Travelling Salesman Problem (TSP)

Q.1. Suppose we have a Travelling Salesman Problem (TSP) problem with 5 cities. The distances between cities are given by the following matrix

        1        2      3        4       5

d =

 Suppose the number of ants, N = 3. 
 Suppose the initial pheromone value τ0, is the same for all edges, which is 1.
 Make the necessary further assumptions whenever they are needed by yourself and clearly state what the assumptions are.

Use the Ant Colony Optimization (ACO) to determine the best route with minimum total distance for one iteration. (40-Marks)

Q.2. Consider that a bus trip from Istanbul to İzmit, which is subject to the followings:

• The distance between the two cities is nearly 100 km;
• The speed can not exceed 110 km/h;
• The traffic is usually heavy and therefore the bus speed is variable;
• The bus usually leaves the bus station in Harem later than the departure time, but the delays never exceed 10 min.

What is the total time (T ) spent on a trip from Istanbul to İzmit by bus under these conditions? (30-Marks)
Hint: Since distance (D) is approximate, you would think that it would be indicated by a Triangular value as 90, 100, and 110. Likewise, the speed (S) is also variable and it could be indicated by a Triangular value as 40, 75, and 110. Further, the bus departs the bus station usually late but delay never exceeds 10 min. This would also be indicated by a Triangular value as 0, 0.05 and 0.1. Use aplha-cut to calculate the approximate travel time.
Q.3. Figure below shows a neural network with one hidden layer for the classification.
Five Boolean inputs correspond to whether holiday destination is Antalya, or Kapadokya, or Ayder, or Istanbul, or Uludağ and a single output corresponds to whether the person likes the sea holiday.
• Initialize the weights and set the learning rate and the stopping criteria by yourself and indicate the assumed figures clearly. Compute the input to each layer and the output of the final layer. Compute the sensitivity and the gradient components and update the weights for just one iteration and display the result. (30-Marks)