解：所有路径有：
(1)A-B-C-D-E-A，费用=10+8+3+9+11=41. (13)A-B-C-E-D-A，费用=10+8+8+9+9=44.
(2)A-B-D-C-E-A，费用=10+12+3+8+11=44. (14)A-B-D-E-C-A，费用=10+12+9+8+2=41.
(3)A-B-E-D-C-A，费用=10+6+9+3+2=30. (15)A-B-E-C-D-A，费用=10+6+8+3+9=36.
(4)A-C-B-D-E-A，费用=2+8+12+9+11=42. (16)A-C-B-E-D-A，费用=2+8+6+9+9=34.
(5)A-C-D-E-B-A，费用=2+3+9+6+10=30. (17)A-C-D-B-E-A，费用=2+3+12+6+11=34.
(6)A-C-E-B-D-A，费用=2+8+6+12+9=37. (18)A-C-E-D-B-A，费用=2+8+9+12+10=41.
(7)A-D-B-C-E-A，费用=9+12+8+8+11=48. (19)A-D-B-E-C-A，费用=9+12+6+8+2=37.
(8)A-D-C-B-E-A，费用=9+3+8+6+11=37. (20)A-D-C-E-B-A，费用=9+3+8+6+10=36.
(9)A-D-E-B-C-A，费用=9+9+6+8+2=34. (21)A-D-E-C-B-A，费用=9+9+8+8+10=44.
(10)A-E-B-C-D-A，费用=11+6+8+3+9=37. (22)A-E-B-D-C-A，费用=11+6+12+3+2=34.
(11)A-E-C-B-D-A，费用=11+8+8+12+9=48. (23)A-E-C-D-B-A，费用=11+8+3+12+10=44.
(12)A-E-D-B-C-A，费用=11+9+12+8+2=42. (24)A-E-D-C-B-A，费用=11+9+3+8+10=41.
可以看出，最优路线是(3)A-B-E-D-C-A，(5)A-C-D-E-B-A，它们费用相同=30.
原文：http://www.cnblogs.com/huangjiajun/p/4357798.html