Dialectic optimization algorithm (DOA): a novel metaheuristic inspired by dialectical philosophy

Efficient optimization methods are essential for addressing large-scale and real-time problems in supercomputing environments. This paper presents the Dialectic Opti mization Algorithm (DOA), a novel population-based metaheuristic inspired by Hegelian and Marxist dialectical philosophy. DOA simulates the ideological dynam ics of three subpopulations: supporters, opponents, and neutrals—using logistic growth equations, influence matrices, contradiction analysis, and synthesis mecha nisms. These components form a structured and adaptive search process that pro motes diversity, mitigates premature convergence, and drives the population toward global optima. A formal algorithm analysis is also provided, including first-order logical axioms, lemmas on population dynamics, and convergence theorems that mathematically validate its soundness and stability. The proposed method is empiri cally evaluated on twelve standard benchmark functions and compared against eleven widely used metaheuristics, including GA, ACO, PSO, WOA, GWO, HHO, SSA, and others. Based on 100 independent runs per function, the DOA consistently outperformed all eleven comparative algorithms in accuracy, robustness, and con vergence speed. A comprehensive statistical evaluation using Kolmogorov–Smirnov with p < 0.01, Mann–Whitney showing no statistical inferiority, Kruskal–Wallis with χ2 > 1 000 and a Friedman test yielding a mean rank of 1.08 confirmed DOA’s superior solution quality, efficiency and consistency across 12 benchmark functions, underscoring its philosophically grounded, formally validated framework for solving complex, multimodal optimization problems.