋‚˜, ํ˜น์€ ์ƒˆ๋กœ์šด ๊ด€์ ์—์„œ์˜ ๋ฌธ์ œ ์ ‘๊ทผ์ด ํ•„์š”ํ•˜๋‹ค๋Š” ๊ฒƒ์ด๋‹ค. ๋ณธ ๋…ผ๋ฌธ์—์„œ๋Š” ์žฌ๋‚œ์ด ๋ฐœ์ƒํ•œ ์ง€์—ญ์— ๋ฌด์ธํ•ญ๊ณต๊ธฐ๋ฅผ ์ด์šฉํ•˜์—ฌ ๊ธด๊ธ‰๋ฌด์„ ๋„คํŠธ์›Œํฌ๋ฅผ ๊ตฌ์„ฑํ•˜๋Š” ๋‘๊ฐ€์ง€ ๋ฌธ์ œ์™€, ๋ฌด์ธํ•ญ๊ณต๊ธฐ๋ฅผ ์ด์šฉํ•˜์—ฌ ์‘๊ธ‰์˜๋ฃŒ์„œ๋น„์Šค๋ฅผ ์ œ๊ณตํ•˜๋Š” ์‹œ์„ค์˜ ์œ„์น˜์„ค์ • ๋ฐ ํ• ๋‹น๋ฌธ์ œ๋ฅผ ์ œ์•ˆํ•œ๋‹ค. ํ™•์žฅ๋ฌธ์ œ๋กœ์˜ ์žฌ๊ณต์‹ํ™”์™€ ๋ถ„์ง€ํ‰๊ฐ€๋ฒ•์„ ํ™œ์šฉํ•˜์—ฌ, ๋ฌด์ธํ•ญ๊ณต๊ธฐ์˜ ํ™œ์šฉ์œผ๋กœ ์ธํ•ด ๋ฐœ์ƒํ•˜๋Š” ๋ฌธ์ œ ํ•ด๊ฒฐ ๋ฐฉ๋ฒ•์˜ ํ•œ๊ณ„๋ฅผ ๊ทน๋ณตํ•˜๊ณ  ์™„ํ™”ํ•œ๊ณ„๋ฅผ ๊ฐœ์„ ํ•˜์˜€๋‹ค. ๊ณต๊ณต ์„œ๋น„์Šค ์˜์—ญ์—์„œ์˜ ๋ฌด์ธํ•ญ๊ณต๊ธฐ ์šด์˜, ๊ด€๋ จ๋œ ๊ธฐ์กด ์—ฐ๊ตฌ์™€ ๋ณธ ๋…ผ๋ฌธ์—์„œ ์‚ฌ์šฉํ•˜๋Š” ๋Œ€๊ทœ๋ชจ ์ตœ์ ํ™” ๊ธฐ๋ฒ•์— ๋Œ€ํ•œ ๊ฐœ๊ด„์ ์ธ ์„ค๋ช…, ์—ฐ๊ตฌ ๋™๊ธฐ ๋ฐ ๊ธฐ์—ฌ์™€ ๋…ผ๋ฌธ์˜ ๊ตฌ์„ฑ์„ 1์žฅ์—์„œ ์†Œ๊ฐœํ•œ๋‹ค. 2์žฅ์—์„œ๋Š” ๋ฌด์ธํ•ญ๊ณต๊ธฐ ์ง‘ํ•ฉ๋ฎ๊ฐœ๋ฌธ์ œ๋ฅผ ์ •์˜ํ•œ๋‹ค. ๋ฌด์ธํ•ญ๊ณต๊ธฐ๋Š” ๋ฏธ๋ฆฌ ์ •ํ•ด์ง„ ์œ„์น˜ ์—†์ด ์ž์œ ๋กญ๊ฒŒ ๋น„ํ–‰ํ•  ์ˆ˜ ์žˆ๊ธฐ ๋•Œ๋ฌธ์— ๋” ํšจ์œจ์ ์ธ ์šด์˜์ด ๊ฐ€๋Šฅํ•˜๋‚˜, ์•ฝํ•œ ์™„ํ™”ํ•œ๊ณ„๋ฅผ ๊ฐ–๊ฒŒ ๋œ๋‹ค. Dantzig-Wolfe ๋ถ„ํ•ด์™€ ๋ถ„์ง€ํ‰๊ฐ€๋ฒ•์„ ํฌํ•จํ•œ ๋Œ€๊ทœ๋ชจ ์ตœ์ ํ™” ๊ธฐ๋ฒ•์„ ํ†ตํ•ด ์™„ํ™”ํ•œ๊ณ„๋ฅผ ๊ฐœ์„ ํ•  ์ˆ˜ ์žˆ์œผ๋ฉฐ, ๋ถ„์ง€๋‚˜๋ฌด์˜ ๋Œ€์นญ์„ฑ์„ ์ค„์—ฌ ์‹ค์ œ ๊ทœ๋ชจ์˜ ๋ฌธ์ œ๋ฅผ ์‹ค์šฉ์ ์ธ ์‹œ๊ฐ„ ์•ˆ์— ํ•ด๊ฒฐํ•  ์ˆ˜ ์žˆ์—ˆ๋‹ค. ์ˆ˜์น˜์  ๋ถˆ์•ˆ์ •์„ฑ์„ ํ”ผํ•˜๊ธฐ ์œ„ํ•˜์—ฌ, ๋‘ ๊ฐ€์ง€ ์„ ํ˜• ๊ทผ์‚ฌ ๋ชจํ˜•์ด ์ œ์•ˆ๋˜์—ˆ์œผ๋ฉฐ, ์ด๋“ค์˜ ๊ทผ์‚ฌ ๋น„์œจ์„ ๋ถ„์„ํ•˜์˜€๋‹ค. 3์žฅ์—์„œ๋Š” ๋ฌด์ธํ•ญ๊ณต๊ธฐ ์ง‘ํ•ฉ๋ฎ๊ฐœ๋ฌธ์ œ๋ฅผ ์ผ๋ฐ˜ํ™”ํ•˜์—ฌ ๋ฌด์ธํ•ญ๊ณต๊ธฐ ๊ฐ€๋ณ€๋ฐ˜๊ฒฝ ์ง‘ํ•ฉ๋ฎ๊ฐœ๋ฌธ์ œ๋ฅผ ์ •์˜ํ•œ๋‹ค. ๋ถ„์ง€ํ‰๊ฐ€๋ฒ•์„ ์ ์šฉํ•˜๋ฉด์„œ ํ•ด๊ฒฐ ๊ฐ€๋Šฅํ•œ ํ‰๊ฐ€ ๋ถ€๋ฌธ์ œ๋ฅผ ์ œ์•ˆํ•˜์˜€์œผ๋ฉฐ, ํœด๋ฆฌ์Šคํ‹ฑ์„ ์„ค๊ณ„ํ•˜์˜€๋‹ค. ์ œ์•ˆํ•œ ํ’€์ด ๋ฐฉ๋ฒ•๋“ค์ด ๊ธฐ์กด ์—ฐ๊ตฌ์—์„œ ์ œ์•ˆํ•œ ๋ฒค์น˜๋งˆํฌ ์œ ์ „ ์•Œ๊ณ ๋ฆฌ์ฆ˜์„ ๋Šฅ๊ฐ€ํ•˜๋Š” ๊ฒฐ๊ณผ๋ฅผ ๋‚˜ํƒ€๋‚ด์—ˆ๋‹ค. 4์žฅ์—์„œ๋Š” ๋ฌด์ธํ•ญ๊ณต๊ธฐ ์‘๊ธ‰์˜๋ฃŒ์„œ๋น„์Šค๋ฅผ ์šด์˜ํ•˜๋Š” ์‹œ์„ค์˜ ์œ„์น˜์„ค์ • ๋ฐ ํ• ๋‹น๋ฌธ์ œ๋ฅผ ์ •์˜ํ•˜์˜€๋‹ค. 2์ฐจ ๊ฐ€๋ณ€๋ฐ˜๊ฒฝ ๋ฒ”์œ„์ œ์•ฝ์ด ์„ ํ˜•์˜ ๋™์น˜์ธ ์ˆ˜์‹์œผ๋กœ ์žฌ๊ณต์‹ํ™”๋˜์—ˆ์œผ๋ฉฐ, ๊ฐ•๊ฑด์ตœ์ ํ™” ๊ธฐ๋ฒ•์œผ๋กœ ์ธํ•ด ๋ฐœ์ƒํ•˜๋Š” ๋น„์„ ํ˜• ๋ฌธ์ œ๋ฅผ ์„ ํ˜•ํ™”ํ•˜์˜€๋‹ค. ๋Œ€๊ทœ๋ชจ ์ตœ์ ํ™” ๊ธฐ๋ฒ•์„ ์ ์šฉํ•˜๋ฉด์„œ, ํ‰๊ฐ€ ๋ถ€๋ฌธ์ œ์˜ ๊ตฌ์กฐ๋ฅผ ๋ถ„์„ํ•˜์—ฌ ๋‘ ๊ฐ€์ง€ ํ’€์ด ๊ธฐ๋ฒ•๊ณผ ํœด๋ฆฌ์Šคํ‹ฑ์„ ์ œ์•ˆํ•˜์˜€๋‹ค. ๋ณธ ์—ฐ๊ตฌ์˜ ๊ฒฐ๊ณผ๋Š” ๋ฌด์ธํ•ญ๊ณต๊ธฐ์™€ ๋น„์Šทํ•œ ํŠน์ง•์„ ๊ฐ€์ง€๋Š” ์‹ค์ œ ์‚ฌ๋ก€์— ์ ์šฉ๋  ์ˆ˜ ์žˆ์œผ๋ฉฐ, ์ถ”์ƒ์ ์ธ ๋ฌธ์ œ๋กœ์จ ๋‹ค์–‘ํ•œ ๋ถ„์•ผ์— ๊ทธ๋Œ€๋กœ ํ™œ์šฉ๋  ์ˆ˜๋„ ์žˆ๋‹ค.Abstract i Contents vii List of Tables ix List of Figures xi Chapter 1 Introduction 1 1.1 Unmanned aerial vehicle operation on public services 1 1.2 Facility location problems 3 1.3 Large-scale optimization techniques 4 1.4 Research motivations and contributions 6 1.5 Outline of the dissertation 12 Chapter 2 Unmanned aerial vehicle set covering problem considering fixed-radius coverage constraint 14 2.1 Introduction 14 2.2 Problem definition 20 2.2.1 Problem description 22 2.2.2 Mathematical formulation 23 2.2.3 Discrete approximation model 26 2.3 Branch-and-price approach for the USCP 28 2.3.1 An extended formulation of the USCP 29 2.3.2 Branching strategies 34 2.3.3 Pairwise-conflict constraint approximation model based on Jung's theorem 35 2.3.4 Comparison of the approximation models 40 2.3.5 Framework of the solution algorithm for the PCBP model 42 2.4 Computational experiments 44 2.4.1 Datasets used in the experiments 44 2.4.2 Algorithmic performances 46 2.5 Solutions and related problems of the USCP 61 2.6 Summary 64 Chapter 3 Unmanned