We present the Traffic Signal Plans Explorer, a framework for visualising and exploring traffic signal plans generated via PDDL+ planning. Designed to support both traffic experts and non-specialists, the tool offers a web-based interface for high-level network analysis and a SUMO-based adapter for detailed simulation. Users can inspect junction settings and link dynamics, and simulate plan execution step by step. The system bridges planning technology with practical traffic control, enhancing the transparency and usability of automatically generated solutions.

Optimising traffic signals is crucial for mitigating urban congestion, and automated planning, particularly with PDDL+, has shown promise for real-world deployment due to its flexibility and centralised perspective. While existing PDDL+ models guarantee deployability on current infrastructure, they face significant limitations: reliance on domain-independent heuristics restricts their applicability and scalability, leading to slow solution generation and unclear plan quality. To overcome these challenges and unlock the widespread adoption of planning-based traffic control, we introduce hCAFE, a domain-specific heuristic for PDDL+-based traffic signal optimisation. Unlike prior approaches, hCAFE is designed to work effectively across multiple problem encodings, addressing a key limitation of traditional domain-specific heuristics. We demonstrate its capabilities on real-world data from a region of the UK, showing significant improvements in solution generation time and search space exploration. Our evaluation also compares the strategies generated by hCAFE against historical data from existing traffic control systems and a non-deployable benchmark, confirming the high quality of the resulting plans.

Uncertainty over model knowledge is a core challenge in planning and has been addressed through various approaches tailored to different scenarios. In this paper, we focus on scenarios where the agent does not initially know the exact outcome of its actions but gains knowledge upon execution, i.e., each action reveals its actual effect, removing uncertainty about future occurrences. We refer to this formulation as Planning with Uncertain Models of Actions (PUMA). We show that PUMA can be compiled in polynomial time in both Fully Observable Non-Deterministic planning and, perhaps more unexpectedly, classical planning, providing a constructive proof that PUMA remains PSPACE-complete despite its apparent exponential uncertainty. Finally, we experimentally evaluate both compilations with benchmark domains that capture the key aspects of the problem. The results show the practical feasibility of our approach and reveal a complementary behavior between the two compilations.

The expressive power of PDDL+ is crucial in a wide range of real-world applications, where it is necessary to represent hybrid discrete-continuous changes and environmental dynamics. Given the complexity of the dynamics that can be modelled in PDDL+ and the scale of the problems involved, the ability to validate plans and simulate their trajectories is essential for assessing the accuracy of the models. In this paper, we present PPS (PDDL Plus Simulator), a Java-based tool that enables seamless validation and simulation of PDDL+ plans under time-discrete semantics.

: Modular Autonomous Customised Bus Systems (MACB) promise to significantly enhance public transport attractiveness and accessibility, leading to improved quality of life and reduced emissions. Compared to traditional bus systems, MACB provides a problem that poses a new set of challenges, ranging from the allocation of vehicles to the optimisation of routes and recharges. The MACB problem is attracting increasing interest within the transport research community, but it presents characteristics and dimensions that lend themselves well to approaches based on planning and combinatorial search. In this paper, with the aim of bridging the gap between different research communities, we provide a crisp definition of the MACB problem and present a planning-based approach to solve a specific variant of the problem, together with a set of benchmarks to foster research on this topic.

It is well known that numeric planning can be made decidable if the domain of all numeric state variables is finite. This bounded formulation can be polynomially compiled into classical planning with Boolean conditions and conditional effects preserving the plan size exactly. However, it remains unclear whether this compilation has any practical utility. To explore this aspect, this work revisits the theoretical compilation framework from a practical perspective, focusing on the fragment of simple numeric planning. Specifically, we introduce three different compilations. The first, called one-hot, aims to systematise the current practice among planning practitioners of modelling numeric planning through classical planning. The other two, termed binary compilations, extend and specialise the logarithmic encoding introduced in previous literature. Our experimental analysis reveals that the overly complex logarithmic encoding can, surprisingly, be made practical with some representational expedients. Among these, the use of axioms is particularly crucial. Furthermore, we identify a class of mildly numeric planning problems where a classical planner, i.e., LAMA, when run on the compiled problem, is highly competitive with state-of-the-art numeric planners.

