General Implementation of Multilevel Parallelization in a Gradient-Based Design Optimization Algorithm

As product designs have become more sophisticated, both the simulation models (e.g., finite element models) and the design optimization models have grown bigger. To keep pace with this increase in problem size, we present and implement an optimization strategy that can run on a computing cluster with demonstrable efficiency. First, parallelism is implemented in the context of gradient calculations using divided differences. Then, parallelism is achieved in the context of both direction-finding and line-search steps. Parallel direction finding improves the convergence rate as opposed to just cutting down the amount of arithmetic. A new algorithm based on method of feasible directions is discussed that obtains better optima and is also computationally faster. Implementation details regarding distribution of computing tasks to improve scalability and load balancing are presented. Numerical examples show the efficiency of the developed methodology on a relatively small computing cluster. Gains of about 7:1 have been obtainable using 16 processors on some test problems. Importantly, the framework presented can be developed by researchers using other gradient-based optimization codes on different computing platforms.