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Influence maximization aims at identifying a limited set of key individuals in a (social) network which spreads information based on some propagation model and maximizes the number of individuals reached. We show that influence maximization based on the probabilistic independent cascade model can be modeled as a stochastic maximal covering location problem. A reformulation based on Benders decomposition is proposed and a relation between obtained Benders optimality cuts and submodular cuts for correspondingly defined subsets is established. We introduce preprocessing tests, which allow us to remove variables from the model and develop efficient algorithms for the separation of Benders cuts. Both aspects are shown to be crucial ingredients of the developed branch-and-cut algorithm since real-life social network instances may be very large. In a computational study, the considered variants of this branch-and-cut algorithm outperform the state-of-the-art approach for influence maximization by orders of magnitude.

We study the multi-depot split-delivery vehicle routing problem (MDSDVRP) that combines the advantages and potential cost savings of multiple depots and split deliveries and develop the first exact algorithm for this problem. We propose an integer programming formulation using a small number of decision variables and several sets of valid inequalities. These inequalities focus on ensuring the vehicles’ capacity limits and that vehicles return to their initial depot. As we show that the new constraints do not guarantee these aspects, our branch-and-cut framework also includes an efficient feasibility check for candidate solutions and explicit feasibility cuts. The algorithm that also uses a comparably simple, yet effective heuristic to compute high-quality initial solutions is tested on the MDSDVRP and two well-known special cases, the split-delivery vehicle routing problem (SDVRP) and the multi-depot traveling salesman problem (MDTSP). The results show that the new inequalities tighten the linear programming relaxation, increase the performance of the branch-and-cut algorithm, and reduce the number of required feasibility cuts. We report the first proven optimal results for the MDSDVRP and show that our algorithm significantly outperforms the state-of-the-art for the MDTSP while being competitive on the SDVRP. For the latter, 20 instances are solved for the first time, and new best primal and dual bounds are found for others. Funding: This work was supported by the Fundação para a Ciência e a Tecnologia [Project UIDB/04561/2020]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.1179 .

Online social networks have become crucial to propagate information. Prominent use cases include marketing campaigns for products or political candidates in which maximizing the expected number of reached individuals is a common objective. The latter can be achieved by incentivizing an appropriately selected seed set of influencers that trigger an influence cascade with expected maximum impact. In real-world settings, competing influence spreads need to be considered frequently. These may, for instance, stem from marketing activities for a substitute product of a different company or bad actors that spread (mis-)information about a political candidate. This article focuses on competitive settings in which the seed individuals of one entity are already known. Another entity wants to choose its seed set of individuals that triggers an influence cascade of maximum impact. The propagation process is modeled by a variant of the probabilistic independent cascade model. An algorithmic framework based on a Benders decomposition is developed that also employs preprocessing and initial heuristics. This framework is used within a sample average approximation scheme that allows to approximate the exact objective function value. The algorithms are tested on real-world instances from the literature and newly-obtained ones from Twitter. A computational study reports on the algorithms’ performance next to providing further insights. The latter are based on analyzing expected losses that are caused by competition, the gain from solving subproblems to optimality using the Benders decomposition based algorithm, and the influence of different seed set choices of the first entity.

Extending the concept of time-space networks, layered graphs associate information about one or multiple resource state values with nodes and arcs. While integer programming formulations based on them allow to model complex problems comparably easy, their large size makes them hard to solve for non-trivial instances. We detail and classify layered graph modeling techniques that have been used in the (recent) scientific literature and review methods to successfully solve the resulting large-scale, extended formulations. Modeling guidelines and important observations concerning the solution of layered graph formulations by decomposition methods are given together with several future research directions.

Low and infrequent demand in rural areas poses a problem for public transport providers to run cost-effective services and individual car use is usually the main means of transportation. We investigate how microtransit services can be integrated with existing public transport solutions (bus, train) as a flexible shared mobility alternative in rural areas and how to make them attractive alternatives to individual car use. We combine large neighborhood search with agent-based modeling and simulation to validate generated schedules for a microtransit service in terms of vulnerability to tardiness in passenger behavior or service provision. This includes the study of how disturbances, such as delays in service provision or late arrivals of passengers affect the stability of a transport schedule concerning a reliable timely delivery to transfer stops. We explore how simulation can be utilized as a means to fine-tune provider policies, e.g., how long vehicles may wait for late passengers before they depart.

In a personal communication with Ruslan Sadykov from Inria, France, we found an implementation error in our code for importing the benchmark instance set MUT leading to wrong numerical results in our original article (Gouveia, Leitner, and Ruthmair, 2017). In this corrigendum we provide corrected results for all experiments on instance set MUT. The general findings and conclusions drawn from the results however do not change.

