Temporal planning by a continuous and differentiable nonlinear optimization formulation and constraint partitioning

In this paper, we study efficient temporal planning based on a continuous and differentiable nonlinear programming transformation of the planning problem. Based on the observation that many large planning problems have constraint locality, we have previously proposed the constraint partitioning approach that utilizes the constraint structure by partitioning the constraints of a planning problem into subproblems and solving each subproblem individually. Constraint partitioning has led to the design of SGPlan, a state-of-the-art planner. However, SGPlan is based on a mixed-integer programming formulation that is computationally expensive to solve. In this paper, we present a continuous and differentiable nonlinear programming formulation for planning problems, and apply the constraint partitioning approach to this formulation. Because the nonlinear programming transformation is continuous and differentiable, we can utilize powerful existing continuous nonlinear optimization packages to solve each subproblem very quickly. We apply the new strategies in solving some planning benchmark problems and demonstrate significant improvements in time and quality.