arXiv subjects

Roberto Montemanni

Publications and source records attributed to Roberto Montemanni.

16 recordsLinked to original sources

arXiv2025

On Solving the Shortest Paths with Exclusive-Disjunction Arc Pairs Conflicts

A variant of the well-known Shortest Path Problem is studied in this paper, where pairs of conflicting arcs are provided, and for each conflicting pair a penalty is paid once neither or both of the arcs are selected. This configures a set of soft-constraints. The problem, which can be used to model real applications, looks for a path from a given origin to a given destination that minimizes the cost of the arcs traversed plus the penalties incurred. In this paper, we consider a compact mixed integer linear program representing the problem and we solve it with the open-source solver CP-SAT, part of the Google OR-Tools computational suite. An experimental campaign on the instances available from the literature indicates that the approach we propose achieves results comparable with those of state-of-the-art solvers, notwithstanding it is a compact model, while the other approaches require the generation of dynamic constraints in order for the models to be competitive. Some best-known results have been improved in this study, and some instances have been closed for the first time.

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arXiv2025

On Solving the Knapsack Problem with Conflicts

A variant of the well-known Knapsack Problem is studied in this paper, where pairs of items are conflicting, and cannot be selected at the same time. This configures a set of hard constraints. The problem, which can be used to model real applications, looks for a selection of items such that the total profit is maximized, the capacity of the container is respected, and no conflict is violated. In this paper, we consider a previously known mixed integer linear program representing the problem and we solve it with the open-source solver CP-SAT, part of the Google OR-Tools computational suite. An experimental campaign on the instances available from the literature and adopted in the last decade, indicate that the approach we propose achieves results comparable with, and often better than, those of state-of-the-art solvers, notwithstanding its intrinsic conceptual and implementation simplicity.

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arXiv2025

On Solving the Assignment Problem with Conflicts

A variant of the well-known Assignment Problem is studied in this paper, where pairs of assignments are conflicting, and cannot be selected at the same time. This configures a set of hard constraints. The problem, which models real applications, looks for a complete assignment that minimizes the total cost, while no conflict is violated. In this paper, we consider a previously known mixed integer linear program representing the problem and we solve it with the open-source solver CP-SAT, part of the Google OR-Tools computational suite. An experimental campaign on the instances available from the literature, indicates that the approach we propose achieves results comparable with, those of state-of-the-art solvers, notwithstanding its intrinsic conceptual and implementation simplicity. The solver adopted is also able to provide heuristic solutions quicker and better than the heuristic methods previously discussed in the literature.

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arXiv2025

On Solving the Minimum Spanning Tree Problem with Conflicting Edge Pairs

The Minimum Spanning Tree with Conflicting Edge Pairs is a generalization that adds conflict constraints to a classical optimization problem on graphs used to model several real-world applications. In the last few years several approaches, both heuristic and exact, have been proposed to attack the problem. In this paper we consider a mixed integer linear program never approached before in the context of the problem under investigation, and we solve it with an open-source solver. Computational results on the benchmark instances commonly used in the literature of the problem are reported. The results indicate that the approach we propose, in its simplicity, obtains results aligned with those of the much more sophisticated approaches available. During the experimental campaign 6 instances have been closed for the first time, with 9 improved best-known lower bounds and 16 improved best-known upper bounds over the 230 instances considered.

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arXiv2025

On Solving the Set Covering Problem with Conflicts on Sets

A variant of the well-known Set Covering Problem is studied in this paper, where subsets of a collection have to be selected, and pairwise conflicts among subsets of items exist. The selection of each subset has a cost, and the inclusion of conflicting subsets is associated with a penalty to be paid. The problem, which can be used to model real applications, looks for a selection of subsets that cover the original collection, while minimizing the sum of covering and penalty costs. In this paper we consider a compact mixed integer linear program and we solve it with an open-source solver. Computational results on the benchmark instances commonly used in the literature of the problem are reported. The results indicate that the new approach we propose is capable of good results, both in terms of lower and upper bounds, although not matching the state-of-the-art on average. The new approach was, however, able to improve 9 best-known heuristic solutions.

