Dialectical search: a cognitively inspired framework for balancing solution quality and computational cost in global optimization

The field of global optimization faces the persistent challenge of developing metaheuristics that are both highly effective and computationally efficient. Motivated by the limitations of many nature-inspired algorithms, which are often susceptible to premature convergence, this research explores formal intellectual processes to create a more robust search mechanism. We propose and formalize the Dialectical Search (DS) framework, a metaheuristic inspired by the philosophical principle of Thesis, Antithesis, and Synthesis. The framework’s efficacy was validated in a comprehensive empirical study where two primary variants, DS-Original and DS-Hybrid, were benchmarked against a diverse suite of seven other classical and state-of-the-art algorithms on multiple real-world datasets. The benchmark revealed that the DS-Original variant consistently achieves a solution quality that is statistically indistinguishable from top-performing algorithms; for instance, on the Breast Cancer Wisconsin dataset, it achieved a cross-validation error of 0.02415, matching the performance of far slower methods. Critically, it delivers this state-of-the-art performance with exceptional computational efficiency, executing approximately 20% faster than the Genetic Algorithm and an order of magnitude faster—48.14 s versus 481.25 s—than the Firefly Algorithm. Furthermore, the simpler DS-Original’s superior practical performance over its more complex hybrid counterpart provides a valuable insight into the No Free Lunch (NFL) theorem. Therefore, we conclude that the Dialectical Search framework, particularly the DS-Original variant, represents a significant contribution to the field, offering a validated and highly advantageous balance of solution accuracy and computational efficiency for solving complex optimization problems.