GENETIC ALGORITHM CROSSOVERS IMPLEMENTATION Distance matrix 1 2 17 3 8 4 27 6 23 40 25 29 5 10 35 31 10 7 29 32 17 21 29 35 25 30 19 17 38 40 15 38 32 38 37 34 8 You want to apply Genetic Algorithm for the TSP instance whose distance matrix is given above. The initial population with size 10 is given as follows; Initial Population Tour 1 8-4-5-2-6-1-7-3 Tour 2 2-7-1-8-6-5-3-4 Tour 3 7-8-5-2-1-6-3-4 Tour 4 7-4-3-1-2-8-6-5 Tour 5 2-1-7-5-3-8-6-4 Tour 6 1-7-8-2-4-6-5-3 Tour 7 3-5-1-8-2-7-6-4 Tour 8 1-4-5-7-6-3-8-2 Tour 9 4-1-3-6-2-8-7-5 Tour 10 2-4-5-6-8-3-1-7 a) Give the ordinal representation for each tour in the initial population. b) Find the 2 offsprings and the corresponding distances for the following scenarios. Note that you must find the corresponding tour using the ordinal representation first before calculating the distances. b-1) Parent 1: Tour 6 b-2) Parent 1: Tour 4 b-3) Parent 1: Tour 10 Parent 2: Tour 5 Parent 2: Tour 1 Parent 2: Tour 2 Cut position: 3 Cut position: 5 Cut position: 3 c) Using the path representation and partially-mapped crossover (PMX), find the offsprings and the corresponding distances for the following scenarios. When finding the offsprings, report each step explicitly. C-1) Parent 1: Tour 3 C-2) Parent 1: Tour 4 C-3) Parent 1: Tour 2 Parent 2: Tour 9 Parent 2: Tour 6 Parent 2: Tour 5 Cut positions: 3,6 Cut positions: 3,5 Cut positions: 2,6 d) Using the path representation and order crossover (OX), find the offsprings and the corresponding distances for the following scenarios. When finding the offsprings, report each step explicitly. d-1) Parent 1: Tour 3 d-2) Parent 1: Tour 4 d-3) Parent 1: Tour 1 Parent 2: Tour 8 Parent 2: Tour 7 Parent 2: Tour 5 Cut positions: 3,6 Cut positions: 2,5 Cut positions: 2,6 GENETIC ALGORITHM CROSSOVERS IMPLEMENTATION Distance matrix 1 2 17 3 8 4 27 6 23 40 25 29 5 10 35 31 10 7 29 32 17 21 29 35 25 30 19 17 38 40 15 38 32 38 37 34 8 You want to apply Genetic Algorithm for the TSP instance whose distance matrix is given above. The initial population with size 10 is given as follows; Initial Population Tour 1 8-4-5-2-6-1-7-3 Tour 2 2-7-1-8-6-5-3-4 Tour 3 7-8-5-2-1-6-3-4 Tour 4 7-4-3-1-2-8-6-5 Tour 5 2-1-7-5-3-8-6-4 Tour 6 1-7-8-2-4-6-5-3 Tour 7 3-5-1-8-2-7-6-4 Tour 8 1-4-5-7-6-3-8-2 Tour 9 4-1-3-6-2-8-7-5 Tour 10 2-4-5-6-8-3-1-7 a) Give the ordinal representation for each tour in the initial population. b) Find the 2 offsprings and the corresponding distances for the following scenarios. Note that you must find the corresponding tour using the ordinal representation first before calculating the distances. b-1) Parent 1: Tour 6 b-2) Parent 1: Tour 4 b-3) Parent 1: Tour 10 Parent 2: Tour 5 Parent 2: Tour 1 Parent 2: Tour 2 Cut position: 3 Cut position: 5 Cut position: 3 c) Using the path representation and partially-mapped crossover (PMX), find the offsprings and the corresponding distances for the following scenarios. When finding the offsprings, report each step explicitly. C-1) Parent 1: Tour 3 C-2) Parent 1: Tour 4 C-3) Parent 1: Tour 2 Parent 2: Tour 9 Parent 2: Tour 6 Parent 2: Tour 5 Cut positions: 3,6 Cut positions: 3,5 Cut positions: 2,6 d) Using the path representation and order crossover (OX), find the offsprings and the corresponding distances for the following scenarios. When finding the offsprings, report each step explicitly. d-1) Parent 1: Tour 3 d-2) Parent 1: Tour 4 d-3) Parent 1: Tour 1 Parent 2: Tour 8 Parent 2: Tour 7 Parent 2: Tour 5 Cut positions: 3,6 Cut positions: 2,5 Cut positions: 2,6