Interval-Based Relaxation for General Numeric Planning

We generalise the interval-based relaxation to sequential numeric planning problems with non-linear conditions and effects, and cyclic dependencies. This effectively removes all the limitations on the problem placed in previous work on numeric planning heuristics, and even allows us to extend the planning language with a wider set of mathematical functions. Heuristics obtained from the generalised relaxation are pruning-safe. We derive one such heuristic and use it to solve discrete-time control-like planning problems with autonomous processes. Few planners can solve such problems, and search with our new heuristic compares favourably with the

Surrogate Search As a Way to Combat Harmful Effects of Ill-behaved Evaluation Functions

Recently, several researchers have found that cost-based satisficing search with A* often runs into problems. Although some "work arounds" have been proposed to ameliorate the problem, there has been little concerted effort to pinpoint its origin. In this paper, we argue that the origins of this problem can be traced back to the fact that most planners that try to optimize cost also use cost-based evaluation functions (i.e., f(n) is a cost estimate). We show that cost-based evaluation functions become ill-behaved whenever there is a wide variance in action costs; something that is all too common in planning domains. The general solution to this malady is what we call a surrogatesearch, where a surrogate evaluation function that doesn't directly track the cost objective, and is resistant to cost-variance, is used. We will discuss some compelling choices for surrogate evaluation functions that are based on size rather that cost. Of particular practical interest is a cost-sensitive version of size-based evaluation function -- where the heuristic estimates the size of cheap paths, as it provides attractive quality vs. speed tradeoffsComment: arXiv admin note: substantial text overlap with arXiv:1103.368

Creating planning portfolios with predictive models

Mención Internacional en el título de doctorSequential planning portfolios are very powerful in exploiting the complementary strength of different automated planners: for each planning task there are one or more base planners that obtain the best solution. Therefore, the main challenge when building a planning portfolio is to ensure that a suitable planner be chosen and that it gets enough planning time. To solve this problem we need firstly to define three elements. The first is the settings or planning conditions: time, memory, or other constraints. The second one is the set of base planners. And finally, a benchmark that provides us with knowledge on how the base planners will behave under the given settings, following some kind of inductive process. Ideally, if the previous elements are correctly defined, when a new planning task arrives, an oracle will be able to tell which base planner to run and for how long. In practice, since no oracle exists, the challenge to choose a sub-set of base planners, is assigning them a running time and deciding the order in which they are run to optimize a planning metric under the predefined settings. Many state-of-the- art portfolios might never achieve an optimal performance because they do not select different planners for the different planning tasks. In addition, these static techniques typically assign a fixed running time to the selected set of planners, independently of the task. besides, the old-fashioned dynamic portfolios present a poor characterization of the planning task and do not have enough knowledge to predict an accurate portfolio configuration in many cases. The aforementioned drawbacks are intensified by the fact that there is an increasing number of planners available to choose from, although many of them are designed following similar approaches, so they are expected to behave similarly. This dissertation is built on two main hypotheses. Firstly that the space of the base planners can be reduced just by selecting a subset of diverse or complementary planners; e.g. that there is a minimal set of planners that ensure that the optimal portfolio can be computed. Secondly, that planning tasks can be characterized, and that the difficulty in solving them can be modelled as a function of these features. To evaluate the first hypothesis, we analyze different metrics that could be used to filter the initial set of base planners. Classical metrics such as coverage, quality or execution time have been chosen by different portfolios in the past. We demonstrate that these selection methods may reduce the diversity of the portfolios, and propose an alternative method based on the Pareto dominance. We then carry out a profound analysis on previous planning task characterizations and show how we could exploit them in current planning paradigms. A group of very informative features are proposed to improve the current feature definition of the planning tasks. These features have enough knowledge to differentiate planning tasks with similar \a priori" complexity. In this thesis we demonstrate that the implicit knowledge can be exploited in the construction of predictive models. These models estimate whether a base planner will be able to solve a given problem and, if so, how long it will take. Nevertheless, the predictive models are not perfect and sometimes provide wrong (or inaccurate) predictions. To solve this kind of problems, we propose different portfolio strategies to combine the number of selected base planners and their times. These strategies take into account the predefined settings and the knowledge learned in previous phases. In conclusion, this thesis sets out a profound analysis of three different mechanisms or steps to create planning portfolios with predictive models, including new proposals for developing: planner filtering, planning task featuring, learning predictive models and portfolio construction strategies. One of the proposed portfolios was the winner of the Sequential Satisficing Track of the International Planning Competition held in 2014Los portfolios de planificadores tienen un gran potencial ya que pueden aprovecharse de los diferentes planificadores automáticos, consiguiendo mejorar el rendimiento de un único planificador. Sin embargo, la creación de un portfolio no es una tarea sencilla, ya que para poder crear uno lo suficientemente bueno, hay que tratar tres problemas fundamentales. El primero de ellos es encontrar qué planificadores hay que seleccionar como componentes del mismo. La segunda es el tiempo que hay que asignar a cada planificador y, la última y no menos importante el orden en el que se tienen que ejecutar. Actualmente en el estado del arte, estas configuraciones, se realizan a partir de los resultados obtenidos por los planificadores en una fase previa de entrenamiento con un conjunto de problemas y restricciones prefijado (tiempo, memoria, etc), consiguiendo una configuración específica tratando de optimizar una métrica. Idealmente, la mejor configuración posible consiste en asignar el tiempo suficiente al mejor planificador para cada tarea de planificación. Sin embargo, esta configuración no siempre es posible, y hay que recurrir a otras aproximaciones como asignar un tiempo fijo a una selección de planificadores. Ésta no es la única simplificación utilizada, existen otras técnicas más cercanas a la óptima, en las cuales se selecciona un planificador o varios en función de la tarea a resolver. Sin embargo, estos sistemas, denominados dinámicos, incluyen una escasa caracterización de las tareas de planificación. En esta tesis se parte de dos hipótesis. La primera de ellas es que existe un conjunto reducido de planificadores que maximiza la diversidad. La segunda de ellas consiste en la posibilidad de crear un conjunto de descriptivos lo suficientemente bueno para caracterizar la tarea de planificación. La caracterización de las tareas de planificación puede estar basada en sus distintas representaciones, así como en sus paradigmas. La primera tarea es seleccionar un conjunto de planificadores; realizando un análisis basado en las métricas clásicas de planificación, como son problemas resueltos, calidad y tiempo para seleccionar un subconjunto de planificadores. Adicionalmente, proponemos como alternativa a estas métricas, una técnica multiobjetivo. Este criterio está basado en la dominancia de Pareto combinando las métricas de tiempo y calidad. Continuando con nuestras hip_otesis es necesario crear un conjunto de características bien informado para la tarea de planificación. Estas características deben ser capaces de diferenciar adecuadamente por problema y para ello sería necesario basarse en los distintos paradigmas de la planificación automática. Este grupo de características tienen que ser úutiles para crear modelos predictivos. Estos modelos podrán darnos además de una selección de planificadores, una aproximación del tiempo asignado a cada componente y el orden de los mismos. Adicionalmente se presentarán una serie de estrategias para explotar el conocimiento obtenido con los modelos predictivos. En conclusión, se plantea y desarrolla un sistema para configurar porfolios de planificadores usando modelos predictivos en tres fases distintas. Una instanciación de este sistema fue el ganador de la competición internacional de planificación en el áarea de satisfacibilidad en el año 2014.Programa Oficial de Doctorado en Ciencia y Tecnología InformáticaPresidente: María Araceli Sanchís de Miguel.- Secretario: Álvaro Torralba Arias de Reyna.- Vocal: Alessandro Saett

