Substance

A Nonlinear Integer/Discrete/Continuous Programming Solver Applied to a New Formulation of a Nine-City Traveling Salesman Problem, Second Edition

Jsun Yui Wong

The following computer program tries to solve the twelve-city traveling salesperson problem on page 807 of Winston and Vankataramanan [10].  The new formulation is partly described by line 194 through line 355.

0 REM DEFDBL A-Z
2 DEFINT I,J,K,X
3 DIM B(99),N(99),A(2002),H(99),L(99),U(99),X(2002),D(111),P(111),PS(33),J44(2002)
8 DIM HR(49,49)
11 FOR IZ=0 TO 8
14 FOR JZ=0 TO 8
16 READ HR(IZ,JZ)
18 NEXT JZ
19 NEXT IZ
21 DATA 999,172,250,127,103,170,264,82,159
22 DATA 172,999,170,177,200,325,178,139,241
23 DATA 250,170,999,206,134,252,201,233,291
24 DATA 127,177,206,999,191,181,184,57,172
25 DATA 103,200,134,191,999,201,144,197,268
26 DATA 170,325,252,181,201,999,229,211,129
27 DATA 264,178,201,184,144,229,999,132,202
28 DATA 82,139,233,57,197,211,132,999,186
29 DATA 159,241,291,172,268,129,202,186,999
68 FOR JJJJ=-32000 TO 32000
69 RANDOMIZE JJJJ
70 M=-1D+37
91  A(1)=1:A(2)=2:A(3)=3:A(4)=4:A(5)=5:A(6)=6:A(7)=7:A(8)=8
126 IMAR=10+FIX(RND*666)
128 FOR I=1 TO IMAR
129 FOR KKQQ=1 TO 8
130 X(KKQQ)=A(KKQQ)
131 NEXT KKQQ
194 J=1+FIX(RND*8)
196 JJ=1+FIX(RND*8)
198 X(J)=A(JJ)
199 X(JJ)=A(J)
305 PDU=0
311 FOR J88=0 TO 7
315 PDU=PDU-HR(X(J88),X(J88+1))
320 NEXT J88
355 POB1=PDU-HR(X(8),0)
444 P1NEWMAY=POB1
466 P=P1NEWMAY
1111 IF P<=M THEN 1670
1452 M=P
1454 FOR KLX=1 TO 8
1455 A(KLX)=X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 IF M<-1236 THEN 1999
1933 PRINT A(1),A(2),A(3),A(4),A(5)
1934 PRINT A(6),A(7),A(8),M,JJJJ
1999 NEXT JJJJ

This BASIC computer program was run with Microsoft's GW BASIC 3.11 interpreter.  The complete output through JJJJ=-31908 is shown below.  What follows is a hand copy of the output on the computer-monitor screen; below there is no rounding by hand.

4   2   1   6   8
5   3   7   -1236   -31999

4   2   1   6   8
5   3   7   -1236   -31988

4   2   1   6   8
5   3   7   -1236   -31985

4   2   1   6   8
5   3   7   -1236   -31983

4   2   1   6   8
5   3   7   -1236   -31978

4   2   1   6   8
5   3   7   -1236   -31977

4   2   1   6   8
5   3   7   -1236   -31975

4   2   1   6   8
5   3   7   -1236   -31974

4   2   1   6   8
5   3   7   -1236   -31971

4   2   1   6   8
5   3   7   -1236   -31964

4   2   1   6   8
5   3   7   -1236   -31961

4   2   1   6   8
5   3   7   -1236   -31955

4   2   1   6   8
5   3   7   -1236   -31951

4   2   1   6   8
5   3   7   -1236   -31933

4   2   1   6   8
5   3   7   -1236   -31917

4   2   1   6   8
5   3   7   -1236   -31916

4   2   1   6   8
5   3   7   -1236   -31912

4   2   1   6   8
5   3   7   -1236   -31911

4   2   1   6   8
5   3   7   -1236   -31910

7   3   5   8   6
1   2   4   -1236   -31908

On a personal computer with an Intel 2.66 chip and the IBM basica/D interpreter, version GW BASIC 3.11, the throughput time (including printing) from JJJJ=-32000 through JJJJ=-31908 was four seconds, real time, not cpu time. 

References

[1] Larry M. Austin, Parviz Ghandforoush, Management Science for Decision Makers.  St. Paul, MN: West Publishing Company, 1993.

[2] Robert Garfinkel, George L. Nemhauser, Integer Programming.  John Wiley and Sons, Inc., 1972.

[3] Frederick S. Hillier, Gerard J. Lieberman, Introduction to Operations Research, 8th Edition.   New York: McGraw-Hill, 2005.

[4] Claude McMillan, Mathematical Programming, Second Edition.  John Wiley and Sons Inc., 1975.

[5] Microsoft Corp., BASIC, Second Edition (May 1982), Version 1.10. Boca Raton, Florida: IBM Corp., Personal Computer, P. O. Box 1328-C, Boca Raton, Florida 33432, 1981.

[6] Ronald L. Rardin, Optimization in Operations Research.  Upper Saddle River, NJ: Prentice Hall, 1998.

[7] Hamdy A. Taha, Integer Programming--Theory, Applications, and Computations.  Academic Press, In., 1975.

[8] Hamdy A. Taha, Operations Research: an Introduction, 8th Edition.  Upper Saddle River, NJ 07458: Pearson Prentice Hall, 2007.

[9] Wayne L. Winston, Operations Research: Applications and Algorithms, Fourth Edition.  Brooks/Cole, a division of Thomson, 2004.

[10] Wayne L. Winston, Munirpallam Venkataramanan, Introduction to Mathematical Programming, Third Edition.  Brooks/Cole, a division of Thomson, 2003.

A Nonlinear Integer/Discrete/Continuous Programming Solver Applied to a New Formulation of an Eleven-City Traveling Salesperson Problem, Fourth Edition

Jsun Yui Wong

The following computer program tries to solve the eleven-city traveling salesman problem on page 454 of Winston and Albright [11].  The new formulation is partly described by line 201 through line 355.

