New Complexity Results and Algorithms for the Minimum Tollbooth Problem

The inefficiency of the Wardrop equilibrium of nonatomic routing games can be eliminated by placing tolls on the edges of a network so that the socially optimal flow is induced as an equilibrium flow. A solution where the minimum number of edges are tolled may be preferable over others due to its ease of implementation in real networks. In this paper we consider the minimum tollbooth (MINTB) problem, which seeks social optimum inducing tolls with minimum support. We prove for single commodity networks with linear latencies that the problem is NP-hard to approximate within a factor of $1.1377$ through a reduction from the minimum vertex cover problem. Insights from network design motivate us to formulate a new variation of the problem where, in addition to placing tolls, it is allowed to remove unused edges by the social optimum. We prove that this new problem remains NP-hard even for single commodity networks with linear latencies, using a reduction from the partition problem. On the positive side, we give the first exact polynomial solution to the MINTB problem in an important class of graphs---series-parallel graphs. Our algorithm solves MINTB by first tabulating the candidate solutions for subgraphs of the series-parallel network and then combining them optimally

A biased random-key genetic algorithm for the capacitated minimum spanning tree problem

This paper focuses on the capacitated minimum spanning tree(CMST)problem.Given a central processor and a set of remote terminals with specified demands for traffic that must flow between the central processor and terminals,the goal is to design a minimum cost network to carry this demand. Potential links exist between any pair of terminals and between the central processor and the terminals. Each potential link can be included in the design at a given cost.The CMST problem is to design a minimum-cost network connecting the terminals with the central processor so that the flow on any arc of the network is at most Q. A biased random-keygenetic algorithm(BRKGA)is a metaheuristic for combinatorial optimization which evolves a population of random vectors that encode solutions to the combinatorial optimization problem.This paper explores several solution encodings as well as different strategies for some steps of the algorithm and finally proposes a BRKGA heuristic for the CMST problem. Computational experiments are presented showing the effectivenes sof the approach:Seven newbest- known solutions are presented for the set of benchmark instances used in the experiments.Peer ReviewedPostprint (author’s final draft

Ant Colony Optimization

Ant Colony Optimization (ACO) is the best example of how studies aimed at understanding and modeling the behavior of ants and other social insects can provide inspiration for the development of computational algorithms for the solution of difficult mathematical problems. Introduced by Marco Dorigo in his PhD thesis (1992) and initially applied to the travelling salesman problem, the ACO field has experienced a tremendous growth, standing today as an important nature-inspired stochastic metaheuristic for hard optimization problems. This book presents state-of-the-art ACO methods and is divided into two parts: (I) Techniques, which includes parallel implementations, and (II) Applications, where recent contributions of ACO to diverse fields, such as traffic congestion and control, structural optimization, manufacturing, and genomics are presented

The correlation of externalities in marginal cost pricing: lessons learned from a real-world case study

Negative externalities cause inefficiencies in the allocation of capacities and resources in a transport system. Marginal social cost pricing allows to correct for these inefficiencies in a simulation environment and to derive real-world policy recommendations. In this context, it has been shown for analytical models considering more than one externality, that the correlation between the externalities needs to be taken into account. Typically, in order to avoid overpricing, this is performed by introducing correction factors which capture the correlation effect. However, the correlation structure between, say, emission and congestion externalities changes for every congested facility over time of day. This makes it close to impossible to calculate the factors analytically for large-scale systems. Hence, this paper presents a simulation-based approach to calculate and internalize the correct dynamic price levels for both externalities simultaneously. For a real-world case study, it is shown that the iterative calculation of prices based on cost estimates from the literature allows to identify the amplitude of the correlation between the two externalities under consideration: for the urban travelers of the case study, emission toll levels—without pricing congestion—turn out to be 4.0% too high in peak hours and 2.8% too high in off-peak hours. In contrary, congestion toll levels—without pricing emissions—are overestimated by 3.0% in peak hours and by 7.2% in off-peak hours. With a joint pricing policy of both externalities, the paper shows that the approach is capable to determine the amplitude of the necessary correction factors for large-scale systems. It also provides the corrected average toll levels per vehicle kilometer for peak and off-peak hours for the case study under consideration: again, for urban travelers, the correct price level for emission and congestion externalities amounts approximately to 38 EURct/km in peak hours and to 30 EURct/km in off-peak hours. These toll levels can be used to derive real-world pricing schemes. Finally, the economic assessment indicators for the joint pricing policy provided in the paper allow to compare other policies to this benchmark state of the transport system

