Global Optimization By Particle Swarm Method: A Fortran Program

Abstract:     
Programs that work very well in optimizing convex functions very often perform poorly when the problem has multiple local minima or maxima. They are often caught or trapped in the local minima/maxima. Several methods have been developed to escape from being caught in such local optima. The Particle Swarm Method of global optimization is one of such methods.

A swarm of birds or insects or a school of fish searches for food, protection, etc. in a very typical manner. If one of the members of the swarm sees a desirable path to go, the rest of the swarm will follow quickly. Every member of the swarm searches for the best in its locality - learns from its own experience. Additionally, each member learns from the others, typically from the best performer among them. Even human beings show a tendency to learn from their own experience, their immediate neighbours and the ideal performers. The Particle Swarm method of optimization mimics this behaviour. Every individual of the swarm is considered as a particle in a multidimensional space that has a position and a velocity. These particles fly through hyperspace and remember the best position that they have seen. Members of a swarm communicate good positions to each other and adjust their own position and velocity based on these good positions.

The Particle Swarm method of optimization testifies the success of bounded rationality and decentralized decisionmaking in reaching at the global optima. It has been used successfully to optimize extremely difficult multimodal functions. Here we give a FORTRAN program to find the global optimum by the Repulsive Particle Swarm method.

Keywords: Bounded rationality, Decentralized decision making Jacobian Elliptic functions, Gielis super-formula, supershapes, Repulsive Particle Swarm method of Global optimization, nonlinear programming, multiple sub-optimum, global, local optima, fit, data, empirical, estimation, parameters, curve fitting

JEL Classifications: C15, C63

Working Paper Series