Consensus based optimization: Difference between revisions

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'''Consensus-based optimization (CBO)'''<ref name=":0">{{Cite journal |last1=Pinnau |first1=René |last2=Totzeck |first2=Claudia |last3=Tse |first3=Oliver |last4=Martin |first4=Stephan |date=January 2017 |title=A consensus-based model for global optimization and its mean-field limit |url=https://www.worldscientific.com/doi/abs/10.1142/S0218202517400061 |journal=Mathematical Models and Methods in Applied Sciences |language=en |volume=27 |issue=1 |pages=183–204 |doi=10.1142/S0218202517400061 |arxiv=1604.05648 |s2cid=119296432 |issn=0218-2025}}</ref> is a multi-agent [[derivative-free optimization]] method, designed to obtain solutions for global optimization problems of the form <math display="block">\min_{x\in \cal{X}} f(x),</math>

[[File:CBORastrigin.gif|thumb|Behavior of CBO on the [[Rastrigin function]]. '''Blue:''' Particles, '''Pink:''' drift vectors and consensus point.]]

where <math>f:\mathcal{X}\to\R</math> denotes the objective function acting on the state space <math>\cal{X}</math>, which we assume to be a [[normed vector space]] in the following. The function <math>f</math> can potentially be nonconvex and nonsmooth. The algorithm employs particles or agents to explore the state space, which communicate with each other to update their positions. Their dynamics follows the paradigm of [[Metaheuristic|metaheuristics]], which blend exporation with exploitation. In this sense, CBO is comparable to [[Ant colony optimization algorithms|ant colony optimization]], wind driven optimization<ref>{{Cite web |title=The Wind Driven Optimization Technique and its Application in Electromagnetics {{!}} IEEE Journals & Magazine {{!}} IEEE Xplore |url=https://ieeexplore.ieee.org/document/6407788 |access-date=2024-02-03 |website=ieeexplore.ieee.org}}</ref>, [[particle swarm optimization]] or [[Simulated annealing]].

== The algorithm ==