Variable Interaction Network Analysis to Enhance Boundary Update Method for Constrained Optimization

The boundary update approach was proposed by Gandomi and Deb [Computer Methods in Applied Mechanics and Engineering, 363, 112,917, 2020] for constrained optimization problems. The boundary update (BU) method defines a dynamic formulation of an optimization problem in order to eliminate the infeasible search space. This study investigates the concept of variable interaction using a differential grouping algorithm, DG2, to evaluate and visualize variable interaction impacted by the boundary update method. Using multiple social network analysis (SNA) metrics, including Average Betweenness Centrality, Average Closeness Centrality, Network Density, and Clustering Coefficient, this research reveals significant structural simplifications in optimization problems under the BU method. Results show significant improvements in some aspects by applying the BU method. For example, it reduces network density by up to 34 %, closeness centrality by over 67 %, and enhances independence among variables by 45 %, simplifying the optimization landscape. Furthermore, a systematic evaluation using the TOPSIS multi-criteria decision-making (MCDM) approach confirms that BU improves convergence efficiency and solution quality by 20%–30 % compared to without BU methods across various benchmark problems. Network visualizations corroborate these findings, demonstrating reduced complexity and improved clarity in variable relationships. This comprehensive analysis establishes the BU method as a transformative framework, significantly advancing constrained optimization through its ability to streamline variable interactions and enhance algorithmic performance.