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Global Optimization by Particle Swarm Method:A Fortran Program

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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. The program has been tested on over 90 benchmark functions of varied dimensions, complexities and difficulty levels.

Suggested Citation

  • Mishra, SK, 2006. "Global Optimization by Particle Swarm Method:A Fortran Program," MPRA Paper 874, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:874
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    File URL: https://mpra.ub.uni-muenchen.de/874/1/MPRA_paper_874.pdf
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    1. Mishra, SK, 2006. "Some Experiments on Fitting of Gielis Curves by Simulated Annealing and Particle Swarm Methods of Global Optimization," MPRA Paper 465, University Library of Munich, Germany.
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    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 classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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