A CASP-based Solution for Traffic Signal Optimisation

In the context of urban traffic control, traffic signal optimisation is the problem of determining the optimal green length for each signal in a set of traffic signals. The literature has effectively tackled such a problem, mostly with automated planning techniques leveraging the PDDL+ language and solvers. However, such language has limitations when it comes to specifying optimisation statements and computing optimal plans. In this paper, we provide an alternative solution to the traffic signal optimisation problem based on Constraint Answer Set Programming (CASP). We devise an encoding in a CASP language, which is then solved by means of clingcon 3, a system extending the well-known ASP solver clingo. We performed experiments on real historical data from the town of Huddersfield in the UK, comparing our approach to the PDDL+ model that obtained the best results for the considered benchmark. The results showed the potential of our approach for tackling the traffic signal optimisation problem and improving the solution quality of the PDDL+ plans.

💡 Research Summary

The paper tackles the urban traffic‑signal optimisation problem by replacing the widely used PDDL+ planning approach with a Constraint Answer Set Programming (CASP) formulation solved by clingcon 3, an extension of the ASP solver clingo that integrates linear constraints. The authors first describe the practical context: a 1.3 km corridor in the Kirklees area of West Yorkshire, comprising six junctions and thirty‑four road links, for which historical traffic data from Huddersfield are available. Traditional PDDL+ models (notably the FIRE model) can generate feasible signal plans but lack explicit optimisation statements, often producing long‑horizon plans without guarantees of quality.

In response, the paper models each junction as a fixed sequence of stages (green phases) and inter‑green periods, with the order immutable and the duration of each stage selectable only from a predefined configuration set—constraints that mirror real‑world legacy traffic‑control hardware. The problem’s objective is to minimise average vehicle delay, operationalised as maximising the total number of passenger‑car‑units (PCU) that traverse the network within a given simulation horizon.

The authors introduce the necessary ASP background and then detail the clingcon 3 language extensions: theory atoms such as &dom, &sum, and optimisation directives &maximize/ &minimize. The CASP encoding begins with a set of facts describing controllable junctions, available configurations, phase limits, link topology, capacities, initial occupancies, and turn‑rates (PCU flow per second for each stage). ASP rules enforce the cyclic ordering of phases, ensure exactly one configuration per junction, and generate choice rules for selecting active phases at each time step. Linear constraints expressed via clingcon atoms model the evolution of link occupancies and the cumulative counters that record how many PCU have passed each link. The optimisation statement &maximize {counter(L)} directs the solver to find a model that yields the highest possible throughput, which directly corresponds to reduced average delay.

Experimental evaluation compares the CASP approach against the best PDDL+ baseline (FIRE) on two tasks: (1) feasibility – can clingcon find solutions of comparable quality within a limited horizon (e.g., 25 seconds), and (2) optimisation – does the explicit maximise directive improve solution quality. Results show that, even with modest horizons, the CASP model matches or exceeds the baseline’s counter values, and when optimisation is activated the improvement is statistically significant. The authors note that extending the horizon further leads to a rapid increase in variables and constraints, causing longer solving times, which highlights a scalability challenge common to declarative approaches.

The discussion emphasizes three main contributions: (i) a clear, declarative representation of traffic‑signal optimisation that naturally incorporates hardware‑imposed configuration limits, (ii) the demonstration that clingcon 3 can efficiently handle the mixed logical‑numeric nature of the problem, delivering high‑quality solutions faster than pure PDDL+ planners, and (iii) the ability to embed optimisation directives directly in the model, guaranteeing that the solver seeks the best possible plan within the defined horizon. Limitations include the dependence on a fixed horizon and the need for further work on hierarchical or decomposition techniques to scale to city‑wide networks.

In conclusion, the paper presents the first successful application of CASP to a real‑world traffic‑signal optimisation benchmark, showing that the approach can outperform state‑of‑the‑art PDDL+ planners both in solution quality and in the expressiveness of the modelling language. Future work is suggested on integrating real‑time sensor feeds, exploring distributed CASP solving for larger networks, and extending the objective to multi‑criteria optimisation such as emissions or fuel consumption. Overall, the study opens a promising research direction for applying declarative constraint programming to complex urban traffic management problems.