In this article we introduce the Quadratic Capacitated Vehicle Routing Problem (QCVRP), a combinatorial optimization problem that arises in practical applications in logistics and transportation. The QCVRP extends two other known problems, the Capacitated Vehicle Routing Problem (CVRP) and the Quadratic Symmetric Traveling Salesman Problem (QSTSP), the former by considering a modified cost matr...

The Capacitated Vehicle Routing Problem (CVRP) is a combinatorial optimization problem where a fleet of delivery vehicles must service known customer demands from a common depot at a minimum transit cost without exceeding the capacity constraint of each vehicle. In this paper, we present a meta-heuristic approach for solving the CVRP based on simulated annealing. The algorithm uses a combinatio...

This paper considers a capacitated vehicle routing problem with fuzzy random travel time and demand (FRVRP). A chance-constrained multiobjective programming is presented based on fuzzy random theory and converted to a crisp equivalent models under some assumptions. To solve such a multiobjective combinatorial optimization problem, this paper presents a hybrid multiobjective particle swarm optim...

The capacitated vehicle routing problem (CVRP) is an interesting combinatorial optimization task, which occurs frequently in real-world applications [28]. The problem deals with scheduling a fleet of vehicles to distribute goods between depots and customers. A set of routes for vehicles should be determined, which are in some sense optimal, e.g. the shortest or the cheapest. Certain constraints...

The Capacitated Clustering Problem (CCP) partitions a set of n items (eg. customer orders) into k disjoint clusters with known capacity. During clustering the items with shortest assigning paths from centroids are grouped together. The summation of grouped items should not exceed the capacity of cluster. All clusters have uniform capacity. The CCP is NP-Complete and Combinatorial optimization p...

The split delivery vehicle routing problem is concerned with serving the demand of a set of customers with a fleet of capacitated vehicles at minimum cost. A customer, contrary to what is assumed in the classical vehicle routing problem, can be served by more than one vehicle, if convenient. We present a solution approach that integrates heuristic search with optimization by using an integer pr...

The vehicle routing problem with simultaneous pickup and delivery (VRPSPD) is a well-known combinatorial optimization problem which addresses provided service to a set of customers using a homogeneous fleet of capacitated vehicles. The objective is to minimize the distance traveled. The VRPSPD is an NP-hard combinatorial optimization problem. Therefore, practical large-scale instances of VRPSPD...

In this paper, we have conducted a literature review on the recent developments and publications involving the vehicle routing problem and its variants, namely vehicle routing problem with time windows (VRPTW) and the capacitated vehicle routing problem (CVRP) and also their variants. The VRP is classified as an NP-hard problem. Hence, the use of exact optimization methods may be difficult to s...

using greedy clustering method to solve capacitated location-routing problem with fuzzy demands abstract in this paper, the capacitated location routing problem with fuzzy demands (clrp_fd) is considered. in clrp_fd, facility location problem (flp) and vehicle routing problem (vrp) are observed simultaneously. indeed the vehicles and the depots have a predefined capacity to serve the customerst...

Combinatorial optimization problems are typically NP-hard, and thus very challenging to solve. In this paper, we present the random key cuckoo search (RKCS) algorithm for solving the famous Travelling Salesman Problem (TSP). We used a simplified random-key encoding scheme to pass from a continuous space (real numbers) to a combinatorial space. We also consider the displacement of a solution in ...