Particle swarm optimization: Difference between revisions

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Another argument in favour of simplifying PSO is that [[metaheuristic]]s can only have their efficacy demonstrated [[empirical]]ly by doing computational experiments on a finite number of optimization problems. This means a metaheuristic such as PSO cannot be [[Program correctness|proven correct]] and this increases the risk of making errors in its description and implementation. A good example of this<ref name=tu04robust/> presented a promising variant of a [[genetic algorithm]] (another popular metaheuristic) but it was later found to be defective as it was strongly biased in its optimization search towards similar values for different dimensions in the search space, which happened to be the optimum of the benchmark problems considered. This bias was because of a programming error, and has now been fixed.<ref name=tu04corrections/>

==== Bare Bones PSO ====

Initialization of velocities may require extra inputs. The Bare Bones PSO variant<ref>{{Cite book|last=Kennedy|first=James|title=Proceedings of the 2003 IEEE Swarm Intelligence Symposium. SIS'03 (Cat. No.03EX706) |chapter=Bare bones particle swarms |date=2003|pages=80–87|doi=10.1109/SIS.2003.1202251|isbn=0-7803-7914-4|s2cid=37185749}}</ref> has been proposed in 2003 by James Kennedy, and does not need to use velocity at all.

In this variant of PSO one dispences with the velocity of the particles and instead updates the positions of the particles using the following simple rule,

:<math>

\vec x_i = G\left(\frac{\vec p_i+\vec g}{2},||\vec p_i-\vec g||\right) \,,

</math>

where <math>\vec x_i</math>, <math>\vec p_i</math> are the position and the best position of the particle <math>i</math>; <math>\vec g</math> is the global best position; <math>G(\vec x,\sigma)</math> is the [[normal distribution]] with the mean <math>\vec x</math> and standard deviation <math>\sigma</math>; and where <math>||\dots||</math> signifies the norm of a vector.

==== Accelerated Particle Swarm Optimization ====

Another simpler variant is the accelerated particle swarm optimization (APSO),<ref>X. S. Yang, S. Deb and S. Fong, [https://arxiv.org/abs/1203.6577 Accelerated particle swarm optimization and support vector machine for business optimization and applications], NDT 2011, Springer CCIS 136, pp. 53-66 (2011).</ref> which also does not need to use velocity and can speed up the convergence in many applications. A simple demo code of APSO is available.<ref>{{Cite web | url=http://www.mathworks.com/matlabcentral/fileexchange/?term=APSO | title=Search Results: APSO - File Exchange - MATLAB Central}}</ref>