Markov Decision Problems, MDPs offer an effective mechanism for planning under uncertainty. However, due to unavoidable uncertainty over models, it is difficult to obtain an exact specification of an MDP. We are interested in solving MDPs, where transition and reward functions are not exactly specified. Existing research has primarily focussed on computing infinite horizon stationary policies when optimizing robustness, regret and percentile based objectives. We focus specifically on finite horizon problems with a special emphasis on objectives that are separable over individual instantiations of model uncertainty (i.e., objectives that can be expressed as a sum over instantiations of model uncertainty): (a) First, we identify two separable objectives for uncertain MDPs: Average Value Maximization (AVM) and Confidence Probability Maximisation (CPM). (b) Second, we provide optimization based solutions to compute policies for uncertain MDPs with such objectives. In particular, we exploit the separability of AVM and CPM objectives by employing Lagrangian dual decomposition(LDD). (c) Finally, we demonstrate the utility of the LDD approach on a benchmark problem from the literature.

The defining characteristic the SDVRP, where vehicle capacity and customer demands of the SDVRP that distinguishes it from the classical are not required to be integer numbers, the number of vehicles vehicle routing problem (VRP) is that each customer is not limited to the minimum possible number, and can be served by more than one vehicle. Obviously, when the customer demands may exceed the vehicle capacity. The the demand of a customer is lager than the vehicle capacity, main contributions are threefold. First, we find a novel way it has to be split and the customer has to be visited more to represent the solutions of the SDVRP, which is the combination than once. As shown by (Dror and Trudeau 1989), when all of a set of vehicle routes and a forest. Second, based customer demands are less than or equal to the vehicle capacity, on this solution representation, we propose three classes of split delivery can also lead to substantial cost savings.

Recent advances in Symbolic Dynamic Programming (SDP) combined withthe extended algebraic decision diagram (XADD) have provided exactsolutions for expressive subclasses of finite-horizon Hybrid MarkovDecision Processes (HMDPs) with mixed continuous and discrete stateand action parameters. Unfortunately, SDP suffers from two majordrawbacks: (1) it solves for all states and can be intractable formany problems that inherently have large optimal XADD value functionrepresentations; and (2) it cannot maintain compact (pruned) XADDrepresentations for domains with nonlinear dynamics and reward due tothe need for nonlinear constraint checking. In this work, wesimultaneously address both of these problems by introducing real-timeSDP (RTSDP). RTSDP addresses (1) by focusing the solution and valuerepresentation only on regions reachable from a set of initial statesand RTSDP addresses (2) by using visited states as witnesses ofreachable regions to assist in pruning irrelevant or unreachable(nonlinear) regions of the value function. To this end, RTSDP enjoysprovable convergence over the set of initial states and substantialspace and time savings over SDP as we demonstrate in a variety of hybrid domains ranging from inventory to reservoir to traffic control.

Merge-and-shrink heuristics crucially rely on effective reduction techniques, such as bisimulation-based shrinking, to avoid the combinatorial explosion of abstractions. We propose the concept of factored symmetries for merge-and-shrink abstractions based on the established concept of symmetry reduction for state-space search. We investigate under which conditions factored symmetry reduction yields perfect heuristics and discuss the relationship to bisimulation. We also devise practical merging strategies based on this concept and experimentally validate their utility.

Heuristic search is a state-of-the-art approach to classical planning. Several heuristic families were developed over the years to automatically estimate goal distance information from problem descriptions. Orthogonally to the development of better heuristics, recent years have seen an increasing interest in symmetry-based state space pruning techniques that aim at reducing the search effort. However, little work has dealt with how the heuristics behave under symmetries. We investigate the symmetry properties of existing heuristics and reveal that many of them are invariant under symmetries.

Many AI applications involve the interaction of multiple autonomous agents, requiring those agents to reason about their own beliefs, as well as those of other agents. However, planning involving nested beliefs is known to be computationally challenging. In this work, we address the task of synthesizing plans that necessitate reasoning about the beliefs of other agents. We plan from the perspective of a single agent with the potential for goals and actions that involve nested beliefs, non-homogeneous agents, co-present observations, and the ability for one agent to reason as if it were another. We formally characterize our notion of planning with nested belief, and subsequently demonstrate how to automatically convert such problems into problems that appeal to classical planning technology. Our approach represents an important first step towards applying the well-established field of automated planning to the challenging task of planning involving nested beliefs of multiple agents.

Goal recognition design involves the offline analysis of goal recognition models by formulating measures that assess the ability to perform goal recognition within a model and finding efficient ways to compute and optimize them. In this work we present goal recognition design for non-optimal agents, which extends previous work by accounting for agents that behave non-optimally either intentionally or naıvely. The analysis we present includes a new generalized model for goal recognition design and the worst case distinctiveness (wcd) measure. For two special cases of sub-optimal agents we present methods for calculating the wcd, part of which are based on novel compilations to classical planning problems. Our empirical evaluation shows the proposed solutions to be effective in computing and optimizing the wcd.

We present a planner named Transition Constraints for Parallel Planning (TCPP). TCPP constructs a new constraint model from domain transition graphs (DTG) of a given planning problem. TCPP encodes the constraint model by using table constraints that allow don't cares or wild cards as cell values. TCPP uses Minion the constraint solver to solve the constraint model and returns the parallel plan. Empirical results exhibit the efficiency of our planning system over state-of-the-art constraint-based planners.

In many practical domains, planning systems are required to reason about durative actions. A common assumption in the literature is that the executor is allowed to decide the duration of each action. However, this assumption may be too restrictive for applications. In this paper, we tackle the problem of temporal planning with uncontrollable action durations. We show how to generate robust plans,that guarantee goal achievement despite the uncontrollability of the actual duration of the actions. We extend the state-space temporalplanning framework, integrating recent techniques for solving temporalproblems under uncertainty. We discuss different ways of lifting the total order plans generated by the heuristic search to partial orderplans, showing (in)completeness results for each of them. We implemented our approach on top of COLIN, a state-of-the-art planner. An experimental evaluation over several benchmark problems shows the practical feasibility of the proposed approach.

Bäckström studied the parameterised complexity of planning when the domain-transition graphs (DTGs) are acyclic. He used the parameters d (domain size), k (number of paths in the DTGs) and w (treewidth of the causal graph), and showed that planning is fixed-parameter tractable (fpt) in these parameters, and fpt in only parameter k if the causal graph is a polytree. We continue this work by considering some additional cases of non-acyclic DTGs. In particular, we consider the case where each strongly connected component (SCC) in a DTG must be a simple cycle, and we show that planning is fpt for this case if the causal graph is a polytree. This is done by first preprocessing the instance to construct an equivalent abstraction and then apply Bäckströms technique to this abstraction. We use the parameters d and k , reinterpreting this as the number of paths in the condensation of a DTG, and the two new parameters c (the number of contracted cycles along a path) and p max (an upper bound for walking around cycles, when not unbounded).