optimization/simulated_annealing.py at master · gisalgs/optimization · GitHub

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"""
A simulated annealing algorithm for the p-median problem

History
    November 17, 2016
        moved some imports to the __main__ part of the code

Contact:
Ningchuan Xiao
The Ohio State University
Columbus, OH
"""

__author__ = "Ningchuan Xiao <ncxiao@gmail.com>"

import math
import random
from copy import deepcopy
from teitz_bart import update_assignment

INF = float('inf')

def evaluate(dist, median, p, N):
    sumdist = 0.0
    for i in range(N):
        dist0 = INF
        for j in range(p):
            if dist[i][median[j]] < dist0:
                dist0 = dist[i][median[j]]
        sumdist += dist0
    return sumdist

# test replacing fr with fi in median without reallocating
# all the nodes
def test_replacement(fi, fr, dist, d1, d2, p, N):
    total = 0.0
    for i in range(N):
        if dist[i][fi]<dist[i][d1[i]]:
            total += dist[i][fi]
        else:
            if fr==d1[i]:
                if dist[i][fi]<dist[i][d2[i]]:
                    total += dist[i][fi]
                else:
                    total += dist[i][d2[i]]
            else:
                total += dist[i][d1[i]]
    return total

def get_new_median(N, p, median):
    samples = []
    for i in range(p):
        s = -1
        while s in median or s in samples:
            s = random.sample(range(N), 1)[0]
        samples.append(s)
    return samples

def bestRandomNeighbor(median, dist, N, p):
    candidates = []
    r_mins = []
    for j in range(p):
        candidates.append(get_new_median(N, p, median))
        r_mins.append(evaluate(dist, candidates[j], p , N))
    r_min = INF
    i_min = -1
    for j in range(p):
        if r_mins[j] < r_min:
            r_min = r_mins[j]
            i_min = j
    return r_min, candidates[i_min]

def bestGeoNeighbor(median, dist, d1, d2, N, p, dthreshold):
    r_min = INF
    for j in range(p):
        r_min_temp = INF
        fi_temp = -1
        for i in range(N): # try replacing j with an i
            if dist[median[j]][i]>dthreshold or i in median:
                continue
            if random.random() > 0.67:
                continue
            r1 = test_replacement(i, median[j], dist, d1, d2, p, N)
            if r1 < r_min_temp:
                r_min_temp = r1
                fi_temp = i
        if r_min_temp < r_min:
            r_min = r_min_temp
            fi = fi_temp
            fr = j
    return r_min, fi, fr

def next(r, T, median, dist, d1, d2, p, N,
         dthreshold, neighbormethod):
    r1 = r
    if neighbormethod == 0:
        r_min, fi, fr = bestGeoNeighbor(median, dist, d1, d2, N, p, dthreshold)
        test = acceptable(10*(r_min-r)/r, T)
        if test[0] > 0:
            median[fr] = fi
            r1 = update_assignment(dist, median,d1,d2,p,N)
        return test[0], r1, median
    else:
        r_min, candidate = bestRandomNeighbor(median, dist, N, p)
        test = acceptable(10*(r_min-r)/r, T)
        if test[0] > 0:
            median = candidate
            r1 = update_assignment(dist, median, d1, d2, p, N)
        return test[0], r1, median

def acceptable(delta, T):
    if delta<0:                 # better solution
        return 1, 1
    if delta==0:                # same solution, no change
        return 0, 0
    prob = math.exp(-delta/T)
    if random.random() < prob:  # worse solution, accept
        return 2, prob
    return 0, prob              # worse solution, reject

def simulated_annealing(dist, p, neighbormethod=0, verbose=False):
    N = len(dist)
    dmax = max([max(dist[i]) for i in range(N)])
    dthreshold = dmax/2
    d1 = [-1 for i in range(N)]
    d2 = [-1 for i in range(N)]

    ## Initialization
    median = random.sample(range(N), p)
    r = update_assignment(dist, median, d1, d2, p , N)
    first = [deepcopy(r), deepcopy(median)]
    best = [r, median]
    if verbose: print first[0]

    accepted_same = 0
    T = 100.0
    while True:
        result = next(r, T, median, dist, d1, d2, p, N,
                      dthreshold, neighbormethod)
        if result[0]>0:
            r = result[1]
            if r < best[0]:
                best = [r, deepcopy(result[2])]
                accepted_same = 0
            if result[0]==2:
                accepted_same += 1
            if r == best[0] and accepted_same > 2:
                break
            T = 0.9*T
            if verbose:
                print r
                if result[0] == 2:
                    print '*',
                print median
        else: break
    return first, best

if __name__ == "__main__":
    import sys
    sys.path.append('../networks')
    from network2listmatrix import network2distancematrix
    from allpairdist import allpairs
    print 'Problem: simple network'
    a = network2distancematrix('../data/network-links', True)
    allpairs(a)
    result = simulated_annealing(a, 2, verbose=True)
    print result[0][0], result[1][0]

    print 'Problem: pmed1 in OR-lib'
    a = network2distancematrix('../data/orlib/pmed1.orlib', False)
    allpairs(a)
    result = simulated_annealing(a, 5, verbose=True)
    print result[0][0], result[1][0]