Assignment I TSP with Simulated Annealing

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Presentation transcript:

Assignment I TSP with Simulated Annealing

Data in Assignment I: You have to solve three TSP problem with 10, 30 and 50 cities. Coordina_10 : coordinates for 10 cities (xi,yi) Coordina_30: coordinates for 30 cities (xi,yi) Coordina_50: coordinates for 50 cities (xi,yi) For example Coordina_10: 2.5346 9.1670 0.5659 7.3454 2.2720 4.8172 0.8226 1.9721 7.7530 8.8111 5.5220 3.8949 2.6775 2.7794 9.2573 7.3441 6.6485 9.5929 8.5379 9.4993

long = 40.3418 Create Cost Matrix: 0 2.6822 4.3577 7.3958 5.2305 6.0597 6.3892 6.9655 4.1359 6.0125 2.6822 0 3.0500 5.3794 7.3350 6.0389 5.0306 8.6914 6.4845 8.2578 4.3577 3.0500 0 3.1930 6.7818 3.3783 2.0778 7.4283 6.4777 7.8220 7.3958 5.3794 3.1930 0 9.7367 5.0776 2.0230 10.0001 9.5926 10.7789 5.2305 7.3350 6.7818 9.7367 0 5.3987 7.8830 2.1012 1.3532 1.0439 6.0597 6.0389 3.3783 5.0776 5.3987 0 3.0554 5.0842 5.8083 6.3644 6.3892 5.0306 2.0778 2.0230 7.8830 3.0554 0 8.0081 7.8862 8.9164 6.9655 8.6914 7.4283 10.0001 2.1012 5.0842 8.0081 0 3.4443 2.2721 4.1359 6.4845 6.4777 9.5926 1.3532 5.8083 7.8862 3.4443 0 1.8917 6.0125 8.2578 7.8220 10.7789 1.0439 6.3644 8.9164 2.2721 1.8917 0 Sample solution: route = 3 7 8 5 1 2 4 9 10 Objective function Value: long = 40.3418

3 7 8 5 1 2 4 9 10 6 10 9 4 2 1 5 8 7 3

Update archive

Search for 10 Cities

Search for 30 Cities

Multi-Objective Simulated Annealing

Update Nondominated Set Update archive Update Nondominated Set

Multi-Objective

Sanghamitra Bandyopadhyay, Sriparna Saha, Ujjwal Maulik and Kalyanmoy Deb. A Simulated Annealing Based Multi-objective Optimization Algorithm: AMOSA , IEEE Transactions on Evolutionary Computation, Volume 12, No. 3, JUNE 2008, Pages 269-283.

Case 1:

Case 2:

Case 3:

? The 0-1 Knapsack Problem Goal: choose subset that weight = 750g profit = 5 weight = 1500g profit = 8 weight = 300g profit = 7 weight = 1000g profit = 3 ? Goal: choose subset that maximizes overall profit minimizes total weight

Update Nondominated Set Update archive Update Nondominated Set

The Solution Space profit weight 500g 1000g 1500g 2000g 2500g 3000g

The 0-1 Multiple Knapsack Problem

Domination For any two solutions x1 and x2 x1 is said to dominate x2 if these conditions hold: x1 is not worse than x2 in all objectives. x1 is strictly better than x2 in at least one objective. If one of the above conditions does not hold x1 does not dominate x2.

Examples for minimization Candidate f1 f2 f3 f4 1 5 6 3 10 2 4 11 9 (dominated by: 2,4,5) (dominated by: 5) (non-dominated) (non-dominated) (non-dominated)

Dominance we say x dominates y if it is at least as good on all criteria and better on at least one Dominated by x f1 f2 Pareto front x

Pareto Optimal Set Non-dominated set: the set of all solutions which are not dominated by any other solution in the sampled search space. Global Pareto optimal set: there exist no other solution in the entire search space which dominates any member of the set.