An Effective Metaheuristic for Multiple Traveling Repairman Problem with Distance Constraints

Multiple Traveling Repairman Problem with Distance Constraints (MTRPD) is an extension of the NP-hard Multiple Traveling Repairman Problem. In MTRPD, a fleet of identical vehicles is dispatched to serve a set of customers with the following constraints. First, each vehicle's travel distance is limited by a threshold. Second, each customer must be visited exactly once. Our goal is to find the visiting order that minimizes the sum of waiting times. To solve MTRPD we propose to combine the Insertion Heuristic (IH), Variable Neighborhood Search (VNS), and Tabu Search (TS) algorithms into an effective two-phase metaheuristic that includes a construction phase and an improvement phase. In the former phase, IH is used to create an initial solution. In the latter phase, we use VNS to generate various neighborhoods, while TS is employed to mainly prohibit from getting trapped into cycles. By doing so, our algorithm can support the search to escape local optima. In addition, we introduce a novel neighborhoods’ structure and a constant time operation which are efficient for calculating the cost of each neighboring solution. To show the efficiency of our proposed metaheuristic algorithm, we extensively experiment on benchmark instances. The results show that our algorithm can find the optimal solutions for all instances with up to 50 vertices in a fraction of seconds. Moreover, for instances from 60 to 80 vertices, almost all found solutions fall into the range of 0.9 %-1.1 % of the optimal solutions' lower bounds in a reasonable duration. For instances with a larger number of vertices, the algorithm reaches good-quality solutions fast. Moreover, in a comparison to the state-of-the-art metaheuristics, our proposed algorithm can find better solutions

Minimizing total weighted latency in home healthcare routing and scheduling with patient prioritization

We study a home healthcare routing and scheduling problem, where multiple healthcare service provider teams should visit a given set of patients at their homes. The problem involves assigning each patient to a team and generating the routes of the teams such that each patient is visited once. When patients are prioritized according to the severity of their condition or their service urgency, the problem minimizes the total weighted waiting time of the patients, where the weights represent the triage levels. In this form, the problem generalizes the multiple traveling repairman problem. To obtain optimal solutions for small to moderate-size instances, we propose a level-based Integer Programming (IP) model on a transformed input network. To solve larger instances, we develop a metaheuristic algorithm that relies on a customized saving procedure and a General Variable Neighborhood Search algorithm. We evaluate the IP model and the metaheuristic on various small, medium, and large-sized instances coming from the vehicle routing literature. While the IP model finds the optimal solutions to all the small and medium-sized instances within three hours of run time, the metaheuristic algorithm achieves the optimal solutions to all instances within merely a few seconds. We also provide a case study involving Covid-19 patients in a district of Istanbul and derive insights for the planners by means of several analyses

The cumulative capacitated vehicle routing problem with min-sum and min-max objectives: An effective hybridisation of adaptive variable neighbourhood search and large neighbourhood search

The cumulative capacitated vehicle routing problem (CCVRP) is a relatively new variant of the classical capacitated vehicle routing problem in which the objective is to minimise the sum of arrival times at customers (min-sum) instead of the total route distance. While the literature for the CCVRP is scarce, this problem has useful applications especially in the area of supplying humanitarian aid after a natural disaster. In this paper, a two-stage adaptive variable neighbourhood search (AVNS) algorithm that incorporates large neighbourhood search (LNS) as a diversification strategy is proposed. When tested on the benchmark data sets, the results show that the proposed AVNS is highly competitive in producing new best known solutions to more than half of the instances. An alternative but related objective that minimises the maximum arrival time (min-max) is also explored in this study demonstrating the flexibility and the effectiveness of the proposed metaheuristic. To the best of our knowledge, this is the first study that exploits the min-max objective of the CCVRP in addition to providing extensive computational results for a large number of instances for the min-sum. As a by-product of this study, managerial insights for decision making are also presented

Distributed task allocation optimisation techniques in multi-agent systems

A multi-agent system consists of a number of agents, which may include software agents, robots, or even humans, in some application environment. Multi-robot systems are increasingly being employed to complete jobs and missions in various fields including search and rescue, space and underwater exploration, support in healthcare facilities, surveillance and target tracking, product manufacturing, pick-up and delivery, and logistics. Multi-agent task allocation is a complex problem compounded by various constraints such as deadlines, agent capabilities, and communication delays. In high-stake real-time environments, such as rescue missions, it is difficult to predict in advance what the requirements of the mission will be, what resources will be available, and how to optimally employ such resources. Yet, a fast response and speedy execution are critical to the outcome. This thesis proposes distributed optimisation techniques to tackle the following questions: how to maximise the number of assigned tasks in time restricted environments with limited resources; how to reach consensus on an execution plan across many agents, within a reasonable time-frame; and how to maintain robustness and optimality when factors change, e.g. the number of agents changes. Three novel approaches are proposed to address each of these questions. A novel algorithm is proposed to reassign tasks and free resources that allow the completion of more tasks. The introduction of a rank-based system for conflict resolution is shown to reduce the time for the agents to reach consensus while maintaining equal number of allocations. Finally, this thesis proposes an adaptive data-driven algorithm to learn optimal strategies from experience in different scenarios, and to enable individual agents to adapt their strategy during execution. A simulated rescue scenario is used to demonstrate the performance of the proposed methods compared with existing baseline methods

Constraint Programming-Based Heuristics for the Multi-Depot Vehicle Routing Problem with a Rolling Planning Horizon

Der Transportmarkt ist sowohl durch einem intensiven Kostenwettbewerb als auch durch hohe Erwartungen der Kunden an den Service geprägt. Die vorliegende Dissertation stellt zwei auf Constraint Programming basierende heuristische Frameworks vor, die eine Reoptimierung bereits geplanter Touren zu festgelegten Zeitpunkten erlauben und so eine Reaktion auf die gesteigerte Wettbewerbsdynamik und den Kostendruck ermöglichen.Actors on the transportation market currently face two contrary trends: Cost pressure caused by intense competition and a need for prompt service. We introduce two heuristic solution frameworks to enable freight carriers to deal with this situation by reoptimizing tours at predefined points in time. Both heuristics are based on Constraint Programming techniques