Enhanced cultural algorithm to solve multi-objective attribute reduction based on rough set theory

Abstract

The paper "Enhanced cultural algorithm to solve multi-objective attribute reduction based on rough set theory," published in Mathematics and Computers in Simulation in 2020, addresses the challenge of high-dimensional data in knowledge discovery by proposing a novel approach to attribute reduction (AR). Authored by Majid Abdolrazzagh-Nezhad, Homa Radgohar, and Seyede Najme Salimian, the research focuses on multi-objective attribute reduction (MOAR) using rough set theory (RST), which quantifies information loss and dependency among attributes. The primary goal is to find a minimal subset of attributes (a reduct) that maximizes the dependency coefficient, thereby preserving essential information while eliminating redundancy—a problem known to be NP-hard.

The study makes two significant contributions. First, it designs a new cost function that effectively combines two conflicting objectives: minimizing the size of the reduct and maximizing its dependency degree. This function penalizes solutions with low dependency and rewards compact, high-quality reducts, enabling the transformation of the multi-objective problem into a single-objective optimization task. Second, the authors enhance the cultural algorithm (CA)—a population-based metaheuristic inspired by societal learning—to handle the discrete nature of the attribute reduction problem. The enhanced CA (ECA) utilizes only normative and situational knowledge components to guide the search, and introduces a discretization mechanism to convert continuous candidate solutions into binary representations suitable for feature selection.

Experimental validation was conducted on twelve well-known UCI datasets of varying sizes, comparing the ECA against five established algorithms: binary genetic algorithm (Bi-GA), particle swarm optimization (PSO), bee colony optimization (BCO), artificial bee colony (ABC), and binary tabu search (Bi-TS). The algorithms were tested with different population sizes to evaluate sensitivity and robustness. Results demonstrated that the ECA consistently achieved competitive reducts, often with the maximum dependency value of one, indicating no information loss. Notably, the ECA exhibited lower sensitivity to population size changes compared to other methods, maintaining stable performance as the population increased from 100 to 200 individuals.

Key positive outcomes include the ECA's efficient convergence, reduced dispersion of results, and its ability to avoid local optima through cultural knowledge sharing. Statistical tests, including T-tests, indicated that the ECA's performance was comparable to or better than that of the other algorithms, particularly PSO, in terms of solution quality and reliability. The proposed cost function also proved effective in steering the search toward high-dependency reducts. These findings highlight the ECA as a robust and scalable method for attribute reduction in high-dimensional data settings, offering a valuable tool for preprocessing in data mining, machine learning, and pattern recognition applications.

In conclusion, the paper successfully integrates rough set theory with an enhanced cultural algorithm to address a complex multi-objective optimization problem. The methodological advancements—both in the design of the cost function and the adaptation of the CA—provide a practical and efficient framework for feature selection. The research opens avenues for future work, such as extending the approach to incomplete or fuzzy rough sets, or applying the ECA to other discrete optimization challenges in data science and beyond.