1 | # _________________________________________________________________________ |
---|
2 | # |
---|
3 | # Coopr: A COmmon Optimization Python Repository |
---|
4 | # Copyright (c) 2010 Sandia Corporation. |
---|
5 | # This software is distributed under the BSD License. |
---|
6 | # Under the terms of Contract DE-AC04-94AL85000 with Sandia Corporation, |
---|
7 | # the U.S. Government retains certain rights in this software. |
---|
8 | # For more information, see the Coopr README.txt file. |
---|
9 | # _________________________________________________________________________ |
---|
10 | |
---|
11 | # this module contains various utilities for creating PH weighted penalty |
---|
12 | # objectives, e.g., through quadratic or linearized penalty terms. |
---|
13 | |
---|
14 | from math import fabs, log, exp |
---|
15 | from coopr.pyomo import * |
---|
16 | from phutils import indexToString |
---|
17 | |
---|
18 | # IMPT: In general, the breakpoint computation codes can return a 2-list even if the lb equals |
---|
19 | # the ub. This case happens quite often in real models (although typically lb=xvag=ub). |
---|
20 | # See the code for constructing the pieces on how this case is handled in the linearization. |
---|
21 | |
---|
22 | # |
---|
23 | # routine to compute linearization breakpoints uniformly between the bounds and the mean. |
---|
24 | # |
---|
25 | |
---|
26 | def compute_uniform_breakpoints(lb, node_min, xavg, node_max, ub, num_breakpoints_per_side, tolerance): |
---|
27 | |
---|
28 | breakpoints = [] |
---|
29 | |
---|
30 | # add the lower bound - the first breakpoint. |
---|
31 | breakpoints.append(lb) |
---|
32 | |
---|
33 | # determine the breakpoints to the left of the mean. |
---|
34 | left_step = (xavg - lb) / num_breakpoints_per_side |
---|
35 | current_x = lb |
---|
36 | for i in range(1,num_breakpoints_per_side+1): |
---|
37 | this_lb = current_x |
---|
38 | this_ub = current_x+left_step |
---|
39 | if (fabs(this_lb-lb) > tolerance) and (fabs(this_lb-xavg) > tolerance): |
---|
40 | breakpoints.append(this_lb) |
---|
41 | current_x += left_step |
---|
42 | |
---|
43 | # add the mean - it's always a breakpoint. unless! |
---|
44 | # the lb or ub and the avg are the same. |
---|
45 | if (fabs(lb-xavg) > tolerance) and (fabs(ub-xavg) > tolerance): |
---|
46 | breakpoints.append(xavg) |
---|
47 | |
---|
48 | # determine the breakpoints to the right of the mean. |
---|
49 | right_step = (ub - xavg) / num_breakpoints_per_side |
---|
50 | current_x = xavg |
---|
51 | for i in range(1,num_breakpoints_per_side+1): |
---|
52 | this_lb = current_x |
---|
53 | this_ub = current_x+right_step |
---|
54 | if (fabs(this_ub-xavg) > tolerance) and (fabs(this_ub-ub) > tolerance): |
---|
55 | breakpoints.append(this_ub) |
---|
56 | current_x += right_step |
---|
57 | |
---|
58 | # add the upper bound - the last breakpoint. |
---|
59 | # the upper bound should always be different than the lower bound (I say with some |
---|
60 | # hesitation - it really depends on what plugins are doing to modify the bounds dynamically). |
---|
61 | breakpoints.append(ub) |
---|
62 | |
---|
63 | return breakpoints |
---|
64 | |
---|
65 | # |
---|
66 | # routine to compute linearization breakpoints uniformly between the current node min/max bounds. |
---|
67 | # |
---|
68 | |
---|
69 | def compute_uniform_between_nodestat_breakpoints(lb, node_min, xavg, node_max, ub, num_breakpoints, tolerance): |
---|
70 | |
---|
71 | breakpoints = [] |