Optimization of vehicular networks in smart cities: from agile optimization to learnheuristics and simheuristics

Vehicular ad hoc networks (VANETs) are a fundamental component of intelligent transportation systems in smart cities. With the support of open and real-time data, these networks of inter-connected vehicles constitute an ‘Internet of vehicles’ with the potential to significantly enhance citizens’ mobility and last-mile delivery in urban, peri-urban, and metropolitan areas. However, the proper coordination and logistics of VANETs raise a number of optimization challenges that need to be solved. After reviewing the state of the art on the concepts of VANET optimization and open data in smart cities, this paper discusses some of the most relevant optimization challenges in this area. Since most of the optimization problems are related to the need for real-time solutions or to the consideration of uncertainty and dynamic environments, the paper also discusses how some VANET challenges can be addressed with the use of agile optimization algorithms and the combination of metaheuristics with simulation and machine learning methods. The paper also offers a numerical analysis that measures the impact of using these optimization techniques in some related problems. Our numerical analysis, based on real data from Open Data Barcelona, demonstrates that the constructive heuristic outperforms the random scenario in the CDP combined with vehicular networks, resulting in maximizing the minimum distance between facilities while meeting capacity requirements with the fewest facilities.Peer ReviewedPostprint (published version

Simulation, optimization, and machine learning in sustainable transportation systems: Models and applications

[EN] The need for effective freight and human transportation systems has consistently increased during the last decades, mainly due to factors such as globalization, e-commerce activities, and mobility requirements. Traditionally, transportation systems have been designed with the main goal of reducing their monetary cost while offering a specified quality of service. During the last decade, however, sustainability concepts are also being considered as a critical component of transportation systems, i.e., the environmental and social impact of transportation activities have to be taken into account when managers and policy makers design and operate modern transportation systems, whether these refer to long-distance carriers or to metropolitan areas. This paper reviews the existing work on different scientific methodologies that are being used to promote Sustainable Transportation Systems (STS), including simulation, optimization, machine learning, and fuzzy sets. This paper discusses how each of these methodologies have been employed to design and efficiently operate STS. In addition, the paper also provides a classification of common challenges, best practices, future trends, and open research lines that might be useful for both researchers and practitioners.This work has been partially supported by the Spanish Ministry of Science, Innovation, and Universities (PID2019-111100RB-C21-C22/AEI/10.13039/501100011033, RED2018-102642-T) and the SEPIE Erasmus+ Program (2019-I-ES01-KA103-062602), and the IoF2020-H2020 (731884) project.Torre-Martínez, MRDL.; Corlu, CG.; Faulin, J.; Onggo, BS.; Juan-Pérez, ÁA. (2021). Simulation, optimization, and machine learning in sustainable transportation systems: Models and applications. Sustainability. 13(3):1-21. https://doi.org/10.3390/su1303155112113

Application of traffic weighted multi-map optimization strategies to traffic assignment

Traffic Assignment Problem (TAP) is a critical issue for transportation and mobility models that deals mainly with the calculus and delivery of best-cost routes for the trips in a traffic network. It is a computationally complex problem focused on finding user equilibrium (UE) and system optimum (SO). The Traffic Weighted Multi-Maps (TWM) technique offers a new perspective for TAP calculus, based on routing decisions using different traffic network views. These TWM are complementary cost maps that combine physical traffic networks, traffic occupation data, and routing policies. This paper shows how evolutionary algorithms can find optimal cost maps that solve TAP from the SO perspective, minimizing total travel time and providing the best-cost routes to vehicles. Several strategies are compared: a baseline algorithm that optimizes the whole network and two algorithms based on extended k-shortest path mappings. Algorithms are analyzed following a simulation-optimization methodology over synthetic and real traffic networks. Obtained results show that TWM algorithms generate solutions close to the static UE traffic assignment methods at a reasonable computational cost. A crucial aspect of TWM is its good performance in terms of optimal routing at the system level, avoiding the need for continuous route calculus based on traffic status data streamin