0 REM DEFDBL A-Z
2 DEFINT I,J,K,X
3 DIM B(99),N(99),A(2002),H(99),L(99),U(99),X(2002),D(111),P(111),PS(33),J44(2002)
8 DIM HR(33,33)
11 FOR IZ=0 TO 10
14 FOR JZ=0 TO 10
16 READ HR(IZ,JZ)
18 NEXT JZ
19 NEXT IZ
21 DATA 99999,0983,1815,1991,3036,1539,0213,2664,0792,2385,2612
22 DATA 0983,99999,1205,1050,2112,1390,0840,1729,0457,2212,2052
23 DATA 1815,1205,99999,0801,1425,1332,1604,1027,1237,1034,2404
24 DATA 1991,1050,0801,99999,1174,2057,1780,0836,1411,1765,1373
25 DATA 3036,2112,1425,1174,99999,2757,2825,0398,2456,0403,1919
26 DATA 1539,1390,1332,2057,2757,99999,1258,2359,1250,3097,3389
27 DATA 0213,0840,1604,1780,2825,1258,99999,2442,0386,3036,2900
28 DATA 2664,1729,1027,0836,0398,2359,2442,99999,2073,0800,1482
29 DATA 0792,0457,1237,1411,2456,1250,0386,2073,99999,2653,2517
30 DATA 2385,2212,1765,1034,0403,3097,3036,0800,2653,99999,0817
31 DATA 2612,2052,2404,1373,1919,3389,2900,1482,2517,0817,99999
52 FOR JJJJ=-32000 TO 32000
54 RANDOMIZE JJJJ
57 M=-1D+37
71 FOR J44=1 TO 10
72 A(J44)=J44
74 NEXT J44
126 IMAR=10+FIX(RND*500)
128 FOR I=1 TO IMAR
129 FOR KKQQ=1 TO 10
130 X(KKQQ)=A(KKQQ)
131 NEXT KKQQ
194 J=1+FIX(RND*11)
196 JJ=1+FIX(RND*11)
198 X(J)=A(JJ)
199 X(JJ)=A(J)
201 FOR J44=1 TO 10
207  IF   (X(J44)) >10 THEN 1670
211  NEXT J44
231 FOR J44=1 TO 10
237  IF   X(J44) <1 THEN 1670
240  NEXT J44
251 FOR J44B=1 TO 9
256 FOR J44A=J44B+1 TO 10
260 IF ABS(X(J44B)-X(J44A))=0 THEN 1670
261 NEXT J44A
262 NEXT J44B
305 PDU=0
311 FOR J88=0 TO 9
315 PDU=PDU-HR(X(J88),X(J88+1))
320 NEXT J88
333 REM
355 POB1=PDU-HR(X(10),0)
444 P1NEWMAY=POB1
466 P=P1NEWMAY
1111 IF P<=M THEN 1670
1452 M=P
1454 FOR KLX=1 TO 10
1455 A(KLX)=X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889  IF M<-9000 THEN 1999
1933 PRINT A(1),A(2),A(3),A(4),A(5)
1934 PRINT A(6),A(7),A(8),A(9),A(10)
1936 PRINT M,JJJJ
1999 NEXT JJJJ

This BASIC computer program was run with Microsoft's GW BASIC 3.11 interpreter.  The complete output through JJJJ=-31943 is shown below.  What follows is a hand copy of the output on the computer-monitor screen; below there is no rounding by hand.

6   8   1   3   10
9   4   7   2   5
-8995   -31976

5   2   7   4   9
10   3   1   8   6
-8995   -31967

5   2   7   4   9
10   3   1   8   6
-8995   -31956

5   2   7   4   9
10   3   1   8   6
-8995   -31949

5   2   7   4   9
10   3   1   8   6
-8995   -31943

On a personal computer with an Intel 2.66 chip and the IBM basica/D interpreter, version GW BASIC 3.11, the throughput time (including printing) from JJJJ=-32000 through JJJJ=-31943 was eight seconds, real time, not cpu time. 

References

[1] Larry M. Austin, Parviz Ghandforoush, Management Science for Decision Makers.  St. Paul, MN: West Publishing Company, 1993.

[2] Robert Garfinkel, George L. Nemhauser, Integer Programming.  John Wiley and Sons, Inc., 1972.

[3] Frederick S. Hillier, Gerard J. Lieberman, Introduction to Operations Research, 8th Edition.   New York: McGraw-Hill, 2005.

[4] Claude McMillan, Mathematical Programming, Second Edition.  John Wiley and Sons Inc., 1975.

[5] Microsoft Corp., BASIC, Second Edition (May 1982), Version 1.10. Boca Raton, Florida: IBM Corp., Personal Computer, P. O. Box 1328-C, Boca Raton, Florida 33432, 1981.

[6] Ronald L. Rardin, Optimization in Operations Research.  Upper Saddle River, NJ: Prentice Hall, 1998.

[7] Hamdy A. Taha, Integer Programming--Theory, Applications, and Computations.  Academic Press, In., 1975.

[8] Hamdy A. Taha, Operations Research: an Introduction, 8th Edition.  Upper Saddle River, NJ 07458: Pearson Prentice Hall, 2007.

[9] Wayne L. Winston, Operations Research: Applications and Algorithms, Fourth Edition.  Brooks/Cole, a division of Thomson, 2004.

[10] Wayne L. Winston, Munirpallam Venkataramanan, Introduction to Mathematical Programming, Fourth Edition.  Brooks/Cole, a division of Thomson, 2003. 

[11] Wayne L. Winston, S. Christian Albright, Practical Management Science, Third Edition. Mason, OH 45040: Thomson Higher Education, 2007. 

A Nonlinear Integer/Discrete/Continuous Programming Solver Applied to a New Formulation of an Eleven-City Traveling Salesperson Problem, Third Edition

Jsun Yui Wong

The following computer program tries to solve the eleven-city traveling salesman problem on page 454 of Winston and Albright [11].  The new formulation is partly described by line 201 through line 355.

Here line 133 is 133 FOR IPP=1 TO (1+FIX(RND*5)) while line 133 of the preceding post is 133 FOR IPP=1 TO (1+FIX(RND*9)); here line 185 is 185 IF J<2003 THEN X(J)=(A(J)+RND*R) ELSE X(J)=CINT(RND) while there line 185 is 185 IF J<2003 THEN X(J)=(A(J)+RND^3*R) ELSE X(J)=CINT(RND).

