Heuristics for a vehicle routing problem with information collection in wireless networks

Abstract

We consider a wireless network where a given set of stations is continuously generating information. A single vehicle, located at a base station, is available to collect the information via wireless transfer. The wireless transfer vehicle routing problem (WTVRP) is to decide which stations should be visited in the vehicle route, how long shall the vehicle stay in each station, and how much information shall be transferred from the nearby stations to the vehicle during each stay. The goal is to collect the maximum amount of information during a time period after which the vehicle returns to the base station. The WTVRP is NP-hard. Although it can be solved to optimality for small size instances, one needs to rely on good heuristic schemes to obtain good solutions for large size instances. In this work, we consider a mathematical formulation based on the vehicle visits. Several heuristics strategies are proposed, most of them based on the mathematical model. These strategies include constructive and improvement heuristics. Computational experiments show that a strategy that combines a combinatorial greedy heuristic to design a initial vehicle route, improved by a fix-and-optimize heuristic to provide a local optimum, followed by an exchange heuristic, affords good solutions within reasonable amount of running time.

Mixed integer formulations for a routing problem with information collection in wireless networks

“…To the best of our knowledge, the authors in [8] and [22] are the only ones to study the design of a vehicle route from scratch together with a wireless transmission planning.…”

“…The problem treated in [22] is a very close version of the VRP addressed in the present work: all but one assumption are the same. In [22] it is assumed that, once a station starts a transmission to the vehicle, all information accumulated in this station at that moment must be transmitted. This assumption is justified in situations where information is safer once it leaves the stations.…”

“…In our problem, transmission of partial information is allowed. Three different strategies adopted in the vehicle routing problem were investigated in [22]: maximizing the total amount of information extracted at the end of the time horizon T ; maximizing the average of the information in the vehicle at each time point; and maximizing the satisfaction of each station at the end of the time horizon T . A MILP formulation was introduced with three different objective functions being discussed.…”

“…The authors presented computational experiments on randomly generated networks with up to 15 stations (|T | ∈ {24, 28}), solved in one hour of computation time 1 . The results discussed in [22] showed the problem becomes more difficult as the total amount of information collected increases. The periodicity on remaining information at the stations (after a sequence of vehicle routings is solved) was studied for each strategy.…”

“…For the example depicted in Figure 1, Range(5) = {4, 7}. We make the same physical and technical assumptions as in [22]. Thus, we assume transmission speed inversely proportional to the square of the distance between nodes depending on two additional factors: the amount of information transmitted and physical factors (as equipments used or obstacles between nodes).…”