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arXiv2025

On Solving the Maximum Flow Problem with Conflict Constraints

The Maximum Flow Problem with Conflict Constraints is a generalization that adds conflict constraints to a classical optimization problem on networks used to model several real-world applications. In the last few years several approaches, both heuristic and exact, have been proposed to attack the problem. In this paper we consider a mixed integer linear program and solve it with an open-source solver. Computational results on the benchmark instances commonly used in the literature of the problem are reported. All the 160 instances benchmark instances normally used in the literature are solved to optimality for the first time, with 28 instances closed for the first time. Moreover, in the process, 6 improvements to the best-known heuristic solutions are also found.

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arXiv2023

Parallel drone scheduling vehicle routing problems with collective drones

We study last-mile delivery problems where trucks and drones collaborate to deliver goods to final customers. In particular, we focus on problem settings where either a single truck or a fleet with several homogeneous trucks work in parallel to drones, and drones have the capability of collaborating for delivering missions. This cooperative behaviour of the drones, which are able to connect to each other and work together for some delivery tasks, enhance their potential, since connected drone has increased lifting capabilities and can fly at higher speed, overcoming the main limitations of the setting where the drones can only work independently. In this work, we contribute a Constraint Programming model and a valid inequality for the version of the problem with one truck, namely the \emph{Parallel Drone Scheduling Traveling Salesman Problem with Collective Drones} and we introduce for the first time the variant with multiple trucks, called the \emph{Parallel Drone Scheduling Vehicle Routing Problem with Collective Drones}. For the latter variant, we propose two Constraint Programming models and a Mixed Integer Linear Programming model. An extensive experimental campaign leads to state-of-the-art results for the problem with one truck and some understanding of the presented models' behaviour on the version with multiple trucks. Some insights about future research are finally discussed.

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arXiv2023

Constraint Programming models for the parallel drone scheduling vehicle routing problem

Drones are currently seen as a viable way for improving the distribution of parcels in urban and rural environments, while working in coordination with traditional vehicles like trucks. In this paper we consider the parallel drone scheduling vehicle routing problem, where the service of a set of customers requiring a delivery is split between a fleet of trucks and a fleet of drones. We consider two variations of the problem. In the first one the problem is more theoretical, and the target is the minimization of the time required to complete the service and have all the vehicles back to the depot. In the second variant more realistic constraints involving operating costs, capacity limitation and workload balance, are considered, and the target is to minimize the total operational costs. We propose several constraint programming models to deal with the two problems. An experimental champaign on the instances previously adopted in the literature is presented to validate the new solving methods. The results show that on top of being a viable way to solve problems to optimality, the models can also be used to derive effective heuristic solutions and high-quality lower bounds for the optimal cost, if the execution is interrupted after its natural end.

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arXiv2023

An Ant Colony System for the Team Orienteering Problem with Time Windows

This paper discusses a heuristic approach for Team Orienteering Problems with Time Windows. The method we propose takes advantage of a solution model based on a hierarchic generalization of the original problem, which is combined with an Ant Colony System algorithm. Computational results on benchmark instances previously adopted in the literature suggest that the algorithm we propose is effective in practice.

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arXiv2022

Precedence-Constrained Arborescences

The minimum-cost arborescence problem is a well-studied problem in the area of graph theory, with known polynomial-time algorithms for solving it. Previous literature introduced new variations on the original problem with different objective function and/or constraints. Recently, the Precedence-Constrained Minimum-Cost Arborescence problem was proposed, in which precedence constraints are enforced on pairs of vertices. These constraints prevent the formation of directed paths that violate precedence relationships along the tree. We show that this problem is NP-hard, and we introduce a new scalable mixed integer linear programming model for it. With respect to the previous models, the newly proposed model performs substantially better. This work also introduces a new variation on the minimum-cost arborescence problem with precedence constraints. We show that this new variation is also NP-hard, and we propose several mixed integer linear programming models for formulating the problem.

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arXiv2021

A New Constructive Heuristic driven by Machine Learning for the Traveling Salesman Problem