0 REM DEFDBL A-Z
2 DEFINT I,J,K,X
3 DIM B(99),N(99),A(2002),H(99),L(99),U(99),X(2002),D(111),P(111),PS(33),J44(2002)
8 DIM HR(33,33)
11 FOR IZ=0 TO 10
14 FOR JZ=0 TO 10
16 READ HR(IZ,JZ)
18 NEXT JZ
19 NEXT IZ
21 DATA 99999,0983,1815,1991,3036,1539,0213,2664,0792,2385,2612
22 DATA 0983,99999,1205,1050,2112,1390,0840,1729,0457,2212,2052
23 DATA 1815,1205,99999,0801,1425,1332,1604,1027,1237,1034,2404
24 DATA 1991,1050,0801,99999,1174,2057,1780,0836,1411,1765,1373
25 DATA 3036,2112,1425,1174,99999,2757,2825,0398,2456,0403,1919
26 DATA 1539,1390,1332,2057,2757,99999,1258,2359,1250,3097,3389
27 DATA 0213,0840,1604,1780,2825,1258,99999,2442,0386,3036,2900
28 DATA 2664,1729,1027,0836,0398,2359,2442,99999,2073,0800,1482
29 DATA 0792,0457,1237,1411,2456,1250,0386,2073,99999,2653,2517
30 DATA 2385,2212,1765,1034,0403,3097,3036,0800,2653,99999,0817
31 DATA 2612,2052,2404,1373,1919,3389,2900,1482,2517,0817,99999
52 FOR JJJJ=-32000 TO 32000
54 RANDOMIZE JJJJ
57 M=-1D+37
71 FOR J44=1 TO 10
72 A(J44)=1+FIX(RND*10)
74 NEXT J44
126 IMAR=10+FIX(RND*10000)
128 FOR I=1 TO IMAR
129 FOR KKQQ=1 TO 10
130 X(KKQQ)=A(KKQQ)
131 NEXT KKQQ
133 FOR IPP=1 TO (1+FIX(RND*5))
181 J=1+FIX(RND*10)
183 R=(1-RND*2)*A(J)
185 IF J<2003 THEN X(J)=(A(J)+RND*R) ELSE X(J)=CINT(RND)
192 NEXT IPP
201 FOR J44=1 TO 10
207  IF   (X(J44)) >10 THEN 1670
211  NEXT J44
231 FOR J44=1 TO 10
237  IF   X(J44) <1 THEN 1670
240  NEXT J44
251 FOR J44B=1 TO 9
256 FOR J44A=J44B+1 TO 10
260 IF ABS(X(J44B)-X(J44A))=0 THEN 1670
261 NEXT J44A
262 NEXT J44B
305 PDU=0
311 FOR J88=0 TO 9
315 PDU=PDU-HR(X(J88),X(J88+1))
320 NEXT J88
333 REM 
355 POB1=PDU-HR(X(10),0)
444 P1NEWMAY=POB1
466 P=P1NEWMAY
1111 IF P<=M THEN 1670
1452 M=P
1454 FOR KLX=1 TO 10
1455 A(KLX)=X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889  IF M<-9120 THEN 1999
1933 PRINT A(1),A(2),A(3),A(4),A(5)
1934 PRINT A(6),A(7),A(8),A(9),A(10)
1936 PRINT M,JJJJ
1999 NEXT JJJJ

This BASIC computer program was run with Microsoft's GW BASIC 3.11 interpreter.  The complete output through JJJJ=-21169 is shown below.  What follows is a hand copy of the output on the computer-monitor screen; below there is no rounding by hand.

6   8   1   3   10
9   4   7   2   5
-8995   -30190

8   1   3   10   9
4   7   2   5   6
-9120   -27959

6   5   2   7   4
9   10   3   1   8
-9120   -27892

5   2   7   4   9
10   3   1   8   6
-8995   -25133

6   8   1   3   10
9   4   7   2   5
-8995   -24042

5   2   7   4   9
10   3   1   8   6
-8995   -21169

On a personal computer with an Intel 2.66 chip and the IBM basica/D interpreter, version GW BASIC 3.11, the throughput time (including printing) from JJJJ=-32000 through JJJJ=-21169 was about 2.5 hours, real time, not cpu time. 

References

[1] Larry M. Austin, Parviz Ghandforoush, Management Science for Decision Makers.  St. Paul, MN: West Publishing Company, 1993.

[2] Robert Garfinkel, George L. Nemhauser, Integer Programming.  John Wiley and Sons, Inc., 1972.

[3] Frederick S. Hillier, Gerard J. Lieberman, Introduction to Operations Research, 8th Edition.   New York: McGraw-Hill, 2005.

[4] Claude McMillan, Mathematical Programming, Second Edition.  John Wiley and Sons Inc., 1975.

[5] Microsoft Corp., BASIC, Second Edition (May 1982), Version 1.10. Boca Raton, Florida: IBM Corp., Personal Computer, P. O. Box 1328-C, Boca Raton, Florida 33432, 1981.

[6] Ronald L. Rardin, Optimization in Operations Research.  Upper Saddle River, NJ: Prentice Hall, 1998.

[7] Hamdy A. Taha, Integer Programming--Theory, Applications, and Computations.  Academic Press, In., 1975.

[8] Hamdy A. Taha, Operations Research: an Introduction, 8th Edition.  Upper Saddle River, NJ 07458: Pearson Prentice Hall, 2007.

[9] Wayne L. Winston, Operations Research: Applications and Algorithms, Fourth Edition.  Brooks/Cole, a division of Thomson, 2004.

[10] Wayne L. Winston, Munirpallam Venkataramanan, Introduction to Mathematical Programming, Fourth Edition.  Brooks/Cole, a division of Thomson, 2003. 

[11] Wayne L. Winston, S. Christian Albright, Practical Management Science, Third Edition. Mason, OH 45040: Thomson Higher Education, 2007. 

A Nonlinear Integer/Discrete/Continuous Programming Solver Applied to a New Formulation of an Eleven-City Traveling Salesperson Problem, Second Edition

Jsun Yui Wong

The following computer program tries to solve the eleven-city traveling salesman problem on page 454 of Winston and Albright [11].  The new formulation is partly described by line 201 through line 333.

