# usr bin env python3 import math import sys usr bin env python3 import

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276``` ```#! /usr/bin/env python3 import math import sys # ! /usr/bin/env python3 import numpy as np class Simplex: def __init__(self, A, b, c, B_idx, N_idx=None): self.A = np.matrix(A) self.b = np.matrix(b) self.c = np.matrix(c) self.B_idx = B_idx if N_idx is None: self.N_idx = [i for i in range(self.A.shape[1]) if i not in self.B_idx] else: self.N_idx = N_idx def getB(self): return self.A[:, self.B_idx] def getCb(self): return self.c[:, self.B_idx] def getCn(self): return self.c[:, self.N_idx] def getN(self): return self.A[:, self.N_idx] def calcZvar(self): InvB = np.linalg.inv(self.getB()) N = self.getN() Cb = self.getCb() Cb_InvB = Cb @ InvB Cb_InvB_b = Cb_InvB @ self.b.T Cb_InvB_N = Cb_InvB @ N bracadddinget_term = Cb_InvB_N - self.getCn() return Cb_InvB_b, -1 * bracadddinget_term def getVector(self): X = self.computeX() res = [0.0] * self.c.shape[1] index = 0 for j in self.B_idx: res[j] = X[index, 0] index += 1 return res def isOptimal(self, z): return all([x <= 0 for x in np.nditer(z)]) def enteringVariable(self, z): # pri('CHOOSE ENTERING')nt max_ascent = -1 * np.inf index = -1 it = np.nditer(z.T, flags=['f_index']) while not it.finished: # print(it[0]) if it[0] > max_ascent: max_ascent = it[0] index = it.index it.iternext() if index != -1: InvB = np.linalg.inv(self.getB()) val = InvB @ self.A[:, self.N_idx[index]] return index, val else: return None, None def computeX(self): InvB = np.linalg.inv(self.getB()) InvB_b = InvB @ self.b.T return InvB_b def exitingVariable(self, entering_pos, ev): X = self.computeX() # print('CHOOSE EXITING') min_value = np.inf index = -1 for idx, cr in enumerate(np.nditer([X, ev])): x, y = cr[0], cr[1] # print(x, y) if y <= 0: continue ratio = x / y if ratio < min_value: min_value = ratio index = idx # print('ratio={}'.format(min_value)) if index != -1: return index else: return None, None def do(self, verbose=False): while True: z, z_var = self.calcZvar() # print(z, z_var) if self.isOptimal(z_var): if verbose: print("solution") return z, self.getVector(), self.B_idx entering_pos, val = self.enteringVariable(z_var) if entering_pos is None: # print('Entering None') # print(self.getVector()) return None, None, None exiting_pos = self.exitingVariable(entering_pos, val) if exiting_pos is None: # print('Exiting None') # print(self.getVector()) return None, None, None self.B_idx[exiting_pos] = self.N_idx[entering_pos] self.N_idx = [i for i in range(self.A.shape[1]) if i not in self.B_idx] def calc_simplex_max(orig_A, orig_b, orig_c): A = [] for l in orig_A: A.append(l.copy()) b = orig_b.copy() c = [0.0] * len(A[0]) base = [i + len(A[0]) for i in range(len(b))] for i, row in enumerate(A): for j in range(len(b)): if i == j: row.append(1.0) else: row.append(0.0) for _ in range(len(b)): c.append(-1.0) # print(A) # print(b) # print(c) # print(base) simplex = Simplex(A, b, c, base) z, res, base = simplex.do() if z is None: return None, None if any([x >= len(orig_c) for x in base]): return None, None A = [] for l in orig_A: A.append(l.copy()) b = orig_b.copy() c = orig_c.copy() # c = simplex.c # notbase = [x for x in notbase if x < len(orig_c)] # print(A) # print(b) # print(c) # print(base) # print(notbase) simplex = Simplex(A, b, c, base) z, res, _ = simplex.do() return z, res def isAlmostEqual(x, y, epsilon=10 ** (-8)): return abs(x - y) <= epsilon def isAlmostEqualLists(x, y, epsilon=10 ** (-8)): return all(isAlmostEqual(x_i, y_i, epsilon) for (x_i, y_i) in zip(x, y)) def isIntList(list): rounded_list = [round(x) for x in list] return isAlmostEqualLists(list, rounded_list) def createBranch(x, index, A, b): A1 = [condition + [0.] for condition in A] new_A1 = [0.] * len(A1[0]) new_A1[index] = 1. new_A1[-1] = 1. A1.append(new_A1) b1 = b.copy() b1.append(math.floor(x[index])) # print('Created: {} {}'.format(A1, b1)) A2 = [condition + [0.] for condition in A] new_A2 = [0.] * len(A1[0]) # new_A2[index] = -1. new_A2[index] = 1. new_A2[-1] = -1. A2.append(new_A2) b2 = b.copy() b2.append(math.floor(x[index]) + 1.) # print('Created: {} {}'.format(A2, b2)) return A1, b1, A2, b2 def process(A, b, c, q, xs): # print('') # print(A) # print(b) # print(c) try: f_val, x_val = calc_simplex_max(A, b, c) except IndexError: print(len(A[0]), len(b), len(c)) raise IndexError # print(f_val, x_val) if f_val is None: return if isIntList(x_val): q.append((f_val, x_val, A, b)) xs.append((f_val, x_val)) else: q.append((f_val, x_val, A, b)) def branchsAndBounds(A, b, c, iterations_max=30): k = 0 f_val, x_val = calc_simplex_max(A, b, c) if f_val is None: return None, None, None q = [(f_val, x_val.copy(), A, b)] xs = [] if isIntList(x_val): return f_val, x_val, k k = 0 while q: # print("Q len = {}".format(len(q))) x_values = [x[1] for x in q] f_values = [x[0] for x in q] max_f_value_index = f_values.index(max(f_values)) _, new_x, c_A, c_b = q.pop(max_f_value_index) frac_parts = [i for i, x in enumerate(new_x) if divmod(x, 1)[1] > 0] if not frac_parts: continue index = frac_parts[0] A1, b1, A2, b2 = createBranch(new_x, index, c_A, c_b) process(A1, b1, c + [0.0] * (len(A1[0]) - len(A[0])), q, xs) process(A2, b2, c + [0.0] * (len(A2[0]) - len(A[0])), q, xs) if k > iterations_max: break k += 1 # sys.stdin.readline() f_values = [x[0] for x in xs] print(f_values) max_val = max(f_values) max_x = xs[f_values.index(max(f_values))][1] return max_val, max_x, k def main(): # A = [[1, 3, 4, -1], [2, 5, 1, 1]] # b = [23, 14] # c = [4, 2, -1, 0] A = [[1.0, 3.0, 4.0, 0.0], [2.0, 5.0, 7.0, 1.0]] b = [28.0, 64.0] c = [3.0, 4.0, -10.0, 0.0] print(branchsAndBounds(A, b, c)) if __name__ == '__main__': main() ```