Since 1992 a popular and appealing technique for solving planning problems has been to use a general purpose solution procedure for Boolean SAT(isfiability) problems. In this setting, a fixed horizon instance of the problem is encoded as a formula in propositional logic. A SAT procedure then computes a satisfying valuation for that formula, or otherwise proves it unsatisfiable. Here, the SAT encoding is constructive in the usual sense that there is a one-to-one correspondence between plans –i.e., solutions to the planning problem– and satisfying valuations of the formula.

One of the biggest drawbacks of this approach is the enormous sized formulae generated by the proposed encodings. In this thesis we mitigate that problem by developing, implementing, and evaluating a novel encoding that uses the techniques of splitting and factoring to develop a compact encoding that is amenable to state-of-the-art SAT procedures. Overall, our approach is the most scalable, and our representation the most compact amongst optimal planning procedures.

We then examine planning with numeric quantities, and in particular optimal planning with action costs. SAT-based procedures have previously been proposed in this setting for the fixed horizon case, where there is a given limit on plan length, however a key challenge has been to develop a SAT-based procedure that can achieve horizon-independent optimal solutions – i.e., the least costly plan irrespective of length. Meeting that challenge, in this thesis we develop a novel horizon-independent optimal procedure that poses partially weighted MaxSAT problems to our own cost-optimising conflict-driven clause learning (CDCL) procedure. We perform a detailed empirical evaluation of our approach, detailing the types of problem structures where it dominates.

Finally, we take the insights gleaned for the classical propositional planning case, and develop a number of encodings of problems that are described using control-knowledge. That control knowledge expresses domain-dependent constraints which: (1) constrain the space of admissible plans, and (2) allow the compact specification of constraints on plans that cannot be naturally or efficiently specified in classical propositional planning. Specifically, in this thesis we develop encodings for planning using temporal logic based constraints, procedural knowledge written in a language based on ConGolog, and Hierarchical Task Network based constraints. Our compilations use the technique of splitting to achieve relatively compact encodings compared to existing compilations. In contrast to similar work in the field of answer set planning, our compilations admit plans in the parallel format, a feature that is crucial for the performance of SAT-based planning.