The 2011 International Planning Competition

After a 3 years gap, the 2011 edition of the IPC involved a total of 55 planners, some of them versions of the same planner, distributed among four tracks: the sequential satisficing track (27 planners submitted out of 38 registered), the sequential multicore track (8 planners submitted out of 12 registered), the sequential optimal track (12 planners submitted out of 24 registered) and the temporal satisficing track (8 planners submitted out of 14 registered). Three more tracks were open to participation: temporal optimal, preferences satisficing and preferences optimal. Unfortunately the number of submitted planners did not allow these tracks to be finally included in the competition. A total of 55 people were participating, grouped in 31 teams. Participants came from Australia, Canada, China, France, Germany, India, Israel, Italy, Spain, UK and USA. For the sequential tracks 14 domains, with 20 problems each, were selected, while the temporal one had 12 domains, also with 20 problems each. Both new and past domains were included. As in previous competitions, domains and problems were unknown for participants and all the experimentation was carried out by the organizers. To run the competition a cluster of eleven 64-bits computers (Intel XEON 2.93 Ghz Quad core processor) using Linux was set up. Up to 1800 seconds, 6 GB of RAM memory and 750 GB of hard disk were available for each planner to solve a problem. This resulted in 7540 computing hours (about 315 days), plus a high number of hours devoted to preliminary experimentation with new domains, reruns and bugs fixing. The detailed results of the competition, the software used for automating most tasks, the source code of all the participating planners and the description of domains and problems can be found at the competition’s web page: http://www.plg.inf.uc3m.es/ipc2011-deterministicThis booklet summarizes the participants on the Deterministic Track of the International Planning Competition (IPC) 2011. Papers describing all the participating planners are included

