We study the problem of determining the worst optimal value and characterizing the corresponding worst-case scenarios in minimum cost network flow problems with interval uncertainty in arc capacities. In this setting, each capacity can take any value within its specified lower and upper bounds. We prove that computing the worst optimal value is a strongly NP-hard problem and remains NP-hard even when restricted to series-parallel graphs. Further, we propose a mixed-integer linear programming formulation that computes the exact worst optimal value, as well as a pseudopolynomial-time algorithm designed for the special case of series-parallel graphs. We also examine the structural properties of the most extremal worst-case scenarios and show that the arcs whose capacities are not fixed at their interval bounds form a forest. This result establishes an upper bound on the number of such arcs, which we show to be tight by constructing a class of instances in which the bound is attained. Finally, we investigate the more-for-less paradox in minimum cost network flow problems with interval capacities, which occurs in instances where increasing the required flow leads to a decrease in the worst-case optimal cost. We provide a general characterization of this phenomenon using augmenting paths and establish a stronger characterization for complete graphs. In addition, we discuss the properties of the cost matrices immune against the paradox and prove that deciding whether a given cost matrix has this property is a strongly co-NP-hard problem.

ABSTRACT This work addresses the paper selection problem that each Italian university and department faced in the context of the research quality evaluation (VQR) of the Italian university system for the period 2020–2024. Given the set of researchers of a university and their associated papers, the problem consists of selecting a fixed number of researcher, paper pairs, as established by the Ministry, while respecting bounds on the minimum and maximum number of papers selectable for each researcher, as well as the maximum number of times a paper can be selected. Each pair is associated with a score, which depends on several bibliometric parameters related to both the paper and the author, and the goal of the problem is to select the pairs so as to maximize the total score. In this paper, we consider two versions of the problem, modeling the departments' and the university's perspectives, and for each of them, we provide an integer linear programming formulation. Moreover, we present two proofs showing that the problem can be solved optimally in polynomial time. The first proof consists of a polynomial‐time reduction to the capacitated minimum cost flow problem and is introduced to allow the problem to be solved without the need for commercial solvers (and the associated license costs); this is the ideal approach for any commercial software that already faces this problem. The second proof shows that the constraint matrices of the two formulations are totally unimodular. This property, together with the integrality of the right‐hand sides, ensures that the linear relaxations yield integer optimal solutions, which can be easily computed using the simplex method.

This work addresses a variant of the maximum flow problem where specific pairs of arcs are not allowed to carry positive flow simultaneously. Such restrictions are known in the literature as negative disjunctive constraints or conflict constraints. The problem is known to be strongly NP-hard and several exact approaches have been proposed in the literature. In this paper, we present a heuristic algorithm for the problem, based on two different approaches: Carousel Greedy and Kernel Search. These two approaches are merged to obtain a fast and effective matheuristic, named Kernousel. In particular, the computational results reveal that exploiting the information gathered by the Carousel Greedy to build the set of most promising variables (the kernel set ), makes the Kernel Search more effective. To validate the performance of the new hybrid method, we compare it with the two components running individually. Results are also evaluated against the best-known solutions available in the literature for the problem. The new hybrid method provides 15 new best-known values on benchmark instances.

The Minimum Spanning Tree Problem with Conflicts consists in finding the minimum conflict-free spanning tree of a graph, i.e., the spanning tree of minimum cost, including no pairs of edges that are in conflict. In this paper, we solve this problem using an enhanced Kernel Search method, which iteratively solves refined problem restrictions. Our approach addresses two central open questions in the kernel search literature: (1) how to determine the affinity between variables to ensure that the restricted problem contains variables that are as compatible as possible, meaning they are more likely to appear together in a feasible solution, and (2) how to construct an initial feasible solution quickly. To this end, we integrate the computation of independent sets from the conflict graph within the algorithm to detect affinities and effectively manage conflicts. Furthermore, we heuristically construct an initial starting point, significantly accelerating the computational process. Although our methodology is designed for MSTC, its principles could be extended to other combinatorial optimization problems with conflicts. Experimental results on benchmark instances demonstrate the efficiency and competitiveness of our approach compared to existing methods in the literature, achieving 17 new best-known values.

We introduce a heuristic rule for calculating the stepsize in the subgradient method for unconstrained convex nonsmooth optimization which, unlike the classic approach, is based on retaining some information from previous iteration. The rule is inspired by the well known two-point stepsize by Barzilai and Borwein (BB) [6] for smooth optimization and it coincides with (BB) in case the function to be minimised is convex quadratic.Under the use of appropriate safeguards we demonstrate that the method terminates at a point that satisfies an approximate optimality condition.The proposed approach is tested in the framework of Lagrangian relaxation for integer linear programming where the Lagrangian dual requires maximization of a concave and nonsmooth (piecewise affine) function. In particular we focus on the relaxation of the Minimum Spanning Tree problem with Conflicting Edge Pairs (MSTC). Comparison with classic subgradient method is presented. The results on some widely used academic test problems are provided too.

