Constrained pressure-vessel design optimization using the scuba diver optimization algorithm: parameter sensitivity and statistical validation

Abstract

The pressure-vessel benchmark is a mixed-discrete nonlinear engineering problem in which shell and head thicknesses follow manufacturing increments while radius and cylindrical length remain continuous. This study applies the Scuba Diver Optimization Algorithm (SDOA) to the standard formulation and examines ten parameter configurations through 30 independent runs each. An oxygen-regulated state model assigns global exploration, moderate exploration, exploitation, fine tuning, or reset, while a repair procedure enforces the 0.0625-in thickness increment, variable bounds, minimum wall thicknesses, and required volume. All 300 runs ended with feasible designs. S7 achieved the best mean rank (4.000), the smallest standard deviation (0.055056), a mean cost of 6059.766062, and a 73.3% success rate within 0.001% of the proven optimum. S9 produced the closest individual design, with cost 6059.714482843 and a relative gap of 0.000002439%. Friedman and Holm-adjusted Wilcoxon analyses confirmed significant configuration effects. The results show that parameter selection mainly affects repeated-run consistency and search-stage allocation rather than attainable best-case accuracy.