Complex System Engineering For Scalable Architectures: A Structural Complexity Optimization Approach

Abstract

The increasing complexity of modern engineered systems arises from tightly coupled components and their interdependent interactions, necessitating robust approaches for scalable and efficient system design. Research presents a Complex System Engineering method that models product architectures as dependency networks, represented through adjacency matrices to capture structural relationships among components. A quantitative structural complexity metric is developed to evaluate and compare different architectural configurations. Data used for experimentation is collected from the Structural Complexity Design Dataset, which consists of 13000 data. The proposed approach integrates preprocessing using Min–Max normalization to scale interaction weights for consistent analysis, and Linear Discriminant Analysis (LDA) to extract the most discriminative structural features that enhance class separability among architectural configurations. The method further integrates multi-objective Non-dominated Sorting Genetic Algorithm II (NSGA-II) optimization to balance modularity, scalability, and complexity distribution across system modules. The method is validated using a gas turbine engine, where multiple architectural configurations were analyzed. Experimental result demonstrates an optimization cost of 0.65, Structural Complexity Index (SCI) of 0.60, Convergence Iterations of 350, Execution Time of 10.2s, and a Scalability Score of 0.89, which is implemented in Python. Furthermore, analysis reveals a non-linear relationship between structural complexity and development cost, emphasizing the need for optimal complexity allocation during early design stages. The proposed method provides a systematic foundation for designing scalable, modular, and cost-efficient complex systems, making it applicable to aerospace, manufacturing, and large-scale engineered infrastructures.