Abstract
AbstractThis paper deals with planning of a tour for a vehicle to clear a certain set of streets in a city of snow. Our previous results on the problem contain a heuristic based on reformulation to an asymmetric traveling salesman problem (ATSP) which yields feasible solutions and upper bounds, and a relaxation of a MIP model for obtaining lower bounds. The goal now is to try to improve the solutions and bounds. In this paper we describe a branch‐and‐dive heuristic which is based on branch‐and‐bound principles. We discuss how branching can be done so that the fixations can be utilized in both the relaxation and the ATSP model, and how the search for better solutions can be done. The heuristic has been implemented and applied to real life city networks. The method is shown to outperform two other heuristics for the ATSP with precedence constraints.
Highlights
Snow removal is an important problem in Nordic countries
After the construction of GT the problem is an asymmetric traveling salesman problem (ATSP) with precedences, and we have compared our method to two methods for that problem, namely an adaptive evolutionary algorithm described in [27], and an ant colony hybrid method including a new local search method, SOP3, described in [8], both claimed to be better than other methods at the time of publication
We have constructed a branch-and-dive heuristic based on branch-and-bound principles, for the problem of finding the best tour for one snow removal vehicle
Summary
Snow removal is an important problem in Nordic countries. In Figure 1 the maximal snow depth (December to April) in Stockholm (Observatorielunden) is given for each year from 1904 to 2018, and the large variation is evident. The horizontal line is the average, and the slightly sloping horizontal line is the linear trend.) The total costs for snow removal in the city of Stockholm for each year from 2008 to 2013 (as reported by Stockholm Stad) were 130, 146, 265, 238, 224, and 192 million SEK (10 SEK ≈ 1 Euro) Note that this is only for one city, not the whole country, and that Stockholm is not situated in the northern parts of Sweden, where there is much more snow. We consider the optimization of the snow removal tour facing a single vehicle (a single snow remover) This means that the relevant size of an area to be covered is decreased even more, since the total area of a contractor is usually divided up between the vehicles.
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