|
Consensus Based Optimization
Consensus-based optimization (CBO) is a multi-agent derivative-free optimization method, designed to obtain solutions for global optimization problems of the form \min_ f(x), where f:\mathcal\to\R denotes the objective function acting on the state space \cal, which is assumed to be a normed vector space. The function f 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, particle swarm optimization or Simulated annealing. Algorithm Consider an ensemble of points x_t = (x_t^1,\dots, x_t^N) \in ^N, dependent of the time t\in[0,\infty). Then the update for the ith particle is formulated as a stochastic differential equation, dx^i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Derivative-free Optimization
Derivative-free optimization (sometimes referred to as blackbox optimization) is a discipline in mathematical optimization that does not use derivative information in the classical sense to find optimal solutions: Sometimes information about the derivative of the objective function ''f'' is unavailable, unreliable or impractical to obtain. For example, ''f'' might be non-smooth, or time-consuming to evaluate, or in some way noisy, so that methods that rely on derivatives or approximate them via finite differences are of little use. The problem to find optimal points in such situations is referred to as derivative-free optimization, algorithms that do not use derivatives or finite differences are called derivative-free algorithms. Introduction The problem to be solved is to numerically optimize an objective function f\colon A\to\mathbb for some set A (usually A\subset\mathbb^n), i.e. find x_0\in A such that without loss of generality f(x_0)\leq f(x) for all x\in A. When applicable, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
