The work, published open access in the journal Applied Intelligence, targets Hierarchical Task Network planning, or HTN planning, a technique prized in artificial intelligence for its speed and its ability to encode rich domain knowledge as recipes. In classical HTN planning, an agent starts with a high-level task, such as delivering a package or capturing a scientific image, and repeatedly decomposes it into smaller subtasks using predefined methods until only directly executable primitive actions remain. This hierarchical structure mirrors how humans organise complex decision-making, which is precisely why the Stuttgart team saw it as a natural home for risk reasoning. Yet, as they document in a sweeping review of prior work, no existing HTN approach models risk in terms of probabilistic action costs, and none reasons about the risk attitude of the planning agent. Existing planners either ignore costs entirely, minimise expected cost in a risk-neutral way, or handle uncertainty over action effects rather than costs, leaving a conceptual gap between what decision theory prescribes and what planning algorithms actually compute.

The theoretical backbone of the new approach comes from expected utility theory, formalised in the mid-twentieth century by von Neumann and Morgenstern. Under this framework, an agent’s tolerance for risk is expressed as a utility function that transforms uncertain monetary or temporal costs into real-valued utilities. A risk-neutral agent uses a linear function and simply minimises expected cost. A risk-seeking agent uses a convex exponential function that rewards the small chance of a cheap, lucky outcome. A risk-averse agent uses a concave function that disproportionately punishes the tail risk of an expensive disaster. The Stuttgart team defines a family of exponential utility functions in which a coefficient called alpha controls the intensity of the attitude: the larger alpha becomes, the more extreme the agent’s risk-seeking or risk-averse behaviour. Crucially, these functions allow the expected utility of a plan to be computed segment by segment, a property called segmentation that makes the mathematics tractable inside a hierarchical planner.

Turning this theory into a working algorithm required solving several technical puzzles that had blocked earlier attempts. First, expected utilities can be negative as well as positive, whereas classical cost-optimal planners assume strictly positive action costs, so existing heuristics could not simply be reused. Second, the exponential utility functions multiply across plan segments, but the A* search algorithm at the heart of the planner adds values. The researchers’ elegant workaround is a logarithmic transformation: by taking the logarithm of the expected utility of each primitive action, the multiplicative aggregation becomes additive, restoring compatibility with A* while preserving the sign of the utility through an attitude-determining coefficient. Third, hierarchical domains often contain cycles, where decomposing a task can lead back to the same task, and a naive maximisation procedure could loop forever through a cycle, inflating expected utility without bound. The team’s preprocessing phase detects such cycles by tracking decomposition paths and assigns negative infinity to the last method in each cycle, forcing the search to prefer alternative decompositions when they exist.

The resulting system, implemented as a prototype planner called RISKIE built on top of the established PANDA planning framework, operates in two phases. In the preprocessing phase, the planner grounds the domain into a graph structure called a Ground Cost-Variable Task Decomposition Graph and computes, bottom-up, an estimate of the expected utility of every task and method. Because a compound task may appear in many different decomposition paths, some of which contain cycles and some of which do not, each task stores a vector of expected utility values rather than a single number, and the maximum is used during search. In the plan generation phase, A* explores partial plans, ordering them by the sum of the expected utilities of their already-refined primitive actions plus a heuristic estimate for the compound tasks still to be decomposed. The authors prove formally that this heuristic is admissible in the maximisation setting, meaning it never underestimates the achievable expected utility, and they establish termination, soundness, completeness, and optimality of the overall algorithm, together with worst-case and best-case complexity bounds.

To test the approach, the researchers evaluated RISKIE on four risk-involving domains: a Self-Driving Car domain modelled in earlier work, a Satellite domain adapted from a classical planning benchmark, and extended versions of the Rover and Transport benchmark domains from the 2020 International Planning Competition. In the Self-Driving Car domain, a vehicle must navigate roads with construction zones, congested pedestrian crossings, and icy stretches, choosing among options such as accelerating without electronic stability control, decelerating with it, or activating stability control but accelerating anyway. In the extended Rover domain, rovers can delegate data transmission to space drones that are fast but prone to crashes, signal loss, and transmission failures. In the extended Transport domain, trucks can choose between ordinary roads and a speedway network that is potentially faster but riskier. Each domain was modelled in three planning languages, including an extension of the standard hierarchical language HDDL that the authors call rHDDL, which allows probability distributions over operator costs to be expressed directly.

The behavioural results are striking. In the Self-Driving Car domain, an extremely risk-averse agent with alpha equal to 0.9 chooses the only route whose every action has a guaranteed outcome, taking the long road and decelerating with stability control engaged on the icy stretch. The extreme risk-seeking agent, by contrast, takes the short road and accelerates on the ice without stability control, accepting an eighty percent chance of slipping for a twenty percent chance of saving four hours. The risk-neutral agent takes the route with the lowest expected cost and is indifferent among several icy-road options. In the Satellite domain, risk-seeking agents power all three instruments simultaneously, accepting the risk of a power failure to skip two switching actions, while risk-averse agents operate instruments one at a time, producing longer but safer plans. In the Transport and Rover domains, the pattern flips: risk-averse agents produce shorter plans because the risky options, speedways and drones, require extra steps, illustrating that the relationship between risk attitude and plan length is domain-dependent rather than universal.

