  The static bike rebalancing problem (SBRP) concerns the task of repositioning
bikes among stations in self-service bike-sharing systems. This problem can be
seen as a variant of the one-commodity pickup and delivery vehicle routing
problem, where multiple visits are allowed to be performed at each station,
i.e., the demand of a station is allowed to be split. Moreover, a vehicle may
temporarily drop its load at a station, leaving it in excess or, alternatively,
collect more bikes from a station (even all of them), thus leaving it in
default. Both cases require further visits in order to meet the actual demands
of such station. This paper deals with a particular case of the SBRP, in which
only a single vehicle is available and the objective is to find a least-cost
route that meets the demand of all stations and does not violate the minimum
(zero) and maximum (vehicle capacity) load limits along the tour. Therefore,
the number of bikes to be collected or delivered at each station should be
appropriately determined in order to respect such constraints. We propose an
iterated local search (ILS) based heuristic to solve the problem. The ILS
algorithm was tested on 980 benchmark instances from the literature and the
results obtained are quite competitive when compared to other existing methods.
Moreover, our heuristic was capable of finding most of the known optimal
solutions and also of improving the results on a number of open instances.
