In our research, we explore two orthogonal but related methodologies of solving planning instances: planning algorithms based on direct but lazy, incremental heuristic search over transition systems and planning as satisfiability. We address numerous challenges associated with solving large planning instances within practical time and memory constraints. This is particularly relevant when solving real-world problems, which often have numeric domains and resources and, therefore, have a large ground representation of the planning instance. Our first contribution is an approximate novelty search, which introduces two novel methods. The first approximates novelty via sampling and Bloom filters, and the other approximates the best-first search using an adaptive policy that decides whether to forgo the expansion of nodes in the open list. For our second work, we present an encoding of the partial order causal link (POCL) formulation of the temporal planning problems into a CP model that handles the instances with required concurrency, which cannot be solved using sequential planners. Our third significant contribution is on lifted sequential planning with lazy constraint generation, which scales very well on large instances with numeric domains and resources. Lastly, we propose a novel way of using novelty approximation as a polynomial reachability propagator, which we use to train the activity heuristics used by the CP solvers.