Evolving Swarm-A Genetically Modified Particle Swarm Optimizer with Localized Pattern Search Capability for Aerospace Propulsion Systems

Abstract

A hybrid particle swarm-pattern search optimizer is combined with a genetic algorithm (GA) to produce a particle swarm model which evolves through time, subject to the laws of natural selection The ability of particle swarm optimization to locate global optimum solutions, combined with the usefulness of pattern search optimization in finding local optimum values is augmented by GA natural selection parameters (e.g., crossover, creep, mutation, tournament selection) Continuous removal of the poorest performing members of the swarm can greatly improve optimizer performance, as characterized by two criteria: (1) “fitness function” accuracy, or how closely solutions meet a specified tolerance, and (2) convergence speed, based on how many calls to the “objective function” are required to meet that tolerance. Design of a star grain solid rocket motor (SRM) to match a specified thrust vs. time curve is used as the objective function. Results are compared with those obtained from a “regular” particle swarm optimizer, a binary encoded genetic algorithm (GA) optimizer, a real code genetic algorithm optimizer, and a hybrid particle swarm/pattern search optimizer. I. Introduction As computer capacity and physical understanding of the mechanisms involved in the physics of aerospace design has increased, modeling and simulation has teamed with optimization techniques to become a powerful design tool. The situation becomes very complex for multi-disciplinary system level design optimization. Optimizers may be based on either stochastic or direct (non-stochastic) methodology, or some combination of both. Stochastic tools include genetic algorithms (GA’s), which are based on survival of the fittest principles, and particle swarm (PSO) algorithms, which are based on the principles of social behavior. Direct solution techniques include pattern search and gradient descent, among others. Interest in the development of hybrid optimizers (a combination of two or more optimizer types) has increased in recent years. Genetic algorithms, particle swarm algorithms, pattern search algorithms and others have been combined in various ways in attempts to improve optimization efficiency for a range of problems, with varying degrees of success. For instance, the authors recently (2010) published a method based on the direct integration of a pattern search technique into a constrained repulsive particle swarm algorithm 1 . The technique was applied to several propulsion-based problems and was shown to compare very favorably with solutions obtained by a binary genetic algorithm, a real coded genetic algorithm, and a standard particle swarm algorithm. Solution accuracy and convergence speed (as measured by number of calls to the objective function) were the comparison criteria. Many hybrid combinations have been proposed. Juang 2 proposed a combination of genetic algorithm and particle swarm optimizers for design