Domain-Independent Dynamic Programming: Generic State Space Search for Combinatorial Optimization
This work addresses the problem of declarative problem-solving in combinatorial optimization for researchers and practitioners, offering a new paradigm that is incremental in its application of DP.
The authors tackled the challenge of making dynamic programming (DP) a generic, model-based approach for combinatorial optimization, proposing domain-independent dynamic programming (DIDP) with a solver that outperforms commercial MIP and CP solvers on several problem classes.
For combinatorial optimization problems, model-based approaches such as mixed-integer programming (MIP) and constraint programming (CP) aim to decouple modeling and solving a problem: the 'holy grail' of declarative problem solving. We propose domain-independent dynamic programming (DIDP), a new model-based paradigm based on dynamic programming (DP). While DP is not new, it has typically been implemented as a problem-specific method. We propose Dynamic Programming Description Language (DyPDL), a formalism to define DP models, and develop Cost-Algebraic A* Solver for DyPDL (CAASDy), a generic solver for DyPDL using state space search. We formalize existing problem-specific DP and state space search methods for combinatorial optimization problems as DP models in DyPDL. Using CAASDy and commercial MIP and CP solvers, we experimentally compare the DP models with existing MIP and CP models, showing that, despite its nascent nature, CAASDy outperforms MIP and CP on a number of common problem classes.