A Model Reference Adaptive Search Method for Global Optimization

Abstract

informs ® doi 10.1287/opre.1060.0367 © 2007 INFORMS Model reference adaptive search (MRAS) for solving global optimization problems works with a parameterized probabilistic model on the solution space and generates at each iteration a group of candidate solutions. These candidate solutions are then used to update the parameters associated with the probabilistic model in such a way that the future search will be biased toward the region containing high-quality solutions. The parameter updating procedure in MRAS is guided by a sequence of implicit probabilistic models we call reference models. We provide a particular algorithm instantiation of the MRAS method, where the sequence of reference models can be viewed as the generalized probability distribution models for estimation of distribution algorithms (EDAs) with proportional selection scheme. In addition, we show that the model reference framework can also be used to describe the recently proposed cross-entropy (CE) method for optimization and to study its properties. Hence, this paper can also be seen as a study on the effectiveness of combining CE and EDAs. We prove global convergence of the proposed algorithm in both continuous and combinatorial domains, and we carry out numerical studies to illustrate the performance of the algorithm

Cumulative weighting optimization

“…Proof Using the argument made for proving Lemma 2 of [19] and the assumption that θ k+1 ∈ , we can prove that Remark 4). The rest of the proof uses the same argument as in Lemma 2.1 of [2].…”

“…We propose several approaches for constructing the weight-update stage. These algorithms build on the theoretical results using the same types of modifications as are found in CE and MRAS (see [11,19,22]). There are seven parameters in Algorithm 2. ρ 0 is the initial percentile threshold, ρ min is the minimum allowed percentile threshold, N 0 is the initial sample size, 2 is the minimal γ k threshold improvement requirement, where γ k is the corresponding value at threshold ρ k .…”

“…They are taken from the website http://www.iwr.uni-heidelberg.de/groups/comopt/ software/TSPLIB95. We follow a similar approach as in Hu et al [19], which is outlined below. The reader is reminded here that Algorithm 2 is designed for maximization problems, whereas we are searching for the minimum distances of ATSPs.…”

Hybrid simulation–optimization methods: A taxonomy and discussion

“…Some examples include Swarm Intelligence (e.g. ant colony optimization [21]), Estimation of Distribution Algorithms [22], Cross-Entropy Method [23] and Model Reference Adaptive Search [24]. These methods are also known as model-based methods, as opposed to the previous methods, which are instance-based [25], and may work either with discrete (MMH a ) or continuous variables (MMH b ).…”

The mathematics of continuous-variable simulation optimization

“…We do not discuss the very important and applicable area of meta-modeling, including the very promising area of kriging, e.g., Barton and Meckesheimer (2006) and Ankenman, Nelson, and Staum (2008). We do not cover the frameworks of the cross-entropy method, e.g., Rubinstein and Kroese (2004), or model-reference adaptive search Hu, Fu, and Marcus (2007). Finally, we do not discuss results related to the difficulty of solving global optimization problems, e.g., Calvin (2004).…”