Temporal logics have been used in autonomous planning to represent and reason about temporal planning problems. However, such techniques have typically been restricted to either (1) representing actions, events, and goals with temporal properties or (2) planning for temporally-extended goals under restrictive assumptions. We introduce Mixed Propositional Metric Temporal Logic (MPMTL) where formulae are built over mixed binary and continuous real variables. We introduce a planner, MTP, that solves MPMTL problems and includes a SAT-solver, model checker for a polynomial fragment of MPMTL, and a forward search algorithm. We extend PDDL 2.1 with MPMTL syntax to create MPDDL and an associated parser. The empirical study shows that MTP outperforms the state-of-the-art PDDL+ planner SMTPlan+ on several domains it performed best on and MTP performs and scales on problem size well for challenging domains with rich temporal properties we create.

Compressed path databases (CPDs) are a state-of-the-art approach to path planning, a core AI problem. In the Grid-based Path Planning Competition, the CPD-based SRC path planning system was the fastest competitor with respect to both computing full optimal paths and computing the first moves of an optimal path. However, on large maps, CPDs can require a significant amount of memory, which can be a serious practical bottleneck. We present an approach that significantly reduces the size of a CPD. Our approach replaces part of the data encoded in a CPD with wildcards ("don’t care" symbols), maintaining the ability to compute optimal paths for all pairs of nodes of an undirected graph. We show that using wildcards in a way that maximizes the memory savings is NP-hard. We consider heuristics that achieve a good performance in practice. We implement our ideas on top of SRC and provide a detailed empirical analysis. Average memory savings can reach a factor of 2. Our first-k-moves lag (i.e., the time before knowing the first k optimal forward moves) increases, but it can be kept within competitive values. The speed of computing full optimal paths improves slightly.

We propose a novel approach for group elevator scheduling by formulating it as the maximization of submodular function under a matroid constraint. In particular, we propose to model the total waiting time of passengers using a quadratic Boolean function. The unary and pairwise terms in the function denote the waiting time for single and pairwise allocation of passengers to elevators, respectively. We show that this objective function is submodular. The matroid constraints ensure that every passenger is allocated to exactly one elevator. We use a greedy algorithm to maximize the submodular objective function, and derive provable guarantees on the optimality of the solution. We tested our algorithm using Elevate 8, a commercial-grade elevator simulator that allows simulation with a wide range of elevator settings. We achieve significant improvement over the existing algorithms.

Axioms can be used to model derived predicates in domain-independent planning models. Formulating models which use axioms can sometimes result in problems with much smaller search spaces than the original model. We propose a method for automatically extracting a particular class of axioms from standard STRIPS PDDL models. More specifically, we identify operators whose effects become irrelevant given some other operator, and generate axioms that capture this relationship. We show that this algorithm can be used to successfully extract axioms from standard IPC benchmark instances, and show that the extracted axioms can be used to significantly improve the performance of satisficing planners.

For example, we may need to (i) perform inverse learning of the cost parameters of a multi-objective reward based on observed agent behavior; (ii) perform sensitivity analyses of policies to various parameter settings; or (iii) analyze and optimize policy performance as a function of policy parameters. When such problems have mixed discrete and continuous state and/or action spaces, this leads to parameterized hybrid MDPs (PHMDPs) that are often approximately solved via discretization, sampling, and/or local gradient methods (when optimization is involved). In this paper we combine two recent advances that allow for the first exact solution and optimization of PHMDPs. We first show how each of the aforementioned use cases can be formalized as PHMDPs, which can then be solved via an extension of symbolic dynamic programming (SDP) even when the solution is piecewise nonlinear. Secondly, we can leverage recent advances in non-convex solvers that require symbolic forms of the objective function for non-convex global optimization in (i), (ii), and (iii) using SDP to derive symbolic solutions for each PHMDP formalization. We demonstrate the efficacy and scalability of our optimal analytical framework on nonlinear examples of each of the aforementioned use cases.

Energy costs are an increasingly important issue in real-world scheduling, for both economic and environmental reasons. This paper deals with a variant of the well-known job shop scheduling problem, where we consider a bi-objective optimization of both the weighted tardiness and the energy costs. To this end, we design a hybrid metaheuristic that combines a genetic algorithm with a novel local search method and a linear programming approach. We also propose an efficient procedure for improving the energy cost of a given schedule. In the experimental study we analyse our proposal and compare it with the state of the art and also with a constraint programming approach, obtaining competitive results.

Diverse action costs are an essential feature of many real-world planning applications. Some recent studies have shown that diversity of action costs makes planning more difficult, and that searching using unit action costs can outperform searching the same domain with diverse action costs. In this paper, we provide experimental evidence and theoretical analysis showing that search can also benefit from action cost diversity. We show that on several IPC problems cost diversity has a positive effect (reduces search effort). We then present a theoretical analysis establishing that these positive cases are not accidental. Our main result is a "No Free Lunch" theorem showing that any negative effects of cost diversity are always perfectly counterbalanced by positive effects. Our theoretical analysis also shows that it is advantageous to have a strongly concentrated distribution of solution costs. In many domains, unit costs will give rise to a more concentrated distribution than diverse costs, but we give an example typifying domains in which the opposite is the case.

In this paper we study bidirectional state space search with consistent heuristics, with a focus on obtaining sufficient conditions for node expansion, that is, conditions characterizing nodes that must be expanded by any admissible bidirectional search algorithm. We provide such conditions for front-to-front and front-to-end bidirectional search. The sufficient conditions are used to prove that the front-to-front bidirectional search algorithm BDS1 is optimally efficient, in terms of node expansion, among a broad class of bidirectional search algorithms, for a specific class of problem instances. Dechter and Pearl's well-known result on sufficient conditions for node expansion by unidirectional algorithms such as A* is shown to be a special case of our results.

When planning in temporal domains with required concurrency, envelopes arise where one or more actions need to occur within the execution of another. Starting an envelope action gives rise to an implicit relative deadline: all of the actions that need to occur within the envelope must complete before it ends. Finding effective heuristic guidance in these domains is challenging: the heuristic must not only consider how to reach the goals, but identify when it is not possible to achieve these implicit deadlines to avoid fruitless search. In this paper, we present an adaptation of a Temporal Relaxed Planning Graph heuristic, that accounts for dependencies between facts and actions in the relaxed planning graph; and the envelopes that are open in the state being evaluated. Results show that our new heuristic significantly improves the performance of a temporal planner on benchmark domains with required concurrency.

Mapping in the GPS-denied environment is an important and challenging task in the field of robotics. In the large environment, mapping can be significantly accelerated by multiple robots exploring different parts of the environment. Accordingly, a key problem is how to integrate these local maps built by different robots into a single global map. In this paper, we propose an approach for simultaneous merging of multiple grid maps by the robust motion averaging. The main idea of this approach is to recover all global motions for map merging from a set of relative motions. Therefore, it firstly adopts the pair-wise map merging method to estimate relative motions for grid map pairs. To obtain as many reliable relative motions as possible, a graph-based sampling scheme is utilized to efficiently remove unreliable relative motions obtained from the pair-wise map merging. Subsequently, the accurate global motions can be recovered from the set of reliable relative motions by the motion averaging. Experimental results carried on real robot data sets demonstrate that proposed approach can achieve simultaneous merging of multiple grid maps with good performances.