in this paper, we study the multi-depot vehiclerouting problem with inter-depot routes, in which the vehicles can replenish atintermediate depots. vehicles leave the origin depot with load on-board andserve customers until out of load. they may visit an intermediate depot toreplenish and finally return to the origin depot, completing their route. weinitiate a mathematical mixed integer programm...

Reinforcement learning has recently shown promise in quality solutions many combinatorial optimization problems. In particular, the attention-based encoder-decoder models show high effectiveness on various routing problems, including Traveling Salesman Problem (TSP). Unfortunately, they perform poorly for TSP with Drone (TSP-D), requiring a heterogeneous fleet of vehicles coordination—a truck a...

An optimal evacuation route plan has to be established to overcome the problem of poor coordination and uneven distribution of vehicles before or during disaster. This article introduces the evacuation vehicle routing problem (EVRP) as a new variant to the vehicle routing problem (VRP). EVRP is a process of moving vehicles from a vehicle location to the potentially flooded area (PFA), and from ...

Vehicle Routing Problem (VRP) has become an integral part in logistic operations which determines optimal routes for several vehicles to serve customers. The basic version of VRP is Capacitated VRP (CVRP) which considers equal capacities for all vehicles. The objective of CVRP is to minimize the total traveling distance of all vehicles to serve all the customers. Various methods are used to sol...

This paper aims to compare a two-echelon and a single-echelon distribution system. A mathematical model for the Single-Echelon Capacitated Vehicle Routing Problem (SE-CVRP) is proposed. This SE-CVRP is the counterpart of Two-Echelon Capacitated Vehicle Routing Problem (2E-CVRP) introduced in the authors’ previous work. The proposed mathematical model is Mixed-Integer Non-Linear Programming (MIN...

Classical combinatorial optimization problems can be generalized in a natural way by considering a related problem relative to a given partition of the nodes of the graph into node sets. In the literature one can find generalized problems such as: generalized minimum spanning tree, generalized traveling salesman problem, generalized Steiner tree problem, generalized vehicle routing problem, etc...

Vehicle routing problems are a class of NP-hard combinatorial optimization which attract lot attention, as they have many practical applications. In recent years there been new developments solving vehicle with the help machine learning, since learning how to automatically solve has potential provide big leap in technology. Prior work on using mainly focused auto-regressive models, connected hi...

The vehicle routing problem (VRP), a well-known combinatorial optimization problem, holds a central place in logistics management. Many meta-heuristic approaches like Simulated Annealing (SA), Genetic Algorithms (GA), Tabu Search (TS), and Ant Colony Optimization (ACO) have been proposed to solve VRP. Ant Algorithm is a distributed meta-heuristic approach that has been applied to various combin...

One of the motivations of hyper-heuristic research is to investigate the development of adaptive decision support systems that can be applied to a range of different problems and different problem instances [5]. One possible approach is to dynamically adjust the preferences of a set of simple lowlevel heuristics (or neighbourhood operators) during the search. Hyper-heuristics have been used to ...

The Capacitated Arc Routing Problem (CARP) is a well-known NP-hard combinatorial optimization problem where, given an undirected graph, the objective is to find a minimum cost set of tours servicing a subset of required edges under vehicle capacity constraints. There are numerous applications for the CARP, such as street sweeping, garbage collection, mail delivery, school bus routing, and meter...