0 REM DEFDBL A-Z
2 DEFINT I,J,K,X
3 DIM B(99),N(99),A(2002),H(99),L(99),U(99),X(2002),D(111),P(111),PS(33),J44(2002)
8 DIM HR(33,33)
11 FOR IZ=0 TO 10
14 FOR JZ=0 TO 10
16 READ HR(IZ,JZ)
18 NEXT JZ
19 NEXT IZ
21 DATA 99999,0983,1815,1991,3036,1539,0213,2664,0792,2385,2612
22 DATA 0983,99999,1205,1050,2112,1390,0840,1729,0457,2212,2052
23 DATA 1815,1205,99999,0801,1425,1332,1604,1027,1237,1034,2404
24 DATA 1991,1050,0801,99999,1174,2057,1780,0836,1411,1765,1373
25 DATA 3036,2112,1425,1174,99999,2757,2825,0398,2456,0403,1919
26 DATA 1539,1390,1332,2057,2757,99999,1258,2359,1250,3097,3389
27 DATA 0213,0840,1604,1780,2825,1258,99999,2442,0386,3036,2900
28 DATA 2664,1729,1027,0836,0398,2359,2442,99999,2073,0800,1482
29 DATA 0792,0457,1237,1411,2456,1250,0386,2073,99999,2653,2517
30 DATA 2385,2212,1765,1034,0403,3097,3036,0800,2653,99999,0817
31 DATA 2612,2052,2404,1373,1919,3389,2900,1482,2517,0817,99999
52 FOR JJJJ=-32000 TO 32000
54 RANDOMIZE JJJJ
57 M=-1D+37
71 FOR J44=1 TO 10
72 A(J44)=1+FIX(RND*10)
74 NEXT J44
126 IMAR=10+FIX(RND*10000)
128 FOR I=1 TO IMAR
129 FOR KKQQ=1 TO 10
130 X(KKQQ)=A(KKQQ)
131 NEXT KKQQ
133 FOR IPP=1 TO (1+FIX(RND*9))
181 J=1+FIX(RND*10)
183 R=(1-RND*2)*A(J)
185 IF J<2003 THEN X(J)=(A(J)+RND^3*R) ELSE X(J)=CINT(RND)
192 NEXT IPP
201 FOR J44=1 TO 10
207  IF   (X(J44)) >10 THEN 1670
211  NEXT J44
231 FOR J44=1 TO 10
237  IF   X(J44) <1 THEN 1670
240  NEXT J44
251 FOR J44B=1 TO 9
256 FOR J44A=J44B+1 TO 10
260 IF ABS(X(J44B)-X(J44A))=0 THEN 1670
261 NEXT J44A
262 NEXT J44B
333 POB1=-HR(0,X(1))-HR(X(1),X(2))-HR(X(2),X(3))-HR(X(3),X(4))-HR(X(4),X(5))-HR(X(5),X(6))-HR(X(6),X(7))-HR(X(7),X(8))-HR(X(8),X(9))-HR(X(9),X(10))-HR(X(10),0)
444 P1NEWMAY=POB1
466 P=P1NEWMAY
1111 IF P<=M THEN 1670
1452 M=P
1454 FOR KLX=1 TO 10
1455 A(KLX)=X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889  IF M<-9333 THEN 1999
1933 PRINT A(1),A(2),A(3),A(4),A(5)
1934 PRINT A(6),A(7),A(8),A(9),A(10)
1936 PRINT M,JJJJ
1999 NEXT JJJJ

This BASIC computer program was run with Microsoft's GW BASIC 3.11 interpreter.  The complete output through JJJJ=-19843 is shown below.  What follows is a hand copy of the output on the computer-monitor screen; below there is no rounding by hand.

6   5   2   7   4
9   10   3   1   8
-9120   -31517

6   8   5   2   7
4   9   10   3   1
-9232   -31027

6   8   1   10   9
4   7   3   2   5
-9234   -28966

5   2   7   4   9
10   3   1   8   6
-8995   -26242

6   8   1   10   9
4   7   3   2   5
-9234   -21585

5   2   7   4   9
10   3   1   8   6
-8995   -19843

On a personal computer with an Intel 2.66 chip and the IBM basica/D interpreter, version GW BASIC 3.11, the throughput time (including printing) from JJJJ=-32000 through JJJJ=-19843 was 2.5 hours, real time, not cpu time. 

References

[1] Larry M. Austin, Parviz Ghandforoush, Management Science for Decision Makers.  St. Paul, MN: West Publishing Company, 1993.

[2] Robert Garfinkel, George L. Nemhauser, Integer Programming.  John Wiley and Sons, Inc., 1972.

[3] Frederick S. Hillier, Gerard J. Lieberman, Introduction to Operations Research, 8th Edition.   New York: McGraw-Hill, 2005.

[4] Claude McMillan, Mathematical Programming, Second Edition.  John Wiley and Sons Inc., 1975.

[5] Microsoft Corp., BASIC, Second Edition (May 1982), Version 1.10. Boca Raton, Florida: IBM Corp., Personal Computer, P. O. Box 1328-C, Boca Raton, Florida 33432, 1981.

[6] Ronald L. Rardin, Optimization in Operations Research.  Upper Saddle River, NJ: Prentice Hall, 1998.

[7] Hamdy A. Taha, Integer Programming--Theory, Applications, and Computations.  Academic Press, In., 1975.

[8] Hamdy A. Taha, Operations Research: an Introduction, 8th Edition.  Upper Saddle River, NJ 07458: Pearson Prentice Hall, 2007.

[9] Wayne L. Winston, Operations Research: Applications and Algorithms, Fourth Edition.  Brooks/Cole, a division of Thomson, 2004.

[10] Wayne L. Winston, Munirpallam Venkataramanan, Introduction to Mathematical Programming, Fourth Edition.  Brooks/Cole, a division of Thomson, 2003. 

[11] Wayne L. Winston, S. Christian Albright, Practical Management Science, Third Edition. Mason, OH 45040: Thomson Higher Education, 2007. 

A Nonlinear Integer/Discrete/Continuous Programming Solver Applied to a New Formulation of an Eleven-City Traveling Salesperson Problem

Jsun Yui Wong

The following computer program tries to solve the eleven-city traveling salesman problem on page 454 of Winston and Albright [11].  The new formulation is partly described by line 201 through line 333.

