Solving the Orienteering Problem through Branch-and-Cut

Bran h-and-Cut Matteo Fis hetti DEI, University of Padova, 35131 Padova, Italy; Email: s h dei.unipd.it Juan Jos e Salazar Gonz alez DEIOC, University of La Laguna, 38271 Tenerife, Spain; Email: jjsalaza ull.es Paolo Toth DEIS, University of Bologna, 40136 Bologna, Italy; Email: ptoth deis.unibo.it Abstra t In the Orienteering Problem (OP) we are given an undire ted graph with edge weights and node prizes. The problem alls for a simple y le whose total edge weight does not ex eed a given threshold, while visiting a subset of nodes with maximum total prize. This NP-hard problem arises in routing and s heduling appli ations. We des ribe a bran h-andut algorithm for nding an optimal OP solution. The algorithm is based on several families of valid inequalities. We also introdu e a family of uts whi h an ut o the optimal OP solution, alled onditional uts, and propose an e e tive way to use them within the overall bran h-andut framework. Exa t and heuristi separation algorithms are des ribed, as well as heuristi pro edures to produ e near-optimal OP solutions. An extensive omputational analysis on several lasses of both real-world and random instan es is reported. The algorithm proved to be able to solve to optimality large-s ale instan es involving up to 500 nodes, within a eptable omputing time. This ompares favourably with previous published methods.