Influence maximization problems aim to identify key players in (social) networks and are typically motivated from viral marketing. In this work, we introduce and study the Generalized Least Cost Influence Problem (GLCIP) that generalizes many previously considered problem variants and allows to overcome some of their limitations. A formulation that is based on the concept of activation functions is proposed together with strengthening inequalities. Exact and heuristic solution methods are developed and compared for the new problem. Our computational results also show that our approaches outperform the state-of-the-art on relevant, special cases of the GLCIP.

We present a rich, bi-objective generalization of the orienteering problem.A modular bi-objective large neighborhood search metaheuristic is proposed.We conduct an extensive computational study on real-life-inspired test instances.Near-optimal Pareto sets are rapidly found on instances solvable to optimality.Solution quality, computation time, and reliability scale well to larger instances. We propose and solve a rich, bi-objective extension of the orienteering problem with time windows (OPTW) to model a combined routing and scheduling problem. Our research is motivated by the problem faced by mobile freelancers who have to integrate irregular appointments and tasks into their daily routines. Those people have a number of tasks which they need to perform at various locations (e.g.meetings with different clients), subject to varying time constraints (e.g.opening hours), and with different levels of importance or urgency (e.g.submitting a deliverable versus cleaning the home office). Furthermore, sets of related tasks may be subject to precedence relations and time dependencies. We explicitly consider the trade-off between planning more tasks and enjoying more free time by means of a bi-objective model. The extension of the OPTW and the bi-objective formulation result in the Personal Planning Problem (PPP). We present a mathematical formulation of the PPP and a metaheuristic based on Large Neighborhood Search (LNS) is developed to generate a set of non-dominated solutions to the problem. Solution quality is analyzed on real-world-inspired test instances. Exact reference sets based on a linear single-commodity flow model are used as benchmarks. Extensive computational experiments show that the proposed metaheuristic generates near-optimal solution sets and scales well to larger instances.

In this paper we study Integer Linear Programming models and develop branch-and-cut algorithms to solve the Black-and-White Traveling Salesman Problem (BWTSP) (Bourgeois, Laporte, & Semet, 2003) which is a variant of the well known Traveling Salesman Problem (TSP). Two strategies to model the BWTSP have been used in the literature. The problem is either modeled on the original graph as TSP using a single set of binary edge variables and with additional non-trivial hop and distance constraints between every pair of black nodes (see Ghiani, Laporte, & Semat, 2006) or as a sequence of constrained paths composed of white nodes connecting pairs of black nodes (see Muter, 2015). In this paper, we study and develop an intermediate approach based on the observation that it is sufficient to guarantee the required distance (and hop) limit of the path from a given black node to the next black node without explicitly stating which one it is. Thus, instead of stating the two constraints (after adding appropriately defined variables) for each pair of black nodes, they are stated for each black node only (that represents the source of each path). Based on this idea we develop several variants of position- and distance-dependent reformulations together with corresponding layered graph representations. Branch-and-cut algorithms are developed for all proposed formulations and empirically compared by an extensive computational study. The obtained results allow us to provide insights into individual advantages and disadvantages of the different models.

International audience; Urban railway transportation organization is a systematic activity that is usually composed of several stages, including network design, line planning, timetabling, rolling stock and staffing. In this paper, we study the optimization of first train timetables for an urban railway network that focuses on designing convenient and smooth timetables for morning passengers. We propose a mixed integer programming (MIP) model for minimizing train arrival time differences and the number of missed trains, i.e., the number of trains without transfers within a reasonable time at interchange stations as an alternative to minimize passenger transfer waiting times. This is interesting from the operator's point of view, and we show that both criteria are equivalent. Starting from an intuitive model for the first train transfer problem, we then linearize the non-linear constraints by utilizing problem specific knowledge. In addition, a local search algorithm is developed to solve the timetabling problem. Through computational experiments involving the Beijing subway system, we demonstrate the computational efficiency of the exact model and the heuristic approach. Finally, three practical suggestions are proposed for the operation and management of the urban railway transit system.

We consider a framework for obtaining a sequence of converging primal and dual bounds based on mixed integer linear programming formulations on layered graphs. The proposed iterative algorithm avoids the typically rather large size of the full layered graph by approximating it incrementally. We focus in particular on this refinement step that extends the graph in each iteration. Novel path-based approaches are compared to existing variants from the literature. Experiments on two benchmark problems—the traveling salesman problem with time windows and the rooted distance-constrained minimum spanning tree problem—show the effectiveness of our new strategies. Moreover, we investigate the impact of a strong heuristic component within the algorithm, both for improving convergence speed and for improving the potential of an employed reduced cost fixing step.