0 REM DEFDBL A-Z
2 DEFINT I,J,K,X
3 DIM B(99),N(99),A(2002),H(99),L(99),U(99),X(2002),D(111),P(111),PS(33),J44(2002)
8 DIM HR(33,33)
11 FOR IZ=0 TO 10
14 FOR JZ=0 TO 10
16 READ HR(IZ,JZ)
18 NEXT JZ
19 NEXT IZ
21 DATA 99999,0983,1815,1991,3036,1539,0213,2664,0792,2385,2612
22 DATA 0983,99999,1205,1050,2112,1390,0840,1729,0457,2212,2052
23 DATA 1815,1205,99999,0801,1425,1332,1604,1027,1237,1034,2404
24 DATA 1991,1050,0801,99999,1174,2057,1780,0836,1411,1765,1373
25 DATA 3036,2112,1425,1174,99999,2757,2825,0398,2456,0403,1919
26 DATA 1539,1390,1332,2057,2757,99999,1258,2359,1250,3097,3389
27 DATA 0213,0840,1604,1780,2825,1258,99999,2442,0386,3036,2900
28 DATA 2664,1729,1027,0836,0398,2359,2442,99999,2073,0800,1482
29 DATA 0792,0457,1237,1411,2456,1250,0386,2073,99999,2653,2517
30 DATA 2385,2212,1765,1034,0403,3097,3036,0800,2653,99999,0817
31 DATA 2612,2052,2404,1373,1919,3389,2900,1482,2517,0817,99999
52 FOR JJJJ=-32000 TO 32000
54 RANDOMIZE JJJJ
57 M=-1D+37
71 FOR J44=1 TO 10
72 A(J44)=1+FIX(RND*10)
74 NEXT J44
126 IMAR=10+FIX(RND*10000)
128 FOR I=1 TO IMAR
129 FOR KKQQ=1 TO 10
130 X(KKQQ)=A(KKQQ)
131 NEXT KKQQ
133 FOR IPP=1 TO (1+FIX(RND*9))
181 J=1+FIX(RND*10)
183 R=(1-RND*2)*A(J)
185 IF J<2003 THEN X(J)=(A(J)+RND^3*R) ELSE X(J)=CINT(RND)
192 NEXT IPP
201 FOR J44=1 TO 10
207  IF   (X(J44)) >10 THEN 1670
211  NEXT J44
231 FOR J44=1 TO 10
237  IF   X(J44) <1 THEN 1670
240  NEXT J44
251 FOR J44B=1 TO 9
256 FOR J44A=J44B+1 TO 10
260 IF ABS(X(J44B)-X(J44A))=0 THEN 1670
261 NEXT J44A
262 NEXT J44B
333 POB1=-HR(0,X(1))-HR(X(1),X(2))-HR(X(2),X(3))-HR(X(3),X(4))-HR(X(4),X(5))-HR(X(5),X(6))-HR(X(6),X(7))-HR(X(7),X(8))-HR(X(8),X(9))-HR(X(9),X(10))-HR(X(10),0)
444 P1NEWMAY=POB1
466 P=P1NEWMAY
1111 IF P<=M THEN 1670
1452 M=P
1454 FOR KLX=1 TO 10
1455 A(KLX)=X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889  IF M<-9333 THEN 1999
1933 PRINT A(1),A(2),A(3),A(4),A(5)
1934 PRINT A(6),A(7),A(8),A(9),A(10)
1936 PRINT M,JJJJ
1999 NEXT JJJJ

This BASIC computer program was run with Microsoft's GW BASIC 3.11 interpreter.  The complete output through JJJJ=-26242 is shown below.  What follows is a hand copy of the output on the computer-monitor screen; below there is no rounding by hand.

6   5   2   7   4
9   10   3   1   8
-9120   -31517

6   8   5   2   7
4   9   10   3   1
-9232   -31027

6   8   1   10   9
4   7   3   2   5
-9234   -28966

5   2   7   4   9
10   3   1   8   6
-8995   -26242

On a personal computer with an Intel 2.66 chip and the IBM basica/D interpreter, version GW BASIC 3.11, the throughput time (including printing) from JJJJ=-32000 through JJJJ=-26242 was seventy minutes, real time, not cpu time. 

References

[1] Larry M. Austin, Parviz Ghandforoush, Management Science for Decision Makers.  St. Paul, MN: West Publishing Company, 1993.

[2] Robert Garfinkel, George L. Nemhauser, Integer Programming.  John Wiley and Sons, Inc., 1972.

[3] Frederick S. Hillier, Gerard J. Lieberman, Introduction to Operations Research, 8th Edition.   New York: McGraw-Hill, 2005.

[4] Claude McMillan, Mathematical Programming, Second Edition.  John Wiley and Sons Inc., 1975.

[5] Microsoft Corp., BASIC, Second Edition (May 1982), Version 1.10. Boca Raton, Florida: IBM Corp., Personal Computer, P. O. Box 1328-C, Boca Raton, Florida 33432, 1981.

[6] Ronald L. Rardin, Optimization in Operations Research.  Upper Saddle River, NJ: Prentice Hall, 1998.

[7] Hamdy A. Taha, Integer Programming--Theory, Applications, and Computations.  Academic Press, In., 1975.

[8] Hamdy A. Taha, Operations Research: an Introduction, 8th Edition.  Upper Saddle River, NJ 07458: Pearson Prentice Hall, 2007.

[9] Wayne L. Winston, Operations Research: Applications and Algorithms, Fourth Edition.  Brooks/Cole, a division of Thomson, 2004.

[10] Wayne L. Winston, Munirpallam Venkataramanan, Introduction to Mathematical Programming, Fourth Edition.  Brooks/Cole, a division of Thomson, 2003. 

[11] Wayne L. Winston, S. Christian Albright, Practical Management Science, Third Edition. Mason, OH 45040: Thomson Higher Education, 2007. 

A Nonlinear Integer/Discrete/Continuous Programming Solver Applied to a New Formulation of a Nine-City Traveling Salesperson Problem

Jsun Yui Wong

The following computer program tries to solve the nine-city traveling salesman problem on page 807 of Winston and Venkataramanan [10].  The new formulation is partly described by line 201 through line 333.

0 REM DEFDBL A-Z
2 DEFINT I,J,K,X
3 DIM B(99),N(99),A(2002),H(99),L(99),U(99),X(2002),D(111),P(111),PS(33),J44(2002)
8 DIM HR(33,33)
11 FOR IZ=0 TO 8
14 FOR JZ=0 TO 8
16 READ HR(IZ,JZ)
18 NEXT JZ
19 NEXT IZ
21 DATA 99999,172,250,127,103,170,264,082,159
22 DATA 172,99999,170,177,200,325,178,139,241
23 DATA 250,170,99999,206,134,252,201,233,291
24 DATA 127,177,206,99999,191,181,184,057,172
25 DATA 103,200,134,191,99999,201,144,197,268
26 DATA 170,325,252,181,201,99999,229,211,129
27 DATA 264,178,201,184,144,229,99999,132,202
28 DATA 082,139,233,057,197,211,132,99999,186
29 DATA 159,241,291,172,268,129,202,186,99999
52 FOR JJJJ=-32000 TO 32000
54 RANDOMIZE JJJJ
57 M=-1D+37
71 FOR J44=1 TO 8
72 A(J44)=1+FIX(RND* 8)
74 NEXT J44
126 IMAR=10+FIX(RND*10000)
128 FOR I=1 TO IMAR
129 FOR KKQQ=1 TO 8
130 X(KKQQ)=A(KKQQ)
131 NEXT KKQQ
133 FOR IPP=1 TO (1+FIX(RND*7))
181 J=1+FIX(RND*8)
183 R=(1-RND*2)*A(J)
185 IF J<2003 THEN X(J)=(A(J)+RND^3*R) ELSE X(J)=RND
192 NEXT IPP
201 FOR J44=1 TO 8
207  IF   (X(J44)) >8 THEN 1670
211  NEXT J44
231 FOR J44=1 TO 8
237  IF   X(J44) <1 THEN 1670
240  NEXT J44
251 FOR J44B=1 TO 7
256 FOR J44A=J44B+1 TO 8
260 IF ABS(X(J44B)-X(J44A))=0 THEN 1670
261 NEXT J44A
262 NEXT J44B
333 POB1=-HR(0,X(1))-HR(X(1),X(2))-HR(X(2),X(3))-HR(X(3),X(4))-HR(X(4),X(5))-HR(X(5),X(6))-HR(X(6),X(7))-HR(X(7),X(8))-HR(X(8),0)
444 P1NEWMAY=POB1
466 P=P1NEWMAY
1111 IF P<=M THEN 1670
1452 M=P
1454 FOR KLX=1 TO 8
1455 A(KLX)=X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889  IF M<-1236 THEN 1999
1933 PRINT A(1),A(2),A(3),A(4),A(5)
1934 PRINT A(6),A(7),A(8)
1936 PRINT M,JJJJ
1999 NEXT JJJJ

