Budgeted Prize-Collecting Traveling Salesman and Minimum Spanning Tree Problems

Paul, Alice; Freund, Daniel; Ferber, Aaron; Shmoys, David B.; Williamson, David P.

doi:10.1287/moor.2019.1002

Cited by 27 publications

(17 citation statements)

References 19 publications

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“…2) show that this postprocessing almost always yields improvements, sometimes by a significant factor, on both the TSPLIB and the Citi Bike data sets. (This is despite the fact that our worst-case analysis only shows that the algorithm that tries all possible guesses for w is a 4-approximation for the rooted case, whereas the algorithm in [19] is a 2-approximation.) The results are summarized in Figure 2…”

Section: Cycle Orienteering Experimentsmentioning

confidence: 84%

“…It is pertinent to compare our results with Paul et al [19], which is the only other work that performs a computational evaluation of a (polytime) approximation algorithm for orienteering. They develop a 2approximation algorithm for cycle orienteering (which they call budgeted prize-collecting TSP), and run computational experiments on two types of datasets: 1) 37 metric TSPLIB instances with at most 400 nodes, each having unit reward; and 2) 37 instances constructed from different weeks of usage of the Citi Bike network of bike sharing stations in New York City, where node rewards correspond to an estimate of the number of broken docks at that station during the week.…”

Section: Cycle Orienteering Experimentsmentioning

confidence: 98%

“…Instead of this, we considered running our algorithms in combination to see if this yields improved solutions for the underlying instances. In particular, we run our algorithm as a fast postprocessing step: we pick an arbitrary node on the solution output by the algorithm in [19] as the root node r, and (in the same spirit) pick the node furthest from r on their solution as our guess w of the furthest node. Our results (see Fig.…”

Section: Cycle Orienteering Experimentsmentioning

confidence: 99%

“…We have omitted one instance each from the TSPLIB and Citi Bike datasets in[19], where our algorithm yields an improvement by a factor exceeding 2. This would seemingly contradict the 2-approximation guarantee of[19], but the discrepancy arises because the implementation in[19] is slightly different from their 2-approximation algorithm[18].…”

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confidence: 99%

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Combinatorial Algorithms for Rooted Prize-Collecting Walks and Applications to Orienteering and Minimum-Latency Problems

Dezfuli¹,

Friggstad²,

Post³

et al. 2021

Preprint

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We consider the rooted prize-collecting walks (PCW) problem, wherein we seek a collection C of rooted walks having minimum prize-collecting cost, which is the (total cost of walks in C) + (total nodereward of the nodes not visited by any walk in C). This problem arises naturally as the Lagrangian relaxation of both orienteering, where we seek a length-bounded walk of maximum reward, and the ℓstroll problem, where we seek a minimum-length walk covering at least ℓ nodes. Our main contribution is to devise a simple, combinatorial algorithm for the PCW problem that returns a rooted tree whose prize-collecting cost is at most the optimum value of the prize-collecting walks problem. This result applies to both directed and undirected graphs, and holds for arbitrary nonnegative edge costs.We present two applications of our result, where we utilize our algorithm to develop combinatorial approximation algorithms for two fundamental vehicle-routing problems (VRPs): (1) orienteering; and(2) k-minimum-latency problem (k-MLP), wherein we seek to cover all nodes using k paths starting at a prescribed root node, so as to minimize the sum of the node visiting times. Our combinatorial algorithm allows us to sidestep the part where we solve a preflow-based LP in the LP-rounding algorithms of [14] for orienteering, and in the state-of-the-art 7.183-approximation algorithm for k-MLP in [20]. Consequently, we obtain combinatorial implementations of these algorithms (with the same approximation factors). Compared to algorithms that achieve the current-best approximation factors for orienteering and k-MLP, our algorithms have substantially improved running time, and achieve approximation guarantees that match (k-MLP), or are slightly worse (orienteering) than the current-best approximation factors for these problems.We report various computational results for our resulting (combinatorial implementations of) orienteering algorithms, which show that the algorithms perform quite well in practice, both in terms of the quality of the solution they return, as also the upper bound they yield on the orienteering optimum (which is obtained by leveraging the workings of our PCW algorithm).

