[Paper Review] Planning and Scheduling in Hybrid Domains Using Answer Set Programming

Sandeep Chintabathina|arXiv (Cornell University)|Jan 8, 2013

Logic, Reasoning, and Knowledge8 references3 citations

TL;DR

This paper presents a novel approach to solving planning and scheduling problems in hybrid domains—systems with both discrete and continuous dynamics—by modeling them using Action Language H and translating the theory into Answer Set Programming (ASP) via A-Prolog. The method enables efficient computation of solutions using the hybrid solver EZCSP, which integrates constraint solving with answer set computation, successfully generating valid plans and schedules for a multi-agent travel scenario within a 330-minute deadline.

ABSTRACT

In this paper we present an Action Language-Answer Set Programming based approach to solving planning and scheduling problems in hybrid domains - domains that exhibit both discrete and continuous behavior. We use action language H to represent the domain and then translate the resulting theory into an A-Prolog program. In this way, we reduce the problem of finding solutions to planning and scheduling problems to computing answer sets of A-Prolog programs. We cite a planning and scheduling example from the literature and show how to model it in H. We show how to translate the resulting H theory into an equivalent A-Prolog program. We compute the answer sets of the resulting program using a hybrid solver called EZCSP which loosely integrates a constraint solver with an answer set solver. The solver allows us reason about constraints over reals and compute solutions to complex planning and scheduling problems. Results have shown that our approach can be applied to any planning and scheduling problem in hybrid domains.

Motivation & Objective

• To address the challenge of planning and scheduling in hybrid domains that combine discrete actions and continuous state changes.
• To overcome limitations of existing formalisms like PDDL+ that lack support for derived predicates and complex causal reasoning.
• To develop a unified framework that models both action effects and continuous fluents using a high-level action language.
• To enable automated solution generation for complex planning problems involving time constraints and continuous dynamics.
• To demonstrate the feasibility and effectiveness of integrating answer set programming with constraint solving for hybrid domains.

Proposed method

• Modeling the domain using Action Language H, which supports time, process fluents, and triggers for continuous and discrete behavior.
• Translating the H theory into an equivalent A-Prolog program under answer set semantics to represent actions, fluents, and constraints.
• Using the hybrid solver EZCSP to compute answer sets that satisfy both logical and continuous constraints over real numbers.
• Encoding time constraints via constraint variables (e.g., start(I) < 330) and using required/1 to enforce temporal bounds.
• Generating plans through choice rules that select action sequences, while scheduling is determined by assigning specific time points to initiating actions.
• Leveraging triggers to automatically determine the timing of terminating actions, reducing the need for explicit scheduling of all events.

Experimental results

Research questions

• RQ1 Can Action Language H effectively represent hybrid domains with both discrete actions and continuous fluents?
• RQ2 How can an H theory be systematically translated into an A-Prolog program for computational reasoning?
• RQ3 Can a hybrid solver like EZCSP efficiently compute answer sets that satisfy both logical and continuous constraints in planning problems?
• RQ4 What is the impact of using derived predicates and triggers in modeling complex causal and temporal dependencies?
• RQ5 How does the proposed approach compare in expressiveness and capability to existing formalisms like PDDL+?

Key findings

• The proposed method successfully generated a valid plan for transporting Scott and Ernie to city d within 330 minutes, with all actions scheduled at specific time points.
• The solution involved 10 actions, including boarding, flying, and refueling, with precise end times computed by EZCSP, such as end(9)=329.0 minutes.
• Refueling was required in city c due to insufficient fuel for direct travel to d, confirming the necessity of intermediate actions.
• The system correctly enforced temporal constraints, ensuring all actions occurred before the 330-minute deadline.
• The use of triggers allowed automatic determination of terminating action times, reducing the search space and improving efficiency.
• The approach demonstrated feasibility for modeling and solving complex hybrid planning and scheduling problems with continuous dynamics.