Improved Particle Swarm Optimization Algorithms for Optimal Designs with Various Decision Criteria

Abstract

Particle swarm optimization (PSO) is an attractive, easily implemented method which is successfully used across a wide range of applications. In this paper, utilizing the core ideology of genetic algorithm and dynamic parameters, an improved particle swarm optimization algorithm is proposed. Then, based on the improved algorithm, combining the PSO algorithm with decision making, nested PSO algorithms with two useful decision making criteria (optimistic coefficient criterion and minimax regret criterion) are proposed . The improved PSO algorithm is implemented on two unimodal functions and two multimodal functions, and the results are much better than that of the traditional PSO algorithm. The nested algorithms are applied on the Michaelis–Menten model and two parameter logistic regression model as examples. For the Michaelis–Menten model, the particles converge to the best solution after 50 iterations. For the two parameter logistic regression model, the optimality of algorithms are verified by the equivalence theorem. More results for other models applying our algorithms are available upon request.