Usage

Import

from quickopt.annealing import anneal_double, anneal_int, anneal_string

anneal_double

Uses simulated annealing to minimize a function of double inputs.

Signature

anneal_double(funct, initial, neighbor, iterations=100, temperature=lambda iter: pow(0.999, iter), acceptance=lambda new_value, current_value, temperature: exp(-(new_value - current_value) / temperature), verbose=1)

Parameters

• funct - function: (input: List[float]) -> float : The function to be minimized. It should take a list of doubles as input and return a double.

• initial - List[float] : The initial guess for the parameters. This is the starting point for the simulated annealing process.

• neighbor - function: (input: List[float]) -> List[float] : The neighbor function that generates a new set of parameters based on the current set. It should take a vector of doubles as input and return a new vector of doubles.

• iterations - int, optional : The number of iterations to run the algorithm. Default is 100.

• temperature - function: (input: int) -> float, optional : The temperature schedule that determines the temperature at each iteration. It should take an iteration number as input and return a temperature double. Default returns 0.999**iteration.

• acceptance - function: (input: float, float, float) -> float, optional : Used to define a custom acceptance probability function, which determines whether to accept a new set of parameters based on the current set and temperature. It should take a new value, the current value, and the temperature - three doubles (new_value, current_value, temperature) - as inputs, and return a double in [0,1]. Default uses the Metropolis-Hastings algorithm in case T=1 and proposal distribution is symmetric.

• verbose - int, optional : The verbosity level. 0 for final output, 1 for output at each iteration. Default is 1.

Output

• best_params - List[float]: The best set of parameters found by the simulated annealing process.

Notes

• Maximization can be achieved by returning the negative of objective function values.
• The temperature function should typically return a value in the range (0, 1] and must be decreasing over iterations.
• The acceptance function must return a value between 0 and 1.
• The neighbor function should handle boundary conditions if necessary.
• Adjust the verbosity level with the verbose parameter to control the amount of output during the iterations.

anneal_int

Uses simulated annealing to minimize a function of integer inputs.

Signature

anneal_int(funct, initial, neighbor, iterations=100, temperature=lambda iter: pow(0.999, iter), acceptance=lambda new_value, current_value, temperature: exp(-(new_value - current_value) / temperature), verbose=1)

Parameters

• funct - function: (input: List[int]) -> float : The function to be minimized. It should take a list of doubles as input and return a double.

• initial - List[int] : The initial guess for the parameters. This is the starting point for the simulated annealing process.

• neighbor - function: (input: List[int]) -> List[float] : The neighbor function that generates a new set of parameters based on the current set. It should take a vector of doubles as input and return a new vector of doubles.

• iterations - int, optional : The number of iterations to run the algorithm. Default is 100.

• temperature - function: (input: int) -> float, optional : The temperature schedule that determines the temperature at each iteration. It should take an iteration number as input and return a temperature double. Default returns 0.999**iteration.

• acceptance - function: (input: int, int, float) -> float, optional : Used to define a custom acceptance probability function, which determines whether to accept a new set of parameters based on the current set and temperature. It should take a new value, the current value, and the temperature - three doubles (new_value, current_value, temperature) - as inputs, and return a double in [0,1]. Default uses the Metropolis-Hastings algorithm in case T=1 and proposal distribution is symmetric.

• verbose - int, optional : The verbosity level. 0 for final output, 1 for output at each iteration. Default is 1.

Output

• best_params - List[int]: The best set of parameters found by the simulated annealing process.

Notes

• Maximization can be achieved by returning the negative of objective function values.
• The temperature function should typically return a value in the range (0, 1] and must be decreasing over iterations.
• The acceptance function must return a value between 0 and 1.
• The neighbor function should handle boundary conditions if necessary.
• Adjust the verbosity level with the verbose parameter to control the amount of output during the iterations.

anneal_string

Uses simulated annealing to minimize a function of string inputs.

Signature

anneal_string(funct, initial, neighbor, iterations=100, temperature=lambda iter: pow(0.999, iter), acceptance=lambda new_value, current_value, temperature: exp(-(new_value - current_value) / temperature), verbose=1)

Parameters

• funct - function: (input: List[str]) -> float : The function to be minimized. It should take a list of doubles as input and return a double.

• initial - List[str] : The initial guess for the parameters. This is the starting point for the simulated annealing process.

• neighbor - function: (input: List[str]) -> List[float] : The neighbor function that generates a new set of parameters based on the current set. It should take a vector of doubles as input and return a new vector of doubles.

• iterations - int, optional : The number of iterations to run the algorithm. Default is 100.

• temperature - function: (input: int) -> float, optional : The temperature schedule that determines the temperature at each iteration. It should take an iteration number as input and return a temperature double. Default returns 0.999**iteration.

• acceptance - function: (input: str, str, float) -> float, optional : Used to define a custom acceptance probability function, which determines whether to accept a new set of parameters based on the current set and temperature. It should take a new value, the current value, and the temperature - three doubles (new_value, current_value, temperature) - as inputs, and return a double in [0,1]. Default uses the Metropolis-Hastings algorithm in case T=1 and proposal distribution is symmetric.

• verbose - int, optional : The verbosity level. 0 for final output, 1 for output at each iteration. Default is 1.

Output

• best_params - List[str]: The best set of parameters found by the simulated annealing process.

Notes

• Maximization can be achieved by returning the negative of objective function values.
• The temperature function should typically return a value in the range (0, 1] and must be decreasing over iterations.
• The acceptance function must return a value between 0 and 1.
• The neighbor function should handle boundary conditions if necessary.
• Adjust the verbosity level with the verbose parameter to control the amount of output during the iterations.