Development of Heuristic Approaches for Last-Mile Delivery TSP with a Truck and Multiple Drones

Unmanned Aerial Vehicles (UAVs) are gaining momentum in many civil and military sectors. An example is represented by the logistics sector, where UAVs have been proven to be able to improve the efficiency of the process itself, as their cooperation with trucks can decrease the delivery time and reduce fuel consumption. In this paper, we first state a mathematical formulation of the Travelling Salesman Problem (TSP) applied to logistic routing, where a truck cooperates synchronously with multiple UAVs for parcel delivery. Then, we propose, implement, and compare different sub-optimal routing approaches to the formulated mFSTSP (multiple Flying Sidekick Travelling Salesman Problem) since the inherent combinatorial computational complexity of the problem makes it unattractable for commercial Mixed-Integer Linear Programming (MILP) solvers. A local search algorithm, two hybrid genetic algorithms that permutate feasible and infeasible solutions, and an alternative ad-hoc greedy method are evaluated in terms of the total delivery time of the output schedule. For the sake of the evaluation, the savings in terms of delivery time over the well-documented truck-only TSP solution are investigated for each proposed routing solution, and this is repeated for two different scenarios. Monte Carlo simulations corroborate the results

Drone-Truck Cooperated Delivery under Time Varying Dynamics

Rapid technological developments in autonomous unmanned aerial vehicles (or drones) could soon lead to their large-scale implementation in the last-mile delivery of products. However, drones have a number of problems such as limited energy budget, limited carrying capacity, etc. On the other hand, trucks have a larger carrying capacity, but they cannot reach all the places easily. Intriguingly, last-mile delivery cooperation between drones and trucks can synergistically improve delivery efficiency. In this paper, we present a drone-truck co-operated delivery framework under time-varying dynamics. Our framework minimizes the total delivery time while considering low energy consumption as the secondary objective. The empirical results support our claim and show that our algorithm can help to complete the deliveries time efficiently and saves energy

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

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

The multi-visit drone-assisted pickup and delivery problem with time windows

We consider a new combined truck-drone routing problem with time windows in the context of last-mile logistics. A fleet of trucks, each equipped with an identical drone, is scheduled to provide both pickup and delivery services to a set of customers with minimum cost. Some customers are paired, in that the goods picked up from one must be delivered to the other on the same route. Drones are launched from and retrieved by trucks at a pool of designated stations, which can be used multiple times. Each drone can serve multiple customers in one flight. We formulate this problem as a large-scale mixed-integer bilinear program, with the bilinear terms used to calculate the load-time-dependent energy consumption of drones. To accelerate the solution process, multiple valid inequalities are proposed. For large-size problems, we develop a customised adaptive large neighbourhood search (ALNS) algorithm, which includes several preprocessing procedures to quickly identify infeasible solutions and accelerate the search process. Moreover, two feasibility test methods are developed for trucks and drones, along with an efficient algorithm to determine vehicles’ optimal waiting time at launch stations, which is important to consider due to the time windows. Extensive numerical experiments demonstrate the effectiveness of the valid inequalities and the strong performance of the proposed ALNS algorithm over two benchmarks in the literature, and highlight the cost-savings of the combined mode over the truck-only mode and the benefits of allowing multiple drone visits

Variable Neighborhood Descent Matheuristic for the Drone Routing Problem with Beehives Sharing

In contemporary urban logistics, drones will become a preferred transportation mode for last-mile deliveries, as they have shown commercial potential and triple-bottom-line performance. Drones, in fact, address many challenges related to congestion and emissions and can streamline the last leg of the supply chain, while maintaining economic performance. Despite the common conviction that drones will reshape the future of deliveries, numerous hurdles prevent practical implementation of this futuristic vision. The sharing economy, referred to as a collaborative business model that foster sharing, exchanging and renting resources, could lead to operational improvements and enhance the cost control ability and the flexibility of companies using drones. For instance, the Amazon patent for drone beehives, which are fulfilment centers where drones can be restocked before flying out again for another delivery, could be established as a shared delivery systems where different freight carriers jointly deliver goods to customers. Only a few studies have addressed the problem of operating such facilities providing services to retail companies. In this paper, we formulate the problem as a deterministic location-routing model and derive its robust counterpart under the travel time uncertainty. To tackle the computational complexity of the model caused by the non-linear energy consumption rates in drone battery, we propose a tailored matheuristic combining variable neighborhood descent with a cut generation approach. The computational experiments show the efficiency of the solution approach especially compared to the Gurobi solver

Implementasi Wahana Tanpa Awak Otomatis Berbasis Drone Quadcopter untuk Pengiriman Makanan

