Enhanced Henry Gas Solubility Optimization for Solving Data and Engineering Design Problems

Many engineering design problems are formulated as constrained optimization tasks that are nonlinear and nonconvex, and often treated as black boxes. In such cases, metaheuristic algorithms are attractive because they can search complex design spaces without requiring gradient information. In this work, we propose an Enhanced Henry Gas Solubility Optimization (eHGSO) algorithm, which is an improved version of the physics-inspired HGSO method. The enhanced variant introduces six main contributions: (i) a more diverse, population-wide initialization strategy to cover the design space more thoroughly; (ii) adaptive temperature/pressure control parameters that automatically shift the search from global exploration to local refinement; (iii) an elitist archive with differential perturbation that accelerates exploitation around high-quality candidate designs; (iv) a simple combination of the global HGSO search moves with a lightweight gradient-free local search to refine promising solutions; (v) a constraint-handling mechanism that explicitly prioritizes feasible solutions while still allowing exploration near the constraint boundaries; and (vi) a complexity and ablation analysis that quantifies the impact of each mechanism and confirms that they introduce only modest computational overhead. We evaluate eHGSO on four classical constrained engineering design problems: the stepped cantilever beam, the tension/compression spring, the welded beam, and the three-bar truss. Its performance is compared with seventeen recent metaheuristic optimizers over multiple independent runs. eHGSO achieves the best average objective value on the cantilever, spring, and welded-beam problems and shares the best average result on the three-bar truss. Compared to the second-best method, the mean objective is improved by about 0.84% for the cantilever beam and 0.35% for the welded beam, while the spring and truss results are essentially equivalent at four significant figures. Convergence and robustness analyses show that eHGSO reaches high-quality solutions quickly and consistently. Overall, the proposed eHGSO algorithm appears to be a competitive and practical tool for constrained engineering design problems.