Efficient Multi-Robot Coverage of a Known Environment

This paper addresses the complete area coverage problem of a known environment by multiple-robots. Complete area coverage is the problem of moving an end-effector over all available space while avoiding existing obstacles. In such tasks, using multiple robots can increase the efficiency of the area coverage in terms of minimizing the operational time and increase the robustness in the face of robot attrition. Unfortunately, the problem of finding an optimal solution for such an area coverage problem with multiple robots is known to be NP-complete. In this paper we present two approximation heuristics for solving the multi-robot coverage problem. The first solution presented is a direct extension of an efficient single robot area coverage algorithm, based on an exact cellular decomposition. The second algorithm is a greedy approach that divides the area into equal regions and applies an efficient single-robot coverage algorithm to each region. We present experimental results for two algorithms. Results indicate that our approaches provide good coverage distribution between robots and minimize the workload per robot, meanwhile ensuring complete coverage of the area.Comment: In proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 201

전기 마이크로 모빌리티 공유 시스템에서의 배터리 교체와 재배치 작업 최적화

학위논문 (석사) -- 서울대학교 대학원 : 공과대학 산업공학과, 2021. 2. 박건수.In this thesis, we consider a battery swapping and mobility inventory rebalancing problem arising in electric micro-mobility sharing systems. Vehicles are equipped with swappable batteries and they are managed by staffs' visiting each vehicle and changing depleted batteries. With the free-floating property of the system, vehicles can locate anywhere in a service area without designated stations, which increases the difficulty to visit and collect every single vehicle. In order to successfully meet user demand during the daytime, operators have to redistribute the vehicles with the right number in the right place and swap batteries with insufficient levels into fully charged ones overnight. Therefore, it is essential that operators take battery charging(swapping), staff routing, rebalancing problem all together into consideration. We aim to satisfy demand as much as possible and at the same time minimize routing and swapping costs. We formulate this problem in a mixed integer linear programming. Target inventory level for rebalancing, an important parameter used in the system, is suggested by analyzing a stochastic process that incorporates demand changes. Being a special case of vehicle routing problem with pickup and delivery, it shares the difficulty and complexity of VRP in practically large size. So as to give efficient solutions in large size problems, we develop a Cluster-first Route-second heuristic where a set partitioning problem considers inventory imbalances and approximates routing distances. We benchmark our heuristic approach on a pure MLIP formulation. The experimental result confirms that the heuristic is good at decomposing a large problem and gives efficient solutions even in practically large instances.본 연구는 교체형 배터리를 이용하는 전기 마이크로 모빌리티 공유 시스템에서의 배터리 교체 및 차량 재배치를 효율적으로 수행하는 방법을 제시하고자 한다. 수요를 성공적으로 충족시키기 위해선 모빌리티의 공급과 이용자의 수요를 맞춰주기 위한 차량 재고 차원에서의 재배치 작업과 배터리 수준을 유지시켜주는 배터리 관리 차원에서의 교체 작업이 필수적이다. 또한 충전소로 차량을 옮길 필요 없이 바로 교체할 수 있으므로 담당 직원이 산발적으로 위치한 각 모빌리티들을 순회하며 위 작업들을 진행해야 한다. 이동하며 작업하는 비용과 시간이 대부분이기 때문에 이동 순서를 함께 최적화하는 것이 비용 개선에 필수적이다. 따라서 작업 결정과 경로 결정을 동시에 고려하는 충전 및 재배치 모형을 제시한다. 이때 free-floating 모빌리티 공유시스템의 이용 수요를 효과적으로 반영하고자 수요를 stochastic process로 모델링하고 이를 이용하여 재배치 목표 수량을 구한다. 문제의 크기가 큰 경우 효율적으로 본 충전 및 재배치 모형의 좋은 해를 얻기 위한 방법으로, 해당 서비스지역의 각 구역들을 클러스터링하고 그 뒤에 스태프들의 경로와 작업을 결정하는 휴리스틱을 제안한다. 여러 스태프를 순회시키는 복잡한 형태를 클러스터링으로써 작은 크기의 문제들로 분해하여 빠르게 문제를 풀고자 한다. 이를 위해 각 클러스터에는 한 명의 스태프가 배정되고, 한 클러스터 내에서 소속된 구역들이 필요로 하는 작업들을 한 명의 스태프가 모두 진행하도록 구성한다. 최소걸침나무 근사법을 적용한 set partitioning 문제를 풀어 클러스터링을 진행한다. 계산실험 결과, 고안된 휴리스틱은 차량의 수가 많아 크기가 큰 상황에서도 빠른 시간내에 더 좋은 해를 냈다.Chapter 1. Introduction 1 1.1 Background 1 1.2 Related literature 6 1.2.1 Rebalancing in bike sharing systems 6 1.2.2 Charging and rebalancing in free-floating electric vehicle(FFEV) sharing 9 1.2.3 Charging of electric micro-mobility with swappable batteries 10 1.3 Motivation and contributions 12 1.4 Organization of the thesis 14 Chapter 2. Mathematical formulations 15 2.1 Basic assumptions and problem description 15 2.2 Demand Modeling and Target Inventory 18 2.3 Mixed integer linear programming formulation 23 Chapter 3. Heuristic approach 30 3.1 Cluster-first route-second approach 31 3.2 Clustering problem with routing cost approximation 33 3.2.1 Minimum spanning tree approximation 33 3.2.2 Clustering problem 35 3.2.3 Cluster-first Route-second heuristic 41 Chapter 4. Computational experiments 42 4.1 Design of experiment 42 4.2 Comparative Analysis 47 Chapter 5. Conclusion 52Maste

