Parallel global optimization with the particle swarm algorithm

Present day engineering optimization problems often impose large computational demands, resulting in long solution times even on a modern high-end processor. To obtain enhanced computational throughput and global search capability, we detail the coarse-grained parallelization of an increasingly popular global search method, the particle swarm optimization (PSO) algorithm. Parallel PSO performance was evaluated using two categories of optimization problems possessing multiple local minima-large-scale analytical test problems with computationally cheap function evaluations and medium-scale biomechanical system identification problems with computationally expensive function evaluations. For load-balanced analytical test problems formulated using 128 design variables, speedup was close to ideal and parallel efficiency above 95% for up to 32 nodes on a Beowulf cluster. In contrast, for load-imbalanced biomechanical system identification problems with 12 design variables, speedup plateaued and parallel efficiency decreased almost linearly with increasing number of nodes. The primary factor affecting parallel performance was the synchronization requirement of the parallel algorithm, which dictated that each iteration must wait for completion of the slowest fitness evaluation. When the analytical problems were solved using a fixed number of swarm iterations, a single population of 128 particles produced a better convergence rate than did multiple independent runs performed using sub-populations (8 runs with 16 particles, 4 runs with 32 particles, or 2 runs with 64 particles). These results suggest that (1) parallel PSO exhibits excellent parallel performance under load-balanced conditions, (2) an asynchronous implementation would be valuable for real-life problems subject to load imbalance, and (3) larger population sizes should be considered when multiple processors are available.

NEWSUMT-A: A General Purpose Program for Constrained Optimization Using Constraint Approximations

The solution of complex constrained optimization problems is often prohibitively expensive because of the computational expense of evaluating the constraints. Under these circumstances the only viable solution is to employ inexpensive constraint approximations accompanied by move-limits that guard against large errors in the approximated constraints. The NEWSUMT-A program is a general purpose optimization program which automates the process of selecting constraint approximations and move-limits to ensure smooth convergence. The present paper describes the theoretical basis and the implementation of the optimization procedure. Examples from the field of structural optimization are presented. These involve stress and displacement constraints which require a costly finite element analysis. Additionally, the performance of two first-order constraint approximations is compared.