Automated planning, a core area of artificial intelligence, aims to generate action sequences that achieve specified goals based on a formal model. In classical planning, where only Boolean state variables are allowed, conditional effects are the standard approach for modelling actions with state-dependent outcomes. However, unlike in the classical setting, relatively little research has focused on developing planning methods for numeric problems with conditional effects. To address this gap in the literature, this work studies numeric planning with conditional effects. We formalise its semantics and revise existing classical planning compilations for conditional effects to account for the specific features of numeric planning. This results in three encodings: two are designed for the full class of numeric planning problems, while the third is specific to tasks with conditional effects that increase or decrease variables by a constant, transforming such problems into instances of Simple Numeric Planning, a well-known and practically significant subclass of numeric tasks. The experimental evaluation compares these compilations across both newly designed and compelling benchmarks as well as existing domains featuring conditional effects. Our empirical findings reveal complementary behaviour among the approaches, highlighting the practical impact of selecting the appropriate compilation for different problem structures.

Real-world applications of planning techniques often deal with dynamic and noisy environments, where sensor readings are often inaccurate, and the world's states can evolve in unexpected ways. This is particularly challenging for hybrid discrete-continuous planning approaches, where processes and events can be strongly affected by even slightly different initial conditions of the world, and planning tasks are notoriously difficult to cope with. In this paper, we introduce the Initial Condition Retrieving (ICR) problem to foster hybrid planning in real-world applications. Given a knowledge model of a planning task and a trace, solving the ICR problem allows identifying the space of all the initial conditions from which the provided plan is guaranteed to reach a goal state. We define three tasks: (i) retrieving any valid initial condition, (ii) fixing only some desired initial values and retrieving a complete initial condition that fills in the unassigned values, or (iii) retrieving the closest achievable initial condition to a fully specified one from which the goal cannot be reached. Experiments on well-known hybrid planning domains demonstrate the efficacy of our approach in solving such tasks. Moreover, given that our approach can be applied to numeric planning without any change, we extend our analysis to numeric domains, where we obtain positive results.

PDDL+ is a planning formalism designed to model mixed continuous-discrete problems. Despite its expressiveness, the absence of a well-established framework for evaluating plan quality makes it challenging to use PDDL+ in applications where plan shape and quality are crucial. This paper addresses this issue by introducing a comprehensive set of plan cost functions tailored for discrete-time PDDL+, along with a cost-preserving translation for generating cost-aware PDDL2.1 planning tasks. The plan cost functions provide a theoretical ground for assessing plan quality, whereas the translation shows their practicability by leveraging the connection between PDDL+ and PDDL2.1.

Automated planning systems are increasingly deployed in real-world applications, often characterised by uncertainty and noise stemming from sensors, actuators, and environmental conditions. Under such circumstances, improving the deployability of generated plans requires assessing their robustness to varying conditions, thereby reducing the need for costly replanning. Replanning can be computationally intensive and may hinder the practical applicability of planning systems. In many domains, such as urban traffic control or underwater exploration, it is often sufficient for plans to reach an acceptable region rather than the exact goal. A key distinction in this context lies between valid plans (which achieve the intended goal under ideal conditions) and executable plans (which remain feasible under uncertainty or perturbation). This paper formalises the notion of execution-invariant planning tasks, in which plans are robust to noise and uncertainty. To foster the adoption of automated planning in real-world settings, we propose a statistical framework for evaluating plan robustness, offering a quantifiable measure of a plan’s ability to reach a goal within a specified tolerance under diverse perturbations or uncertainty. We validate our approach in two real-world domains, demonstrating its effectiveness.

