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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