How to plan your visit as a tourist using OR?

I planned to visit city X, which is known for its numerous attractions, including museums, markets, theaters, churches, and castles. To make things easier, I identified the top 50 attractions in the city. My hotel is located at node 1.

The dictionary contains information for each node in the form (x, y, T). Here, x and y denote the location coordinates of the node, and T represents the time required for visiting.

{1: (0.5, 0.5, 0),
 2: (0.603, 0.756, 20),
 3: (0.075, 0.739, 18),
 4: (0.225, 0.202, 13),
 5: (0.377, 0.994, 16),
 6: (0.997, 0.652, 7),
 7: (0.014, 0.246, 3),
 8: (0.455, 0.788, 13),
 9: (0.557, 0.667, 14),
 10: (0.371, 0.799, 1),
 11: (0.131, 0.149, 3),
 12: (0.179, 0.283, 10),
 13: (0.646, 0.341, 19),
 14: (0.792, 0.566, 12),
 15: (0.255, 0.158, 14),
 16: (0.311, 0.65, 13),
 17: (0.721, 0.707, 9),
 18: (0.974, 0.995, 7),
 19: (0.345, 0.047, 6),
 20: (0.287, 0.139, 3),
 21: (0.736, 0.618, 18),
 22: (0.056, 0.752, 18),
 23: (0.469, 0.232, 19),
 24: (0.067, 0.934, 4),
 25: (0.379, 0.508, 19),
 26: (0.213, 0.954, 3),
 27: (0.283, 0.308, 16),
 28: (0.589, 0.868, 10),
 29: (0.967, 0.832, 5),
 30: (0.803, 0.073, 20),
 31: (0.937, 0.226, 4),
 32: (0.607, 0.376, 10),
 33: (0.469, 0.324, 5),
 34: (0.409, 0.176, 16),
 35: (0.63, 0.638, 10),
 36: (0.394, 0.249, 19),
 37: (0.556, 0.88, 20),
 38: (0.438, 0.86, 14),
 39: (0.828, 0.659, 1),
 40: (0.132, 0.047, 5),
 41: (0.695, 0.556, 5),
 42: (0.825, 0.208, 19),
 43: (0.731, 0.797, 19),
 44: (0.872, 0.081, 15),
 45: (0.97, 0.286, 4),
 46: (0.899, 0.608, 1),
 47: (0.706, 0.317, 2),
 48: (0.413, 0.051, 13),
 49: (0.498, 0.919, 16),
 50: (0.998, 0.53, 8)}        

TTP approach

Initially I decided to visit all these beautiful places in one day. The question I had to answer was how should this be done? Obviousley it's a traveling tourist problem !

I used ORTools to find the optimal path.

Result

The OF (total path) is 582.

TRP approach

I realized that visiting all these places in one day would be extremely tiring, so I decided to tackle the Tourist Routing Problem by dividing my visits over 4 days. For each day, I dedicated a limited amount of time as follows:

Time limit = {0:150, 1:190, 2:130, 3:170}         

I used ORTools to find the optimal path in each day.

The coding concept is to assign each node to one day and find the tour for each day.

results:

Tired Tourist Problem:

Upon reviewing the path obtained from my previous approach, I realized that on some days, I would need to visit 10-12 nodes, which is beyond my limits. However, I still wanted to visit these locations and check them off my list. Then I thought, what if I visit most of them and just pass very close to some of them?

So, I decided that each day I would visit at most 7 locations. These locations would be carefully selected to ensure that the non-visited locations are close enough to them.

so each node is eigther visisted or it is close to a visited node.

Results:

We can also limit the daily visit time

Some observations:

• Specifying the non-possible connections can help improve the solution speed. This can be determined based on the distance between two nodes.
• Choosing the covering distance also affects the optimal path for each day.
• An interesting reference regarding the CSP is here : Current, John R., and David A. Schilling. "The covering salesman problem." Transportation science 23.3 (1989): 208-213.