This BASIC computer program was run with Microsoft's GW BASIC 3.11 interpreter.  The complete output through JJJJ=-30853 is shown below.  What follows is a hand copy of the output on the computer-monitor screen; below there is no rounding by hand.

7   3   5   8   6
1   2   4
-1236   -31999

4   2   1   6   8
5   3   7
-1236   -31151

7   3   5   8   6
1   2   4
-1236   -30853

On a personal computer with an Intel 2.66 chip and the IBM basica/D interpreter, version GW BASIC 3.11, the throughput time (including printing) from JJJJ=-32000 through JJJJ=-30853 was twelve minutes, real time, not cpu time. 

References

[1] Larry M. Austin, Parviz Ghandforoush, Management Science for Decision Makers.  St. Paul, MN: West Publishing Company, 1993.

[2] Robert Garfinkel, George L. Nemhauser, Integer Programming.  John Wiley and Sons, Inc., 1972.

[3] Frederick S. Hillier, Gerard J. Lieberman, Introduction to Operations Research, 8th Edition.   New York: McGraw-Hill, 2005.

[4] Claude McMillan, Mathematical Programming, Second Edition.  John Wiley and Sons Inc., 1975.

[5] Microsoft Corp., BASIC, Second Edition (May 1982), Version 1.10. Boca Raton, Florida: IBM Corp., Personal Computer, P. O. Box 1328-C, Boca Raton, Florida 33432, 1981.

[6] Ronald L. Rardin, Optimization in Operations Research.  Upper Saddle River, NJ: Prentice Hall, 1998.

[7] Hamdy A. Taha, Integer Programming--Theory, Applications, and Computations.  Academic Press, In., 1975.

[8] Hamdy A. Taha, Operations Research: an Introduction, 8th Edition.  Upper Saddle River, NJ 07458: Pearson Prentice Hall, 2007.

[9] Wayne L. Winston, Operations Research: Applications and Algorithms, Fourth Edition.  Brooks/Cole, a division of Thomson, 2004.

[10] Wayne L. Winston, Munirpallam Venkataramanan, Introduction to Mathematical Programming, Fourth Edition.   Pacific Grove, CA 93950: Brooks/Cole--Thomson Learning Inc., 2003. 

A Nonlinear Integer/Discrete/Continuous Programming Solver Applied to a New Formulation of the Traveling Salesperson Problem, Fifth Edition

Jsun Yui Wong

The following computer program tries to solve the five-city traveling salesman problem on page 573 of Reference 3.  The new formulation is partly described by line 201 through line 333.

0 REM DEFDBL A-Z
2 DEFINT I,J,K
3 DIM B(99),N(99),A(2002),H(99),L(99),U(99),X(2002),D(111),P(111),PS(33),J44(2002)
8 DIM HR(33,33)
11 FOR IZ=0 TO 4
14 FOR JZ=0 TO 4
16 READ HR(IZ,JZ)
18 NEXT JZ
19 NEXT IZ
24 DATA 999,20,4,10,25
25 DATA 20,999,5,30,10
26 DATA 4,5,999,6,6
27 DATA 10,25,6,999,20
28 DATA 35,10,6,20,999
52 FOR JJJJ=-32000 TO 32000
54 RANDOMIZE JJJJ
56 M=-1D+37
71 FOR J44=1 TO 4
72 A(J44)=1+FIX(RND*4)
74 NEXT J44
126 IMAR=10+FIX(RND*10)
128 FOR I=1 TO IMAR
129 FOR KKQQ=1 TO 4
130 X(KKQQ)=A(KKQQ)
131 NEXT KKQQ
133 FOR IPP=1 TO (1+FIX(RND*3))
181 J=1+FIX(RND*4)
183 R=(1-RND*2)*A(J)
185 IF J<2003 THEN X(J)=CINT(A(J)+RND^3*R) ELSE X(J)=CINT(RND)
192 NEXT IPP
201 FOR J44=1 TO 4
207  IF   (X(J44)) >4 THEN 1670
211  NEXT J44
231 FOR J44=1 TO 4
237  IF   X(J44) <1 THEN 1670
241  NEXT J44
251 IF ABS(X(1)-X(2))=0 THEN 1670
253 IF ABS(X(1)-X(3))=0 THEN 1670
257 IF ABS(X(1)-X(4))=0 THEN 1670
260 IF ABS(X(2)-X(3))=0 THEN 1670
261 IF ABS(X(2)-X(4))=0 THEN 1670
266 IF ABS(X(3)-X(4))=0 THEN 1670
333 POB1=-HR(0,X(1))-HR(X(1),X(2))-HR(X(2),X(3))-HR(X(3),X(4))-HR(X(4),0)
444 P1NEWMAY=POB1
466 P=P1NEWMAY
1111 IF P<=M THEN 1670
1452 M=P
1454 FOR KLX=1 TO 4
1455 A(KLX)=X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 IF M<-52 THEN 1999
1933 PRINT A(1),A(2),A(3),A(4)
1936 PRINT M,JJJJ
1999 NEXT JJJJ

This BASIC computer program was run with Microsoft's GW BASIC 3.11 interpreter.  The complete output through JJJJ=-31907 is shown below.  What follows is a hand copy of the output on the computer-monitor screen; below there is no rounding by hand.

