Multi-agent pathfinding (MAPF) is an NP-hard problem. As such, dense maps may be very hard to solve optimally. In such scenarios, compilation-based approaches, via Boolean satisfiability (SAT) and answer set programming (ASP), have been shown to outperform heuristic-search-based approaches, such as conflict-based search (CBS). In this paper, we propose a new Boolean encoding for MAPF, and show how to implement it in ASP and MaxSAT. A feature that distinguishes our encoding from existing ones is that swap and follow conflicts are encoded using binary clauses, which can be exploited by current conflict-driven clause learning (CDCL) solvers. In addition, the number of clauses used to encode swap and follow conflicts do not depend on the number of agents, allowing us to scale better. For MaxSAT, we study different ways in which we may combine the MSU3 and LSU algorithms for maximum performance. In our experimental evaluation, we used square grids, ranging from 20 x 20 to 50 x 50 cells, and warehouse maps, with a varying number of agents and obstacles. We compared against representative solvers of the state-of-the-art, including the search-based algorithm CBS, the ASP-based solver ASP-MAPF, and the branch-and-cut-and-price hybrid solver, BCP. We observe that the ASP implementation of our encoding, ASP-MAPF2 outperforms other solvers in most of our experiments. The MaxSAT implementation of our encoding, MtMS shows best performance in relatively small warehouse maps when the number of agents is large, which are the instances with closer resemblance to hard puzzle-like problems.

A popular approach for sequential decision-making is to perform simulator-based search guided with Machine Learning (ML) methods like policy learning. On the other hand, model-relaxation heuristics can guide the search effectively if a full declarative model is available. In this work, we consider how a practitioner can improve ML-based black-box planning on settings where a complete symbolic model is not available. We show that specifying an incomplete STRIPS model that describes only part of the problem enables the use of relaxation heuristics. Our findings on several planning domains suggest that this is an effective way to improve ML-based black-box planning beyond collecting more data or tuning ML architectures.

Many interesting search problems can be formulated as bi-objective search problems; for example, transportation problems where both travel distance and time need to be minimized. Multi-objective best-first search algorithms need to maintain the set of undominated paths from the start state to each state to compute a set of paths from a given start state to a given goal state (the Pareto-optimal solutions) such that no path in the set is dominated by another path in the set. Each time they find a new path to a state n, they perform a dominance check to determine whether such a path dominates any of the previously found paths to n. Existing algorithms do not perform these checks efficiently, requiring at least a full iteration over the Open list per check. In this paper, we present the first multi-objective algorithm that performs these checks efficiently. Indeed, Bi-Objective A* (BOA*)—our algorithm—requires constant time to check for dominance. Our experimental evaluation shows that BOA*is orders-of-magnitude faster than state-of-the-art search algorithms, such as NAMOA*, Bi-Objective Dijkstra, and Bidirectional Bi-Objective Dijkstra.

Multipath Generalized Adaptive A* (MPGAA*) is an A*- based incremental search algorithm for dynamic terrain that can outperform D* for the (realistic) case of limited visibility ranges. A first contribution of this paper is a brief analysis studying why MPGAA* has poor performance for extended visibility ranges, which concludes that MPGAA* carries out an excessive number of heuristic updates. Our second contribution is a method to reduce the number of heuristic updates that preserves optimality. Finally, a third contribution is a variant of MPGAA*, MPGAA*-back, which we show outperforms MPGAA* and D* on a wide range of dynamic grid pathfinding scenarios, and visibility ranges.

