개미알고리즘을 이용한 드론의 제설 경로 최적화

학위논문(석사) -- 서울대학교대학원 : 공과대학 건설환경공학부, 2022.2. 김동규.Drones can overcome the limitation of ground vehicles by replacing the congestion time and allowing rapid service. For sudden snowfall with climate change, a quickly deployed drone can be a flexible alternative considering the deadhead route and the labor costs. The goal of this study is to optimize a drone arc routing problem (D-ARP), servicing the required roads for snow removal. A D-ARP creates computational burden especially in large network. The D-ARP has a large search space due to its exponentially increased candidate route, arc direction decision, and continuous arc space. To reduce the search space, we developed the auxiliary transformation method in ACO algorithm and adopted the random walk method. The contribution of the work is introducing a new problem and optimization approach of D-ARP in snow removal operation and reduce its search space. The optimization results confirmed that the drone travels shorter distance compared to the truck with a reduction of 5% to 22%. Furthermore, even under the length constraint model, the drone shows 4% reduction compared to the truck. The result of the test sets demonstrated that the adopted heuristic algorithm performs well in the large size networks in reasonable time. Based on the results, introducing a drone in snow removal is expected to save the operation cost in practical terms.드론은 혼잡시간대를 대체하고 빠른 서비스를 가능하게 함으로써 지상차량의 한계를 극복할 수 있다. 최근 기후변화에 따른 갑작스런 강설의 경우에, 드론과 같이 빠르게 투입할 수 있는 서비스는 운행 경로와 노동비용을 고려했을 때도 유연한 운영 옵션이 될 수 있다. 본 연구의 목적은 드론 아크 라우팅(D-ARP)을 최적화하는 것이며, 이는 제설에 필요한 도로를 서비스하는 경로를 탐색하는 것이다. 드론 아크 라우팅은 특히 큰 네트워크에서 컴퓨터 부하를 생성한다. 다시 말해D-ARP는 큰 검색공간을 필요로 하며, 이는 기하급수적으로 증가하는 후보 경로 및 호의 방향 결정 그리고 연속적인 호의 공간으로부터 기인한다. 검색공간을 줄이기 위해, 우리는 개미알고리즘에 보조변환방법을 적용하는 방안을 도입하였으며 또한 랜덤워크 기법을 채택하였다. 본 연구의 기여는 제설 운영에 있어 D-ARP라는 새로운 문제를 설정하고 최적화 접근법을 도입하였으며 검색공간을 최소화한 것이다. 최적화 결과, 드론은 지상트럭에 비해 약 5% ~ 22%의 경로 비용 감소를 보였다. 나아가 길이 제약 모델에서도 드론은 4%의 비용 감소를 보였다. 또한 실험결과는 적용한 휴리스틱 알고리즘이 큰 네트워크에서도 합리적 시간 내에 최적해를 찾음을 입증하였다. 이러한 결과를 바탕으로, 드론을 제설에 도입하는 것은 미래에 제설 운영 비용을 실질적으로 감소시킬 것으로 기대된다.Chapter 1. Introduction 4 1.1. Study Background 4 1.2. Purpose of Research 6 Chapter 2. Literature Review 7 2.1. Drone Arc Routing problem 7 2.2. Snow Removal Routing Problem 8 2.3. The Classic ARPs and Algorithms 9 2.4. Large Search Space and Arc direction 11 Chapter 3. Method 13 3.1. Problem Statement 13 3.2. Formulation 16 Chapter 4. Algorithm 17 4.1. Overview 17 4.2. Auxilary Transformation Method 18 4.3. Ant Colony Optimization (ACO) 20 4.4. Post Process for Arc Direction Decision 23 4.5. Length Constraint and Random Walk 24 Chapter 5. Results 27 5.1. Application in Toy Network 27 5.2. Application in Real-world Networks 29 5.3. Application of the Refill Constraint in Seoul 31 Chapter 6. Conclusion 34 References 35 Acknowledgment 40석

Two-Echelon Vehicle and UAV Routing for Post-Disaster Humanitarian Operations with Uncertain Demand