3   4   1   2
-49   -31996

3   2   4   1  
-52   -31989

2   1   4   3
-49   -31941

3   4   1   2
-49   -31929

2   1   4   3
-49   -31907

On a personal computer with an Intel 2.66 chip and the IBM basica/D interpreter, version GW BASIC 3.11, the throughput time (including printing) from JJJJ=-32000 through JJJJ=-31907 was one second, real time, not cpu time.

References

[1] Robert Garfinkel, George L. Nemhauser, Integer Programming.  John Wiley and Sons, Inc., 1972.

[2] Microsoft Corp., BASIC, Second Edition (May 1982), Version 1.10. Boca Raton, Florida: IBM Corp., Personal Computer, P. O. Box 1328-C, Boca Raton, Florida 33432, 1981.

[3] Research and Education Association, The Operations Research Problem Solver. Research and Education Association, 1983 (revised printing 1989).

[4] Hamdy A. Taha, Integer Programming--Theory, Applications, and Computations.  Academic Press, In., 1975.

[5] Hamdy A. Taha, Operations Research: an Introduction, 8th Edition.  Upper Saddle River, NJ 07458: Pearson Prentice Hall, 2007.

[6] Wayne L. Winston, Operations Research: Applications and Algorithm, Fourth Edition.  Brooks/Cole, a division of Thomson, 2004.

A Nonlinear Integer/Discrete/Continuous Programming Solver Applied to a New Formulation of the Traveling Salesperson Problem, Fourth Edition

Jsun Yui Wong

The following computer program tries to solve the five-city traveling salesmman problem on page 310 of Taha [2].  The new formulation is partly described by line 201 through line 333.

0 REM DEFDBL A-Z
2 DEFINT I,J,K
3 DIM B(99),N(99),A(2002),H(99),L(99),U(99),X(2002),D(111),P(111),PS(33),J44(2002)
8 DIM HR(33,33)
11 FOR IZ=0 TO 4
14 FOR JZ=0 TO 4
16 READ HR(IZ,JZ)
18 NEXT JZ
19 NEXT IZ
24 DATA 999,2,0,6,1
25 DATA 1,999,4,4,2
26 DATA 5,3,999,1,5
27 DATA 4,7,2,999,1
28 DATA 2,6,3,6,999
52 FOR JJJJ=-32000 TO 32000
54 RANDOMIZE JJJJ
56 M=-1D+37
71 FOR J44=1 TO 4
72 A(J44)=1+FIX(RND*4)
74 NEXT J44
126 IMAR=10+FIX(RND*10)
128 FOR I=1 TO IMAR
129 FOR KKQQ=1 TO 4
130 X(KKQQ)=A(KKQQ)
131 NEXT KKQQ
133 FOR IPP=1 TO (1+FIX(RND*3))
181 J=1+FIX(RND*4)
183 R=(1-RND*2)*A(J)
185 IF J<2003 THEN X(J)=CINT(A(J)+RND^3*R) ELSE X(J)=CINT(RND)
192 NEXT IPP
201 FOR J44=1 TO 4
207  IF   (X(J44)) >4 THEN 1670
211  NEXT J44
231 FOR J44=1 TO 4
237  IF   X(J44) <1 THEN 1670
241  NEXT J44
251 IF ABS(X(1)-X(2))=0 THEN 1670
253 IF ABS(X(1)-X(3))=0 THEN 1670
257 IF ABS(X(1)-X(4))=0 THEN 1670
260 IF ABS(X(2)-X(3))=0 THEN 1670
261 IF ABS(X(2)-X(4))=0 THEN 1670
266 IF ABS(X(3)-X(4))=0 THEN 1670
333 POB1=-HR(0,X(1))-HR(X(1),X(2))-HR(X(2),X(3))-HR(X(3),X(4))-HR(X(4),0)
444 P1NEWMAY=POB1
466 P=P1NEWMAY
1111 IF P<=M THEN 1670
1452 M=P
1454 FOR KLX=1 TO 4
1455 A(KLX)=X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 IF M<-9 THEN 1999
1933 PRINT A(1),A(2),A(3),A(4)
1936 PRINT M,JJJJ
1999 NEXT JJJJ

This BASIC computer program was run with Microsoft's GW BASIC 3.11 interpreter.  The complete output through JJJJ=-31426 is shown below.  What follows is a hand copy of the output on the computer-monitor screen; below there is no rounding by hand.

2   3   4   1
-9   -31976

2   3   4   1
-9   -31445

2   3   4   1
-9   -31434

2   3   4   1
-9   -31426

On a personal computer with an Intel 2.66 chip and the IBM basica/D interpreter, version GW BASIC 3.11, the throughput time (including printing) from JJJJ=-32000 through JJJJ=-31426 was one second, real time, not cpu time.

References

[1] Robert Garfinkel, George L. Nemhauser, Integer Programming.  John Wiley and Sons, Inc., 1972.

[2] Hamdy A. Taha, Integer Programming--Theory, Applications, and Computations.  Academic Press, In., 1975.

[3] Hamdy A. Taha, Operations Research: an Introduction, 8th Edition.  Upper Saddle River, NJ 07458: Pearson Prentice Hall, 2007.

[4] Microsoft Corp., BASIC, Second Edition (May 1982), Version 1.10. Boca Raton, Florida: IBM Corp., Personal Computer, P. O. Box 1328-C, Boca Raton, Florida 33432, 1981.

A Nonlinear Integer/Discrete/Continuous Programming Solver Applied to a New Formulation of the Traveling Salesperson Problem, Third Edition

Jsun Yui Wong

The following computer program tries to solve the six-city traveling salesman problem on page 86 of Fabrycky, Ghare, and Torgersen [1].  The new formulation is partly described by line 201 through line 333.

