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Stochastic Optimization
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Stochastic Optimization - University of Warwick · PDF fileStochastic Optimization. ... Ant Colony Optimization Knapsack problem: Which boxes ... Quantum Tunneling Configuration Temperature:

Feb 20, 2018

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Page 1: Stochastic Optimization - University of Warwick · PDF fileStochastic Optimization. ... Ant Colony Optimization Knapsack problem: Which boxes ... Quantum Tunneling Configuration Temperature:

Stochastic Optimization

Page 2: Stochastic Optimization - University of Warwick · PDF fileStochastic Optimization. ... Ant Colony Optimization Knapsack problem: Which boxes ... Quantum Tunneling Configuration Temperature:

Simmulated Annealing

Page 3: Stochastic Optimization - University of Warwick · PDF fileStochastic Optimization. ... Ant Colony Optimization Knapsack problem: Which boxes ... Quantum Tunneling Configuration Temperature:

Greedy algorithms can get stuck in local optima, and depend on initial conditions :(

Simmulated Annealing

Energy

- Initial configuration i with

- Choose random (nearby) state j with

- Accept change with probability

Simmulated Annealing procedure:

- Gradually decrease T according to a “cooling schedule”

Page 4: Stochastic Optimization - University of Warwick · PDF fileStochastic Optimization. ... Ant Colony Optimization Knapsack problem: Which boxes ... Quantum Tunneling Configuration Temperature:

Simmulated Annealing

Page 5: Stochastic Optimization - University of Warwick · PDF fileStochastic Optimization. ... Ant Colony Optimization Knapsack problem: Which boxes ... Quantum Tunneling Configuration Temperature:

Quantum Annealing

Page 6: Stochastic Optimization - University of Warwick · PDF fileStochastic Optimization. ... Ant Colony Optimization Knapsack problem: Which boxes ... Quantum Tunneling Configuration Temperature:

Swarm intelligence

Page 7: Stochastic Optimization - University of Warwick · PDF fileStochastic Optimization. ... Ant Colony Optimization Knapsack problem: Which boxes ... Quantum Tunneling Configuration Temperature:

Swarm intelligence

Page 8: Stochastic Optimization - University of Warwick · PDF fileStochastic Optimization. ... Ant Colony Optimization Knapsack problem: Which boxes ... Quantum Tunneling Configuration Temperature:

Ant Colony Optimization

Swarm intelligence

Page 9: Stochastic Optimization - University of Warwick · PDF fileStochastic Optimization. ... Ant Colony Optimization Knapsack problem: Which boxes ... Quantum Tunneling Configuration Temperature:

Ant Colony Optimization

Page 10: Stochastic Optimization - University of Warwick · PDF fileStochastic Optimization. ... Ant Colony Optimization Knapsack problem: Which boxes ... Quantum Tunneling Configuration Temperature:

Ant Colony Optimization

TSP: Which is the shortest path that visits each city exactly once?

Page 11: Stochastic Optimization - University of Warwick · PDF fileStochastic Optimization. ... Ant Colony Optimization Knapsack problem: Which boxes ... Quantum Tunneling Configuration Temperature:

Ant Colony Optimization

Page 12: Stochastic Optimization - University of Warwick · PDF fileStochastic Optimization. ... Ant Colony Optimization Knapsack problem: Which boxes ... Quantum Tunneling Configuration Temperature:

Ant Colony Optimization

Page 13: Stochastic Optimization - University of Warwick · PDF fileStochastic Optimization. ... Ant Colony Optimization Knapsack problem: Which boxes ... Quantum Tunneling Configuration Temperature:

Ant Colony Optimization

Knapsack problem: Which boxes should be chosen to maximize the amount of money while still keeping the overall weight under or equal to 15 kg?

Page 14: Stochastic Optimization - University of Warwick · PDF fileStochastic Optimization. ... Ant Colony Optimization Knapsack problem: Which boxes ... Quantum Tunneling Configuration Temperature:

Ant Colony Optimization

Page 15: Stochastic Optimization - University of Warwick · PDF fileStochastic Optimization. ... Ant Colony Optimization Knapsack problem: Which boxes ... Quantum Tunneling Configuration Temperature:

Which boxes should be chosen to maximize the amount of money while still keeping the overall weight under or equal to 15 kg?

Knapsack problem: Travelling salesman problem:

Which is the shortest path that visits each city exactly once?