Merge pull request #24 from padix-key/optimization

New parameters for the optimizer

Author: padix-key

LICENSE.rst

@@ -1,7 +1,7 @@
 BSD 3-Clause License
 --------------------
 
-Copyright 2019 - 2021, Patrick Kunzmann, Benjamin Mayer
+Copyright 2019 - 2022, Patrick Kunzmann, Benjamin Mayer
 All rights reserved.
 
 Redistribution and use in source and binary forms, with or without modification,

doc/cli.rst

@@ -71,12 +71,15 @@ In order to increase the quality of the scheme tha amount of optimization steps
 (``--nsteps``) or the number of runs (``--nruns``) can be increased.
 However, increasing these values also extends the runtime of the optimization.
 Note that ``--nruns`` can take advantage of multiple cores.
+The number of used cores is set with ``--nthreads``
 
 The simulated annealing can be adjusted even more fine grained by setting
-the initial reverse temperature (``--beta``) and the rate of its exponential
-growth (``--rate``). The step size decreases in the course of the simulated
+the inverse temperature at the first (``--beta-start``) and last
+(``--beta-end``) step of the optimization.
+For the steps in between the inverse temperature is interpolated exponentially.
+The step size decreases in the course of the simulated
 annealing also in an exponential manner, which can be parameterized via
-``--step-size-start`` and ``--step-size-end``.
+``--stepsize-start`` and ``--stepsize-end``.
 The seed for the random number generator used by the algorithm is set with
 the ``--seed`` option.
 However, these parameters address the more advanced users.

doc/plotgen.py

@@ -65,7 +65,7 @@ def plot_generator(function):
 def plot_main_example_alignment():
     scheme_file = biotite.temp_file("json")
     gecli.main(args=[
-        "--seed", "0",
+        "--seed", "3",
         "--matrix", "BLOSUM62",
         "--lmin", "60",
         "--lmax", "75",

doc/theory.rst

@@ -173,12 +173,7 @@ an exponential schedule for the step size
 The step size is used for perturbing the current solution in each step of the
 SA algorithm to find a new candidate solution.
 So the idea for using the schedule here is to start with relatively large 
-step size :math:`\delta_{start}` and to chose the rate  according to an 
-target step size :math:`\delta_{end}`.
-An according rate is easily derived  by claiming
-:math:`\delta(N_{max})=\delta_{end}` which leads to
-
-.. math:: \gamma = \frac{1}{N_{max}}\log \left( \frac{\delta_{end}}{\delta_{start}} \right).
+step size and reduce it over the course of the simulation.
 
 
 Monte-Carlo algorithm

pyproject.toml

@@ -1,6 +1,6 @@
 [tool.poetry]
 name = "gecos"
-version = "1.3.0"
+version = "2.0.0"
 description = "Generated color schemes for sequence alignment visualizations"
 readme = "README.rst"
 license = "BSD-3-Clause"

src/gecos/__init__.py

@@ -2,7 +2,7 @@
 # under the 3-Clause BSD License. Please see 'LICENSE.rst' for further
 # information.
 
-__version__ = "1.3.0"
+__version__ = "2.0.0"
 __author__ = "Patrick Kunzmann"
 
 from .colors import *

src/gecos/cli.py

@@ -1,5 +1,6 @@
 from multiprocessing import Pool
 from os.path import join, dirname, realpath, isfile
+import itertools
 import argparse
 import copy
 import sys
@@ -37,22 +38,18 @@ class InputError(Exception):
     pass
 
 
-def _optimize(optline):
+def _optimize(seed, alphabet, score_func, space, constraints, 
+              nsteps, beta_start, beta_end, stepsize_start, stepsize_end):
     """
-    Worker function used for parallel execution of simulated annealing
-    optimizer with optline being a tuple containing the needed data
+    Worker function used for parallel execution of simulated annealing.
     """
-    (
-        alphabet, score_func, space, constraints, 
-        nsteps, beta, rate, step_size_start, step_size_end,
-        seed 
-    ) = optline
-    
     np.random.seed(seed)
     optimizer = ColorOptimizer(
         alphabet, score_func, space, constraints
     )
-    optimizer.optimize(nsteps, beta, rate, step_size_start, step_size_end)
+    optimizer.optimize(
+        nsteps, beta_start, beta_end, stepsize_start, stepsize_end
+    )
     return optimizer.get_result()
 