0 REM DEFDBL A-Z
2 DEFINT I,J,K
3 DIM B(99),N(99),A(2002),H(99),L(99),U(99),X(2002),D(111),P(111),PS(33),J44(2002)
8 DIM HR(33,33)
11 FOR IZ=0 TO 5
14 FOR JZ=0 TO 5
16 READ HR(IZ,JZ)
18 NEXT JZ
19 NEXT IZ
24 DATA 999,20,23,27,29,34
25 DATA 21,999,19,26,31,24
26 DATA 26,28,999,15,36,26
27 DATA 25,16,25,999,23,18
28 DATA 23,40,23,31,999,10
29 DATA 27,18,12,35,16,999
52 FOR JJJJ=-32000 TO 32000
54 RANDOMIZE JJJJ
56 M=-1D+37
71 FOR J44=1 TO 5
72 A(J44)=1+FIX(RND*5)
74 NEXT J44
126 IMAR=10+FIX(RND*10)
128 FOR I=1 TO IMAR
129 FOR KKQQ=1 TO 5
130 X(KKQQ)=A(KKQQ)
131 NEXT KKQQ
133 FOR IPP=1 TO (1+FIX(RND*4))
181 J=1+FIX(RND*5)
183 R=(1-RND*2)*A(J)
185 IF J<2003 THEN X(J)=CINT(A(J)+RND^3*R) ELSE X(J)=CINT(RND)
192 NEXT IPP
201 FOR J44=1 TO 5
207  IF   (X(J44)) >5 THEN 1670
211  NEXT J44
231 FOR J44=1 TO 5
237  IF   X(J44) <1 THEN 1670
241  NEXT J44
251 IF ABS(X(1)-X(2))=0 THEN 1670
253 IF ABS(X(1)-X(3))=0 THEN 1670
257 IF ABS(X(1)-X(4))=0 THEN 1670
258 IF ABS(X(1)-X(5))=0 THEN 1670
260 IF ABS(X(2)-X(3))=0 THEN 1670
261 IF ABS(X(2)-X(4))=0 THEN 1670
262 IF ABS(X(2)-X(5))=0 THEN 1670
266 IF ABS(X(3)-X(4))=0 THEN 1670
267 IF ABS(X(3)-X(5))=0 THEN 1670
268 IF ABS(X(4)-X(5))=0 THEN 1670
333 POB1=-HR(0,X(1))-HR(X(1),X(2))-HR(X(2),X(3))-HR(X(3),X(4))-HR(X(4),X(5))-HR(X(5),0)
444 P1NEWMAY=POB1
466 P=P1NEWMAY
1111 IF P<=M THEN 1670
1452 M=P
1454 FOR KLX=1 TO 5
1455 A(KLX)=X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 IF M<-110 THEN 1999
1933 PRINT A(1),A(2),A(3),A(4),A(5)
1936 PRINT M,JJJJ
1999 NEXT JJJJ

This BASIC computer program was run with Microsoft's GW BASIC 3.11 interpreter.  The complete output through JJJJ=-30372 is shown below.  What follows is a hand copy of the output on the computer-monitor screen; below there is no rounding by hand.

4   5   2   3   1
-103   -31048

2   3   4   5   1
-110   -30946

2   3   4   5   1
-110   -30901

4   5   2   3   1
-103   -30372

On a personal computer with an Intel 2.66 chip and the IBM basica/D interpreter, version GW BASIC 3.11, the throughput time (including printing) from JJJJ=-32000 through JJJJ=-30372 was two seconds, real time, not cpu time.

References

[1] W. J. Fabrycky, P. M. Ghare, R. E. Torgersen, Applied Operations Research and Management Science.  Englewood Cliffs, N. J.: Prentice-Hall, 1984.

[2] Robert Garfinkel, George L. Nemhauser, Integer Programming.  John Wiley and Sons, Inc., 1972.

[3] Microsoft Corp., BASIC, Second Edition (May 1982), Version 1.10. Boca Raton, Florida: IBM Corp., Personal Computer, P. O. Box 1328-C, Boca Raton, Florida 33432, 1981.

A Nonlinear Integer/Discrete/Continuous Programming Solver Applied to a New Formulation of the Traveling Salesperson Problem, Second Edition

Jsun Yui Wong

The following computer program tries to solve the traveling salesman problem on page 162 of Bronson and Naadimuthu [1].  The new formulation is partly described by line 201 through line 333.

0 REM DEFDBL A-Z
2 DEFINT I,J,K
3 DIM B(99),N(99),A(2002),H(99),L(99),U(99),X(2002),D(111),P(111),PS(33),J44(2002)
8 DIM HR(33,33)
11 FOR IZ=0 TO 3
14 FOR JZ=0 TO 3
16 READ HR(IZ,JZ)
18 NEXT JZ
19 NEXT IZ
24 DATA 999,65,53,37
25 DATA 65,999,95,999
26 DATA 53,95,999,81
27 DATA 37,999,81,999
52 FOR JJJJ=-32000 TO 32000
54 RANDOMIZE JJJJ
56 M=-1D+37
71 FOR J44=1 TO 3
72 A(J44)=1+FIX(RND*3)
74 NEXT J44
126 IMAR=10+FIX(RND*10)
128 FOR I=1 TO IMAR
129 FOR KKQQ=1 TO 3
130 X(KKQQ)=A(KKQQ)
131 NEXT KKQQ
133 FOR IPP=1 TO (1+FIX(RND*2))
181 J=1+FIX(RND*3)
183 R=(1-RND*2)*A(J)
185 IF J<2003 THEN X(J)=CINT(A(J)+RND^3*R) ELSE X(J)=CINT(RND)
192 NEXT IPP
201 FOR J44=1 TO 3
207  IF   (X(J44)) >3 THEN 1670
211  NEXT J44
231 FOR J44=1 TO 3
237  IF   X(J44) <1 THEN 1670
241  NEXT J44
251 IF ABS(X(1)-X(2))=0 THEN 1670
253 IF ABS(X(1)-X(3))=0 THEN 1670
257 IF ABS(X(2)-X(3))=0 THEN 1670
333 POB1=-HR(0,X(1))-HR(X(1),X(2))-HR(X(2),X(3))-HR(X(3),0)
444 P1NEWMAY=POB1
466 P=P1NEWMAY
1111 IF P<=M THEN 1670
1452 M=P
1454 FOR KLX=1 TO 3
1455 A(KLX)=X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 IF M<-800 THEN 1999
1933 PRINT A(1),A(2),A(3)
1936 PRINT M,JJJJ
1999 NEXT JJJJ

This BASIC computer program was run with Microsoft's GW BASIC 3.11 interpreter.  The complete output through JJJJ=-31981 is shown below.  What follows is a hand copy of the output on the computer-monitor screen; below there is no rounding by hand.

1   2   3
-278   -31988

3   2   1
-278   -31986

1   2   3
-278   -31984

3   2   1
-278   -31981

On a personal computer with an Intel 2.66 chip and the IBM basica/D interpreter, version GW BASIC 3.11, the throughput time (including printing) from JJJJ=-32000 through JJJJ=-31981 was one second, real time, not cpu time.

References

[1]  Richard Bronson, Govindasami Naadimuthu, Operations Research, Second Edition.  Schaum's Outlines.  McGraw-Hill, 1997.

[2] Microsoft Corp. BASIC, Second Edition (May 1982), Version 1.10. Boca Raton, Florida: IBM Corp., Personal Computer, P. O. Box 1328-C, Boca Raton, Florida 33432, 1981.