In this study we address the Set Orienteering Problem, which is a generalization of the Orienteering Problem where customers are clustered in groups. Each group is associated with a profit which is gained in case at least one customer in the group is served. A single vehicle is available to serve the customers. The aim is to find the vehicle route that maximizes the profit collected without exceeding a maximum route cost, which can be interpreted also as route duration. The problem was introduced in Archetti (2018) together with a mathematical programming formulation. In this paper, we propose a new formulation which uses less variables. We also derive different classes of valid inequalities to strengthen the formulation. In addition, separation algorithms are developed, some of which are new with respect to those presented in the literature. A branch-and-cut algorithm is implemented to solve the problem and tests are made on benchmark instances. The results show that the branch-and-cut algorithm is effective in solving instances with up to 100 customers. Moreover, the difficulty of solving the problem largely depends on the maximum route duration. We also show that valid inequalities are effective in speeding up the solution process. Finally, a comparison with two exact benchmark approaches proposed in the literature shows that the branch-and-cut algorithm proposed in this paper is the new state-of-the-art exact approach for solving the Set Orienteering Problem.

In this paper, we analyze a new variant of the well-known NP -hard Set Covering Problem, characterized by pairwise conflicts among subsets of items. Two subsets in conflict can belong to a solution provided that a positive penalty is paid. The problem looks for the optimal collection of subsets representing a cover and minimizing the sum of covering and penalty costs. We introduce two integer linear programming formulations and a quadratic one for the problem and provide a parallel GRASP (Greedy Randomized Adaptive Search Procedure) that, during parallel executions of the same basic procedure, shares information among threads. We tailor such a parallel processing to address the specific problem in an innovative way that allows us to prevent redundant computations in different threads, ultimately saving time. To evaluate the performance of our algorithm, we conduct extensive experiments on a large set of new instances obtained by adapting existing instances for the Set Covering Problem. Computational results show that the proposed approach is extremely effective and efficient providing better results than Gurobi (tackling three alternative mathematical formulations of the problem) in less than 1/6 of the computational time.

This article addresses the 2-edge-connected minimum branch vertices problem, a variant of the minimum branch vertices problem in which the spanning subgraph is required to be 2-edge-connected for survivability reasons. The problem has been recently introduced and finds application in optical networks design scenarios, where branch vertices are associated to switch devices that allow to split the entering light signals and send them to several adjacent vertices. An exact approach to the problem has been proposed in the literature. In this paper, we formally prove its NP-completeness and propose a genetic algorithm, which exploits some literature-provided procedures for efficiently checking and restoring solutions feasibility, and makes use of novel ad-hoc designed operators aiming to improve their values, reducing the number of branch vertices. The computational tests show that, on the benchmark instances, the genetic algorithm very often finds the optimal solution. Moreover, in order to further investigate the effectiveness and the performance of our algorithm, we generated a new set of random instances where the optimal solution is known a priori.

The seismic analysis of reinforced concrete (RC) structures generally requires significant computational effort, which can be challenging or at least time-consuming also for the modern computing systems. Particularly, huge computational effort is required for running optimisation procedures intended at selecting the “best” retrofitting solution among the wide set of technical feasible ones. Therefore, this paper proposes the use of Machine Learning instead of the mechanistic analyses executed as part of an optimisation procedure for seismic retrofitting of RC existing structures recently proposed by the authors. Specifically, an Artificial Neural Network is trained and employed as a possible substitute of finite element analysis for a rapid and accurate assessment of the relevant performance exhibited by the enhanced configurations of an RC existing building typology. The obtained results demonstrate the effectiveness of an artificial neural network as a computational model to approximate a finite element analysis in seismic retrofitting of RC structures by considering several structural configurations. The proposed methodology can be used to speed-up the search of a viable RC strengthening configuration within the whole parametric field of relevance, which can be subsequently refined using more detailed and computationally expensive FE methods.

This article addresses the minimum spanning tree problem with conflicting edge pairs, a variant of the classical minimum spanning tree where, given a list of conflicting edges, the goal is to find the cheapest spanning tree with no edges in conflict. We adopt a Lagrangian relaxation approach together with a dual ascent and a subgradient procedure to find tight lower bounds on the optimal solution. The algorithm is also equipped with a heuristic approach which provides an upper bound by removing the conflicts from possible infeasible solutions met during the calculation of the lower bounds. The computational results, carried out on benchmark instances, show that the proposed algorithm finds the optimal solutions on several instances. Moreover, the lower bounds it provides are much more accurate than ones provided by other Lagrangian approaches available in the literature and they are computed in much less time.

This paper deals with the Constrained Forward Shortest Path Tour Problem, an NP‐complete variant of the Forward Shortest Path Tour Problem. Given a directed weighted graph G = (V, A), where the set of nodes V is partitioned into clusters T1, …, TN, the aim is determining a shortest path between two given nodes, s and d, with the properties that clusters must be visited according to a given order, and each arc can be crossed at most once. We introduce a mathematical formulation of the problem, and a reduction procedure to reduce the number of variables involved in the model. Furthermore, we propose a Greedy Randomized Adaptive Search Procedure (GRASP) algorithm to solve large instances of the problem. Computational tests show that the reduction procedure is very effective and its application significantly speeds up the resolution of the model. Moreover, the computational results certify the effectiveness of GRASP that often finds the optimal solution and, in general, provides quickly high‐quality sub‐optimal solutions.