Humanitarian logistics service providers have two major responsibilities immediately after a disaster: locating trapped people and routing aid to them. These difficult operations are further hindered by failures in the transportation and telecommunications networks, which are often rendered unusable by the disaster at hand. In this work, we propose two-echelon vehicle routing frameworks for performing these operations using aerial uncrewed autonomous vehicles (UAVs or drones) to address the issues associated with these failures. In our proposed frameworks, we assume that ground vehicles cannot reach the trapped population directly, but they can only transport drones from a depot to some intermediate locations. The drones launched from these locations serve to both identify demands for medical and other aids (e.g., epi-pens, medical supplies, dry food, water) and make deliveries to satisfy them. Specifically, we present two decision frameworks, in which the resulting optimization problem is formulated as a two-echelon vehicle routing problem. The first framework addresses the problem in two stages: providing telecommunications capabilities in the first stage and satisfying the resulting demands in the second. To that end, two types of drones are considered. Hotspot drones have the capability of providing cell phone and internet reception, and hence are used to capture demands. Delivery drones are subsequently employed to satisfy the observed demand. The second framework, on the other hand, addresses the problem as a stochastic emergency aid delivery problem, which uses a two-stage robust optimization model to handle demand uncertainty. To solve the resulting models, we propose efficient and novel solution approaches

An ACO-Inspired, Probabilistic, Greedy Approach to the Drone Traveling Salesman Problem

In recent years, major companies have done research on using drones for parcel delivery. Research has shown that this can result in significant savings, which has led to the formulation of various truck and drone routing and scheduling optimization problems. This paper explains and analyzes a new approach to the Drone Traveling Salesman Problem (DTSP) based on ant colony optimization (ACO). The ACO-based approach has an acceptance policy that maximizes the usage of the drone. The results reveal that the pheromone causes the algorithm to converge quickly to the best solution. The algorithm performs comparably to the MIP model, CP model, and EA of Rich & Ham (2018), especially in instances with a larger number of stops

트럭을 이동형 드론 기지로 사용하는 한정용량 트럭-드론 경로 배정 문제

학위논문(석사) -- 서울대학교대학원 : 공과대학 건설환경공학부, 2022.2. 김동규.Drones initially received attention for military purposes as a collective term for unmanned aerial vehicles (UAVs), but recently, efforts to use them in logistics have been actively underway. If drones are put into places where low-weight and high-value items are currently difficult to deliver by existing delivery means, it will have the effect of greatly reducing costs. However, the disadvantages of drones in delivery are also clear. In order to improve the delivery capacity of drones, the size of drones must increase when drones are equipped with large-capacity batteries. This thesis introduced two methods and presented algorithms for each method among VRP-D. First of all, CVP-D is a method in which carriers such as trucks and ships with large capacity and slow speed carry robots and drones with small capacity. Next, in the CVRP-D, the vehicle and the drone move different paths simultaneously, and the drone can visit multiple nodes during one sortie. The two problems are problems in which restrictions are added to the vehicle route problem (VRP), known as the NP-hard problem. The algorithm presented in this study derived drone-truck routes for two problems within a reasonable time. In addition, sensitivity analysis was conducted to observe changes in the appropriate network structure for the introduction of drone delivery and the main parameters of the drone. In addition, the validity of the proposed algorithm was verified through comparison with the data used as a benchmark in previous studies. These research results will contribute to the creation of delivery routes quickly, considering the specification of a drone.드론은 무인항공기(UAV)의 통칭으로 초기에는 군사적 목적으로 주목을 받았으나 최근 물류에서 사용하려는 노력이 적극적으로 진행되고 있다. 드론이 저중량-고가치 물품을 배송에서 현재 기존 배송수단에 의해 배송이 어려운 곳에 투입이 된다면 큰 비용절감의 효과가 있을 것이다. 하지만 배송에 있어서 드론의 단점도 명확하다. 드론의 배송능력을 향상시키기 위해서는 드론이 대용량 배터리를 탑재하면 드론 크기가 증가하여야 한다. 이러한 단점을 극복하기 위해서 드론과 트럭을 결합하여 운영하는 방식이 연구되어왔다. 이러한 방식 중 본 연구에서는 두 가지 방식을 소개하고, 각각의 방식에 대한 알고리즘을 제시하였다. 먼저, CVP-D는 용량이 크고 속도가 느린 트럭이나 배 등의 캐리어가 용량이 작은 로봇, 드론 등을 싣고 다니면서 배송을 하는 방식이다. 다음으로, CVRP-D는 차량과 드론이 동시에 각기 다른 경로를 이동하며, 드론은 1회 비행(sortie)시 다수의 노드를 방문하는 것이 가능하다. 두 문제는 차량경로문제(VRP)에 제약이 더해진 문제이다. VRP는 대표적인 NP-hard 문제로 해를 구하기 위해서 휴리스틱 알고리즘이 요구된다. 본 연구에서 제시하는 알고리즘은 합리적인 시간 내 두문제의 드론-트럭 경로를 도출하였다. 또한 민감도 분석을 실시하여 드론 배송 도입을 위한 적절한 네트워크 구조 및 드론의 주요 파라미터에 변화에 따른 변화를 관찰하였다. 이는 차후 드론의 성능에 관한 의사결정 시 고려해야 할 요소들에 대한 기준이 될 수 있을 것으로 기대된다. 또한 선행연구에서 벤치마크로 사용되는 데이터와의 비교를 통해 제안하는 알고리즘의 타당성을 검증하였다. 본 연구는 드론 도입이 배송시간을 감소시키며, 운영방법에 따라서 배송시간의 차이가 발생함을 보였다. 이러한 연구 성과는 드론 배송 시 환경과 기계적 성능을 고려한 배송 경로를 단시간내 생성하여 상업적으로 이용가능 할 것이다.Chapter 1. Introduction 1 1.1 Research Background 1 1.2 Research Purpose 3 1.3 Contribution of Research 4 Chapter 2. Literature review 5 2.1 Vehicle Routing Problems with Drone 5 2.2 Carrier Vehicle Problem with Drone(CVP-D) 10 2.3 Capacitated VRP with Drone(CVRP-D) 12 Chapter 3. Mathematical Formulation 14 3.1 Terminology 14 3.2 CVP-D Formulation 15 3.3 CVRP-D Formulation 19 Chapter 4. Proposed Algorithms 23 4.1 Heuristic Algorithm 23 4.1.1 Knapsack Problem 23 4.1.2 Parallel Machine Scheduling (PMS) 25 4.1.3 Set Covering Location Problem (SCLP) 27 4.1.4 Guided Local Search (GLS) Algorithm 28 4.1.5 Genetic Algorithm (GA) 29 4.2 Proposed Heuristic Algorithm : GA-CVPD 30 4.3 Proposed Heuristic Algorithm : GA-CVRPD 33 Chapter 5. Numerical Analysis 36 5.1 Data Description 36 5.2 Numerical experiment 37 5.3 Sensitivity analysis 39 5.3.1 Analysis on GA-CVPD 39 5.3.2 Analysis on GA-CVRPD 42 5.3.3 Result on different Instances 45 Chapter 6. Conclusion 48 Bibliography 50 Abstract in Korean 53 4.1.5 Genetic Algorithm (GA) 29 4.2 Proposed Heuristic Algorithm : GA-CVPD 30 4.3 Proposed Heuristic Algorithm : GA-CVRPD 33 Chapter 5. Numerical Analysis 36 5.1 Data Description 36 5.2 Numerical experiment 37 5.3 Sensitivity analysis 42 5.3.1 Analysis on GA-CVPD 39 5.3.2 Analysis on GA-CVRPD 42 5.3.3 Result on different Instances 45 Chapter 6. Conclusion 48 Bibliography 50 Abstract in Korean 53석

