The time-dependent orienteering problem is dual to the time-dependent traveling salesman problem. It consists of visiting a maximum number of sites within a given deadline. The traveling time between two sites is in general dependent on the starting time. For any ε > 0, we provide a (2 + ε)-approximation algorithm for the time-dependent orienteering problem which runs in polynomial time if the ...

In the last years, a growing number of challenging applications in navigation, logistics, and tourism were modeled as orienteering problems. This problem has been proposed relation to sport race where certain control points must be visited minimal time. kind these competitions, choice order for are left competitor. We propose an original approach solve based on hybrid control. The continuous st...

We consider the rooted orienteering problem: Given a set P of n points in the plane, a starting point r ∈ P , and a length constraint B, one needs to find a path starting from r that visits as many points of P as possible and of length not exceeding B. We present a (1 − ε)-approximation algorithm for this problem that runs in nO(1/ε) time; the computed path visits at least (1 − ε)kopt points of...

Team Orienteering with Decreasing Profits (DP-TOP) extends the classical Team Orienteering problem (TOP) by considering the profit of each client as a decreasing function of time. It consists of maximizing the sum of collected profit by a fixed number K of vehicles, visiting each client at most once. In this work, we present lower bounds based on a Dantzig-Wolfe decomposition and column generat...

We tackle the thief orienteering problem (ThOP), an academic multi-component that combines two classical combinatorial problems, namely Knapsack Problem and Orienteering Problem. In ThOP, a has time limit to steal items distributed in given set of cities. While traveling, collects by storing them their knapsack, which turn reduces travel speed. The as objective maximize total profit stolen item...

The team orienteering problem (TOP) is the generation to the case of multi tours of the Orienteering Problem (OP). A pair of origin and destination is specified and a set of potential customers with profits are provided. A single path’s initial construction which is considered as the main procedure for feasible solution initialization for the TOP is formulated as an integer program, then the BS...