An application of the greedy heuristic of set cover to traffic checks

Abstract

Set cover, Greedy heuristic, Traffic checks, Traffic assignment, Shortest paths,

Empirical study of the greedy heuristic as applied to the link selection problem

“…The checking process is realized in such way that it does not change the flow of traffic. A greedy heuristic was applied to solve a large size problem, but the qualification of this heuristic was demonstrated only on small (10 loaded links) networks [6]. The optimal solution of the link selection problem can be calculated with binary integer programming models as well.…”

“…The link selection problem has got two similar but slightly different optimization tasks. We define the problem and its heuristic more generally than it was described in [6].…”

“…In the first case the weights were the demands of travel and in the second case the weights were calculated by the demands of travel multiplied by the lengths of the paths (that resulted larger weights and larger differences between them). In the first case the weights give the traffic (see Traffic data in the figures) and in the second With using traffic performance we prefer to check those vehicles that travel longer distances on the networks (as it has been done in [6]).…”

“…The problem of link selection as an effective traffic check was introduced in [6]. The input data of a real life situation were produced with a traffic assignment model [5], and the problem was solved with an algorithm that is based on the greedy heuristic of set cover [1,2,3].…”