Dealing with planning problems with both discrete logical relations and continuous numeric changes in real-world dynamic environments is challenging. Existing numeric planning systems for the problem often discretize numeric variables or impose convex quadratic constraints on numeric variables, which harms the performance when solving the problem. In this paper, we propose a novel algorithm framework to solve the numeric planning problems mixed with discrete and continuous actions based on gradient descent. We cast the numeric planning with discrete and continuous actions as an optimization problem by integrating a heuristic function based on discrete effects. Specifically, we propose a gradient-based framework to simultaneously optimize continuous parameters and actions of candidate plans. The framework is combined with a heuristic module to estimate the best plan candidate to transit initial state to the goal based on relaxation. We repeatedly update numeric parameters and compute candidate plan until it converges to a valid plan to the planning problem. In the empirical study, we exhibit that our algorithm framework is both effective and efficient, especially when solving non-convex planning problems.

We present the domain-independent HRFF algorithm, which solves goal-oriented HMDPs by incrementally aggregating plans generated by the Metric-FF planner into a policy defined over discrete and continuous state variables. HRFF takes into account non-monotonic state variables, and complex combinations of many discrete and continuous probability distributions. We introduce new data structures and algorithmic paradigms to deal with continuous state spaces: hybrid hierarchical hash tables, domain determinization based on dynamic domain sampling or on static computation of probability distributions' modes, optimization settings under Metric-FF based on plan probability and length. We compare with HAO* on the Rover domain and show that HRFF outperforms HAO* by many order of magnitudes in terms of computation time and memory usage. We also experiment challenging and combinatorial HMDP versions of benchmarks from numeric classical planning, with continuous dead-ends and non-monotonic continuous state variables.

We present the domain-independent HRFF algorithm, which solves goal-oriented HMDPs by incrementally aggregating plans generated by the METRIC-FF planner into a policy defined over discrete and continuous state variables. HRFF takes into account non-monotonic state variables, and complex combinations of many discrete and continuous probability distributions. We introduce new data structures and algorithmic paradigms to deal with continuous state spaces: hybrid hierarchical hash tables, domain determinization based on dynamic domain sampling or on static computation of probability distributions' modes, optimization settings under METRIC-FF based on plan probability and length. We deeply analyze the behavior of HRFF on a probabilistically-interesting structured navigation problem with continuous dead-ends and non-monotonic continuous state variables. We compare with HAO* on the Rover domain and show that HRFF outperforms HAO* by many order of magnitudes in terms of computation time and memory usage. We also experiment challenging and combinatorial HMDP versions of benchmarks from numeric classical planning.

In particular, modeling context dependent eects, concurrent execution of actions with dierent duration, and continuous resources are all awkward, or impossible, within the STRIPS language. To overcome the rst of these limitations, Pednault (1989) dened the (nowadays widely accepted) ADL language, which amongst other things allows for conditional eects (eects that only occur when their condition holds true in the state of execution). To overcome (one or both of) the latter two limitations, various proposals have been made (e.g., Ghallab & Laruelle, 1994; Koehler, 1998; Smith & Weld, 1999). The most recent eort in this direction is the PDDL2.1 language dened by Fox and Long (2002) as the input language for the 3rd International Planning Competition (IPC-3). The IPC series is a biennial challenge for the planning community, inviting planning systems to participate in a large scale publicly accessible evaluation. IPC-3 was hosted at AIPS-2002, and stressed planning beyond the STRIPS formalism, featuring tracks for temporal and numeric planners. This article describes the approach behind one of the planners that participated in IPC-3, Metric-FF. Metric-FF is an extension of the FF system (that can handle ADL) to numeric constructs.

In this paper, we present the partitioning of mutual-exclusion (mutex) constraints in temporal planning problems and its implementation in the SGPlan4 planner. Based on the strong locality of mutex constraints observed in many benchmarks of the Fourth International Planning Competition (IPC4), we propose to partition the constraints of a planning problem into groups based on their subgoals. Constraint partitioning leads to significantly easier subproblems that are similar to the original problem and that can be efficiently solved by the same planner with some modifications to its objective function. We present a partition-and-resolve strategy that looks for locally optimal subplans in constraint-partitioned temporal planning subproblems and that resolves those inconsistent global constraints across the subproblems. We also discuss some implementation details of SGPlan4, which include the resolution of violated global constraints, techniques for handling producible resources, landmark analysis, path finding and optimization, search-space reduction, and modifications of Metric-FF when used as a basic planner in SGPlan4. Last, we show results on the sensitivity of each of these techniques in quality-time trade-offs and experimentally demonstrate that SGPlan4 is effective for solving the IPC3 and IPC4 benchmarks.