The comparative evaluation pitted RISKIE against four state-of-the-art HTN planners spanning the full spectrum of cost awareness: SH and HyperTensioN, which ignore costs entirely, and SHOP2 and PANDA, which optimise costs in a risk-neutral fashion. Across 440 experiments covering eleven risk-attitude settings per problem instance, RISKIE solved every instance in every domain within a ten-minute timeout, achieving coverage on par with or better than the established planners despite optimising a considerably more complex objective. By construction, RISKIE’s plans always matched or exceeded the expected utility of plans produced by the other planners when scored with the same utility function. Plan-overlap analysis revealed that the risk-neutral configuration of RISKIE agreed most often with the conventional planners, as expected, while risk-seeking configurations frequently diverged, producing plans no baseline planner could find. An ablation study confirmed that varying alpha meaningfully changes behaviour in domains rich with risky alternatives, while in domains offering only binary risk choices, all attitudes converge on the same plan.

The authors are candid about limitations and open challenges. The current approach assumes a static risk attitude and utility functions that permit segmentation; arbitrary utility functions could, in the worst case, require enumerating every possible plan trajectory. Scalability bottlenecks emerge when the branching factor is high or when the heuristic becomes uninformative, and the team points to landmark guidance and greedy pre-passes as promising remedies. Dynamic risk attitudes that shift with remaining battery or elapsed time, and multi-agent settings where a self-driving car must adapt to the risk preferences of surrounding human drivers, remain future work. Still, the significance of the contribution is hard to overstate: for the first time, a hierarchical AI planner can be handed a risk attitude the way a human client hands a financial adviser a risk profile, and it will return a provably optimal plan for that personality. As autonomous vehicles, satellites, and robots move from laboratories into the messy, probabilistic real world, planners that understand risk may become not a luxury but a necessity.

Subject of Research: Risk-aware hierarchical task network planning using expected utility theory

Article Title: Solving risk-aware HTN planning problems: algorithmic, formal, and empirical results

Article References: Alnazer, E., Georgievski, I., & Aiello, M. (2026). Solving risk-aware HTN planning problems: algorithmic, formal, and empirical results. Applied Intelligence, 56(15), Article 468. https://doi.org/10.1007/s10489-026-07450-4

Image Credits: AI Generated

DOI: 10.1007/s10489-026-07450-4

Keywords: HTN planning, risk-aware planning, expected utility, AI planning, autonomous vehicles, decision theory, heuristic search, probabilistic action costs, RISKIE planner, risk attitudes, A* search, Applied Intelligence

The motivation behind the work lies in the convergence of two technological currents. Graph pangenomics and long-read sequencing, the authors argue, together hold the promise of integrating read mapping directly with variant calling. A single long read, spanning thousands of DNA letters in one continuous stretch, can provide strong evidence not only for single nucleotide variants but also for larger or more complex structural variations that are notoriously difficult to detect with short reads. Short-read sequencers chop the genome into fragments of a few hundred bases, and when a structural variant spans a region longer than a single fragment, the evidence is scattered and easily missed. Long reads, by contrast, can traverse an entire rearranged segment, carrying the signal for the variant within one molecule. To fully realize this potential, however, the classical algorithms used to align sequences against graphs must be extended to account for recombination events among haplotypes, all while maintaining the practical efficiency that large-scale sequencing projects demand.

Recombination is not a rare curiosity in genome biology; it is a fundamental force that reshapes chromosomes in every generation. When a read originates from a haplotype that inherited one segment from one ancestral path through the pangenome and an adjacent segment from another, an aligner that insists on a single coherent path through the graph will either misalign the read or miss the true origin altogether. Capturing such events formally is what the authors call the R-bounded Recombination-Aware Alignment Problem, abbreviated R-RAAP in the paper. The task is to find the best alignment of a query sequence to a path through a variation graph while allowing a bounded number of recombinations, that is, switches between distinct haplotype paths embedded in the graph. Solving this problem exactly with classical dynamic programming quickly becomes intractable as the number of allowed recombinations grows, because the search space of possible path combinations explodes combinatorially.

The team’s answer to this computational wall is an algorithmic strategy borrowed from artificial intelligence: the A* search framework. A* is a best-first search method that explores a space of possible solutions by prioritizing states that look most promising according to a heuristic function, an estimate of the remaining cost to reach a goal. When the heuristic is admissible, meaning it never overestimates the true remaining cost, A* is guaranteed to find an optimal solution while typically examining only a small fraction of the full search space. RecAlign applies this idea to sequence-to-graph alignment, steering the search through the variation graph toward the alignments that are most likely to be optimal and pruning away the vast regions of the search space that cannot contribute to the best answer. The result, according to the study, is an aligner that is both accurate and fast, and that can efficiently manage two or more recombination events when aligning a read against a variation graph.