We present a sensitivity analysis for a mechanical model, which is used to estimate the energy demand of battery electric vehicles. This model is frequently used in literature, but its parameters are often chosen incautiously, which can lead to inaccurate energy demand estimates. We provide a novel prioritization of parameters and quantify their impact on the accuracy of the energy demand estimation, to enable better decision making during the model parameter selection phase. We furthermore determine a subset of parameters, which has to be defined, in order to achieve a desired estimation accuracy. The analysis is based on recorded GPS tracks of a battery electric vehicle under various driving conditions, but results are equally applicable for other BEVs. Results show that the uncertainty of vehicle efficiency and rolling friction coefficient have the highest impact on accuracy. The uncertainty of power demand for heating and cooling the vehicle also strongly affects the estimation accuracy, but only at low speeds. We also analyze the energy shares related to each model component including acceleration, air drag, rolling and grade resistance and auxiliary energy demand. Our work shows that, while some components make up a large share of the overall energy demand, the uncertainty of parameters related to these components does not affect the accuracy of energy demand estimation significantly. This work thus provides guidance for implementing and calibrating an energy demand estimation based on a longitudinal dynamics model.

We address the one-to-one multi-commodity pickup and delivery traveling salesman problem (m-PDTSP) which is a generalization of the TSP and arises in several transportation and logistics applications. The objective is to find a minimum-cost directed Hamiltonian path which starts and ends at given depot nodes and such that the demand of each given commodity is transported from the associated source to its destination and the vehicle capacity is never exceeded. In contrast, the many-to-many one-commodity pickup and delivery traveling salesman problem (1-PDTSP) just considers a single commodity and each node can be a source or target for units of this commodity. We show that the m-PDTSP is equivalent to the 1-PDTSP with additional precedence constraints defined by the source-destination pairs for each commodity and explore several models based on this equivalence. In particular, we consider layered graph models for the capacity constraints and introduce new valid inequalities for the precedence relations. Especially for tightly capacitated instances with a large number of commodities our branch-and-cut algorithms outperform the existing approaches. For the uncapacitated m-PDTSP (which is known as the sequential ordering problem) we are able to solve to optimality several open instances from the TSPLIB and SOPLIB. HighlightsWe present models for pickup and delivery traveling salesman problems.Important relations between different problem variants are shown.New valid inequalities for precedence relations are introduced.Our branch-and-cut algorithms outperform existing approaches.Several open instances for the sequential ordering problem are solved.

We study the directed network design problem with relays (DNDPR) whose aim is to construct a minimum cost network that enables the communication of a given set of origin-destination pairs. Thereby, expensive signal regeneration devices need to be placed to cover communication distances exceeding a predefined threshold. Applications of the DNDPR arise in telecommunications and transportation. We propose two new integer programming formulations for the DNDPR. The first one is a flow-based formulation with a pseudo-polynomial number of variables and constraints and the second is a cut-based formulation with an exponential number of constraints. Fractional distance values are handled efficiently by augmenting both models with an exponentially-sized set of infeasible path constraints. We develop branch-and-cut algorithms and also consider valid inequalities to strengthen the obtained dual bounds and to speed up convergence. The results of our extensive computational study on diverse sets of benchmark instances show that our algorithms outperform the previous state-of-the-art method based on column generation.

There are many ways of modeling the Asymmetric Traveling Salesman Problem (ATSP) and the related Precedence Constrained ATSP (PCATSP). In this paper we present new formulations for the two problems that result from combining precedence variable based formulations with network flow based formulations. The motivation for this work is a property of the so-called GDDL inequalities (Gouveia and Pesneau, Networks 48, 77–89, 2006), the “disjoint sub-paths” property, that is explored to create formulations that combine two (or more) disjoint path network flow based formulations. Several sets of projected inequalities, in the space of the arc and precedence variables, and in the spirit of many inequalities presented in Gouveia and Pesneau (Networks 48, 77–89, 2006), are obtained by projecting these network flow based formulations. Computational results are given for the PCATSP and the ATSP to evaluate the quality of the new inequalities. © 2017 Wiley Periodicals, Inc. NETWORKS, 2017

International audience; Electric vehicles are gaining importance and help to reduce dependency on oil, increase energy efficiency of transportation, reduce carbon emissions and noise, and avoid tail pipe emissions. Because of short driving distances, high mileages, and intermediate waiting times, fossil-fuelled taxi vehicles are ideal candidates for being replaced by battery electric vehicles (BEVs). Moreover, taxis as BEVs would increase visibility of electric mobility and therefore encourage others to purchase an electric vehicle. Prior to replacing conventional taxis with BEVs, a suitable charging infrastructure has to be established. This infrastructure, which is a prerequisite for the use of BEVs in practice, consists of a sufficiently dense network of charging stations taking into account the lower driving ranges of BEVs. In this case study we propose a decision support system for placing charging stations to satisfy the charging demand of electric taxi vehicles. Operational taxi data from about 800 vehicles is used to identify and estimate the charging demand for electric taxis based on frequent origins and destinations of trips. Next, a variant of a set covering problem is formulated and solved, aiming at satisfying as much charging demand as possible with a limited number of charging stations. Already existing charging locations are considered in the optimization problem. In this work, we focus on finding regions in which charging stations should be placed, rather than exact locations. The exact location within an area is identified in a post-optimization phase (e.g., by authorities), where environmental conditions are considered, e.g., the capacity of the power network, availability of space, and legal issues. Our approach is implemented in the city of Vienna, Austria, in the course of an applied research project conducted in 2014. Local authorities, power network operators, representatives of taxi driver guilds as well as a radio taxi provider participated in the project and identified exact locations for charging stations based on our decision support system.

