Department of Mathematics and Computer Science

Domain-independent dynamic programming (DIDP) is a recently proposed framework for modeling combinatorial optimization problems using dynamic programming and solving them with a general purpose solver. Initial results show strong performance using a heuristic state-based search solver, thus demonstrating the success of problem solving approaches developed in Artificial Intelligence (AI) on problems traditionally studied in Operations Research (OR). This project seeks to develop the theory and practice of DIDP-based problem solving by characterizing DIDP from computational and knowledge representation perspectives; by understanding its relationship to the problem solving paradigms embodied in constraint programming, satisfiability, and AI planning; and by developing novel domain-independent heuristics for DIDP through the adaptation and extension of techniques from AI planning, state abstraction in OR, and decision diagram-based optimization.

Automated planning, also known as factored state-space search, is a fundamental problem in AI with numerous applications in computer science and elsewhere. There are three dominant algorithmic paradigms: heuristic search, symbolic search, and SAT planning. While important theoretical results exist to explain and improve the performance of some of these algorithms, almost nothing is known about the connections between them.

We build a unified theory of factored state-space search that identifies a common reasoning core encompassing all three algorithmic paradigms that allows us to directly relate these algorithms to each other in theory and build hybridized algorithms combining their individual strengths in practice. Identifying such a core also allows us to better understand the trade-off involved between representational expressiveness and efficiency of reasoning and design better algorithms to address this trade-off.