Efficient Metaheuristics for the Mixed Team Orienteering Problem with Time Windows

Abstract

Given a graph whose nodes and edges are associated with a profit, a visiting (or traversing) time and an admittance time window, the Mixed Team Orienteering Problem with Time Windows (MTOPTW) seeks for a specific number of walks spanning a subset of nodes and edges of the graph so as to maximize the overall collected profit. The visit of the included nodes and edges should take place within their respective time window and the overall duration of each walk should be below a certain threshold. In this paper we introduce the MTOPTW, which can be used for modeling a realistic variant of the Tourist Trip Design Problem where the objective is the derivation of near-optimal multiple-day itineraries for tourists visiting a destination which features several points of interest (POIs) and scenic routes. Since the MTOPTW is a NP-hard problem, we propose the first metaheuristic approaches to tackle it. The effectiveness of our algorithms is validated through a number of experiments on POI and scenic route sets compiled from the city of Athens (Greece).

Optimizing practical orienteering problems with stochastic time-dependent travel times: towards congestion free routes

“…The most recent work is from Gavalas et al [55] and Gavalas et al [56]. Actually, this work was published after we published our research on the TD-OP [151], which we will discuss in Chapter 4.…”

“…These problems are called tourist trip design problems. Apart from our own research [152], this problem was studied by [53,56,118,124,126,[148][149][150]155]. Gavalas et al [54] present the most recent survey on algorithmic approaches for this class of problems.…”

“…The time-dependent variant of the OP is relatively new and has, to the best of our knowledge, only been studied in [1,48,53,55,56,89,90]. Fomin and Lingas [48] were the first authors to mention the TD-OP and state that it is NP-hard because the OP is NP-hard.…”

User Transition Pattern Analysis for Travel Route Recommendation

“…(19), the reward function R(p j |p i ) now includes both nodes and edges of the POI graph, which leads the objective function Eq. (1) to be a mixed orienteering problem (MOP) [6]. Although this is quite different from the original OP, it can still be treated as a mixed integer linear problem, which can be solved by optimization tools such as Gurobi † or lp solve † † .…”

“…Therefore, we extract transition patterns from users' travel route data and use them to compute rewards on edges. This changes the OP to a mixed orienteering problem (MOP) [6]: both nodes and edges are assigned rewards. We recommend travel routes by solving this MOP, aiming to maximize the total reward from both nodes and edges.…”