Implementation of Digital Pheromones in Particle Swarm Optimization for Constrained Optimization Problems

This paper presents a model for digital pheromone implementation of Particle Swarm Optimization (PSO) to solve constrained optimization problems. Digital pheromones are models simulating real pheromones produced by insects for communication to indicate a source of food or a nesting location. When integrated within PSO, this principle of communication and organization between swarm members offer substantial improvement in search accuracy, efficiency and reliability. Multiple pheromones are released in the design space, and the strength of a pheromone in a region of the design space is determined through empirical proximity analysis, and. The swarm then reacts accordingly based on the probability that this region may contain an optimum. The addition of a pheromone component to the velocity vector equation demonstrated substantial success in solving unconstrained problems. The research presented in this paper explores the suitability of the developed method to solve constrained optimization problems. A sequential unconstrained minimization technique – Augmented Lagrange Multiplier (ALM) method has been implemented to address constrained optimization problems. ALM has been chosen because of its relative insensitivity to whether the initial design points for a pseudo objective function are feasible or infeasible. The development of the method and results from solving several constrained test problems are presented.