---|
72 | |
---|
73 | # add the lower bound - the first breakpoint. |
---|
74 | breakpoints.append(lb) |
---|
75 | |
---|
76 | # add the node-min - the second breakpoint. but only if it is different than the lower bound and the mean. |
---|
77 | if (fabs(node_min-lb) > tolerance) and (fabs(node_min-xavg) > tolerance): |
---|
78 | breakpoints.append(node_min) |
---|
79 | |
---|
80 | step = (node_max - node_min) / num_breakpoints |
---|
81 | current_x = node_min |
---|
82 | for i in range(1,num_breakpoints+1): |
---|
83 | this_lb = current_x |
---|
84 | this_ub = current_x+step |
---|
85 | if (fabs(this_lb-node_min) > tolerance) and (fabs(this_lb-node_max) > tolerance) and (fabs(this_lb-xavg) > tolerance): |
---|
86 | breakpoints.append(this_lb) |
---|
87 | current_x += step |
---|
88 | |
---|
89 | # add the node-max - the second-to-last breakpoint. but only if it is different than the upper bound and the mean. |
---|
90 | if (fabs(node_max-ub) > tolerance) and (fabs(node_max-xavg) > tolerance): |
---|
91 | breakpoints.append(node_max) |
---|
92 | |
---|
93 | # add the upper bound - the last breakpoint. |
---|
94 | breakpoints.append(ub) |
---|
95 | |
---|
96 | # add the mean - it's always a breakpoint. unless! - |
---|
97 | # it happens to be equal to (within tolerance) the lower or upper bounds. |
---|
98 | # sort to insert it in the correct place. |
---|
99 | if (fabs(xavg - lb) > tolerance) and (fabs(xavg - ub) > tolerance): |
---|
100 | breakpoints.append(xavg) |
---|
101 | breakpoints.sort() |
---|
102 | |
---|
103 | return breakpoints |
---|
104 | |
---|
105 | # |
---|
106 | # routine to compute linearization breakpoints using "Woodruff" relaxation of the compute_uniform_between_nodestat_breakpoints. |
---|
107 | # |
---|
108 | |
---|
109 | def compute_uniform_between_woodruff_breakpoints(lb, node_min, xavg, node_max, ub, num_breakpoints, tolerance): |
---|
110 | |
---|
111 | breakpoints = [] |
---|
112 | |
---|
113 | # add the lower bound - the first breakpoint. |
---|
114 | breakpoints.append(lb) |
---|
115 | |
---|
116 | # be either three "differences" from the mean, or else "halfway to the bound", whichever is closer to the mean. |
---|
117 | left = max(xavg - 3.0 * (xavg - node_min), xavg - 0.5 * (xavg - lb)) |
---|
118 | right = min(xavg + 3.0 * (node_max - xavg), xavg + 0.5 * (ub - xavg)) |
---|
119 | |
---|
120 | # add the left bound - the second breakpoint. but only if it is different than the lower bound and the mean. |
---|
121 | if (fabs(left-lb) > tolerance) and (fabs(left-xavg) > tolerance): |
---|
122 | breakpoints.append(left) |
---|
123 | |
---|
124 | step = (right - left) / num_breakpoints |
---|
125 | current_x = left |
---|
126 | for i in range(1,num_breakpoints+1): |
---|
127 | this_lb = current_x |
---|
128 | this_ub = current_x+step |
---|
129 | if (fabs(this_lb-left) > tolerance) and (fabs(this_lb-right) > tolerance) and (fabs(this_lb-xavg) > tolerance): |
---|
130 | breakpoints.append(this_lb) |
---|
131 | current_x += step |
---|
132 | |
---|
133 | # add the right bound - the second-to-last breakpoint. but only if it is different than the upper bound and the mean. |
---|
134 | if (fabs(right-ub) > tolerance) and (fabs(right-xavg) > tolerance): |
---|
135 | breakpoints.append(right) |
---|
136 | |
---|
137 | # add the upper bound - the last breakpoint. |
---|
138 | breakpoints.append(ub) |
---|
139 | |
---|
140 | # add the mean - it's always a breakpoint. |
---|