Recent systems applying Machine Learning (ML) to solve the Traveling Salesman Problem (TSP) exhibit issues when they try to scale up to real case scenarios with several hundred vertices. The use of Candidate Lists (CLs) has been brought up to cope with the issues. The procedure allows to restrict the search space during solution creation, consequently reducing the solver computational burden. So far, ML were engaged to create CLs and values on the edges of these CLs expressing ML preferences at solution insertion. Although promising, these systems do not clearly restrict what the ML learns and does to create solutions, bringing with them some generalization issues. Therefore, motivated by exploratory and statistical studies, in this work we instead use a machine learning model to confirm the addition in the solution just for high probable edges. CLs of the high probable edge are employed as input, and the ML is in charge of distinguishing cases where such edges are in the optimal solution from those where they are not. . This strategy enables a better generalization and creates an efficient balance between machine learning and searching techniques. Our ML-Constructive heuristic is trained on small instances. Then, it is able to produce solutions, without losing quality, to large problems as well. We compare our results with classic constructive heuristics, showing good performances for TSPLIB instances up to 1748 cities. Although our heuristic exhibits an expensive constant time operation, we proved that the computational complexity in worst-case scenario, for the solution construction after training, is $O(n^2 \log n^2)$, being $n$ the number of vertices in the TSP instance.

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arXiv2021

Machine Learning Constructives and Local Searches for the Travelling Salesman Problem

The ML-Constructive heuristic is a recently presented method and the first hybrid method capable of scaling up to real scale traveling salesman problems. It combines machine learning techniques and classic optimization techniques. In this paper we present improvements to the computational weight of the original deep learning model. In addition, as simpler models reduce the execution time, the possibility of adding a local-search phase is explored to further improve performance. Experimental results corroborate the quality of the proposed improvements.

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arXiv2021

Benchmark Instances and Optimal Solutions for the Traveling Salesman Problem with Drone

The use of drones in logistics is gaining more and more interest, and drones are becoming a more viable and common way of distributing parcels in an urban environment. As a consequence, there is a flourishing production of articles in the field of operational optimization of the combined use of trucks and drones for fulfilling customers requests. The aim is minimizing the total time required to service all the customers, since this has obvious economical impacts. However in the literature there is not yet a widely recognized basic model, and there are not well assessed sets of instances and optimal solutions that can be considered as a benchmark to prove the effectiveness of new solution methods. The aim of this paper is to fill this gap. On one side we will clearly describe some of the most common components of the truck/drone routing problems and we will define nine basic problem settings, by combining these components. On the other side we will consider some of the instances used by many researchers and we will provide optimal solutions for all the problem settings previously identified. Instances and detailed solutions are then organized into benchmarks made publicly available as validation tools for future research methods.

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arXiv2019

Models and algorithms for the Flying Sidekick Traveling Salesman Problem

This paper presents a set of new formulations for the Flying Sidekick Traveling Salesman Problem, where a truck and a drone cooperate to delivery parcels to customers minimizing the completion time. The new formulations improve the results of the literature by solving to optimality several benchmark instances for which an optimal solution was previously unknown. A matheuristic algorithm, strongly based on the new models, is also discussed. Experimental results show that this method is able to provide good quality solutions in short time even for the larger instances, on which the mathematical models struggle to provide either good heuristic solution or strong lower bounds.

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arXiv2019

Matheuristic algorithms for the parallel drone scheduling traveling salesman problem

In a near future drones are likely to become a viable way of distributing parcels in a urban environment. In this paper we consider the parallel drone scheduling traveling salesman problem, where a set of customers requiring a delivery is split between a truck and a fleet of drones, with the aim of minimizing the total time required to service all the customers. We present a set of matheuristic methods for the problem. The new approaches are validated via an experimental campaign on two sets of benchmarks available in the literature. It is shown that the approaches we propose perform very well on small/medium size instances. Solving a mixed integer linear programming model to optimality leads to the first optimality proof for all the instances with 20 customers considered, while the heuristics are shown to be fast and effective on the same dataset. When considering larger instances with 48 to 229 customers, the results are competitive with state-of-the-art methods and lead to 28 new best known solutions out of the 90 instances considered.

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arXiv2019

Drone-assisted deliveries: new formulations for the Flying Sidekick Traveling Salesman Problem

In this paper we consider a problem related to deliveries assisted by an unmanned aerial vehicle, so-called drone. In particular we consider the Flying Sidekick Traveling Salesman Problem, where a truck and a drone cooperate to delivery parcels to customers minimizing the completion time. In the following we improve the formulation found in the related literature. We propose three-indexed and two-indexed formulations and a set of inequalities that can be implemented in a branch-and-cut fashion. We could find the optimal solutions for most of the literature instances. Moreover, we consider two versions of the problem: one in which the drone is allowed to wait at the customers, as in the literature, and one where waiting is allowed only in flying mode. The solving methodologies are adapted to both versions. A comparison between the two versions is provided.

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