Optimal Planning with State Constraints

In the classical planning model, state variables are assigned values in the initial state and remain unchanged unless explicitly affected by action effects. However, some properties of states are more naturally modelled not as direct effects of actions but instead as derived, in each state, from the primary variables via a set of rules. We refer to those rules as state constraints. The two types of state constraints that will be discussed here are numeric state constraints and logical rules that we will refer to as axioms. When using state constraints we make a distinction between primary variables, whose values are directly affected by action effects, and secondary variables, whose values are determined by state constraints. While primary variables have finite and discrete domains, as in classical planning, there is no such requirement for secondary variables. For example, using numeric state constraints allows us to have secondary variables whose values are real numbers. We show that state constraints are a construct that lets us combine classical planning methods with specialised solvers developed for other types of problems. For example, introducing numeric state constraints enables us to apply planning techniques in domains involving interconnected physical systems, such as power networks. To solve these types of problems optimally, we adapt commonly used methods from optimal classical planning, namely state-space search guided by admissible heuristics. In heuristics based on monotonic relaxation, the idea is that in a relaxed state each variable assumes a set of values instead of just a single value. With state constraints, the challenge becomes to evaluate the conditions, such as goals and action preconditions, that involve secondary variables. We employ consistency checking tools to evaluate whether these conditions are satisfied in the relaxed state. In our work with numerical constraints we use linear programming, while with axioms we use answer set programming and three value semantics. This allows us to build a relaxed planning graph and compute constraint-aware version of heuristics based on monotonic relaxation. We also adapt pattern database heuristics. We notice that an abstract state can be thought of as a state in the monotonic relaxation in which the variables in the pattern hold only one value, while the variables not in the pattern simultaneously hold all the values in their domains. This means that we can apply the same technique for evaluating conditions on secondary variables as we did for the monotonic relaxation and build pattern databases similarly as it is done in classical planning. To make better use of our heuristics, we modify the A* algorithm by combining two techniques that were previously used independently – partial expansion and preferred operators. Our modified algorithm, which we call PrefPEA, is most beneficial in cases where heuristic is expensive to compute, but accurate, and states have many successors

Efficient Automated Planning with New Formulations

Problem solving usually strongly relies on how the problem is formulated. This fact also applies to automated planning, a key field in artificial intelligence research. Classical planning used to be dominated by STRIPS formulation, a simple model based on propositional logic. In the recently introduced SAS+ formulation, the multi-valued variables naturally depict certain invariants that are missed in STRIPS, make SAS+ have many favorable features. Because of its rich structural information SAS+ begins to attract lots of research interest. Existing works, however, are mostly limited to one single thing: to improve heuristic functions. This is in sharp contrast with the abundance of planning models and techniques in the field. On the other hand, although heuristic is a key part for search, its effectiveness is limited. Recent investigations have shown that even if we have almost perfect heuristics, the number of states to visit is still exponential. Therefore, there is a barrier between the nice features of SAS+ and its applications in planning algorithms. In this dissertation, we have recasted two major planning paradigms: state space search and planning as Satisfiability: SAT), with three major contributions. First, we have utilized SAS+ for a new hierarchical state space search model by taking advantage of the decomposable structure within SAS+. This algorithm can greatly reduce the time complexity for planning. Second, planning as Satisfiability is a major planning approach, but it is traditionally based on STRIPS. We have developed a new SAS+ based SAT encoding scheme: SASE) for planning. The state space modeled by SASE shows a decomposable structure with certain components independent to others, showing promising structure that STRIPS based encoding does not have. Third, the expressiveness of planning is important for real world scenarios, thus we have also extended the planning as SAT to temporally expressive planning and planning with action costs, two advanced features beyond classical planning. The resulting planner is competitive to state-of-the-art planners, in terms of both quality and performance. Overall, our work strongly suggests a shifting trend of planning from STRIPS to SAS+, and shows the power of formulating planning problems as Satisfiability. Given the important roles of both classical planning and temporal planning, our work will inspire new developments in other advanced planning problem domains

Short Term Unit Commitment as a Planning Problem

‘Unit Commitment’, setting online schedules for generating units in a power system to ensure supply meets demand, is integral to the secure, efficient, and economic daily operation of a power system. Conflicting desires for security of supply at minimum cost complicate this. Sustained research has produced methodologies within a guaranteed bound of optimality, given sufficient computing time. Regulatory requirements to reduce emissions in modern power systems have necessitated increased renewable generation, whose output cannot be directly controlled, increasing complex uncertainties. Traditional methods are thus less efficient, generating more costly schedules or requiring impractical increases in solution time. Meta-Heuristic approaches are studied to identify why this large body of work has had little industrial impact despite continued academic interest over many years. A discussion of lessons learned is given, and should be of interest to researchers presenting new Unit Commitment approaches, such as a Planning implementation. Automated Planning is a sub-field of Artificial Intelligence, where a timestamped sequence of predefined actions manipulating a system towards a goal configuration is sought. This differs from previous Unit Commitment formulations found in the literature. There are fewer times when a unit’s online status switches, representing a Planning action, than free variables in a traditional formulation. Efficient reasoning about these actions could reduce solution time, enabling Planning to tackle Unit Commitment problems with high levels of renewable generation. Existing Planning formulations for Unit Commitment have not been found. A successful formulation enumerating open challenges would constitute a good benchmark problem for the field. Thus, two models are presented. The first demonstrates the approach’s strength in temporal reasoning over numeric optimisation. The second balances this but current algorithms cannot handle it. Extensions to an existing algorithm are proposed alongside a discussion of immediate challenges and possible solutions. This is intended to form a base from which a successful methodology can be developed