 @handle_error
@@ -201,29 +198,35 @@ def main(args=None, result_container=None, show_plots=True):
     )
     opt_group.add_argument(
         "--nruns", default=16, type=int,
-        help="Number of parallel optimization algorithms runs that are to be "
-             "executed.",
+        help="Number of optimizations to run. "
+             "From these runs, the color scheme with the best score is "
+             "selected.",
+        metavar="NUMBER"
+    )
+    opt_group.add_argument(
+        "--nthreads", type=int,
+        help="Number of optimization runs to run in parallel. "
+             "By default this is equal to the number of CPUs.",
         metavar="NUMBER"
     )
     opt_group.add_argument(
-        "--beta", default=1e-7, type=float,
-        help="Inverse start temperature for simulated annealing algorithm.",
+        "--beta-start", default=1, type=float,
+        help="Inverse temperature at start of simulated annealing.",
         metavar="FLOAT",
     )
     opt_group.add_argument(
-        "--rate", default=1, type=float,
-        help="Rate controlling the exponential annealing schedule, "
-             "for the annealing of the inverse temperature.",
+        "--beta-end", default=500, type=float,
+        help="Inverse temperature at end of simulated annealing.",
         metavar="FLOAT",
     )   
     opt_group.add_argument(
-        "--step-size-start", default=20, type=float,
-        help="Start step size for simulated annealing algorithm.",
+        "--stepsize-start", default=10, type=float,
+        help="Step size temperature at start of simulated annealing.",
         metavar="FLOAT",
     )
     opt_group.add_argument(
-        "--step-size-end", default=0.1, type=float,
-        help="End step size for simulated annealing algorithm.",
+        "--stepsize-end", default=0.2, type=float,
+        help="Step size temperature at end of simulated annealing.",
         metavar="FLOAT",
     )     
 
@@ -318,30 +321,26 @@ def main(args=None, result_container=None, show_plots=True):
 
     score_func = DefaultScoreFunction(matrix, args.contrast, args.delta)   
 
-    # Simulated annealing
-    n_parallel = args.nruns      
+    # Simulated annealing     
     if args.seed is not None:
         np.random.seed(int(args.seed))
-    # Different randomly seed for each run
-    seeds = np.random.randint(0, 1000000, size=n_parallel)
-    opt_data = [
-        (
-            matrix.get_alphabet1(),
-            score_func,
-            space,
-            constraints,
-            args.nsteps, 
-            args.beta,
-            args.rate,
-            args.step_size_start,
-            args.step_size_end,
-            seeds[i])
-        for i in range(n_parallel)
-    ]
-
-    with Pool(n_parallel) as p:
-        results = p.map(_optimize, opt_data)
-    best_result = sorted(results, key=lambda x: x.score)[0]
+    # Different random seed for each run
+    seeds = np.random.randint(0, 1000000, size=args.nruns)
+
+    with Pool(args.nthreads) as p:
+        results = p.starmap(_optimize, zip(
+            seeds,
+            itertools.repeat(matrix.get_alphabet1()),
+            itertools.repeat(score_func),
+            itertools.repeat(space),
+            itertools.repeat(constraints),
+            itertools.repeat(args.nsteps), 
+            itertools.repeat(args.beta_start),
+            itertools.repeat(args.beta_end),
+            itertools.repeat(args.stepsize_start),
+            itertools.repeat(args.stepsize_end),
+        ))
+    best_result = min(results, key=lambda x: x.score)
 
     scores = np.array([result.scores for result in results])
     scores_mean = np.mean(scores, axis=0)

src/gecos/optimizer.py

@@ -166,78 +166,62 @@ def _set_coordinates(self, coord, score=None):
             score = self._score_func(coord)
         self._scores.append(score)
 
-    def optimize(self, n_steps,
-                 beta_start, rate_beta, stepsize_start, stepsize_end):
+    def optimize(self, n_steps=20000,
+                 beta_start=1, beta_end=500,
+                 stepsize_start=10, stepsize_end=0.2):
         r"""
-        Perform a Simulated Annealing optimization on the current
+        Perform a simulated annealing optimization on the current
         coordinate to minimize the score returned by the score function.
         
