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. 2026 Apr 30;16:20059. doi: 10.1038/s41598-026-50836-0

Table 2.

Representative allocation ranges and associated objective values across the Pareto spectrum.

Allocation region Inline graphic Inline graphic​ Inline graphic​ Inline graphic Inline graphic​ Inline graphic​
Concentrated end 0.65–0.69 0.23–0.28 0.06–0.09 1.80–1.84 0.21–0.24 0.020–0.029
Near-knee region ≈ 0.60 ≈ 0.30 ≈ 0.10 1.82–1.90 0.17–0.21 0.02–0.03
Dispersed end 0.40–0.47 0.28–0.33 0.19–0.32 2.20–2.60 0.04–0.09 0.09–0.30

The near-knee region denotes solutions where marginal improvement in any single objective induces disproportionate deterioration in others, representing a stability zone for multi-objective performance. Lower f₁ indicates shorter response time, lower f₂ indicates more balanced workload, and lower f₃ indicates reduced expected burned area.