An Adaptive Random Search for Unconstrained Global Optimization

Abstract

Adaptive Gibbs Sampling (AGS) algorithm is a new heuristic for unconstrained global optimization. AGS algorithm is a population-based method that uses a random search strategy to generate a set of new potential solutions. Random search combines the one-dimensional Metropolis-Hastings algorithm with the multidimensional Gibbs sampler in such a way that the noise level can be adaptively controlled according to the landscape providing a good balance between exploration and exploitation over all search space. Local search strategies can be coupled to the random search methods in order to intensify in the promising regions. We have performed experiments on three well known test problems in a range of dimensions with a resulting testbed of 33 instances. We compare the AGS algorithm against two deterministic methods and three stochastic methods. Results show that the AGS algorithm is robust in problems that involve central aspects which is the main reason of global optimization problem difficulty including high-dimensionality, multi-modality and non-smoothness.

An adaptive random search for short term generation scheduling with network constraints

“…In this paper, we extend the AGS algorithm (see [ 22 ]) for continuous optimization to tackle mixed-variable optimization problems. First, the LR was used just for bounding purposes, and then the AGS algorithm was used to construct feasible solutions in reasonable computational times.…”

“…In order to improve the obtained solutions, we consider coupling a local search into a random search process. The algorithm is well described and implement for unconstrained global optimization problems in [ 22 ]. A brief summary of the AGS method is given in Algorithm 2 below.…”

“…Thus, the noise intensity allows exploring the entire search space, and noise-reduction allows exploitation in the promising regions where local optima exist. The algorithm is well described and compared in unconstrained global optimization problems by [ 22 ]. The effectiveness and robustness of this method was proved in several complex problems in order to find reasonable quality solutions for global optimization problems.…”