We study the problem of determining the bounds of the optimal cost of a transportation problem when the capacity of the suppliers and the demand of the customers vary over an interval. We consider transportation costs such that the transportation paradox does not arise. We design a new heuristic approach based on some polyhedral properties of the problem and provide a novel integer linear programming mathematical formulation to solve it exactly. Our computational results, carried out on benchmark instances from the literature and on some new instances, show that our heuristic algorithm greatly outperforms the best solution approaches currently used. (C) 2021 Elsevier Ltd. All rights reserved.

This paper addresses the Set Orienteering Problem which is a generalization of the Orienteering Problem where the customers are grouped in clusters, and the profit associated with each cluster is collected by visiting at least one of the customers in the respective cluster. The problem consists of finding a tour that maximizes the collected profit but, since the cost of the tour is limited by a threshold, only a subset of clusters can usually be visited. We propose a Biased Random-Key Genetic Algorithm for solving the Set Orienteering Problem in which three local search procedures are applied to improve the fitness of the chromosomes. In addition, we introduced three rules useful to reduce the size of the instances and to speed up the resolution of the problem. Finally, a hashtable is used to quickly retrieve the information that are required several times during the computation. The computational results, carried out on benchmark instances, show that our algorithm is significantly faster than the other algorithms, proposed in the literature, and it provides solutions very close to the best-known ones. (C) 2020 Elsevier B.V. All rights reserved.

The All-Colors Shortest Path (ACSP) is a recently introduced NP-Hard optimization problem, in which a color is assigned to each vertex of an edge weighted graph, and the aim is to find the shortest path spanning all colors. The solution path can be not simple, that is it is possible to visit multiple times the same vertices if it is a convenient choice. The starting vertex can be constrained (ACSP) or not (ACSP-UE). We propose a reduction heuristic based on the transformation of any ACSP-UE instance into an Equality Generalized Traveling Salesman Problem one. Computational results show the algorithm to outperform the best previously known one.

The maximum network lifetime is a well known and studied optimization problem. The aim is to appropriately schedule the activation intervals of the individual sensing devices composing a wireless sensor network used for monitoring purposes, in order to keep the network operational for the longest period of time (network lifetime). In this work, we extend this problem by taking into account the issue of charging the sensor batteries. More specifically, it has to be decided how much charge should be provided to each sensor, given the existence of a charging device with limited energy availability. An exact column generation algorithm embedding a genetic algorithm for the subproblem is proposed. Computational results reveal that by appropriately choosing the charge levels, remarkable network lifetime improvements can be obtained, in particular when the available energy is scarce.

This article introduces the Generalized Minimum Branch Vertices problem. Given an undirected graph, where the set of vertices is partitioned into clusters, the Generalized Minimum Branch Vertices problem consists of finding a tree spanning exactly one vertex for each cluster and having the minimum number of branch vertices, namely vertices with degree greater than two. When each cluster is a singleton, the problem reduces to the well-known Minimum Branch Vertices problem, which is NP-hard. We show some properties that any feasible solution to the problem has to satisfy. Some of these properties can be used to determine useless vertices or edges, which can be removed to reduce the size of the instances. We propose an integer linear programming formulation for the problem, we derive the dimension of the polytope, we study the trivial inequalities and introduce two new classes of valid inequalities, that are proved to be facet-defining.

Reinforced Concrete (RC) structures built in the past decades in earthquake-prone regions do not generally meet the seismic safety standards requested by the current codes. Therefore, they generally need to be retrofitted with the aim to reduce their seismic vulnerability within acceptably low levels. Although several technical solutions are nowadays available on the market, the design of retrofitting interventions is mainly based on the so-called "engineering judgment" and, hence, it is highly subjective in nature, yet being bound to respecting strict code provisions. This paper proposes a rational procedure, based on the application of Genetic Algorithms (GAs), intended at selecting the "cheapest" retrofitting solution among the technically feasible ones. The paper shows how the main GA operators (namely, selection, crossover, and mutation) operate on the candidate retrofitting solutions, which, in principle, may consist of a combination of both member- and structure-level techniques. Details about the numerical implementation of the proposed procedure are reported, along with the summary of some relevant applications to RC frames representative of a wide class of buildings currently existing in South European Countries, such as Italy and Greece.

This paper addresses a variant of the minimum spanning tree problem in which, given a list of conflicting edges, the primary goal is to find a spanning tree with the minimum number of conflicting edge pairs and the secondary goal is to minimize the weight of spanning trees without conflicts. The problem is NP-hard and it finds applications in the design of offshore wind farm networks. We propose a multiethnic genetic algorithm for the problem in which the fitness function is designed to simultaneously manage the two goals of the problem. Moreover, we introduce three local search procedures to improve the solutions inside the population during the computation. Computational results performed on benchmark instances reveal that our algorithm outperforms the other heuristic approach, proposed in the literature, for this problem.