aerial vehicle variable radius set covering problem 66 3.1 Introduction 66 3.2 Problem definition 70 3.2.1 Mathematical model 72 3.3 Branch-and-price approach to the UVCP 76 3.4 Minimum covering circle-based approach 79 3.4.1 Formulation of the pricing subproblem II 79 3.4.2 Equivalence of the subproblem 82 3.5 Fixed-radius heuristic 84 3.6 Computational experiments 86 3.6.1 Datasets used in the experiments 88 3.6.2 Solution algorithms 91 3.6.3 Algorithmic performances 94 3.7 Summary 107 Chapter 4 Facility location-allocation problem for unmanned aerial vehicle emergency medical service 109 4.1 Introduction 109 4.2 Related literature 114 4.3 Location-allocation model for UEMS facility 117 4.3.1 Problem definition 118 4.3.2 Mathematical formulation 120 4.3.3 Linearization of the quadratic variable coverage distance function 124 4.3.4 Linear reformulation of standard formulation 125 4.4 Solution algorithms 126 4.4.1 An extended formulation of the ULAP 126 4.4.2 Branching strategy 129 4.4.3 Robust disjunctively constrained integer knapsack problem 131 4.4.4 MILP reformulation approach 132 4.4.5 Decomposed DP approach 133 4.4.6 Restricted master heuristic 136 4.5 Computational experiments 137 4.5.1 Datasets used in the experiments 137 4.5.2 Algorithmic performances 140 4.5.3 Analysis of the branching strategy and the solution approach of the pricing subproblem 150 4.6 Summary 157 Chapter 5 Conclusions and future research 160 5.1 Summary 160 5.2 Future research 163 Appendices 165 A Comparison of the computation times and objective value of the proposed algorithms 166 Bibliography 171 ๊ตญ๋ฌธ์ดˆ๋ก 188 ๊ฐ์‚ฌ์˜ ๊ธ€ 190Docto

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