Nash Equilibria, collusion in games and the coevolutionary particle swarm algorithm

In recent work, we presented a deterministic algorithm to investigate collusion between players in a game where the players’ payoff functions are subject to a variational inequality describing the equilibrium of a transportation system. In investigating the potential for collusion between players, the diagonalization algorithm returned a local optimum. In this paper, we apply a coevolutionary particle swarm optimization (PSO) algorithm developed in earlier research in an attempt to return the global maximum. A numerical experiment is used to verify the performance of the algorithm in overcoming local optimum

A Coevolutionary Particle Swarm Algorithm for Bi-Level Variational Inequalities: Applications to Competition in Highway Transportation Networks

A climate of increasing deregulation in traditional highway transportation, where the private sector has an expanded role in the provision of traditional transportation services, provides a background for practical policy issues to be investigated. One of the key issues of interest, and the focus of this chapter, would be the equilibrium decision variables offered by participants in this market. By assuming that the private sector participants play a Nash game, the above problem can be described as a Bi-Level Variational Inequality (BLVI). Our problem differs from the classical Cournot-Nash game because each and every player’s actions is constrained by another variational inequality describing the equilibrium route choice of users on the network. In this chapter, we discuss this BLVI and suggest a heuristic coevolutionary particle swarm algorithm for its resolution. Our proposed algorithm is subsequently tested on example problems drawn from the literature. The numerical experiments suggest that the proposed algorithm is a viable solution method for this problem

A bilevel multi-objective road pricing model for economic, environmental and health sustainability

We propose a bilevel multi-objective approach to optimise tolls in a road network. Multiple objectives have been considered at either the upper or lower level in the literature but not both. We consider three objectives at the upper level: minimising system travel time; total vehicle emissions; and negative health impacts, modelled as the level of pollutant uptake. For the lower level, we adopt a time surplus maximisation bi-objective user equilibrium model, assuming all users have two objectives: minimising travel time and toll. The complete bilevel optimisation problem is solved using a combination of a metaheuristic and a classical optimisation algorithm

Road network maintenance and repair considering day-to-day traffic dynamics and transient congestion

Road maintenance and repair (M&R) are essential for keeping the performance of traffic infrastructure at a satisfactory level, and extending their lifetime to the fullest extent possible. For road networks, effective M&R plans should not be constructed in a myopic or ad-hoc fashion regardless of the subsequent benefits and costs associated with those projects considered. A hallmark of road M&R studies is the use of user equilibrium (UE) models to predict network traffic for a given set of road conditions with or without M&R. However, UE approaches ignore the traffic disequilibrium states and transient congestion as a result of M&R derived disruptions to network traffic on a day-to-day (DTD) time scale, which could produce additional substantial travel costs. As shown in the numerical studies on a M&R plan of the Sioux Falls network, the additional maintenance derived travel cost is about 4 billion, which is far exceed the actual M&R construction cost of 0.2 billion. Therefore, it is necessary to recognise the substantial social costs induced by maintenance-derived disruptions in the form of transient congestion when planning M&R. This realistic and pressing issue is not properly addressed by the road M&R planning problems with traffic equilibrium constraints. This thesis proposes a dual-time-scale road network M&R model aiming to simultaneously capture the long-term effects of M&R activities under traffic equilibria, and the maintenance-derived transient congestion using day-to-day (DTD) traffic evolutionary dynamics. The notion of ‘day’ is arbitrarily defined (e.g. weeks or months). The proposed M&R model consists of three sub-models: (1) a within-day dynamic network loading (DNL) model; (2) a day-to-day dynamic traffic assignment (DTD DTA) model; and (3) a day-to-day road quality model. The within-day traffic dynamics is captured by the Lighthill-Whitham-Richards (LWR) fluid dynamic network loading model. The day-to-day phase of the traffic dynamics specify travellers’ route and departure time choices in a stochastic manner based on a sequential mixed multinomial or nested Logit model. Travel information sharing behaviour is further integrated into this macroscopic doubly dynamic (both within-day and day-to-day dynamic) traffic assignment (DDTA) model to account for the impact of incomplete information on travel experiences. A deterministic day-to-day road quality model based on an exponential form of traffic flow is employed to govern the road deterioration process, where a quarter-car index (QI) is applied. All these dynamics are incorporated in a holistic dual-time-scale M&R model, which captures realistic phenomena associated with short-term and long-term effects of M&R, including physical queuing and spillback, road capacity reduction, temporal-spatial shift of congestion due to on-going M&R activities, and the tendency to converge to an equilibrium after M&R actions. Following the dual-time-scale road network M&R model, a bi-level road M&R optimisation model is proposed, where the aforementioned three sub-models are incorporated into the lower-level problem, while the upper-level is to minimise M&R expenditure and network travel costs while maintaining a satisfactory level of road quality. The M&R planning horizon is long yet finite (e.g. years or decades). A ‘quality-usage’ feedback mechanism is investigated in the proposed bi-level M&R model, namely, (1) the DTD road quality evolution as a result of DTD traffic loads and the M&R effectiveness; and (2) the evolution of DTD traffic in response to both DTD road deterioration and the improved road quality after M&R activities. The effectiveness of developed M&R optimisation model is demonstrated through case studies on the Sioux Falls network. A metaheuristic Genetic Algorithm (GA) approach is employed to solve the M&R problems given its highly nonlinear, nonconvex and non-differentiable nature. Explicit travellers’ choice behaviour dynamics and complex traffic phenomena such as network paradoxes arising from M&R activities are illustrated. Through a comparison with the results under the dynamic user equilibrium (DUE) method, the proposed DTD method achieves significant reduction in network travel cost of $ 25 million, approximately 20% of the total cost. This points to the benefit of using the DTD dynamics for capturing network’s responses to M&R in a more realistic way. The M&R model proposed in this thesis could provide valuable managerial insights for road M&R planning agencies.Open Acces

