Scaling Up Estimation of Distribution Algorithms for Continuous Optimization

Abstract

Since Estimation of Distribution Algorithms (EDA) were proposed, many attempts have been made to improve EDAs' performance in the context of global optimization. So far, the studies or applications of multivariate probabilistic model based continuous EDAs are still restricted to rather low dimensional problems (smaller than 100D). Traditional EDAs have difficulties in solving higher dimensional problems because of the curse of dimensionality and their rapidly increasing computational cost. However, scaling up continuous EDAs for higher dimensional optimization is still necessary, which is supported by the distinctive feature of EDAs: Because a probabilistic model is explicitly estimated, from the learnt model one can discover useful properties or features of the problem. Besides obtaining a good solution, understanding of the problem structure can be of great benefit, especially for black box optimization.We propose a novel EDA framework with Model Complexity Control (EDA-MCC) to scale up EDAs. By using Weakly dependent variable Identification (WI) and Subspace Modeling (SM), EDA-MCC shows significantly better performance than traditional EDAs on high dimensional problems. Moreover, the computational cost and the requirement of large population sizes can be reduced in EDA-MCC. In addition to being able to find a good solution, EDA-MCC can also produce a useful problem structure characterization. EDA-MCC is the first successful instance of multivariate model based EDAs that can be effectively applied a general class of up to 500D problems. It also outperforms some newly developed algorithms designed specifically for large scale optimization. In order to understand the strength and weakness of EDA-MCC, we have carried out extensive computational studies of EDA-MCC. Our results have revealed when EDA-MCC is likely to outperform others on what kind of benchmark functions.Index Terms-Estimation of distribution algorithm, large scale optimization, model complexity control.

Data-driven analysis of variables and dependencies in continuous optimization problems and estimation of distribution algorithms

“…In addition to this, another set of problems, the Real-Parameter Black-Box Optimization Benchmarking (BBOB) experiment set [76] are used in Chapter 6 to findout the model parameters for 2 different proposed algorithm (sEDA and sEDA-lite). In addition to these sets of problems, another set of problems from [41] has been used in Chapter 6 to compare different algorithms.…”

“…For example the EDA framework with Model Complexity Control (EDA-MCC) [41] was proposed, which uses EMNA global for each subset of the variables, to perform well in high dimensional problems. A number of advanced Gaussian based EDAs like Adaptive-Variance scaling, Standard-Deviation Ratio triggering, Anticipated Mean Shift, which results in AMaLGAM uses the maximum likelihood estimates of EDAs [20].…”

“…For example, more recently, Dong et al [41] proposed the EDA Model Complexity Control (EDA-MCC) to scale up continuous EDAs using a sparse covariance matrix, which is used for solving high dimensional problems very efficiently with less computational cost as well as less population sizes. EDA-MCC uses EMNA global for each subset of the variables.…”

“…A threshold value of 0.3 has been set here for measuring the high correlation between variables [41]. In a 2-dimensional problem, the correlation between two variables has been determined by checking the correlation coefficient values.…”

“…Therefore the model agrees with the properties of problems of type category 1. Literature shows that UMDA c is performing better in this type of function ( [43,41], Chapter 8 of [15]). …”