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Using Augmented Lagrangian Particle Swarm Optimization for Constrained Problems in Engineering

  • Peter Eberhard
  • Kai Sedlaczek
Chapter
Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 511)

Abstract

The general nonlinear optimization problem is given by the nonlinear objective function f, which is to be minimized with respect to the design variables x and the nonlinear equality and inequality constraints. This can be formulated by
$$ \mathop {minimize}\limits_p \psi (p), p \in \mathbb{D} \cap \mathbb{F}, \mathbb{D} \subseteq \mathbb{R}^n $$
(12.1)
subject to the nonlinear equality and inequality constraints
$$ g(p) = 0, g :\mathbb{R}^n \to \mathbb{R}^{m_e } , $$
(12.2)
$$ h(p) \leqslant 0, h :\mathbb{R}^n \to \mathbb{R}^{m_i } $$
(12.3)
which define the feasible region \( \mathbb{F} \) and the search space \( \mathbb{D} \) is additionally bounded by the simple bounds
$$ p_l \leqslant p \leqslant p_u $$
(12.4)

Keywords

Particle Swarm Optimization Lagrange Multiplier Particle Swarm Penalty Factor Tangential Stiffness Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© CISM, Udine 2009

Authors and Affiliations

  • Peter Eberhard
    • 1
  • Kai Sedlaczek
    • 1
  1. 1.Institute of Engineering and Computational MechanicsUniversity of StuttgartGermany

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