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.

Automated planners are computer tools that allow autonomous agents to make strategies and decisions by determining a set of actions for the agent that to take, which will carry a system from a given initial state to the desired goal state. Many planners are domain-independent, allowing their deployment in a variety of domains. Such is the broad family of OPTIC planners. These planners perform Forward Search and call a Linear Programming (LP) solver multiple times at every state to check for consistency and to set bounds on the numeric variables. These checks can be computationally costly, especially in real-life applications. This paper suggests a method for identifying information about the specific state being evaluated, allowing the formulation of the equations to facilitate better solver selection and faster LP solving. The usefulness of the method is demonstrated in six domains and is shown to enhance performance significantly.

We adapt the relaxation heuristics h max , h add and h FF to interval based numeric relaxation frameworks, combining them with two different relaxation techniques and with two different search techniques. In contrast to previous approaches, the heuristics presented here are not limited to a subset of numeric planning and support action costs.

In this paper we describe COLIN, a forward-chaining heuristic search planner, capable of reasoning with COntinuous LINear numeric change, in addition to the full temporal semantics of PDDL. Through this work we make two advances to the state-of-the-art in terms of expressive reasoning capabilities of planners: the handling of continuous linear change, and the handling of duration-dependent effects in combination with duration inequalities, both of which require tightly coupled temporal and numeric reasoning during planning. COLIN combines FF-style forward chaining search, with the use of a Linear Program (LP) to check the consistency of the interacting temporal and numeric constraints at each state. The LP is used to compute bounds on the values of variables in each state, reducing the range of actions that need to be considered for application. In addition, we develop an extension of the Temporal Relaxed Planning Graph heuristic of CRIKEY3, to support reasoning directly with continuous change. We extend the range of task variables considered to be suitable candidates for specifying the gradient of the continuous numeric change effected by an action. Finally, we explore the potential for employing mixed integer programming as a tool for optimising the timestamps of the actions in the plan, once a solution has been found. To support this, we further contribute a selection of extended benchmark domains that include continuous numeric effects. We present results for COLIN that demonstrate its scalability on a range of benchmarks, and compare to existing state-of-the-art planners.

Over the last few years there has been a revival of interest in the idea of least-commitment planning with a number of researchers returning to the partial-order planning approaches of UCPOP and VHPOP. In this paper we explore the potential of a forward-chaining state-based search strategy to support partial-order planning in the solution of temporal-numeric problems. Our planner, POPF, is built on the foundations of grounded forward search, in combination with linear programming to handle continuous linear numeric change. To achieve a partial ordering we delay commitment to ordering decisions, timestamps and the values of numeric parameters, managing sets of constraints as actions are started and ended. In the context of a partially ordered collection of actions, constructing the linear program is complicated and we propose an efficient method for achieving this. Our late-commitment approach achieves flexibility, while benefiting from the informative search control of forward planning, and allows temporal and metric decisions to be made - as is most efficient - by the LP solver rather than by the discrete reasoning of the planner. We compare POPF with the approach of constructing a sequenced plan and then lifting a partial order from it, showing that our approach can offer improvements in terms of makespan, and time to find a solution, in several benchmark domains.

We consider the problem of planning in domains with continuous linear numeric change. Such change cannot always be adequately modelled by discretisation and is a key facet of many interesting problems. We show how a forward-chaining temporal planner can be extended to reason with actions with continuous linear effects. We extend a temporal planner to handle numeric values using linear programming. We show how linear continuous change can be integrated into the same linear program and we discuss how a temporal-numeric heuristic can be used to provide the search guidance necessary to underpin continuous planning. We present results to show that the approach can effectively handle duration-dependent change and numeric variables subject to continuous linear change.