The diagram shows a solution for an optimal tour through 33 cities in a 1962 Procter and Gamble contest. Yes, it is optimal.

If you did not read the article, you should not criticize.

BTW, companies like MapQuest calculate and store in data bases the shortest distances between thousands of US cities. In that way they have converted a problem like the TSP which requires exponentially increasing computer time as the number of cities increases into a problem which increases in polynomial fashion with number of cities. The secret to all clever optimization problems is to avoid recomputing and to store data on the fly to be used later.

If one is interested, one could listen in to the MIT open courseware classes which are filmed MIT undergraduate classes. (It’s a bit hokey, as you will see for yourself if you watch, but it is interesting if one has the time and curiosity.) A discussion of optimization problems in general and the 0/1 Knapsack problem in particular starts at