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Section: Cycle Orienteering Experimentsmentioning

confidence: 84%

Section: Cycle Orienteering Experimentsmentioning

confidence: 98%

Section: Cycle Orienteering Experimentsmentioning

confidence: 99%

mentioning

confidence: 99%

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Combinatorial Algorithms for Rooted Prize-Collecting Walks and Applications to Orienteering and Minimum-Latency Problems

Dezfuli¹,

Friggstad²,

Post³

et al. 2021

Preprint

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show abstract

“…The reader may notice that some literature (for example, [13,10,38,42]) mention the result of Feigenbaum et al [16] as an inapproximability result for the undirected prize-collecting Steiner tree problem. Although not explicitly mentioned by Feigenbaum et al [16], their gadget can be easily updated to work on undirected graphs [41].…”

Section: Dual Separationmentioning

confidence: 99%

On the Request-Trip-Vehicle Assignment Problem

Mori¹,

Samaranayake²

2021

SIAM Conference on Applied and Computational Discrete Algorithms (ACDA21)

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The request-trip-vehicle assignment problem is at the heart of a popular decomposition strategy for online vehicle routing. In this framework, assignments are done in batches in order to exploit any shareability among vehicles and incoming travel requests. We study a natural ILP formulation and its LP relaxation. Our main result is an LP-based randomized rounding algorithm that, whenever the instance is feasible, leverages mild assumptions to return an assignment whose: i) expected cost is at most that of an optimal solution, and ii) expected fraction of unassigned requests is at most 1/e. If trip-vehicle assignment costs are α-approximate, we pay an additional factor of α in the expected cost. We can relax the feasibility requirement by considering the penalty version of the problem, in which a penalty is paid for each unassigned request. We find that, whenever a request is repeatedly unassigned after a number of rounds, with high probability it is so in accordance with the sequence of LP solutions and not because of a rounding error. We additionally introduce a deterministic rounding heuristic inspired by our randomized technique. Our computational experiments show that our rounding algorithms achieve a performance similar to that of the ILP at a reduced computation time, far improving on our theoretical guarantee. The reason for this is that, although the assignment problem is hard in theory, the natural LP relaxation tends to be very tight in practice.

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Hybrid genetic algorithm for undirected traveling salesman problems with profits

Hao

2023

Networks

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The orienteering problem (OP) and prize‐collecting traveling salesman problem (PCTSP) are two typical TSPs with profits, in which each vertex has a profit and the goal is to visit several vertices to optimize the collected profit and travel costs. The OP aims to collect the maximum profit without exceeding the given travel cost. The PCTSP seeks to minimize the travel costs while ensuring a minimum profit threshold. This study introduces a hybrid genetic algorithm that addresses both the OP and PCTSP under a unified framework. The algorithm combines an extended edge‐assembly crossover operator to produce promising offspring solutions, and an effective local search to ameliorate each offspring solution. The algorithm is further enforced by diversification‐oriented mutation and population‐diversity management. Extensive experiments demonstrate that the method competes favorably with the best existing methods in terms of both the solution quality and computational efficiency. Additional experiments provide insights into the roles of the key components of the proposed method.

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Budgeted Prize-Collecting Traveling Salesman and Minimum Spanning Tree Problems

Cited by 27 publications

References 19 publications

Combinatorial Algorithms for Rooted Prize-Collecting Walks and Applications to Orienteering and Minimum-Latency Problems

Combinatorial Algorithms for Rooted Prize-Collecting Walks and Applications to Orienteering and Minimum-Latency Problems

On the Request-Trip-Vehicle Assignment Problem

Hybrid genetic algorithm for undirected traveling salesman problems with profits

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