141 | # sort to insert it in the correct place. |
---|
142 | breakpoints.append(xavg) |
---|
143 | breakpoints.sort() |
---|
144 | |
---|
145 | return breakpoints |
---|
146 | |
---|
147 | # |
---|
148 | # routine to compute linearization breakpoints based on an exponential distribution from the mean in each direction. |
---|
149 | # |
---|
150 | |
---|
151 | def compute_exponential_from_mean_breakpoints(lb, node_min, xavg, node_max, ub, num_breakpoints_per_side, tolerance): |
---|
152 | |
---|
153 | breakpoints = [] |
---|
154 | |
---|
155 | # add the lower bound - the first breakpoint. |
---|
156 | breakpoints.append(lb) |
---|
157 | |
---|
158 | # determine the breakpoints to the left of the mean. |
---|
159 | left_delta = xavg - lb |
---|
160 | base = exp(log(left_delta) / num_breakpoints_per_side) |
---|
161 | current_offset = base |
---|
162 | for i in range(1,num_breakpoints_per_side+1): |
---|
163 | current_x = xavg - current_offset |
---|
164 | if (fabs(current_x-lb) > tolerance) and (fabs(current_x-xavg) > tolerance): |
---|
165 | breakpoints.append(current_x) |
---|
166 | current_offset *= base |
---|
167 | |
---|
168 | # add the mean - it's always a breakpoint. |
---|
169 | breakpoints.append(xavg) |
---|
170 | |
---|
171 | # determine the breakpoints to the right of the mean. |
---|
172 | right_delta = ub - xavg |
---|
173 | base = exp(log(right_delta) / num_breakpoints_per_side) |
---|
174 | current_offset = base |
---|
175 | for i in range(1,num_breakpoints_per_side+1): |
---|
176 | current_x = xavg + current_offset |
---|
177 | if (fabs(current_x-xavg) > tolerance) and (fabs(current_x-ub) > tolerance): |
---|
178 | breakpoints.append(current_x) |
---|
179 | current_offset *= base |
---|
180 | |
---|
181 | # add the upper bound - the last breakpoint. |
---|
182 | breakpoints.append(ub) |
---|
183 | |
---|
184 | return breakpoints |
---|
185 | |
---|
186 | # |
---|
187 | # a utility to create piece-wise linear constraint expressions for a given variable, for |
---|
188 | # use in constructing the augmented (penalized) PH objective. lb and ub are the bounds |
---|
189 | # on this piece, variable is the actual instance variable, and average is the instance |
---|
190 | # parameter specifying the average of this variable across instances sharing passing |
---|
191 | # through a common tree node. lb and ub are floats. |
---|
192 | # IMPT: There are cases where lb=ub, in which case the slope is 0 and the intercept |
---|
193 | # is simply the penalty at the lower(or upper) bound. |
---|
194 | # |
---|
195 | |
---|
196 | def create_piecewise_constraint_expression(lb, ub, instance_variable, variable_average, quad_variable, tolerance): |
---|
197 | |
---|
198 | penalty_at_lb = (lb - value(variable_average)) * (lb - value(variable_average)) |
---|
199 | penalty_at_ub = (ub - value(variable_average)) * (ub - value(variable_average)) |
---|
200 | slope = None |
---|
201 | if fabs(ub-lb) > tolerance: |
---|
202 | slope = (penalty_at_ub - penalty_at_lb) / (ub - lb) |
---|
203 | else: |
---|
204 | slope = 0.0 |
---|
205 | intercept = penalty_at_lb - slope * lb |
---|
206 | expression = (0.0, quad_variable - slope * instance_variable - intercept, None) |
---|
207 | |
---|
208 | return expression |
---|
209 | |
---|
210 | # |
---|
211 | # form the baseline objective. really just a wrapper around a clone |
---|
212 | # operation at this point. |
---|
213 | # |
---|
214 | |
---|
