Is a good solution absolute or relative?

Suppose we have the problem of answering questions based on the simple facts, such as following :

1. James was a man.
2. James was a pompeian.
3. James was born in 50 A.D
4. All men are mortal.
5. All pompeian died when volcano erupted in 79 A.D.
6. No mortals lives longer than 150 years.
7. It is now 1991 A.D.

Consider we ask the question “Is james alive?”. By going through each of these facts, we can easily find the answer to the question. Suppose, two paths leads to the answer but we are interested in is the answer to the question, it does not matter which path we follow.

But now consider again the traveling salesman problem.In that we need to find the best solution (shortest path) among all of other solution.