Abstract
This paper presents a quantum-behaved neurodynamic swarm optimization approach to solve the nonconvex optimization problems with inequality constraints. Firstly, the general constrained optimization problem is addressed and a high-performance feedback neural network for solving convex nonlinear programming problems is introduced. The convergence of the proposed neural network is also proved. Then, combined with the quantum-behaved particle swarm method, a quantum-behaved neurodynamic swarm optimization (QNSO) approach is presented. Finally, the performance of the proposed QNSO algorithm is evaluated through two function tests and three applications including the hollow transmission shaft, heat exchangers and crank–rocker mechanism. Numerical simulations are also provided to verify the advantages of our method.
Highlights
Constrained optimization problems arise in many scientific and engineering applications including robot control [1], regression analysis [2], economic forecasting [3], filter design [4] and so on
As pointed out in [6], the dynamic behaviors of a neural network could change drastically and become unpredictable, when applying neurodynamic optimization to deal with general nonconvex optimization problems
In order to improve the convergence speed of the optimization algorithm, we explore a quantum-behaved neurodynamic approach combining the quantum-behaved particle swarm optimization (QPSO) algorithm with the feedback neural network model (7) for nonconvex programming problems with general constraints
Summary
Constrained optimization problems arise in many scientific and engineering applications including robot control [1], regression analysis [2], economic forecasting [3], filter design [4] and so on. Yan et al [6] presented a collective neurodynamic optimization approach by combining the traditional PSO algorithm and a projection neural network to solve nonconvex optimization problems with box constraints. Inspired by [6,14,29], we employ the feedback neural network and present a quantum-behaved neurodynamic swarm approach for solving the nonconvex optimization problems with inequality constraints efficiently. The proposed QNSO approach combining the QPSO algorithm [30] and the feedback neural network is applied to deal with constrained optimization problems with multiple global minima.
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