The theoretical underpinnings of the work draw on a rich toolkit of combinatorial algorithms and data structures. The abbreviations section of the paper alone signals the depth of the machinery involved: dynamic programming, the longest increasing subsequence problem, the Ferragina-Manzini index better known as the FM-index, and the directed acyclic graph structure that underlies most variation graph representations. The authors also invoke the Strong Exponential Time Hypothesis, a central conjecture in computational complexity theory, which suggests that the recombination-aware alignment problem is unlikely to admit dramatically faster exact algorithms in the worst case. This complexity barrier makes the heuristic-guided pruning of A* not merely a convenience but a necessity: without a way to focus the search, exact recombination-aware alignment would remain confined to toy examples rather than chromosome-scale graphs.

Efficiency alone would not matter if the tool could not be deployed in realistic pipelines. A key contribution of the study is the integration of RecAlign into a chain-and-extend framework, an architectural pattern familiar from classical read aligners, in which short high-confidence matches are first chained together into larger anchors and the alignment is then extended around those anchors. Within this framework, the authors report that RecAlign is currently the only recombination-aware tool that can be used in practice to align long reads against chromosome-wide pangenome graphs. That distinction matters because chromosome-wide graphs, such as those built from the collections of haplotypes assembled by the Human Pangenome Reference Consortium, are precisely the scale at which modern pangenome analyses operate. Tools that can only handle gene-sized or region-sized graphs, however accurate, cannot serve as the mapping engine for whole-genome sequencing experiments.

The biological payoff of recombination-aware alignment is expected to be greatest in the most complex and clinically important regions of the genome. The paper’s list of abbreviations points to the human leukocyte antigen region and the major histocompatibility complex, the hyper-polymorphic immune loci where haplotype diversity is extreme and where short-read mapping has historically struggled most. It also references non-allelic homologous recombination, the mutational mechanism behind many recurrent structural variants, and the Graphical Fragment Assembly and Graph Alignment Format standards that allow graph-based results to flow between tools. By explicitly modeling recombinations among the haplotypes embedded in a variation graph, RecAlign can in principle place reads onto the correct combination of ancestral paths, sharpening downstream variant calling in regions where a linear reference would systematically mislead.

The work did not emerge in isolation. The authors acknowledge helpful discussions with Davide Cozzi and Simone Ciccolella during the development of the project, and the research was carried out within a substantial European funding framework. Monti, Riccardi, Della Vedova, Rizzi and Bonizzoni received support from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement PANGAIA, number 872539, a network dedicated to pangenome algorithms and data structures. The work was further supported by the Horizon Europe programme under project FORGENOM II, identifier 101160008, and partially by the Italian Ministry of University and Research through the Dipartimenti di Eccellenza 2023-2027 grant of the Department of Informatics, Systems and Communication at the University of Milano-Bicocca. Bonizzoni, Della Vedova and Rizzi contributed equally to the study, reflecting a collaboration that spans algorithmic theory and practical bioinformatics engineering.

Consistent with the norms of the field, the implementation is open source and freely available on GitHub under the AlgoLab organization, in the RecGraph repository on the a_star branch, allowing other developers to inspect, reuse and extend the code. The authors declare no competing interests, and all data used in the study were either taken from public repositories or simulated, so no new human subject data were generated. The article is published open access under a Creative Commons Attribution 4.0 International license and was released as a citable, peer-reviewed accepted manuscript with a permanent DOI, subject to further editorial production before the final version of record.

For the broader genomics community, RecAlign represents a step toward a long-standing goal: mapping reads in a way that respects the true evolutionary structure of the population from which they came. As pangenome references grow to encompass ever more diverse haplotypes, and as long-read sequencing becomes routine in clinical and research settings, the algorithms that connect these technologies will determine how much of the genome’s complexity can actually be read out of the data. By showing that recombination-aware alignment can be made fast enough for chromosome-wide graphs, the Milano-Bicocca and UC Santa Cruz team has removed one of the practical obstacles standing between graph pangenomics and its everyday use, and has provided a concrete, tested tool that other groups can now build upon.

Subject of Research: Recombination-aware sequence-to-graph alignment for pangenome read mapping

Article Title: Faster and accurate recombination-aware sequence-to-graph aligner

Article References: Monti, D. C., Riccardi, B., Sirén, J., Bonizzoni, P., Della Vedova, G., & Rizzi, R. (2026). Faster and accurate recombination-aware sequence-to-graph aligner. BMC Bioinformatics. https://doi.org/10.1186/s12859-026-06640-8

Image Credits: AI Generated

DOI: 10.1186/s12859-026-06640-8

Keywords: pangenomics, variation graphs, sequence-to-graph alignment, long-read sequencing, recombination, A* search, RecAlign, BMC Bioinformatics, variant calling, FM-index, Human Pangenome Reference Consortium, computational biology