Journal of Uncertainty Analysis and Applications

Table 4 Optimal solutions with different α and β ( δ=5 )

From: A bi-objective model for uncertain multi-modal shortest path problems

	Parameters	Optimal objective values	Shortest path
Single	α=0.6	g ₁(x)=37.2	0→33→34→27→28→29→23→24→25→26→21→46
Objective	β=0.6	g ₂(x,y)=35.8	0→1→3→12→13→8→10→31→20→21→46
Double	δ=5	g ₁(x)=42.0	0→1→2→28→22→23→30→31→20→21→46
Objectives		g ₂(x,y)=38.6
Single	α=0.7	g ₁(x)=42.4	0→33→34→27→28→29→23→24→25→26→21→46
Objective	β=0.7	g ₂(x,y)=39.6	0→1→3→12→13→8→10→31→20→21→46
Double	δ=5	g ₁(x)=47.2	0→1→3→5→23→24→25→26→21→46
Objectives		g ₂(x,y)=42.8
Single	α=0.8	g ₁(x)=46.4	0→1→2→28→29→23→24→25→26→21→46
Objective	β=0.8	g ₂(x,y)=43.4	0→1→3→12→13→8→10→31→20→21→46
Double	δ=5	g ₁(x)=50.8	0→1→3→5→23→24→25→26→21→46
Objectives		g ₂(x,y)=46.2
Single	α=0.9	g ₁(x)=50.2	0→1→2→28→29→23→24→25→26→21→46
Objective	β=0.9	g ₂(x,y)=47.2	0→1→3→12→13→8→10→31→20→21→46
Double	δ=5	g ₁(x)=54.4	0→1→3→5→23→24→25→26→21→46
Objectives		g ₂(x,y)=49.6
Single	α=1.0	g ₁(x)=54.0	0→1→2→28→29→23→24→25→26→21→46
Objective	β=1.0	g ₂(x,y)=51.0	0→1→3→12→13→8→10→31→20→21→46
Double	δ=5	g ₁(x)=59.0	0→1→3→5→23→30→31→20→21→46
Objectives		g ₂(x,y)=52.0

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