215 | def form_standard_objective(instance_name, instance, original_objective_expression, scenario_tree): |
---|
216 | |
---|
217 | objective_name = instance.active_components(Objective).keys()[0] |
---|
218 | objective = instance.active_components(Objective)[objective_name] |
---|
219 | # clone the objective, because we're going to augment (repeatedly) the original objective. |
---|
220 | objective_expression = original_objective_expression.clone() |
---|
221 | objective_expression.simplify(instance) |
---|
222 | instance.active_components(Objective)[objective_name]._data[None].expr = objective_expression |
---|
223 | instance.active_components(Objective)[objective_name]._quad_subexpr = None |
---|
224 | |
---|
225 | # |
---|
226 | # form the penalized PH objective, guided by various options. |
---|
227 | # returns the list of components added to the instance, e.g., |
---|
228 | # in the case of constraints required to implement linearization. |
---|
229 | # |
---|
230 | |
---|
231 | def form_ph_objective(instance_name, instance, original_objective_expression, scenario_tree, \ |
---|
232 | linearize_nonbinary_penalty_terms, drop_proximal_terms, \ |
---|
233 | retain_quadratic_binary_terms, breakpoint_strategy, \ |
---|
234 | tolerance, simplify_expressions): |
---|
235 | |
---|
236 | new_instance_attributes = [] |
---|
237 | |
---|
238 | objective_name = instance.active_components(Objective).keys()[0] |
---|
239 | objective = instance.active_components(Objective)[objective_name] |
---|
240 | # clone the objective, because we're going to augment (repeatedly) the original objective. |
---|
241 | objective_expression = original_objective_expression.clone() |
---|
242 | # the quadratic expression is really treated as just a list - eventually should be treated as a full expression. |
---|
243 | quad_expression = 0.0 |
---|
244 | |
---|
245 | # print "ORIGINAL OBJECTIVE EXPRESSION:" |
---|
246 | # original_objective_expression.pprint() |
---|
247 | |
---|
248 | # print "CLONED OBJECTIVE EXPRESSION:" |
---|
249 | # objective_expression.pprint() |
---|
250 | |
---|
251 | # foobar |
---|
252 | |
---|
253 | # for each blended variable (i.e., those not appearing in the final stage), |
---|
254 | # add the linear and quadratic penalty terms to the objective. |
---|
255 | |
---|
256 | for stage in scenario_tree._stages[:-1]: # skip the last stage, as no blending occurs |
---|
257 | |
---|
258 | variable_tree_node = None |
---|
259 | for node in stage._tree_nodes: |
---|
260 | for scenario in node._scenarios: |
---|
261 | if scenario._name == instance_name: |
---|
262 | variable_tree_node = node |
---|
263 | break |
---|
264 | |
---|
265 | for (reference_variable, index_template) in stage._variables: |
---|
266 | |
---|
267 | variable_name = reference_variable.name |
---|
268 | variable_type = reference_variable.domain |
---|
269 | |
---|
270 | w_parameter_name = "PHWEIGHT_"+variable_name |
---|
271 | w_parameter = instance.active_components(Param)[w_parameter_name] |
---|
272 | |
---|
273 | average_parameter_name = "PHAVG_"+variable_name |
---|
274 | average_parameter = instance.active_components(Param)[average_parameter_name] |
---|
275 | |
---|
276 | rho_parameter_name = "PHRHO_"+variable_name |
---|
277 | rho_parameter = instance.active_components(Param)[rho_parameter_name] |
---|
278 | |
---|
279 | blend_parameter_name = "PHBLEND_"+variable_name |
---|
280 | blend_parameter = instance.active_components(Param)[blend_parameter_name] |
---|
281 | |
---|
