Topic
Multi-swarm optimization
About: Multi-swarm optimization is a research topic. Over the lifetime, 19162 publications have been published within this topic receiving 549725 citations.
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TL;DR: A hybrid PSO (HPSO) with a feasibility-based rule is proposed to solve constrained optimization problems and it is shown that the rule requires no additional parameters and can guide the swarm to the feasible region quickly.
437 citations
06 Jul 1999
TL;DR: This paper takes the next step, generalizing to obtain closed form equations for trajectories of particles in a multi-dimensional search space.
Abstract: A new optimization method has been proposed by J. Kennedy and R.C. Eberhart (1997; 1995), called Particle Swarm Optimization (PSO). This approach combines social psychology principles and evolutionary computation. It has been applied successfully to nonlinear function optimization and neural network training. Preliminary formal analyses showed that a particle in a simple one-dimensional PSO system follows a path defined by a sinusoidal wave, randomly deciding on both its amplitude and frequency (Y. Shi and R. Eberhart, 1998). The paper takes the next step, generalizing to obtain closed form equations for trajectories of particles in a multi-dimensional search space.
434 citations
TL;DR: The pyOpt framework as discussed by the authors is an object-oriented framework for formulating and solving nonlinear constrained optimization problems in an efficient, reusable and portable manner, which allows for easy integration of optimization software programmed in Fortran, C, C+?+, and other languages.
Abstract: We present pyOpt, an object-oriented framework for formulating and solving nonlinear constrained optimization problems in an efficient, reusable and portable manner. The framework uses object-oriented concepts, such as class inheritance and operator overloading, to maintain a distinct separation between the problem formulation and the optimization approach used to solve the problem. This creates a common interface in a flexible environment where both practitioners and developers alike can solve their optimization problems or develop and benchmark their own optimization algorithms. The framework is developed in the Python programming language, which allows for easy integration of optimization software programmed in Fortran, C, C+?+, and other languages. A variety of optimization algorithms are integrated in pyOpt and are accessible through the common interface. We solve a number of problems of increasing complexity to demonstrate how a given problem is formulated using this framework, and how the framework can be used to benchmark the various optimization algorithms.
434 citations
TL;DR: This letter presents a formal stochastic convergence analysis of the standard particle swarm optimization (PSO) algorithm, which involves with randomness.
433 citations
01 Jan 2004
TL;DR: Results show Discrete PSO is certainly not as powerful as some specific algorithms, but, on the other hand, it can easily be modified for any discrete/combinatorial problem for which the authors have no good specialized algorithm.
Abstract: The classical Particle Swarm Optimization is a powerful method to find the minimum of a numerical function, on a continuous definition domain. As some binary versions have already successfully been used, it seems quite natural to try to define a framework for a discrete PSO. In order to better understand both the power and the limits of this approach, we examine in detail how it can be used to solve the well known Traveling Salesman Problem, which is in principle very “bad” for this kind of optimization heuristic. Results show Discrete PSO is certainly not as powerful as some specific algorithms, but, on the other hand, it can easily be modified for any discrete/combinatorial problem for which we have no good specialized algorithm.
429 citations