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Discrete Dynamics in Nature and Society
Volume 2005 (2005), Issue 3, Pages 257-279

On the optimal control of single-stage hybrid manufacturing systems via novel and different variants of particle swarm optimization algorithm

Faculty of Engineering & Technology (FET), Multimedia University (Melaka Campus), Jalan Ayer Keroh Lama, Bukit Beruang, Melaka 75450, Malaysia

Received 1 March 2005

Copyright © 2005 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents several novel approaches of particle swarm optimization (PSO) algorithm with new particle velocity equations and three variants of inertia weight to solve the optimal control problem of a class of hybrid systems, which are motivated by the structure of manufacturing environments that integrate process and optimal control. In the proposed PSO algorithm, the particle velocities are conceptualized with the local best (or pbest) and global best (or gbest) of the swarm, which makes a quick decision to direct the search towards the optimal (fitness) solution. The inertia weight of the proposed methods is also described as a function of pbest and gbest, which allows the PSO to converge faster with accuracy. A typical numerical example of the optimal control problem is included to analyse the efficacy and validity of the proposed algorithms. Several statistical analyses including hypothesis test are done to compare the validity of the proposed algorithms with the existing PSO technique, which adopts linearly decreasing inertia weight. The results clearly demonstrate that the proposed PSO approaches not only improve the quality but also are more efficient in converging to the optimal value faster.