Fan Yang 6.338 Final Project Professor Edelman Outline 2 - - PowerPoint PPT Presentation
Fan Yang 6.338 Final Project Professor Edelman Outline 2 Introduction I. The Traveling Salesman Problem A. Simulated Annealing B. Genetic Algorithm C. II. Methods III. Results Running Time A. Parallel Speedup B. Optimization C. Rate of
Fan Yang 6.338 Final Project Professor Edelman
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Figure 1: An example of the traveling salesman problem.
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Initialization: Generate a random candidate route
Repeat following steps:
Neighbor function: Generate a neighbor route by
Acceptance function: Evaluate the neighbor route for
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Initialization: Generate a random candidate route
Repeat following steps:
if ITERATION_COUNT != CONVERGING_COUNT
Neighbor function: Generate a neighbor route by exchanging a pair of cities.
Acceptance function: Evaluate the neighbor route for acceptance - if accepted, replace current route with neighbor route
Else
MPI_BARRIER: share the best result among threads by sending all the results to root and have root broadcast the best result
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Initialization: Generate N random candidate
Repeat following steps:
Selection: Select two best candidate routes. Reproduction: Reproduce two routes from the best
Generate new population: Replace the two worst
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Initialization: Generate N random candidate routes and
Repeat following steps:
if ITERATION_COUNT != CONVERGING_COUNT
Selection: Select two best candidate routes.
Reproduction: Reproduce two routes from the best routes.
Generate new population: Replace the two worst routes with the new routes.
Else
MPI_BARRIER: share the best result among threads by sending all the results to root and have root broadcast the best result
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C with MPI on Beowulf cluster
Genetic Algorithm:
Iterations: 100,000 population count: 1000
Simulated Annealing
Iterations: 1,000,000 Start temperature: 10.0 Cooling constant: 0.9999
For each condition, we conducted a
Distances were computed as
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CITIES COORDINATES (X, Y) a (110, 54) b (236, 110) c (153, 151) d (227, 49) e (307, 176) f (220, 211) g (341, 90) h (149, 91) i (335, 40) j (371, 150) k (218, 161) l (334, 239) m (148, 227) n (49, 128)
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Figure 2: Simulated annealing algorithm running time. The running time decreases as the number of processors increases.
Figure 3: Genetic algorithm running time. The running time decreases as the number of processors increases.
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Figure 4: Simulated annealing algorithm parallel speedup. There is a near- linear parallel speedup. The curve approximates an ideal linear line at all points.
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Figure 5: Genetic algorithm parallel speedup. There is a near-linear parallel
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Figure 6: Simulated annealing algorithm distance results. The distance of the shortest route decreases as the number of processors increases. The anomaly at processor #5 is most likely due to an outlier in the raw data points, which is also indicated by the large standard deviation.
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Figure 7: Genetic algorithm distance results. The distance of the shortest route decreases as the number of processors increases.
Figure 8: Simulated annealing algorithm convergence running time. There is a gradual increase in running time as the rate of convergence increases. The running time exceeds the serial implementation at a convergence rate of 35%.
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Figure 9: Genetic algorithm convergence running time. There is a gradual increase in running time as the rate of convergence increases. The running time exceeds the serial implementation at a convergence rate of 15%.
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Figure 10: Simulated annealing convergence distance results. The distance of the shortest route decreases as we increase the rate of convergence. The shortest distance plateaus beginning at a 10% rate of convergence.
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Figure 11: Genetic algorithm convergence distance results. The distance of the shortest route decreases as we increase the convergence rate. The shortest distance plateaus beginning at a 5% rate of convergence.
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Good parallel speedup in both algorithms Genetic algorithm achieves slightly better
Higher rate of convergence improves route