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Questions and Answers
What does the variable $p$ represent in the Metropolis rule?
What does the variable $p$ represent in the Metropolis rule?
- The energy difference between the new and old configurations
- The random variable generated to decide acceptance or rejection
- The total number of configurations available
- The probability of accepting a move to a new configuration (correct)
Which condition results in a move being accepted in the Metropolis rule?
Which condition results in a move being accepted in the Metropolis rule?
- When the temperature $T$ is lowered
- When $Random(0, 1) < e^{(E/T)}$ (correct)
- When the energy difference $E$ is negative
- When the energy of the new configuration is higher than current
What happens when the probability $p$ equals 1 in the Metropolis rule?
What happens when the probability $p$ equals 1 in the Metropolis rule?
- The new configuration is always accepted (correct)
- The energy levels are constant
- The new configuration is never accepted
- No new configurations can be generated
What does a positive energy difference ($ riangle E > 0$) imply for the acceptance probability in local search?
What does a positive energy difference ($ riangle E > 0$) imply for the acceptance probability in local search?
What is indicated by a rejection probability of $1 - p$ in the Metropolis rule?
What is indicated by a rejection probability of $1 - p$ in the Metropolis rule?
What happens to the acceptance of fitness degradation as the temperature increases during the simulated annealing process?
What happens to the acceptance of fitness degradation as the temperature increases during the simulated annealing process?
How is the exploration phase characterized in simulated annealing?
How is the exploration phase characterized in simulated annealing?
What role does the temperature play in the simulated annealing process?
What role does the temperature play in the simulated annealing process?
What is the effect of a gradual decrease in temperature during simulated annealing?
What is the effect of a gradual decrease in temperature during simulated annealing?
What is the initial state after setting the initial configuration in simulated annealing?
What is the initial state after setting the initial configuration in simulated annealing?
In the context of the Metropolis probability rule, what does the term ΔE represent?
In the context of the Metropolis probability rule, what does the term ΔE represent?
What is indicated by the cooling schedule in simulated annealing?
What is indicated by the cooling schedule in simulated annealing?
How does the probability p in the Metropolis algorithm generally behave as temperature T decreases?
How does the probability p in the Metropolis algorithm generally behave as temperature T decreases?
What do simulated annealing and physical annealing have in common?
What do simulated annealing and physical annealing have in common?
What is a key difference between annealing and quenching processes in metallurgy?
What is a key difference between annealing and quenching processes in metallurgy?
During the simulated annealing process, at what temperature range does the system explore a wider range of available states?
During the simulated annealing process, at what temperature range does the system explore a wider range of available states?
What role does temperature play in the simulated annealing algorithm?
What role does temperature play in the simulated annealing algorithm?
What happens to the system as the temperature decreases in the simulated annealing process?
What happens to the system as the temperature decreases in the simulated annealing process?
Which of the following is NOT a principle of the simulated annealing algorithm?
Which of the following is NOT a principle of the simulated annealing algorithm?
What is the outcome of the quenching process compared to mainly annealing?
What is the outcome of the quenching process compared to mainly annealing?
What is the primary objective of the simulated annealing algorithm?
What is the primary objective of the simulated annealing algorithm?
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Study Notes
Simulated Annealing
- Simulated annealing (SA) is a metaheuristics inspired by a metallurgical process called annealing.
- Annealing is a gradual cooling process that improves metal ductility, leading to a global minimum.
- Quenching is a rapid cooling process that improves hardness but leads to a local minimum.
- SA's goal is to find the global minimum of an objective function, often represented as 'E'.
- SA utilizes a process similar to natural systems that minimize energy by exploring possible states.
- At high "temperature" (a dynamic parameter in SA), the system explores a wider range of states.
- Lower "temperatures" constrain the system, promoting exploitation and driving it towards a global minimum.
Principles of SA Algorithm
- SA follows core metaheuristics principles:
- Selecting an initial, arbitrary solution.
- Setting an initial "temperature" value.
- Moving from the current configuration to its 'neighbouring' configurations with a probability 'p'.
- The probability 'p' is determined by the Metropolis rule:
p = min(1, exp(-E / T)), whereEis the energy difference between the new and current configurations, andTis the "temperature".- New configurations are accepted if a randomly generated value between 0 and 1 is less than the probability,
p.
Temperature T
- Temperature is a dynamic parameter in SA, guiding its search process.
- A high initial temperature allows the algorithm to explore a wider range of states.
- As the temperature decreases, the acceptance of fitness degradation (increasing 'E') decreases.
- This controlled reduction in temperature, known as a "cooling schedule", promotes exploitation and drives the search towards better solutions.
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