Phoenix-OC: Applied Optimal Control using Advanced Structure Exploitation and Multi-Level Parallelism

This paper introduces Phoenix-OC, a novel optimal control software for the solution of large-scale, multi-phase Optimal Control (OC) problems. Phoenix-OC employs segmented collocation methods for the state discretization and B-Splines for the control parameteriza- tion. Each of the parameterized controls is allowed to have a distinct degree and knot grid. Additionally, control derivatives of arbitrary order can be utilized in the model, as well as constraint and cost functions. User-defined functions can be modeled either through an automatic differentiation framework or via a generic C interface supporting the utilization of virtually arbitrary functions, external models, etc. Among other features, the software inherently supports table data interpolation, the computation of post-optimal sensitivities for parametric OC problems, bi-level optimization, homotopy formulations, parallel batch runs, and job dependencies. Furthermore, jobs can be executed locally or through a job scheduler on computer clusters. Phoenix-OC operates on the Phoenix-CORE engine - a generic sparse evaluation frame- work for both the evaluation and derivative computation of vector-valued functions. Cen- tral to this computational engine is the notion of an Extended Sparsity Pattern (ESP). This novel type of sparsity pattern extends traditional binary-valued sparsity patterns to a new type of floating-point pattern, allowing for advanced structure exploitation. The ex- ploitation of sparse structures based on the ESP, combined with the multi-level parallelism implemented in Phoenix-OC, yields high performance across a range of representative benchmarks from engineering applications.