An Evolutionary Method for the Minimum Toll Booth Problem: the Methodology

This paper considers the minimum toll booth problem (MINTB) for determining a tolling strategy in a transportation network that requires the least number of toll locations, and simultaneously causes the most efficient use of the network. The paper develops a methodology for using the genetic algorithm to solve MINTB and presents the algorithm GAMINTB. The proposed method is tested and validated through a computational study with six example networks. Additional numerical test discovers some interesting properties for the proposed method, and provides guidelines for further application of the GAMINTB

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 Parameterized Complexity Analysis of Bi-level Optimisation with Evolutionary Algorithms

Bi-level optimisation problems have gained increasing interest in the field of combinatorial optimisation in recent years. With this paper, we start the runtime analysis of evolutionary algorithms for bi-level optimisation problems. We examine two NP-hard problems, the generalised minimum spanning tree problem (GMST), and the generalised travelling salesman problem (GTSP) in the context of parameterised complexity. For the generalised minimum spanning tree problem, we analyse the two approaches presented by Hu and Raidl (2012) with respect to the number of clusters that distinguish each other by the chosen representation of possible solutions. Our results show that a (1+1) EA working with the spanning nodes representation is not a fixed-parameter evolutionary algorithm for the problem, whereas the global structure representation enables to solve the problem in fixed-parameter time. We present hard instances for each approach and show that the two approaches are highly complementary by proving that they solve each other's hard instances very efficiently. For the generalised travelling salesman problem, we analyse the problem with respect to the number of clusters in the problem instance. Our results show that a (1+1) EA working with the global structure representation is a fixed-parameter evolutionary algorithm for the problem

Optimal On‑Ramp Metering of Urban Freeway Network for the Coronavirus Disease Control

The outbreak of COVID-19 disrupted our everyday life. Many local authorities enforced a cordon sanitaire for the protection of sensitive areas. Travellers can only pass the cordon after tested. This paper aims to propose a method to design an on-ramp control scheme to maximise urban freeway network throughput with a predetermined queuing delay constraint at all off-ramps around cordon sanitaire. A bi-level programming model is formulated where the lower-level is a transportation system equilibrium to predict traffic flow, and the upper-level is onramp metering optimisation that is nonlinear programming. A stochastic queuing model is used to represent the waiting phenomenon at each off-ramp where testing is conducted, and a heuristic algorithm is designed to solve the proposed bi-level model where a method of successive averages (MSA) is adopted for the lower-level model; A genetic algorithm (GA) with elite strategy is adopted for the upper-level model. An experimental study is conducted to demonstrate the effectiveness of the proposed method and algorithm. The results show that the methods can find a good heuristic optimal solution. These methods are useful for freeway operators to determine the optimal on-ramp control for disease control and prevention

Contingency-Constrained Unit Commitment With Intervening Time for System Adjustments

The N-1-1 contingency criterion considers the con- secutive loss of two components in a power system, with intervening time for system adjustments. In this paper, we consider the problem of optimizing generation unit commitment (UC) while ensuring N-1-1 security. Due to the coupling of time periods associated with consecutive component losses, the resulting problem is a very large-scale mixed-integer linear optimization model. For efficient solution, we introduce a novel branch-and-cut algorithm using a temporally decomposed bilevel separation oracle. The model and algorithm are assessed using multiple IEEE test systems, and a comprehensive analysis is performed to compare system performances across different contingency criteria. Computational results demonstrate the value of considering intervening time for system adjustments in terms of total cost and system robustness.Comment: 8 pages, 5 figure

Assessing the Value of Time Travel Savings – A Feasibility Study on Humberside.

It is expected that the opening of the Humber Bridge will cause major changes to travel patterns around Humberside; given the level of tolls as currently stated, many travellers will face decisions involving a trade-off between travel time, money outlay on tolls or fares and money outlay on private vehicle running costs; this either in the context of destination choice, mode choice or route choice. This report sets out the conclusions of a preliminary study of the feasibility of inferring values of travel time savings from observations made on the outcomes of these decisions. Methods based on aggregate data of destination choice are found t o be inefficient; a disaggregate mode choice study i s recommended, subject to caveats on sample size

A Parameterised Complexity Analysis of Bi-level Optimisation with Evolutionary Algorithms

Bi-level optimisation problems have gained increasing interest in the field of combinatorial optimisation in recent years. In this paper, we analyse the runtime of some evolutionary algorithms for bi-level optimisation problems. We examine two NP-hard problems, the generalised minimum spanning tree problem and the generalised travelling salesperson problem in the context of parameterised complexity. For the generalised minimum spanning tree problem, we analyse the two approaches presented by Hu and Raidl (2012) with respect to the number of clusters that distinguish each other by the chosen representation of possible solutions. Our results show that a (1+1) evolutionary algorithm working with the spanning nodes representation is not a fixed-parameter evolutionary algorithm for the problem, whereas the problem can be solved in fixed-parameter time with the global structure representation. We present hard instances for each approach and show that the two approaches are highly complementary by proving that they solve each other’s hard instances very efficiently. For the generalised travelling salesperson problem, we analyse the problem with respect to the number of clusters in the problem instance. Our results show that a (1+1) evolutionary algorithm working with the global structure representation is a fixed-parameter evolutionary algorithm for the problem

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