282 | node_min_parameter = variable_tree_node._minimums[variable_name] |
---|
283 | node_max_parameter = variable_tree_node._maximums[variable_name] |
---|
284 | |
---|
285 | quad_penalty_term_variable = None |
---|
286 | if linearize_nonbinary_penalty_terms > 0: |
---|
287 | quad_penalty_term_variable_name = "PHQUADPENALTY_"+variable_name |
---|
288 | quad_penalty_term_variable = instance.active_components(Var)[quad_penalty_term_variable_name] |
---|
289 | |
---|
290 | instance_variable = instance.active_components(Var)[variable_name] |
---|
291 | |
---|
292 | variable_indices = variable_tree_node._variable_indices[variable_name] |
---|
293 | |
---|
294 | for index in variable_indices: |
---|
295 | |
---|
296 | if (instance_variable[index].status is not VarStatus.unused) and (instance_variable[index].fixed is False): |
---|
297 | |
---|
298 | # add the linear (w-weighted) term is a consistent fashion, independent of variable type. |
---|
299 | # if maximizing, here is where you would want "-=" - however, if you do this, the collect/simplify process chokes for reasons currently unknown. |
---|
300 | objective_expression += (value(w_parameter[index]) * instance_variable[index]) |
---|
301 | |
---|
302 | # there are some cases in which a user may want to avoid the proximal term completely. |
---|
303 | # it's of course only a good idea when there are at least bounds (both lb and ub) on |
---|
304 | # the variables to be blended. |
---|
305 | if drop_proximal_terms is False: |
---|
306 | |
---|
307 | # deal with binaries |
---|
308 | if isinstance(variable_type, BooleanSet) is True: |
---|
309 | |
---|
310 | if retain_quadratic_binary_terms is False: |
---|
311 | # this rather ugly form of the linearized quadratic expression term is required |
---|
312 | # due to a pyomo bug - the form (rho/2) * (x+y+z) chokes in presolve when distributing |
---|
313 | # over the sum. |
---|
314 | new_term = (value(blend_parameter[index]) * value(rho_parameter[index]) / 2.0 * instance_variable[index]) - \ |
---|
315 | (value(blend_parameter[index]) * value(rho_parameter[index]) * value(average_parameter[index]) * instance_variable[index]) + \ |
---|
316 | (value(blend_parameter[index]) * value(rho_parameter[index]) / 2.0 * value(average_parameter[index]) * value(average_parameter[index])) |
---|
317 | if objective.sense is minimize: |
---|
318 | objective_expression += new_term |
---|
319 | else: |
---|
320 | objective_expression -= new_term |
---|
321 | else: |
---|
322 | quad_expression += (blend_parameter[index] * rho_parameter[index] * (instance_variable[index] - average_parameter[index]) ** 2) |
---|
323 | |
---|
324 | # deal with everything else |
---|
325 | else: |
---|
326 | |
---|
327 | if linearize_nonbinary_penalty_terms > 0: |
---|
328 | |
---|
329 | # the variables are easy - just a single entry. |
---|
330 | if objective.sense is minimize: |
---|
331 | objective_expression += (rho_parameter[index] / 2.0 * quad_penalty_term_variable[index]) |
---|
332 | else: |
---|
333 | objective_expression -= (rho_parameter[index] / 2.0 * quad_penalty_term_variable[index]) |
---|
334 | |
---|
335 | # the constraints are somewhat nastier. |
---|
336 | |
---|
337 | # TBD - DEFINE CONSTRAINTS ON-THE-FLY?? (INDIVIDUALLY NAMED FOR NOW - CREATE INDEX SETS!) - OR A LEAST AN INDEX SET PER "PIECE" |
---|
338 | xavg = average_parameter[index] |
---|
339 | x = instance_variable[index] |
---|
340 | |
---|
341 | if x.lb is None or x.ub is None: |
