Empirical problem decomposition — the key to the evolutionary effectiveness in solving a large-scale non-binary discrete real-world problem

Abstract

In this paper, we consider an NP-hard, real-world optimization problem from the field of computer networks. The problem refers to the network survivability and may be considered hard due to its scale. Such problems are usually successfully solved by various Genetic Algorithms (GAs). The recent advances in the development of Evolutionary Algorithms (EAs) dedicated to solving discrete-encoded problems show that GAs employing modern linkage learning techniques seem to have exceptional potential in proposing high-quality results. Many of such GAs are the state-of-the-art methods for various optimization problems, including various domain types and single- and multi-objective optimization problems. These GAs have also been shown effective in solving theoretical and practical problems. Thus, linkage learning development may lead to proposing GAs that are significantly more effective than their predecessors. Therefore, we develop the recently proposed linkage learning technique, namely the linkage learning based on local optimization (3LO) that is (to the best of our knowledge) based on fundamentally different ideas than all other linkage-based problem decomposition techniques. Due to these differences, 3LO has some exceptional features — it is proven that it will never commit some of the possible problem decomposition inconsistencies. However, 3LO was only proposed for binary-encoded problems. Therefore, to fill this gap and adjust 3LO to the considered problem, we propose linkage learning based on local optimization for discrete non-binary search spaces (3LO-nb). The obtained results show that 3LO-nb allows for reaching excellent results. Additionally, our proposition is generic, and its effectiveness may be verified on other non-binary discrete problems.