frigidum 0.2.3

Simulated Annealing using tqdm

Simulated Annealing package for Python, using tqdm

Installation

pip install frigidum

Basic Example Usage

import frigidum

import random

def random_start():
    return 50 + random.random()

def random_small_step(x):
    return x + 0.1 * (random.random() - .5)

def random_big_step(x):
    return x + 10 * (random.random() - .5)

def obj(x):
    return x**2

local_opt = frigidum.sa(random_start=random_start, 
                        neighbours=[random_small_step, random_big_step], 
                        objective_function=obj, 
                        T_start=100, 
                        T_stop=0.000001, 
                        repeats=10**4, 
                        copy_state=frigidum.annealing.naked)

Arguments:

• random_start : function which returns a random start / state.
• objective_function : objective function to minimize.
• neighbours : list of neighbour functions, for one use [neighbour]. For each proposal, a neighbour is randomly selected (equal weights).
• T_start : Starting temperature.
• T_stop : Stopping temperature.
• alpha : Lower temperature by this factor, after repeats proposals.
• repeats : at each temperature lowering by factor alpha, do repeats proposals.
• copy = frigidum.annealing.copy, frigidum.annealing.deepcopy, frigidum.annealing.naked, or custom - the copy method.

Movements

A movement is a when a proposed state is accepted, and the objective function has changed. For each batch of repeats, the proportion of movements are displayed.

• In the early phase of annealing, movements should happen >90%.

• In the last phase of annealing, movements should happen <10%.

Movements are useful to determine the starting- and stopping temperature; T_start & T_stop, with the above guidelines.

Copy'ing of States

3 most important copy methods are included in the annealing module,

def copy(state):
	return state.copy()

def deepcopy(state):
	return state.deepcopy()

def naked(state):
	return state

In the example, naked with the argument copy_state=frigidum.annealing.naked is used,

• use copy_state=frigidum.annealing.copy for copy(),
• use copy_state=frigidum.annealing.deepcopy for deepcopy(),
• use copy_state=frigidum.annealing.naked if a = b would already create a copy.

General Advice with Simulated Annealing

• Focus on the neighbour function, not the cooling scheme or acceptance variations.
• To get inspiration for random neighbours, try solve a similar problem yourself.
• Try multiple neighbours together, combinations usually work well. The neighbours argument expects a list of neighbours.
• Try add neighbours, that might work well when cold.
• Try add neighbours, that might work well when warm.
• Try add neighbours, that find a local minima with local greedy algorithm.
• Try add neighbours, that break/remove a local solution and fix it again.
• Try add neighbours, that overwrite a part of the solution rigorously.
• It is difficult to predict the effect of a random neighbour, ideas usually don't survive the outcome of experiments.
• When conditions apply, stay within the feasible zone when possible. -or-
• Only anneal on either condition or objective, not both at the same time.

Examples

Rastrigin Function

https://en.wikipedia.org/wiki/Rastrigin_function

from frigidum.examples import rastrigin

frigidum.sa(random_start=rastrigin.random_start,
           objective_function=rastrigin.rastrigin_function,
           neighbours=[rastrigin.random_small_step, rastrigin.random_big_step],
           copy_state=frigidum.annealing.naked,
           T_start=100,
           T_stop=0.00001,
           repeats=10**4)

To-Do:

• Add TSP as example
• Multi threading (N simultaneous anneals)
• Drilling (after repeats, re-repeat with low temp)
• Re-Annealing
• (?) Auto-set start Temperature (Based on >90% movements)
• (?) Auto-stop (Based on <10% movements)