International audience; Car-sharing systems are increasingly employing environmentally-friendly electric vehicles. The design and management of Ecar-sharing systems poses several additional challenges with respect to those based on traditional combustion vehicles, mainly related with the limited autonomy allowed by current battery technology. We review the main optimization problems arising in Ecar-sharing systems at strategic, tactical and operational levels, and discuss the existing approaches often developed for similar problems, for example in car-sharing systems with traditional vehicles. We also outline open problems and fruitful research directions.

We consider a rather generic class of network design problems in which a set or subset of given terminal nodes must be connected to a dedicated root node by simple paths and a variety of resource and/or quality of service constraints must be respected. These extensions of the classical Steiner tree problem on a graph can be well modeled by a path formulation in which individual variables are used for all feasible paths. To solve this formulation in practice, branch-and-price is used. It turns out, however, that a naive implementation of column generation suffers strongly from certain degeneracies of the pricing subproblem, leading to excessive running times. After analyzing these computational problems, we propose two methods to accelerate and stabilize column generation by using alternative dual-optimal solutions. The resulting branch-and-price approach is practically tested on the rooted delay-constrained Steiner tree problem and a quota-constrained version of it. Results indicate that the proposed methods in general speed-up the solution process dramatically, far more than a piecewise linear stabilization to which we compare. Furthermore, our branch-and-price approach exhibits on most test instances a better performance than a state-of-the-art branch-and-cut approach based on layered graphs. As the new stabilization technique utilizing alternative dual-optimal solutions is generic in the sense that it easily adapts to the inclusion of a large variety of further constraints and different objective functions, the proposed method is highly promising for a large class of network design problems. © 2012 Wiley Periodicals, Inc. NETWORKS, 2013

We investigate a so far not examined problem called the Interdependent Lock Scheduling Problem. A Variable Neighborhood Search approach is proposed for finding lock schedules along the Austrian part of the Danube River in order to minimize the overall ship travel times. In computational experiments the performance of our approach is assessed and compared to real-world ship trajectories. Notable improvements can be achieved. In addition, the number of (empty) lockages can be significantly reduced when taking them into account during optimization without loosing too much of quality in travel time optimization.

In this paper, we introduce and study a generalization of the degree constrained minimum spanning tree problem where we may install one of several available transmission systems (each with a different cost value) in each edge. The degree of the endnodes of each edge depends on the system installed on the edge. We also discuss a particular case that arises in the design of wireless mesh networks (in this variant the degree of the endnodes of each edge depend on the transmission system installed on it as well as on the length of the edge). We propose three classes of models using different sets of variables and compare from a theoretical perspective as well as from a computational point of view, the models and the corresponding linear programming relaxations. The computational results show that some of the proposed models are able to solve to optimality instances with 100 nodes and different scenarios.

This work deals with the application of metaheuristics to the fuel consumption minimization problem of hybrid electric vehicles (HEV) considering exactly specified driving cycles. A genetic algorithm, a downhill-simplex method and an algorithm based on swarm intelligence are used to find appropriate parameter values aiming at fuel consumption minimization. Finally, the individual metaheuristics are combined to a hybrid optimization algorithm taking into account the strengths and weaknesses of the single procedures. Due to the required time-consuming simulations it is crucial to keep the number of candidate solutions to be evaluated low. This is partly achieved by starting the heuristic search with already meaningful solutions identified by a Monte-Carlo procedure. Experimental results indicate that the implemented hybrid algorithm achieves better results than previously existing optimization methods on a simplified HEV model.

We present a memetic algorithm for a combinatorial optimization problem called rooted delay-constrained minimum spanning tree problem arising for example in centralized broadcasting networks where quality of service constraints are of concern. The memetic algorithm is based on a specialized solution representation and a simple and effective decoding mechanism. Solutions are locally improved by a variable neighborhood descent in two neighborhood structures. Furthermore, to tackle the problem of repeated examination of already visited solutions we investigate a simple hash-based method to only detect duplicates or, alternatively, a trie-based complete solution archive to additionally derive new unvisited solutions. Experimental results show that our memetic algorithm outperforms existing heuristic approaches for this problem in most cases. Including the hash-based duplicate detection mostly further improves solution quality whereas the solution archive can only rarely obtain better results due to its operational overhead.