Arc routing problems: A review of the past, present, and future

[EN] Arc routing problems (ARPs) are defined and introduced. Following a brief history of developments in this area of research, different types of ARPs are described that are currently relevant for study. In addition, particular features of ARPs that are important from a theoretical or practical point of view are discussed. A section on applications describes some of the changes that have occurred from early applications of ARP models to the present day and points the way to emerging topics for study. A final section provides information on libraries and instance repositories for ARPs. The review concludes with some perspectives on future research developments and opportunities for emerging applicationsThis research was supported by the Ministerio de Economia y Competitividad and Fondo Europeo de Desarrollo Regional, Grant/Award Number: PGC2018-099428-B-I00. The Research Council of Norway, Grant/Award Numbers: 246825/O70 (DynamITe), 263031/O70 (AXIOM).Corberán, Á.; Eglese, R.; Hasle, G.; Plana, I.; Sanchís Llopis, JM. (2021). Arc routing problems: A review of the past, present, and future. Networks. 77(1):88-115. https://doi.org/10.1002/net.21965S8811577

Delivery by Drones with Arbitrary Energy Consumption Models: A New Formulation Approach

This paper presents a new approach for formulating the delivery problem by drones with general energy consumption models where the drones visit a set of places to deliver parcels to customers. Drones can perform multiple trips that start and end at a central depot while visiting several customers along their paths. The problem determines the routing and scheduling decisions of the drones in order to minimize the total transportation cost of serving customers. For the first time, the new formulation approach enables us to use the best available energy consumption model without the need of any extra approximations. Though the approach works in a very general setting including non-convex energy consumption models, it is also computationally efficient as the resulting optimization model has a linear relaxation. A numerical study on 255 benchmark instances with up to 50 customers and a specific energy function indicate that all the instances can be solved 20 times faster on average using the new formulation when compared to the best existing branch-and-cut algorithm. All the 15 benchmark instances with 50 customers are solved exactly, whereas none of them has been solved optimally before. Moreover, new instances with up to 150 customers are solved with small error bounds within a few hours. The new approach can be simply applied to consider the extra energy required when a drone needs to continue hovering until opening the delivery time window. It can also be applied to the case where the flight time is dependent on the drone's payload weight. Owing to the flexibility of the new approach, these challenging extensions are formulated as linear optimization models for the first time