Teknologi drone sudah mulai berkembang dengan pesat, banyak pengguna drone yang sudah menggunakan teknologi drone untuk pekerjaan, pendidikan, dan bahkan militer memanfaatkan teknologi ini. Dalam bidang pengiriman barang sudah mulai dikembangkan pengiriman menggunakan teknologi drone namun belum terlalu populer karena terkait keamanan saat proses pengiriman yang masih menjadi isu penggunaan drone. Selain digunakan untuk komersil, pemanfaatan drone seharusnya juga dapat digunakan dalam penanggulangan suatu kejadian bencana yang terkadang sulit untuk ditangani karena kondisi medan yang berat. Dimana saat terjadi bencana salah satu yang menjadi perhatian adalah pengiriman logistik baik berupa makanan ataupun obat-obatan yang merupakan kebutuhan utama bagi korban terdampak bencana. Melihat dari manfaat penggunaan drone yang cukup luas, maka dari sini peneliti ingin mengimplementasikan drone sebagai wahana pengirim makanan secara otomatis sehingga dapat mempermudah konsumen yang ingin membeli makanan tanpa harus membuang waktu dan tenaga di perjalanan. Dari hasil penelitian yang sudah dilakukan peneliti berhasil membuat drone pengirim makanan yang mampu mengirimkan makanan dengan tingkat presisi pendaratan pengiriman sebesar 83% serta rata-rata eror jarak pendaratan dengan aslinya sebesar 21 cm. Untuk waktu yang ditempuh juga cukup konstan dengan rata-rata pengiriman sejauh 214 m sebesar 4 menit 20,1 detik

Adjustment Factors and Applications for Analytic Approximations of Tour Lengths

The shortest tour distance for visiting all points exactly once and returning to the origin is computed by solving the well-known Traveling Salesman Problem (TSP). Due to the large computational effort needed for optimizing TSP tours, researchers have developed approximations that relate the average length of TSP tours to the number of points n visited per tour. The most widely used approximation formula has a square root form: √n multiplied by a coefficient β. Although the existing models can effectively approximate the distance for conventional vehicles with large capacities (e.g., delivery trucks) where n is large, approximations that seek to cover large ranges of n, possibly to infinity, tend to yield poorer results for the small n values. Thus, this dissertation focuses on approximation models for the small n values, which are needed for many practical applications, such as for some recent delivery alternatives (e.g., drones). The proposed models show promise in analyzing the real-world problems in which actual tours serve few customers due to limited vehicle capacity and incorporate realistic constraints, such as the effects of a starting point location, geographical restrictions on movements, demand patterns, and service area shapes. The dissertation may open new research avenues for analyzing the new transportation alternatives and provide guidelines to planners for choosing appropriate models in designing or evaluating transportation problems. Approximation models are estimated from the following experiments: 1) a total of 60 cases are developed by considering various factors, such as point distributions and shapes of service areas. 2) Solution methods for TSP instances are compared and chosen. 3) After the TSPs are optimized for each n, the TSP tour lengths are averaged. 4) Lastly, models for the averaged TSP tour lengths are fitted with ordinary least squares (OLS) regression. After the approximations are developed, some possible extensions are explored. First, adjustment factors are designed to integrate the 60 cases within one equation. With those factors, it can be understood how approximation varies with each classification. Next, the approximations considering stochastic customer presence (i.e., probabilistic TSP) are proposed. Third, the approximated tour lengths are compared with the optimal solutions of vehicle routing problem (VRP) in actual rural and urban delivery networks. Here, some additional factors, such as a circuity factor and service zone shape, are discussed. Lastly, the proposed methodology is applied to formulate and explore various types of existing and hypothetical delivery alternatives

Delivery Route Management based on Dijkstra Algorithm

بالنسبة للشركات التي تقدم خدمات التوصيل، فإن كفاءة عملية التسليم من حيث الالتزام بالمواعيد مهمة للغاية. بالإضافة إلى زيادة ثقة العملاء ، فإن الإدارة الفعالة للمسار والاختيار مطلوبة لتقليل تكاليف وقود السيارة وتسريع التسليم. لا تزال بعض الشركات الصغيرة والمتوسطة تستخدم الأساليب التقليدية لإدارة طرق التسليم. لا تستخدم قرارات إدارة جداول التسليم والمسارات أي طرق محددة لتسريع عملية تسوية التسليم. هذه العملية غير فعالة وتستغرق وقتًا طويلاً وتزيد التكاليف وتكون عرضة للأخطاء. لذلك ، تم استخدام خوارزمية Dijkstra لتحسين عملية إدارة التسليم. تم تطوير نظام إدارة التسليم لمساعدة المديرين والسائقين على جدولة طرق فعالة لتسليم طلبات المنتجات إلى المستلمين. بناءً على الاختبار ، عملت خوارزمية Dijkstra التي تم تضمينها في أقرب وظيفة بحث عن المسار لعملية التسليم بشكل جيد. من المتوقع أن يؤدي هذا النظام إلى تحسين الإدارة الفعالة وتسليم الطلبات.For businesses that provide delivery services, the efficiency of the delivery process in terms of punctuality is very important. In addition to increasing customer trust, efficient route management, and selection are required to reduce vehicle fuel costs and expedite delivery. Some small and medium businesses still use conventional methods to manage delivery routes. Decisions to manage delivery schedules and routes do not use any specific methods to expedite the delivery settlement process. This process is inefficient, takes a long time, increases costs and is prone to errors. Therefore, the Dijkstra algorithm has been used to improve the delivery management process. A delivery management system was developed to help managers and drivers schedule efficient ways to deliver product orders to recipients. Based on testing, the Dijkstra algorithm that has been included in the nearest route search function for the delivery process has worked well. This system is expected to improve the efficient management and delivery of orders