A Study On The Split Delivery Vehicle Routing Problem

This dissertation examines the Split Delivery Vehicle Routing Problem (SDVRP), a relaxed version of classical capacitated vehicle routing problem (CVRP) in which the demand of any client can be split among the vehicles that visit it. We study both scenarios of the SDVRP in this dissertation. For the SDVRP with a fixed number of the vehicles, we provide a Two-Stage algorithm. This approach is a cutting-plane based exact method called Two-Stage algorithm in which the SDVRP is decomposed into two stages of clustering and routing. At the first stage, an assignment problem is solved to obtain some clusters that cover all demand points and get the lower bound for the whole problem; at the second stage, the minimal travel distance of each cluster is calculated as a traditional Traveling Salesman Problem (TSP), and the upper bound is obtained. Adding the information obtained from the second stage as new cuts into the first stage, we solve the first one again. This procedure stops when there are no new cuts to be created from the second stage. Several valid inequalities have been developed for the first stage to increase the computational speed. A valid inequality is developed to completely solve the problem caused by the index of vehicles. Another strong valid inequality is created to provide a valid distance lower bound for each set of demand points. This algorithm can significantly outperform other exact approaches for the SDVRP in the literature. If the number of the vehicles in the SDVRP is a variable, we present a column generation based branch and price algorithm. First, a restricted master problem (RMP) is presented, which is composed of a finite set of feasible routes. Solving the linear relaxation of the RMP, values of dual variables are thus obtained and passed to the sub-problem, the pricing problem, to generate a new column to enter the base of the RMP and solve the new RMP again. This procedure repeats until the objective function value of the pricing problem is greater than or equal to zero (for minimum problem). In order to get the integer feasible (optimal) solution, a branch and bound algorithm is then performed. Since after branching, it is not guaranteed that the possible favorable column will appear in the master problem. Therefore, the column generation is performed again in each node after branching. The computational results indicate this approach is promising in solving the SDVRP in which the number of the vehicles is not fixed

Column generation approaches to ship scheduling with flexible cargo sizes

We present a Dantzig-Wolfe procedure for the ship scheduling problem with flexible cargo sizes. This problem is similar to the well-known pickup and delivery problem with time windows, but the cargo sizes are defined by an interval instead of a fixed value. We show that the introduction of flexible cargo sizes to the column generation framework is not straightforward, and we handle the flexible cargo sizes heuristically when solving the subproblems. This leads to convergence issues in the branch-and-price search tree, and the optimal solution cannot be guaranteed. Hence we have introduced a method that generates an upper bound on the optimal objective. We have compared our method with an a priori column generation approach, and our computational experiments on real world cases show that the Dantzig-Wolfe approach is faster than the a priori generation of columns, and we are able to deal with larger or more loosely constrained instances. By using the techniques introduced in this paper, a more extensive set of real world cases can be solved either to optimality or within a small deviation from optimalityTransportation; integer programming; dynamic programming

A Literature Review On Combining Heuristics and Exact Algorithms in Combinatorial Optimization

There are several approaches for solving hard optimization problems. Mathematical programming techniques such as (integer) linear programming-based methods and metaheuristic approaches are two extremely effective streams for combinatorial problems. Different research streams, more or less in isolation from one another, created these two. Only several years ago, many scholars noticed the advantages and enormous potential of building hybrids of combining mathematical programming methodologies and metaheuristics. In reality, many problems can be solved much better by exploiting synergies between these approaches than by “pure” classical algorithms. The key question is how to integrate mathematical programming methods and metaheuristics to achieve such benefits. This paper reviews existing techniques for such combinations and provides examples of using them for vehicle routing problems