Sensibility of Linkage Information and Effectiveness of Estimated Distributions

Abstract

The probabilistic model building performed by estimation of distribution algorithms (EDAs) enables these methods to use advanced techniques of statistics and machine learning for automatic discovery of problem structures. However, in some situations, it may not be possible to completely and accurately identify the whole problem structure by probabilistic modeling due to certain inherent properties of the given problem. In this work, we illustrate one possible cause of such situations with problems consisting of structures with unequal fitness contributions. Based on the illustrative example, we introduce a notion that the estimated probabilistic models should be inspected to reveal the effective search directions and further propose a general approach which utilizes a reserved set of solutions to examine the built model for likely inaccurate fragments. Furthermore, the proposed approach is implemented on the extended compact genetic algorithm (ECGA) and experiments are performed on several sets of additively separable problems with different scaling setups. The results indicate that the proposed method can significantly assist ECGA to handle problems comprising structures of disparate fitness contributions and therefore may potentially help EDAs in general to overcome those situations in which the entire problem structure cannot be recognized properly due to the temporal delay of emergence of some promising partial solutions.

Multivariate multi-model approach for globally multimodal problems

“…To demonstrate this composition, consider our first test problem, F1, which is formed by concatenating ten 4-bit trap or inverse trap functions and one switch variable, s41, 1000 to 10000, and each of these experiments was repeated for 50 times. Tournament selection is adopted as selection method, and we set the tournament size to 16 (which has been reported suitable for ECGA to handle the range of 40-to 80-bit concatenated trap problems [4].) In these experiments, the stopping criterion is set such that a run is terminated when all solutions in the population converge to the same fitness value.…”

A Review of Population-Based Metaheuristics for Large-Scale Black-Box Global Optimization—Part II

“…This characteristic, which is often called the imbalance problem, can have a detrimental effect on the optimization performance if not handled properly. For example, Chuang and Chen [139] showed that the model building process of EDAs is affected by the imbalance problem. They reported that the selected individuals based on which the probabilistic model of EDAs is updated lacks the necessary information about the linkage structure of some parts of the problem.…”

Pairwise independence and its impact on Estimation of Distribution Algorithms

“…Sadowski et al [36] faced similar difficulties when applying the LTGA to the MAX-SAT. According to the literature, such bad results could be caused by a high degree of interactions [30] or the non-uniformity of fitness contributions associated with subsets of variables [37]. However, few studies have followed in such a direction [38,39].…”