To boldly go:an occam-π mission to engineer emergence

Future systems will be too complex to design and implement explicitly. Instead, we will have to learn to engineer complex behaviours indirectly: through the discovery and application of local rules of behaviour, applied to simple process components, from which desired behaviours predictably emerge through dynamic interactions between massive numbers of instances. This paper describes a process-oriented architecture for fine-grained concurrent systems that enables experiments with such indirect engineering. Examples are presented showing the differing complex behaviours that can arise from minor (non-linear) adjustments to low-level parameters, the difficulties in suppressing the emergence of unwanted (bad) behaviour, the unexpected relationships between apparently unrelated physical phenomena (shown up by their separate emergence from the same primordial process swamp) and the ability to explore and engineer completely new physics (such as force fields) by their emergence from low-level process interactions whose mechanisms can only be imagined, but not built, at the current time

Modelling shared space users via rule-based social force model

The promotion of space sharing in order to raise the quality of community living and safety of street surroundings is increasingly accepted feature of modern urban design. In this context, the development of a shared space simulation tool is essential in helping determine whether particular shared space schemes are suitable alternatives to traditional street layouts. A simulation tool that enables urban designers to visualise pedestrians and cars trajectories, extract flow and density relation in a new shared space design and achieve solutions for optimal design features before implementation. This paper presents a three-layered microscopic mathematical model which is capable of representing the behaviour of pedestrians and vehicles in shared space layouts and it is implemented in a traffic simulation tool. The top layer calculates route maps based on static obstacles in the environment. It plans the shortest path towards agents' respective destinations by generating one or more intermediate targets. In the second layer, the Social Force Model (SFM) is modified and extended for mixed traffic to produce feasible trajectories. Since vehicle movements are not as flexible as pedestrian movements, velocity angle constraints are included for vehicles. The conflicts described in the third layer are resolved by rule-based constraints for shared space users. An optimisation algorithm is applied to determine the interaction parameters of the force-based model for shared space users using empirical data. This new three-layer microscopic model can be used to simulate shared space environments and assess, for example, new street designs

A Study of Problems Modelled as Network Equilibrium Flows

This thesis presents an investigation into selfish routing games from three main perspectives. These three areas are tied together by a common thread that runs through the main text of this thesis, namely selfish routing games and network equilibrium flows. First, it investigates methods and models for nonatomic selfish routing and then develops algorithms for solving atomic selfish routing games. A number of algorithms are introduced for the atomic selfish routing problem, including dynamic programming for a parallel network and a metaheuristic tabu search. A piece-wise mixed-integer linear programming problem is also presented which allows standard solvers to solve the atomic selfish routing problem. The connection between the atomic selfish routing problem, mixed-integer linear programming and the multicommodity flow problem is explored when constrained by unsplittable flows or flows that are restricted to a number of paths. Additionally, some novel probabilistic online learning algorithms are presented and compared with the equilibrium solution given by the potential function of the nonatomic selfish routing game. Second, it considers multi-criteria extensions of selfish routing and the inefficiency of the equilibrium solutions when compared with social cost. Models are presented that allow exploration of the Pareto set of solutions for a weighted sum model (akin to the social cost) and the equilibrium solution. A means by which these solutions can be measured based on the Price of Anarchy for selfish routing games is also presented. Third, it considers the importance and criticality of components of the network (edges, vertices or a collection of both) within a selfish routing game and the impact of their removal. Existing network science measures and demand-based measures are analysed to assess the change in total travel time and issues highlighted. A new measure which solves these issues is presented and the need for such a measure is evaluated. Most of the new findings have been disseminated through conference talks and journal articles, while others represent the subject of papers currently in preparation