It is well known that numeric planning can be made decidable if the domain of all numeric state variables is finite. This bounded formulation can be polynomially compiled into classical planning with Boolean conditions and conditional effects preserving the plan size exactly. However, it remains unclear whether this compilation has any practical utility. To explore this aspect, this work revisits the theoretical compilation framework from a practical perspective, focusing on the fragment of simple numeric planning. Specifically, we introduce three different compilations. The first, called one-hot, aims to systematise the current practice among planning practitioners of modelling numeric planning through classical planning. The other two, termed binary compilations, extend and specialise the logarithmic encoding introduced in previous literature. Our experimental analysis reveals that the overly complex logarithmic encoding can, surprisingly, be made practical with some representational expedients. Among these, the use of axioms is particularly crucial. Furthermore, we identify a class of mildly numeric planning problems where a classical planner, i.e., LAMA, when run on the compiled problem, is highly competitive with state-of-the-art numeric planners.

The problem of traffic signal optimisation has been successfully tackled using the PDDL+ planning formalism, which also provides an ideal ground for simulating traffic behaviour and performing what-if analysis to assess and compare alternative scenarios. This line of research leads to approaches that can efficiently generate high-quality signal plans with significant benefits in terms of congestion and emissions reduction, as demonstrated both in simulations and real-world deployments. Existing models for automated planning-based traffic signal control can be roughly divided into two classes. (i) Models maximising the flexibility of the traffic controller, where the planning system can dynamically adjust the duration of traffic stages without constraints on the overall cycles and on the differences between subsequent cycles. (ii) Models that guarantee the deployability of traffic signal control techniques also on legacy infrastructure, by forcing the AI approach to select the cycle configurations of traffic signals for the controlled junctions from a given pre-defined set. Of course, both classes offer valuable properties and benefits: the extreme flexibility helps shed light on the potential gains achievable through investment in brand-new infrastructure, whereas the deployable approaches ensure the immediate usability of tools to maximise short-term impact. To bridge the gap between different model classes and explore the trade-off between flexibility and deployability, we present the Trade model. It enables the enforcement of key constraints required for deployability while preserving a level of flexibility that surpasses the capabilities of traditional traffic control infrastructure.

The paper introduces a novel polynomial compilation technique for the sound and complete removal of conditional effects in classical planning problems. Similar to Nebel's polynomial compilation of conditional effects, our solution also decomposes each action with conditional effects into several simpler actions. However, it does so more effectively by exploiting the actual structure of the given conditional effects. We characterise such a structure using a directed graph and leverage it to significantly reduce the number of additional atoms required, thereby shortening the size of valid plans. Our experimental analysis indicates that this approach enables the effective use of polynomial compilations, offering benefits in terms of modularity and reusability of existing planners. It also demonstrates that a compilation-based approach can be more efficient, either independently or in synergy with state-of-the-art optimal planners that directly support conditional effects.

The PDDL+ formalism allows the use of planning techniques in applications that require the ability to perform hybrid discrete-continuous reasoning. PDDL+ problems are notoriously challenging to tackle, and to reason upon them a well-established approach is discretisation. Existing systems rely on a single discretisation delta or, at most, two: a simulation delta to model the dynamics of the environment, and a planning delta, that is used to specify when decisions can be taken. However, there exist cases where this rigid schema is not ideal, for instance when agents with very different speeds need to cooperate or interact in a shared environment, and a more flexible approach that can accommodate more deltas is necessary. To address the needs of this class of hybrid planning problems, in this paper we introduce a reformulation approach that allows the encapsulation of different levels of discretisation in PDDL+ models, hence allowing any domain-independent planning engine to reap the benefits. Further, we provide the community with a new set of benchmarks that highlights the limits of fixed discretisation.

The use of planning techniques in traffic signal optimisation has proven effective in managing unexpected traffic conditions as well as typical traffic patterns. However, significant challenges concerning the deployability of generated signal strategies remain, as existing approaches tend not to consider constraints and features of the actual real-world infrastructure on which they will be implemented. To address this challenge, we introduce a range of PDDL+ models embodying technological requirements as well as insights from domain experts. The proposed models have been extensively tested on historical data using a range of well-known search strategies and heuristics, as well as alternative encodings. Results demonstrate their competitiveness with the state of the art.