-        This is basically a Monte-Carlo optimization where the
-        temperature is varied according to a so called annealing
-        schedule over the course of the optimization. 
+        This is basically a Metropolis-Monte-Carlo optimization where
+        the inverse temperature and step size is varied according to
+        exponential annealing schedule over the course of the
+        optimization.                            
+        
+        Parameters
+        ----------
+        n_steps : int
+            The number of simulated annealing steps.
+        beta_start, beta_end : float
+            The inverse temperature in the first and last step of the
+            optimization, respectively.
+            Higher values allow less increase of score, i.e. result
+            in a steering into the local minimum.
+            Must be positive.
+        stepsize_start, stepsize_end : float
+            The step size in the first and last step of the
+            optimization, respectively.
+            it is the radius in which the coordinates are randomly
+            altered at in each optimization step.
+            Must be positive.
+
+        Notes
+        -----
         The algorithm is a heuristic thats motivated by the physical
         process of annealing.
         If we, e.g., cool steel than a slow cooling can yield a superior
         quality, whereas for a fast cooling the steel can become
         brittle.
         The same happens here within the search space for the given
-        minimization task.                              
-        
-        Parameters
-        ----------
-        n_steps : int
-            The number of Simulated-Annealing steps.
-        beta_start : float
-            The inverse start temperature, where the start temperature
-            would be :math:`T_{start} = 1/(k_b \cdot \beta_{start})` with
-            :math:`k_b` being the boltzmann constant.            
-        rate_beta: float
-            The rate controls how fast the inverse temperature is
-            increased within the annealing schedule.
-            Here the exponential schedule is chosen so we have
-            :math:`\beta (t) = \beta_0 \cdot \exp(rate \cdot t)`.
-        stepsize_start : float
-            The radius in which the coordinates are randomly altered at
-            the beginning of the simulated anneling algorithm.
-            Like the inverse temperature the step size follows an
-            exponential schedule, enabling the algorithm
-            to do large perturbartions at the beginning of the algorithm
-            run and increasingly smaller ones afterwards.
-        stepsize_end : float
-            The radius in which the coordinates are randomly altered at
-            the end of the simulated annealing algorithm run.          
+        minimization task.       
         """
-        # Calculate the max value 'i' can reach so that
-        # 'np.exp(rate_beta*i)' does not overflow
-        max_i = np.log(np.finfo(np.float64).max) / rate_beta
-        beta = lambda i: beta_start*np.exp(rate_beta*i) \
-                         if i < max_i else np.inf
-
-        #  Choose rate so that stepsize_end reached after n_steps
-        #  derived from step_size(N_steps) = steps_end
-        if stepsize_start == stepsize_end:
-            rate_stepsize = 0
-        else:        
-            rate_stepsize = np.log(stepsize_end / stepsize_start) / n_steps
-        step_size = lambda i: stepsize_start * np.exp(rate_stepsize * i)
+        betas = _calculate_schedule(n_steps, beta_start, beta_end)
+        stepsizes = _calculate_schedule(n_steps, stepsize_start, stepsize_end)
 
         for i in range(n_steps):
-        
             score = self._scores[-1]
             new_coord = self._sample_coord(
                 self._coord,
-                lambda c: c + (random.rand(*c.shape)-0.5) * 2 * step_size(i)
+                lambda c: c + (random.rand(*c.shape)-0.5) * 2 * stepsizes[i]
             )
             new_score = self._score_func(new_coord)
 
             if new_score < score:
                 self._set_coordinates(new_coord, new_score)
 
             else:
-                p_accept = np.exp( -beta(i) * (new_score-score))
-                p = random.rand()
-                
-                if p <= p_accept:
+                p_accept = np.exp( -betas[i] * (new_score-score))
+                if random.rand() <= p_accept:
                     self._set_coordinates(new_coord, new_score)
                 else:
                     self._set_coordinates(self._coord, score)
@@ -292,6 +276,15 @@ def _apply_constraints(self, coord):
         coord[self._constraint_mask] = self._constraints[self._constraint_mask]
 
 
+def _calculate_schedule(n_steps, start, end):
+    """
+    Calculate the values for each step in an exponential schedule.
+    """
+    # Use float 64
+    return start * (end/start)**np.linspace(0, 1, n_steps, dtype=np.float64)
+
+
+
 class ScoreFunction(metaclass=abc.ABCMeta):
     """
     Abstract base class for a score function.
@@ -396,19 +389,18 @@ def __call__(self, coord):
     @staticmethod
     def _calculate_distances(tri_indices, coord, distance_formula):
         ind1, ind2 = tri_indices
-        if distance_formula == "CIEDE76":
-            dist = skimage.color.deltaE_ciede94(
-                coord[ind1], coord[ind2]
+        if distance_formula == "CIE76":
+            return np.sqrt(
+                np.sum((coord[ind1, :] - coord[ind2, :])**2, axis=-1)
             )
         elif distance_formula == "CIEDE94":
-            dist = skimage.color.deltaE_cie76(
+            return skimage.color.deltaE_ciede94(
                 coord[ind1], coord[ind2]
             )
         else: #"CIEDE2000"
-            dist = skimage.color.deltaE_ciede2000(
+            return skimage.color.deltaE_ciede2000(
                 coord[ind1], coord[ind2]
             )
-        return dist
 
     @staticmethod
     def _calculate_ideal_distances(tri_indices, substitution_matrix):
@@ -419,4 +411,4 @@ def _calculate_ideal_distances(tri_indices, substitution_matrix):
         distances = dist_matrix[ind_i, ind_j]
         # Scale, so that average distance is 1
         distances /= np.average(distances)
-        return distances
+        return distances