## Neural networks Applications in optimization

**Applications of Particle Swarm Optimization**

**Nonconvex Search Spaces**

The Rastrigin function from the post In-depth details of the algorithm is a nonconvex function and therefore has a nonconvx search space. Convexity is extremely important in optimization algorithms because it has nice properties involving gradients that can make optimization guaranteed. In a space like the Rastrigin function, particle swarm optimization is able to deal with the local minima and in many cases finds the global optimum.

**Integer or Discontinuous Search Spaces**In a similar vein, integer search spaces are difficult for traditional optimization algorithms. In problems that involve integer variables, the search space is discontinuous and gradient information is rarely effective. Particle swarm optimization does not require the space to be continuous but precautions need to be taken to position particles exactly on specific values. For more information see, “An improved PSO algorithm for solving non-convex NLP/MINLP problems with equality constraints” by Yiqing et al.

**Neural Networks**

One could treat the neural network weight space as a high dimensional particle swarm optimization search space. In this application of PSO, particles could be a swarm of **neural networks** attempting to find the lowest error on some classification or regression task. See “Particle Swarm Optimization of Neural Network Architectures and Weights” by Carvalho et al.

**Source:** Adam Maus

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