The PDDL+ formalism allows the use of planning techniques in applications that require the ability to perform hybrid discrete-continuous reasoning. PDDL+ problems are notoriously challenging to tackle, and to reason upon them a well-established approach is discretisation. Existing systems rely on a single discretisation delta or, at most, two: a simulation delta to model the dynamics of the environment, and a planning delta, that is used to specify when decisions can be taken. However, there exist cases where this rigid schema is not ideal, for instance when agents with very different speeds need to cooperate or interact in a shared environment, and a more flexible approach that can accommodate more deltas is necessary. To address the needs of this class of hybrid planning problems, in this paper we introduce a reformulation approach that allows the encapsulation of different levels of discretisation in PDDL+ models, hence allowing any domain-independent planning engine to reap the benefits. Further, we provide the community with a new set of benchmarks that highlights the limits of fixed discretisation.

The use of planning techniques in traffic signal optimisation has proven effective in managing unexpected traffic conditions as well as typical traffic patterns. However, significant challenges concerning the deployability of generated signal plans remain, as planning systems need to consider constraints and features of the actual real-world infrastructure on which they will be implemented. To address this challenge, we introduce a range of PDDL+ models embodying technological requirements as well as insights from domain experts. The proposed models have been extensively tested on historical data using a range of well-known search strategies and heuristics, as well as alternative encodings. Results demonstrate their competitiveness with the state of the art.

Conditional effects are a key feature in classical planning, enabling the description of actions whose outcomes are state-dependent. It is well known that the polynomial removal of conditional effects necessarily increases the size of a valid plan by a polynomial factor while preserving exactly the plan size requires an exponential encoding of the problem. The paper proposes and empirically evaluates optimisations for existing polynomial compilations. These optimisations aim to make the resulting compilations more suitable for planners while limiting the increase in plan size, which is inevitable if we want to keep the compilation polynomial. Specifically, the paper introduces a polynomial compilation technique that expands conditional effects when their number is below a certain threshold and sequentialises them otherwise. Additionally, the paper demonstrates that even straightforward optimisations can have a notable impact.

There is a growing interest in the use of AI techniques for urban traffic control, with a particular focus on traffic signal optimisation. Model-based approaches such as planning demonstrated to be capable of dealing in real-time with unexpected or unusual traffic conditions, as well as with the usual traffic patterns. Further, the knowledge models on which such techniques rely to generate traffic signal strategies are in fact simulation models of traffic, hence can be used by traffic authorities to test and compare different approaches. In this work, we present a framework that relies on automated planning to generate and simulate traffic signal strategies in a urban region. To demonstrate the capabilities of the framework, we consider real-world data collected from sensors deployed in a major corridor of the Kirklees region of the United Kingdom.

PDDL+ is an expressive formalism that allows for the use of planning in hybrid discrete-continuous domains. To cope with unexpected situations, it is crucial for deployed planning-based systems to efficiently repair existing plans. In this paper, we revisit a recently proposed FIXABILITY framework for expressing and solving problems from validation to rescheduling of actions in PDDL+ plans.

In multi-agent planning, preserving the agents' privacy has become an increasingly popular research topic. For preserving the agents' privacy, agents jointly compute a plan that achieves mutual goals by keeping certain information private to the individual agents. Unfortunately, this can severely restrict the accuracy of the heuristic functions used while searching for solutions. It has been recently shown that, for centralized planning, blind search algorithms such as width-based search can solve instances of many existing domains in low polynomial time when they feature atomic goals. Moreover, the performance of goal-oriented search can be improved by combining it with width-based search. In this paper, we investigate the usage of width-based search in the context of (decentralised) collaborative multi-agent privacy-preserving planning, addressing the challenges related to the agents' privacy and performance. In particular, we show that width-based search is a very effective approach over several benchmark domains, even when the search is driven by heuristics that roughly estimate the distance from goal states, computed without using the private information of other involved agents. Moreover, we show that the use of width-based techniques can significantly reduce the number of messages transmitted among the agents, better preserving their privacy and improving their performance. An experimental study presented in the paper analyses the effectiveness of our techniques, and compares them with the state-of-the-art of collaborative multi-agent planning.