Optimizing Vaccine Supply Chains with Drones in Less-Developed Regions: Multimodal Vaccine Distribution in Vanuatu

In recent years, many less-developed countries (LDCs) have been exploring new opportunities provided by drones, such as the capability to deliver items with minimal infrastructure, fast speed, and relatively low cost, especially for high value-added products such as lifesaving medical products and vaccines. This dissertation optimizes the delivery network and operations for routine childhood vaccines in LDCs. It analyzes two important problems using mathematical programming, with an application in the South Pacific nation of Vanuatu. The first problem is to optimize the nation-wide multi-modal vaccine supply chain with drones to deliver vaccines from the national depot to all health zones in an LDC. The second problem is to optimize vaccine delivery using drones within a single health zone while considering the synchronization of drone deliveries with health worker outreach trips to remote clinics. Both problems consider a cold chain time limit to ensure vaccine viability. The two research problems together provide a holistic solution at the strategic and operational levels for the vaccine supply chain network in LDCs. Results from the first problem show that drones can reduce cost and delivery time simultaneously by replacing expensive and/or slow modes. The use of large drones is shown to save up to 60% of the delivery cost and the use of small drones is shown to save up to 43% of the delivery cost. The research highlights the tradeoff between delivery cost and service, with tighter cold chain limits providing faster delivery to health zones at the expense of added cost. Results from the second problem show that adding drones to delivery plans can save up to 40% of the delivery cost and improve the service time simultaneously by resupplying vaccines when the cold chain and payload limit of health workers are reached. This research contributes to both literature and practice. It develops innovative methodologies to model drone paths with relay stations and to optimize synchronized multi-stop drone trips with health worker trips. The models are tested with real-world data for an island nation (Vanuatu), which provides data for a geographic setting new to the literature on drone delivery and vaccine distribution

Exact methods for the traveling salesman problem with multiple drones

Drone delivery is drawing increasing attention in last-mile delivery. Effective solution methods to solve decision-making problems arising in drone delivery allow to run and assess drone delivery systems. In this paper, we focus on delivery systems with a single traditional vehicle and multiple drones working in tandem to fulfill customer requests. We address the Traveling Salesman Problem with Multiple Drones (TSP-MD) and investigate the modeling challenges posed by the presence of multiple drones, which have proven to be hard to handle in the literature. We propose a compact Mixed-Integer Linear Programming (MILP) model to formulate the TSP-MD and several families of valid inequalities. Moreover, we illustrate an exact decomposition approach based on the compact MILP and a branch-and-cut algorithm. We show that this exact approach can solve instances with up to 24 customers to proven optimality, improving upon existing exact methods that can solve similar problems with up to ten customers only

Adaptive large neighborhood search algorithm – performance evaluation under parallel schemes & applications

Adaptive Large Neighborhood Search (ALNS) is a fairly recent yet popular single-solution heuristic for solving discrete optimization problems. Even though the heuristic has been a popular choice for researchers in recent times, the parallelization of this algorithm is not widely studied in the literature compared to the other classical metaheuristics. To extend the existing literature, this study proposes several different parallel schemes to parallelize the basic/sequential ALNS algorithm. More specifically, seven different parallel schemes are employed to target different characteristics of the ALNS algorithm and the capability of the local computers. The schemes of this study are implemented in a master-slave architecture to manage and assign loads in processors of the local computers. The overall goal is to simultaneously explore different areas of the search space in an attempt to escape the local minima, taking effective steps toward the optimal solution and, to the end, accelerating the convergence of the ALNS algorithm. The performance of the schemes is tested by solving a capacitated vehicle routing problem (CVRP) with available wellknown test instances. Our computational results indicate that all the parallel schemes are capable of providing a competitive optimality gap in solving CVRP within our investigated test instances. However, the parallel scheme (scheme 1), which runs the ALNS algorithm independently within different slave processors (e.g., without sharing any information with other slave processors) until the synchronization occurs only when one of the processors meets its predefined termination criteria and reports the solution to the master processor, provides the best running time with solving the instances approximately 10.5 times faster than the basic/sequential ALNS algorithm. These findings are applied in a real-life fulfillment process using mixed-mode delivery with trucks and drones. Complex but optimized routes are generated in a short time that is applicable to perform last-mile delivery to customers