Cooperative receding horizon strategies for the multivehicle routing problem

Abstract

SummaryThis paper deals with the dynamic Euclidean Multivehicle Routing Problem (MVRP) in both deterministic and uncertain scenarios. The objective of MVRP is to find the best paths for a fleet of vehicles that are cooperative to visit a set of targets. Based on the cooperative receding horizon (CRH) approach proposed in some previous works, which is vehicle-oriented, in this paper, we consider a target-oriented CRH, named tCRH, and then we propose a switching scheme, named sCRH, which is able to dynamically adjust the vehicle behaviors according to the time-varying configuration of both vehicles and targets, as well as to handle the situation with the appearance of unknown targets. The proposed sCRH counteracts the oscillation problem of CRH and improves the overall routing performances by adopting the advantages of both CRH and tCRH approach. Convergence results and simulation results are provided to validate the proposed approach.KEYWORDS cooperative control, multivehicle routing, receding horizon control | INTRODUCTIONVehicle Routing Problem (VRP) is a generalization of the classical Travel Salesman Problem, and it consists of finding the optimal (or near-optimal) path for a vehicle to visit a set of locations. If the distance between 2 locations is the Euclidean distance, the problem is referred as Euclidean VRP. The VRP was first studied by Dantzig and Ramser, 1 and it is still a topic of research now because of the intrinsic hard combinatorial nature. Recent developments in computer technology and wireless communications opened numerous possibilities for lining up networks of mobile vehicles capable of interacting with the environment to accomplish specific objectives. The multiple vehicles are also capable of cooperating with each other to complete the mission. In this paper, we consider M-vehicles operating in a limited two-dimensional space and traveling to visit a set of N targets. Each target is assigned with a value representing the reward of visiting that target. This mission is characterized by the process of visiting all the targets with the available set of vehicles, and the goal is to accomplish the mission as well as to collect the maximum reward. This is the so-called Multivehicle Routing Problem (MVRP), and we will deal with the dynamic Euclidean MVRP in both deterministic and uncertain scenarios in this paper.The MVRP is a complex combinatorial problem where an exact solution is computationally expensive, and it is inapt to solve the problem online. Several algorithms to solve MVRP problems were proposed in the literature (see the recent survey 2 and references therein). Dynamic and deterministic routing problems have been solved by using exact (eg, Baldacci et al and Robert 3,4 ) or approximated methods (eg, Hsueh et al 5 ); dynamic and stochastic routing problems have been solved by using heuristic technique (eg, references herein 6-11 ) or by using partitioning policies, as in Yao et al,12 where the optimality guarantees in light-and heavy-load conditions were proved. Most algorithms pro...

Receding horizon path planning of automated guided vehicles using a time‐space network model

“…In principle, RHP utilizes a dynamical model to obtain planned routes by minimizing an objective over a finite receding horizon 23 . A similar methodology, which is referred to as receding horizon control, has been successfully used in the industrial process and transportation 24,25 .…”