PDDL+ models are advanced models of hybrid systems and the resulting problems are notoriously difficult for planning engines to cope with. An additional limiting factor for the exploitation of PDDL+ approaches in real-world applications is the restricted number of domain-independent planning engines that can reason upon those models. With the aim of deepening the understanding of PDDL+ models, in this work, we study a novel mapping between a time discretisation of pddl+ and numeric planning as for PDDL2.1 (level 2). The proposed mapping not only clarifies the relationship between these two formalisms but also enables the use of a wider pool of engines, thus fostering the use of hybrid planning in real-world applications. Our experimental analysis shows the usefulness of the proposed translation and demonstrates the potential of the approach for improving the solvability of complex PDDL+ instances.

Automated planning is a prominent Artificial Intelligence (AI) challenge that has been extensively studied for decades, which has led to the development of powerful domain-independent planning systems. The performance of domain-independent planning systems are strongly affected by the structure of the search space, that is dependent on the application domain and on its encoding.This paper proposes and investigates a novel way of combining machine learning and heuristic search to improve domain-independent planning. On the learning side, we use learning to predict the plan cost of a good solution for a given instance. On the planning side, we propose a bound-sensitive heuristic function that exploits such a prediction in a state-space planner. Our function combines the input prediction (derived inductively) with some pieces of information gathered during search (derived deductively). As the prediction can sometimes be grossly inaccurate, the function also provides means to recognise when the provided information is actually misguiding the search. Our experimental analysis demonstrates the usefulness of the proposed approach in a standard heuristic best-first search schema.

The aim of decentralised multi-agent (DMA) planning is to coordinate a set of agents to jointly achieve a goal while preserving their privacy. Blind search algorithms, such as width-based search, have recently proved to be very effective in the context of centralised automated planning, especially when combined with goal-oriented techniques. In this paper, we discuss a recent line of research in which the usage of width-based search has been extensively studied in the context of DMA planning, addressing the challenges related to the agents' privacy and performance.

PDDL+ is an expressive planning formalism that enables the modelling of hybrid discrete-continuous domains. The resulting models are notoriously difficult to cope with, and few planning engines are natively supporting PDDL+. To foster the use of PDDL+, this paper revisits a set of recently proposed translations allowing to reformulate a PDDL+ task into a PDDL2.1 one. Such translations permit the use of a wider set of engines to solve complex hybrid problems.

In multi-agent planning, agents jointly compute a plan that achieves mutual goals, keeping certain information private to the individual agents. Agents' coordination is achieved through the transmission of messages, but they can be a source of privacy leakage as they can permit a malicious agent to collect information about other agents' search processes and states. In this paper, we investigate the usage of novelty techniques in the context of (decentralised) multi-agent privacy preserving planning, addressing the challenges related to the agents' privacy and performance. In particular, we show that novelty based techniques allow a significant reduction on the number of messages transmitted among agents, increasing their privacy levels and also their performances. An experimental study analyses the effectiveness of our techniques and compares them with the state of-the-art. Finally, we examine the robustness of our approach considering different delays in the messages transmission as would occur in overloaded networks, due for example to massive attacks or critical situations.

Admissible heuristics are essential for optimal planning in the context of search algorithms like A*, and they can also be used in the context of suboptimal planning in order to find quality-bounded solutions. In satisfacing planning, on the other hand, admissible heuristics are not exploited by the best-first search algorithms of existing planners even when a time window is available for improving the first solution found. For example, in the well-know planner LAMA, better solutions within such a time window are sought by restarting a Weighted-A* search guided by inadmissible heuristics, each time a better solution is found. In this paper, we investigate the use of admissible heuristics in the context of LAMA for pruning nodes that cannot lead to better solutions. The revised search of LAMA is experimentally evaluated using two alternative admissible heuristics for pruning and three types of problems: planning with soft goals, planning with action costs, and planning with both action costs and soft goals. Soft goals are compiled into hard goals following the approach of Keyder and Geffner. The empirical results show that the use of admissible heuristics in LAMA can be of great help to improve the planner performance.