---|
342 | var = variable_name + indexToString(index) |
---|
343 | msg = "Missing bound for '%s'\n" \ |
---|
344 | 'Both lower and upper bounds required when' \ |
---|
345 | ' piece-wise approximating quadratic ' \ |
---|
346 | 'penalty terms' |
---|
347 | raise ValueError, msg % var |
---|
348 | lb = x.lb() |
---|
349 | ub = x.ub() |
---|
350 | |
---|
351 | node_min = value(node_min_parameter[index]) |
---|
352 | node_max = value(node_max_parameter[index]) |
---|
353 | |
---|
354 | # compute the breakpoint sequence according to the specified strategy. |
---|
355 | try: |
---|
356 | strategy = ( |
---|
357 | compute_uniform_breakpoints, |
---|
358 | compute_uniform_between_nodestat_breakpoints, |
---|
359 | compute_uniform_between_woodruff_breakpoints, |
---|
360 | compute_exponential_from_mean_breakpoints, |
---|
361 | )[ breakpoint_strategy ] |
---|
362 | args = ( lb, node_min, value(xavg), node_max, ub, \ |
---|
363 | linearize_nonbinary_penalty_terms, tolerance ) |
---|
364 | breakpoints = strategy( *args ) |
---|
365 | except ValueError, e: |
---|
366 | msg = 'A breakpoint distribution strategy (%s) ' \ |
---|
367 | 'is currently not supported within PH!' |
---|
368 | raise ValueError, msg % breakpoint_strategy |
---|
369 | |
---|
370 | for i in range(0,len(breakpoints)-1): |
---|
371 | |
---|
372 | this_lb = breakpoints[i] |
---|
373 | this_ub = breakpoints[i+1] |
---|
374 | |
---|
375 | piece_constraint_name = "QUAD_PENALTY_PIECE_"+str(i)+"_"+variable_name+str(index) |
---|
376 | if hasattr(instance, piece_constraint_name) is False: |
---|
377 | # this is the first time the constraint is being added - add it to the list of PH-specific constraints for this instance. |
---|
378 | new_instance_attributes.append(piece_constraint_name) |
---|
379 | |
---|
380 | piece_constraint = Constraint(name=piece_constraint_name) |
---|
381 | piece_constraint.model = instance |
---|
382 | piece_expression = create_piecewise_constraint_expression(this_lb, this_ub, x, xavg, \ |
---|
383 | quad_penalty_term_variable[index], \ |
---|
384 | tolerance) |
---|
385 | piece_constraint.add(None, piece_expression) |
---|
386 | setattr(instance, piece_constraint_name, piece_constraint) |
---|
387 | |
---|
388 | else: |
---|
389 | |
---|
390 | quad_expression += (blend_parameter[index] * rho_parameter[index] * (instance_variable[index] - average_parameter[index]) ** 2) |
---|
391 | |
---|
392 | # simplification should actually not be required, at least for LPs and MIPs - repeating variables |
---|
393 | # is not problematic in this context. it may be, though, in the land of NLPs. hence, the option. |
---|
394 | if simplify_expressions is True: |
---|
395 | objective_expression.simplify(instance) |
---|
396 | |
---|
397 | # assign the new expression to the objective. |
---|
398 | instance.active_components(Objective)[objective_name]._data[None].expr = objective_expression |
---|
399 | |
---|
400 | # if we are linearizing everything, then nothing will appear in the quadratic expression - |
---|
401 | # don't add the empty "0.0" expression to the objective. otherwise, the output file won't |
---|
402 | # be properly generated. |
---|
403 | if quad_expression != 0.0: |
---|
404 | instance.active_components(Objective)[objective_name]._quad_subexpr = quad_expression |
---|
405 | else: |
---|
406 | instance.active_components(Objective)[objective_name]._quad_subexpr = None |
---|
407 | |
---|
408 | return new_instance_attributes |
---|