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

Metaheuristic for Solving the Delivery Man Problem with Drone

Delivery Man Problem with Drone (DMPD) is a variant of Delivery Man Problem (DMP). The objective of DMP is to minimize the sum of customers' waiting times. In DMP, there is only a truck to deliver materials to customers while the delivery is completed by collaboration between truck and drone in DMPD. Using a drone is useful when a truck cannot reach some customers in particular circumstances such as narrow roads or natural disasters. For NP-hard problems, metaheuristic is a natural approach to solve medium to large-sized instances. In this paper, a metaheuristic algorithm is proposed. Initially, a solution without drone is created. Then, it is an input of split procedure to convert DMP-solution into DMPD-solution. After that, it is improved by the combination of Variable Neighborhood Search (VNS) and Tabu Search (TS). To explore a new solution space, diversification is applied. The proposed algorithm balances diversification and intensification to prevent the search from local optima. The experimental simulations show that the proposed algorithm reaches good solutions fast, even for large instances

The multi-depot k-traveling repairman problem

In this paper, we study the multi-depot k-traveling repairman problem. This problem extends the traditional traveling repairman problem to the multi-depot case. Its objective, similar to the single depot variant, is the minimization of the sum of the arrival times to customers. We propose two distinct formulations to model the problem, obtained on layered graphs. In order to find feasible solutions for the largest instances, we propose a hybrid genetic algorithm where initial solutions are built using a splitting heuristic and a local search is embedded into the genetic algorithm. The efficiency of the mathematical formulations and of the solution approach are investigated through computational experiments. The proposed models are scalable enough to solve instances up to 240 customers

Efficient GRASP+VND and GRASP+VNS metaheuristics for the traveling repairman problem

The traveling repairman problem is a customer-centric routing problem, in which the total waiting time of the customers is minimized, rather than the total travel time of a vehicle. To date, research on this problem has focused on exact algorithms and approximation methods. This paper presents the first metaheuristic approach for the traveling repairman problem

Applied (Meta)-Heuristic in Intelligent Systems

Engineering and business problems are becoming increasingly difficult to solve due to the new economics triggered by big data, artificial intelligence, and the internet of things. Exact algorithms and heuristics are insufficient for solving such large and unstructured problems; instead, metaheuristic algorithms have emerged as the prevailing methods. A generic metaheuristic framework guides the course of search trajectories beyond local optimality, thus overcoming the limitations of traditional computation methods. The application of modern metaheuristics ranges from unmanned aerial and ground surface vehicles, unmanned factories, resource-constrained production, and humanoids to green logistics, renewable energy, circular economy, agricultural technology, environmental protection, finance technology, and the entertainment industry. This Special Issue presents high-quality papers proposing modern metaheuristics in intelligent systems

Hybrid Metaheuristics for the Clustered Vehicle Routing Problem

The Clustered Vehicle Routing Problem (CluVRP) is a variant of the Capacitated Vehicle Routing Problem in which customers are grouped into clusters. Each cluster has to be visited once, and a vehicle entering a cluster cannot leave it until all customers have been visited. This article presents two alternative hybrid metaheuristic algorithms for the CluVRP. The first algorithm is based on an Iterated Local Search algorithm, in which only feasible solutions are explored and problem-specific local search moves are utilized. The second algorithm is a Hybrid Genetic Search, for which the shortest Hamiltonian path between each pair of vertices within each cluster should be precomputed. Using this information, a sequence of clusters can be used as a solution representation and large neighborhoods can be efficiently explored by means of bi-directional dynamic programming, sequence concatenations, by using appropriate data structures. Extensive computational experiments are performed on benchmark instances from the literature, as well as new large scale ones. Recommendations on promising algorithm choices are provided relatively to average cluster size.Comment: Working Paper, MIT -- 22 page