Despite its success, the delete relaxation has significant pitfalls. Recent work has devised the red-black planning framework, where red variables take the relaxed semantics (accumulating their values), while black variables take the regular semantics. Provided the red variables are chosen so that red-black plan generation is tractable, one can generate such a plan for every search state, and take its length as the heuristic distance estimate. Previous results were not suitable for this purpose because they identified tractable fragments for red-black plan existence, as opposed to red-black plan generation. We identify a new fragment of red-black planning, that fixes this issue. We devise machinery to efficiently generate red-black plans, and to automatically select the red variables. Experiments show that the resulting heuristics can significantly improve over standard delete relaxation heuristics.

Planning is a notoriously difficult computational problem of high worst-case complexity. Researchers have been investing significant efforts to develop heuristics or restrictions to make planning practically feasible. Case-based planning is a heuristic approach where one tries to reuse previous experience when solving similar problems in order to avoid some of the planning effort. Plan reuse may offer an interesting alternative to plan generation in some settings. We provide theoretical results that identify situations in which plan reuse is provably tractable. We perform our analysis in the framework of parameterized complexity, which supports a rigorous worst-case complexity analysis that takes structural properties of the input into account in terms of parameters. A central notion of parameterized complexity is fixed-parameter tractability which extends the classical notion of polynomial-time tractability by utilizing the effect of parameters. We draw a detailed map of the parameterized complexity landscape of several variants of problems that arise in the context of case-based planning. In particular, we consider the problem of reusing an existing plan, imposing various restrictions in terms of parameters, such as the number of steps that can be added to the existing plan to turn it into a solution of the planning instance at hand.

Many practical planning problems necessitate the generation of a plan under incomplete information about the state of the world. In this paper we propose the notion of Assumption-Based Planning. Unlike conformant planning, which attempts to find a plan under all possible completions of the initial state, an assumption-based plan supports the assertion of additional assumptions about the state of the world, often resulting in high quality plans where no conformant plan exists. We are interested in this paradigm of planning for two reasons: 1) it captures a compelling form of \emph{commonsense planning}, and 2) it is of great utility in the generation of explanations, diagnoses, and counter-examples -- tasks which share a computational core with We formalize the notion of assumption-based planning, establishing a relationship between assumption-based and conformant planning, and prove properties of such plans. We further provide for the scenario where some assumptions are more preferred than others. Exploiting the correspondence with conformant planning, we propose a means of computing assumption-based plans via a translation to classical planning. Our translation is an extension of the popular approach proposed by Palacios and Geffner and realized in their T0 planner. We have implemented our planner, A0, as a variant of T0 and tested it on a number of expository domains drawn from the International Planning Competition. Our results illustrate the utility of this new planning paradigm.

Timelines are a formalism to model planning domains where the  temporal aspects are predominant, and have been used in many  real-world applications. Despite their practical success, a major limitation is the inability  to model temporal uncertainty, i.e. the plan executor cannot decide  the duration of some activities. In this paper we make two key contributions. First, we propose a comprehensive, semantically well founded framework that  (conservatively) extends with temporal uncertainty the state of the  art timeline approach. Second, we focus on the problem of producing time-triggered plans  that are robust with respect to temporal uncertainty, under a  bounded horizon. In this setting, we present the first complete  algorithm, and we show how it can be made practical by leveraging  the power of Satisfiability Modulo Theories.

We describe a model for competitive online scheduling algorithms. Two servers, each with a single observable queue, compete for customers. Upon arrival, each customer strategically chooses the queue with minimal expected wait time. Each scheduler wishes to maximize its number of customers, and can strategically select which scheduling algorithm, such as First-Come-First-Served (FCFS), to use for its queue. This induces a game played by the servers and the customers. We consider a non-Bayesian setting, where servers and customers play to maximize worst-case payoffs. We show that there is a unique subgame perfect safety-level equilibrium and we describe the associated scheduling algorithm (which is not FCFS). The uniqueness result holds for both randomized and deterministic algorithms, with a different equilibrium algorithm in each case. When the goal of the servers is to minimize competitive ratio, we prove that it is an equilibrium for each server to apply FCFS: each server obtains the optimal competitive ratio of 2.

AI Planning is inherently hard and hence it is desirable to derive as much information as we can from the structure of the planning problem and let this information be exploited by a planner. Many recent planners use the finite-domain state-variable representation of the problem instead of the traditional propositional representation. However, most planning problems are still specified in the propositional representation due to the widespread modeling language PDDL and it is hard to generate a compact and computationally efficient state variable representation from the propositional model. In this paper we propose a novel method for automaticallygenerating an efficient state-variable representation from the propositional representation. This method groups sets of propositions into state variables based onthe mutex relations introduced in the planning graph. As we shall show experimentally, our method outperforms the current state-of-the-art method both in the smaller number of generated state variables and in the increased performance of planners.

In Automated Planning, learning and exploiting additional knowledge within a domain model, in order to improve plan generation speed-up and increase the scope of problems solved, has attracted much research. Reformulation techniques such as those based on macro-operators or entanglements are very promising because they are to some extent domain model and planning engine independent. This paper aims to exploit recent work on inner entanglements, relations between pairs of planning operators and predicates encapsulating exclusivity of predicate `achievements` or `requirements', for generating macro-operators. We discuss conditions which are necessary for generating such macro-operators and conditions that allow removing primitive operators without compromising solvability of a given (class of) problem(s). The effectiveness of our approach will be experimentally shown on a set of well-known benchmark domains using several high-performing planning engines.

Analysing the structures of solution plans generated by AI Planning engines is helpful in improving the generative planning process, as well as shedding light in the study of its theoretical foundations. We investigate a specific property of solution plans, that we called linearity, which refers to a situation where each action achieves an atom (or atoms) for a directly following action, or achieves goal atom(s). Similarly, linearity can be defined for parallel plans where each action in a set of actions executed at some time step, achieves either goal atom(s) or atom(s) for some action executed in the directly following time step. In this paper, we present a general and problem-independent theoretical framework focusing on the analysis of planning operator schema, namely relations of achiever, clobberer and independence, in order to determine whether solvable planning problems using a given operator schema have as solutions optimal (parallel) plans which are linear. The findings presented in this paper deepen current theoretical knowledge, provide helpful information to engineers of new planning domain models, and suggest new ways of improving the performance of state-of-the-art (optimal) planning engines.

In this paper, we consider the problem of planning any-angle paths with small numbers of turns on grid maps. We propose a novel heuristic search algorithm called Link* that returns paths containing fewer turns at the cost of slightly longer path lengths. Experimental results demonstrate that Link* can produce paths with fewer turns than other any-angle path planning algorithms while still maintaining comparable path lengths. Because it produces this type of path, artificial agents can take advantage of Link* when the cost of turns is expensive.

Monte-Carlo search is successfully used in simulation-based planning for various large-scale sequential decision problems, and the UCT algorithm seems to be the choice in most (if not all) such recent success stories. Based on some recent discoveries in theory and empirical analysis of Monte-Carlo search, here we argue that, if online sequential decision making is your problem, and Monte-Carlo tree search is your way to go, then UCT is unlikely to be the best fit for your needs.