## Particle Swarm Optimization: A Physics-based ApproachThis work aims to provide new introduction to the particle swarm optimization methods using a formal analogy with physical systems. By postulating that the swarm motion behaves similar to both classical and quantum particles, we establish a direct connection between what are usually assumed to be separate fields of study, optimization and physics. Within this framework, it becomes quite natural to derive the recently introduced quantum PSO algorithm from the Hamiltonian or the Lagrangian of the dynamical system. The physical theory of the PSO is used to suggest some improvements in the algorithm itself, like temperature acceleration techniques and the periodic boundary condition. At the end, we provide a panorama of applications demonstrating the power of the PSO, classical and quantum, in handling difficult engineering problems. The goal of this work is to provide a general multi-disciplinary view on various topics in physics, mathematics, and engineering by illustrating their interdependence within the unified framework of the swarm dynamics. Table of Contents: Introduction / The Classical Particle Swarm Optimization Method / Boundary Conditions for the PSO Method / The Quantum Particle Swarm Optimization / Bibliography /Inde |

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### Contents

1 | |

12 Why PhysicsBased Approach | 4 |

13 The Philosophy of the Book | 5 |

The Classical Particle Swarm Optimization Method | 7 |

22 Particle Swarm Optimization and ElectroMagnetics | 10 |

Physical Formalism for Particle Swarm Optimization | 13 |

33 Extraction of Information from Swarm Dynamics | 20 |

34 Thermodynamic Analysis of the PSO Environment | 21 |

43 The Hard Boundary Conditions | 44 |

45 Hybrid Periodic Boundary Condition for the PSO Environment | 46 |

The Quantum Particle Swarm Optimization | 57 |

52 The Choice of the Potential Well Distribution | 59 |

53 The Collapse of the Wave Function | 60 |

54 Selecting the Parameters of the Algorithm | 61 |

55 The QPSO Algorithm | 62 |

56 Application of the QPSO Algorithm to Array Antenna Synthesis Problems | 63 |

35 Acceleration Technique for the PSO Algorithm | 30 |

36 Diffusion Model for the PSO Algorithm | 32 |

37 Markov Model for Swarm Optimization Techniques | 35 |

Boundary Conditions for the PSO Method | 41 |

42 The Soft Conditions | 43 |

57 Infinitesimal Dipoles Equivalent to Practical Antennas | 69 |

58 Conclusion | 76 |

79 | |

85 | |

### Other editions - View all

Particle Swarm Optimizaton: A Physics-Based Approach Said M. Mikki,Ahmed A. Kishk Limited preview - 2008 |

### Common terms and phrases

Antennas Propagat Antennas Wireless Propagat artiﬁcial average basic PSO boundary conditions characteristic length computational conditional pdf conﬁne control parameter convergence curves Cost Function criterion current distribution deﬁned deﬁnition Dielectric Resonator Dielectric Resonator Antenna diffusion equation electromagnetic energy ergodicity hypothesis Figure ﬁnal ﬁnd ﬁrst formulation global optimum hybrid IEEE Antennas Wireless inﬁnite inﬁnitesimal dipoles interacting ith particle Lagrangian Lett linear array antenna linearly from 0.9 Markov chains molecular dynamics Newtonian number of iterations number of particles objective function obtained optimization method optimization problem particle hits Particle Swarm Optimization performance permission from IEEE physical systems position primary cell probability density function PSO algorithm PSO environment PSO method QDPSO QPSO QSPSO quantum mechanics quantum PSO random variable Rastigrin reﬂect Reprinted Rosenbrock Schrödinger equation solution speciﬁc sphere function stochastic swarm dynamics temperature theory thermal equilibrium thermodynamic trajectory update equations vector velocity Vmax