Initial unconnected cities
subtour=ALB; unadded=ALB,MHT,BDL,ORH,PVD,HVN

Starting with 2 farthest cities
subtour=ALB-PVD-ALB; unadded=BDL,ORH,MHT,HVN

Find distance from each city not yet in the tour to all cities in the tour

BDL-ALB=128.81; BDL-PVD=106.96
distance from BDL to tour = shortest = BDL-PVD=106.96
ORH-ALB=167.13; ORH-PVD=70.82
distance from ORH to tour = shortest = ORH-PVD=70.82
MHT-ALB=194.50; MHT-PVD=134.28
distance from MHT to tour = shortest = MHT-PVD=134.28
HVN-ALB=181.55; HVN-PVD=132.08
distance from HVN to tour = shortest = HVN-PVD=132.08

MHT had the longest distance to the tour; finding the place to insert it (thin lines represent the segment to remove; medium lines indicate the segments that replace it)

replacing ALB-PVD with ALB-MHT-PVD replaces a leg of length 226.61 with two of total length 194.50+134.28=328.78 for an increase of 102.18
replace ALB-PVD with ALB-MHT-PVD;
increase=194.50+134.28-226.61=102.18
replacing PVD-ALB with PVD-MHT-ALB replaces a leg of length 226.61 with two of total length 134.28+194.50=328.78 for an increase of 102.18
replace PVD-ALB with PVD-MHT-ALB;
increase=134.28+194.50-226.61=102.18

Adding MHT to tour at point that minimizes increase in distance
subtour=ALB-MHT-ALB; unadded=PVD,BDL,ORH,HVN

Find distance from each city not yet in the tour to all cities in the tour

BDL-ALB=128.81; BDL-MHT=150.72; BDL-PVD=106.96
distance from BDL to tour = shortest = BDL-PVD=106.96
ORH-ALB=167.13; ORH-MHT=82.27; ORH-PVD=70.82
distance from ORH to tour = shortest = ORH-PVD=70.82
HVN-ALB=181.55; HVN-MHT=220.84; HVN-PVD=132.08
distance from HVN to tour = shortest = HVN-PVD=132.08

HVN had the longest distance to the tour; finding the place to insert it (thin lines represent the segment to remove; medium lines indicate the segments that replace it)

replacing ALB-MHT with ALB-HVN-MHT replaces a leg of length 194.50 with two of total length 181.55+220.84=402.39 for an increase of 207.89
replace ALB-MHT with ALB-HVN-MHT;
increase=181.55+220.84-194.50=207.89
replacing MHT-PVD with MHT-HVN-PVD replaces a leg of length 134.28 with two of total length 220.84+132.08=352.91 for an increase of 218.63
replace MHT-PVD with MHT-HVN-PVD;
increase=220.84+132.08-134.28=218.63
replacing PVD-ALB with PVD-HVN-ALB replaces a leg of length 226.61 with two of total length 132.08+181.55=313.63 for an increase of 87.02
replace PVD-ALB with PVD-HVN-ALB;
increase=132.08+181.55-226.61=87.02

Adding HVN to tour at point that minimizes increase in distance
subtour=ALB-MHT-PVD-ALB; unadded=HVN,BDL,ORH

Find distance from each city not yet in the tour to all cities in the tour

BDL-ALB=128.81; BDL-MHT=150.72; BDL-PVD=106.96; BDL-HVN=76.90
distance from BDL to tour = shortest = BDL-HVN=76.90
ORH-ALB=167.13; ORH-MHT=82.27; ORH-PVD=70.82; ORH-HVN=139.61
distance from ORH to tour = shortest = ORH-PVD=70.82

BDL had the longest distance to the tour; finding the place to insert it (thin lines represent the segment to remove; medium lines indicate the segments that replace it)

replacing ALB-MHT with ALB-BDL-MHT replaces a leg of length 194.50 with two of total length 128.81+150.72=279.53 for an increase of 85.03
replace ALB-MHT with ALB-BDL-MHT;
increase=128.81+150.72-194.50=85.03
replacing MHT-PVD with MHT-BDL-PVD replaces a leg of length 134.28 with two of total length 150.72+106.96=257.68 for an increase of 123.40
replace MHT-PVD with MHT-BDL-PVD;
increase=150.72+106.96-134.28=123.40
replacing PVD-HVN with PVD-BDL-HVN replaces a leg of length 132.08 with two of total length 106.96+76.90=183.85 for an increase of 51.78
replace PVD-HVN with PVD-BDL-HVN;
increase=106.96+76.90-132.08=51.78
replacing HVN-ALB with HVN-BDL-ALB replaces a leg of length 181.55 with two of total length 76.90+128.81=205.70 for an increase of 24.15
replace HVN-ALB with HVN-BDL-ALB;
increase=76.90+128.81-181.55=24.15

Adding BDL to tour at point that minimizes increase in distance
subtour=ALB-MHT-PVD-HVN-ALB; unadded=BDL,ORH

Find distance from each city not yet in the tour to all cities in the tour

ORH-ALB=167.13; ORH-MHT=82.27; ORH-PVD=70.82; ORH-HVN=139.61; ORH-BDL=76.11
distance from ORH to tour = shortest = ORH-PVD=70.82

ORH had the longest distance to the tour; finding the place to insert it (thin lines represent the segment to remove; medium lines indicate the segments that replace it)

replacing ALB-MHT with ALB-ORH-MHT replaces a leg of length 194.50 with two of total length 167.13+82.27=249.40 for an increase of 54.90
replace ALB-MHT with ALB-ORH-MHT;
increase=167.13+82.27-194.50=54.90
replacing MHT-PVD with MHT-ORH-PVD replaces a leg of length 134.28 with two of total length 82.27+70.82=153.09 for an increase of 18.80
replace MHT-PVD with MHT-ORH-PVD;
increase=82.27+70.82-134.28=18.80
replacing PVD-HVN with PVD-ORH-HVN replaces a leg of length 132.08 with two of total length 70.82+139.61=210.43 for an increase of 78.35
replace PVD-HVN with PVD-ORH-HVN;
increase=70.82+139.61-132.08=78.35
replacing HVN-BDL with HVN-ORH-BDL replaces a leg of length 76.90 with two of total length 139.61+76.11=215.72 for an increase of 138.82
replace HVN-BDL with HVN-ORH-BDL;
increase=139.61+76.11-76.90=138.82
replacing BDL-ALB with BDL-ORH-ALB replaces a leg of length 128.81 with two of total length 76.11+167.13=243.23 for an increase of 114.43
replace BDL-ALB with BDL-ORH-ALB;
increase=76.11+167.13-128.81=114.43

Adding ORH to tour at point that minimizes increase in distance
subtour=ALB-MHT-ORH-PVD-HVN-ALB; unadded=BDL
Tour produced by -insert farthest
subtour=ALB-MHT-ORH-PVD-HVN-BDL-ALB; unadded= -insert farthest : 685.37 ALB MHT ORH PVD HVN BDL ALB