Grid pathfinding, an old AI problem, is central for the development of navigation systems for autonomous agents. A surprising fact about the vast literature on this problem is that very limited neighborhoods have been studied. Indeed, only the 4- and 8-neighborhoods are usually considered, and rarely the 16-neighborhood. This paper describes three contributions that enable the construction of effective grid path planners for extended 2 k -neighborhoods. First, we provide a simple recursive definition of the 2 k -neighborhood in terms of the 2 k –1 -neighborhood. Second, we derive distance functions, for any k >1, which allow us to propose admissible heurisitics which are perfect for obstacle-free grids. Third, we describe a canonical ordering which allows us to implement a version of A* whose performance scales well when increasing k . Our empirical evaluation shows that the heuristics we propose are superior to the Euclidean distance (ED) when regular A* is used. For grids beyond 64 the overhead of computing the heuristic yields decreased time performance compared to the ED. We found also that a configuration of our A*-based implementation, without canonical orders, is competitive with the "any-angle" path planner Theta$^*$ both in terms of solution quality and runtime.

Temporally extended goals are critical to the specification of a diversity of real-world planning problems. Here we examine the problem of non-deterministic planning with temporally extended goals specified in linear temporal logic (LTL), interpreted over either finite or infinite traces. Unlike existing LTL planners, we place no restrictions on our LTL formulae beyond those necessary to distinguish finite from infinite interpretations. We generate plans by compiling LTL temporally extended goals into problem instances described in the Planning Domain Definition Language that are solved by a state-of-the-art fully observable non-deterministic planner. We propose several different compilations based on translations of LTL to (Büchi) alternating or (Büchi) non-deterministic finite state automata, and evaluate various properties of the competing approaches. We address a diverse spectrum of LTL planning problems that, to this point, had not been solvable using AI planning techniques, and do so in a manner that demonstrates highly competitive performance.

Linear temporal logic (LTL) is an expressive language that allows specifying temporally extended goals and preferences. A general approach to dealing with general LTL properties in planning is by ``compiling them away''; i.e., in a pre-processing phase, all LTL formulas are converted into simple, non-temporal formulas that can be evaluated in a planning state. This is accomplished by first generating a finite-state automaton for the formula, and then by introducing new fluents that are used to capture all possible runs of the automaton. Unfortunately, current translation approaches are worst-case exponential on the size of the LTL formula. In this paper, we present a polynomial approach to compiling away LTL goals. Our method relies on the exploitation of alternating automata. Since alternating automata are different from non-deterministic automata, our translation technique does not capture all possible runs in a planning state and thus is very different from previous approaches. We prove that our translation is sound and complete, and evaluate it empirically showing that it has strengths and weaknesses. Specifically, we find classes of formulas in which it seems to outperform significantly the current state of the art.

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.

RTAA* is probably the best-performing real-time heuristic search algorithm at path-finding tasks in which the environ- ment is not known in advance or in which the environment is known and there is no time for pre-processing. As most real- time search algorithms do, RTAA∗ performs poorly in presence of heuristic depressions, which are bounded areas of the search space in which the heuristic is too low with respect to their border. Recently, it has been shown that LSS-LRTA∗, a well-known real-time search algorithm, can be improved when search is actively guided away of depressions. In this paper we investigate whether or not RTAA∗ can be improved in the same manner. We propose aRTAA∗ and daRTAA∗, two algorithms based on RTAA∗ that avoid heuristic depressions. Both algorithms outperform RTAA∗ on standard path-finding tasks, obtaining better-quality solutions when the same time deadline is imposed on the duration of the planning episode. We prove, in addition, that both algorithms have good theoretical properties

In this paper we examine the general problem of generating preferred explanations for observed behavior with respect to a model of the behavior of a dynamical system. This problem arises in a diversity of applications including diagnosis of dynamical systems and activity recognition. We provide a logical characterization of the notion of an explanation. To generate explanations we identify and exploit a correspondence between explanation generation and planning. The determination of good explanations requires additional domain-specific knowledge which we represent as preferences over explanations. The nature of explanations requires us to formulate preferences in a somewhat retrodictive fashion by utilizing Past Linear Temporal Logic. We propose methods for exploiting these somewhat unique preferences effectively within state-of-the-art planners and illustrate the feasibility of generating (preferred) explanations via planning.