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Parameter Sensitivity Analysis of the Multi-Verse Optimizer for Nonlinear Biological Model Identification

Year: 2026
Type: article
Abstract: This study presents a full-factorial sensitivity analysis of the Multi-Verse Optimizer (MVO) for nonlinear biological model identification. The parameter space comprises 256 configurations formed by eight values of the minimum wormhole existence probability (WEPmin), four population sizes (n), and eight exploitation-accuracy values (p), with 30 independent stochastic runs per configuration. Three complementary response measures are used, all computed as between-run statistics over the 30 independent runs of each configuration: the per-run best objective (BestObj), the mean of the per-run objective values (MeanObj), and the standard deviation of the per-run objective values (StdObj), which quantifies run-to-run reproducibility. A reduced factorial ANOVA shows that the exploitation accuracy p is the dominant control parameter for the per-run best objective, MeanObj, and StdObj (partial ηp2=0.16, 0.90, and 0.63, respectively), followed by WEPmin and n. For BestObj as the minimum over runs, the p main effect is smaller but still significant (ηp2=0.22), while the WEPmin main effect is not significant. No two-way or three-way interaction reaches significance within the tested grid, so the parameters act approximately additively. Holm-corrected post-hoc comparisons on the top-10 configurations show that the MeanObj and StdObj leaders are not statistically distinguishable at 30 independent runs (0/45 significant pairs in each case), while for BestObj the minima of 30 runs cannot be compared formally at this sample size. The three criteria therefore produce different point-estimate rankings rather than statistically separated optima. The recommended configuration (WEPmin,n,p)=(0.15,100,36) is a representative point within a favorable parameter region. Its selection rests on the rank-1 point estimate and its position in the favorable region on the E. coli MC4110 problem; the cross-process validation on the E. coli BL21(DE3)pPhyt109 problem is an independent test of that selection. The recommended configuration was transferred without additional tuning to the E. coli BL21(DE3)pPhyt109 problem, where it was non-inferior to the best alternative within a prespecified margin of 0.5 objective units (d=+0.110, one-sided upper bound +0.338, p=0.002, equivalence confirmed by two one-sided tests) and achieved the best single objective value of the five tested configurations. The results demonstrate that MVO parameter selection should distinguish exceptional solution discovery from typical run-to-run performance, and that a favorable parameter region should be preferred to a single universally optimal point when the objective surface is shallow near its optimum.
Source: Mathematics
DOI: 10.3390/math14224145
Language: English
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W7225795783
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