We consider the vehicle routing problem with stochastic demands (VRPSD). We give randomized approximation algorithms achieving approximation guarantees of 1 + for split-delivery VRPSD, and 2 + for unsplit-delivery VRPSD; here  is the best approximation guarantee for the traveling salesman problem. These bounds match the best known for even the respective deterministic problems [Altinkemer, K...

We present an end-to-end framework for solving Vehicle Routing Problem (VRP) using deep reinforcement learning. In this approach, we train a single model that finds near-optimal solutions for problem instances sampled from a given distribution, only by observing the reward signals and following feasibility rules. Our model represents a parameterized stochastic policy, and by applying a policy g...

The problem of designing a set of routes with minimum cost to serve a collection of customers with a fleet of vehicles is a fundamental challenge when the number of customers to be dropped or picked up is not known during the planning horizon. The purpose of this paper is to develop a vehicle routing Problem (VRP) model that addresses stochastic simultaneous pickup and delivery in the urban pub...

The objective of the Vehicle Routing Problem (VRP) is to construct a minimum cost set of vehicle routes that visits all customers and satisfies demands without violating the vehicle capacity constraints. The Stochastic Vehicle Routing Problem (SVRP) results when one or more elements of the VRP are modeled as random variables. In this paper, we present a set-partitioning-based modeling framework...

Vehicle-routing problems (VRP), which can be considered a generalization of TSP, have been studied in depth. Many variants of the problem exist, most of them trying to find a set of routes with the shortest distance or time possible for a fleet of vehicles. This paper combines two important variants, the stochastic time-dependent VRP and the multi-objective VRP. A genetic algorithm for solving ...

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 ...

In this paper the classical Vehicle Routing Problem (VRP) is extended to cover the more realistic case of uncertainty about customer demands. This case is modelled as a VRP with stochastic demands and tackled with a heuristic solution approach based on Ant Colony Optimization (ACO). The main issues studied in this paper are the modelling of the uncertainty (i) in terms of its influence on the p...

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...

in this paper, a stochastic multi-depot multi-objective vehicle routing problem (vrp) is studied. based on observations in real-world problems, we develop an aspect of the problem, such as stochastic availability of routes. to solve the problem in this situation, a two-objective mathematical model is developed, in which the related objective functions are: (1) minimizing transportation costs an...