1 /* Copyright (c) 2007-2018. The SimGrid Team. All rights reserved. */
3 /* This program is free software; you can redistribute it and/or modify it
4 * under the terms of the license (GNU LGPL) which comes with this package. */
7 * Modeling the proportional fairness using the Lagrangian Optimization Approach. For a detailed description see:
8 * "ssh://username@scm.gforge.inria.fr/svn/memo/people/pvelho/lagrange/ppf.ps".
10 #include "src/kernel/lmm/maxmin.hpp"
12 #include "xbt/sysdep.h"
18 XBT_LOG_NEW_DEFAULT_SUBCATEGORY(surf_lagrange, surf, "Logging specific to SURF (lagrange)");
19 XBT_LOG_NEW_SUBCATEGORY(surf_lagrange_dichotomy, surf_lagrange, "Logging specific to SURF (lagrange dichotomy)");
21 static constexpr double VEGAS_SCALING = 1000.0;
22 static constexpr double RENO_SCALING = 1.0;
23 static constexpr double RENO2_SCALING = 1.0;
29 System* make_new_lagrange_system(bool selective_update)
31 return new Lagrange(selective_update);
34 bool Lagrange::check_feasible(bool warn)
36 for (Constraint const& cnst : active_constraint_set) {
38 for (Element const& elem : cnst.enabled_element_set) {
39 Variable* var = elem.variable;
40 xbt_assert(var->sharing_weight > 0);
44 if (double_positive(tmp - cnst.bound, sg_maxmin_precision)) {
46 XBT_WARN("The link (%p) is over-used. Expected less than %f and got %f", &cnst, cnst.bound, tmp);
49 XBT_DEBUG("Checking feasability for constraint (%p): sat = %f, lambda = %f ", &cnst, tmp - cnst.bound, cnst.lambda);
52 for (Variable const& var : variable_set) {
53 if (not var.sharing_weight)
57 XBT_DEBUG("Checking feasability for variable (%p): sat = %f mu = %f", &var, var.value - var.bound, var.mu);
59 if (double_positive(var.value - var.bound, sg_maxmin_precision)) {
61 XBT_WARN("The variable (%p) is too large. Expected less than %f and got %f", &var, var.bound, var.value);
68 double Lagrange::new_value(const Variable& var)
72 for (Element const& elem : var.cnsts) {
73 tmp += elem.constraint->lambda;
77 XBT_DEBUG("\t Working on var (%p). cost = %e; Weight = %e", &var, tmp, var.sharing_weight);
78 // uses the partial differential inverse function
79 return func_fpi(var, tmp);
82 double Lagrange::new_mu(const Variable& var)
87 for (Element const& elem : var.cnsts) {
88 sigma_i += elem.constraint->lambda;
90 mu_i = func_fp(var, var.bound) - sigma_i;
96 double Lagrange::dual_objective()
100 for (Variable const& var : variable_set) {
101 double sigma_i = 0.0;
103 if (not var.sharing_weight)
106 for (Element const& elem : var.cnsts)
107 sigma_i += elem.constraint->lambda;
112 XBT_DEBUG("var %p : sigma_i = %1.20f", &var, sigma_i);
114 obj += func_f(var, func_fpi(var, sigma_i)) - sigma_i * func_fpi(var, sigma_i);
117 obj += var.mu * var.bound;
120 for (Constraint const& cnst : active_constraint_set)
121 obj += cnst.lambda * cnst.bound;
126 // solves the proportional fairness using a Lagrangian optimization with dichotomy step
127 void Lagrange::lagrange_solve()
129 /* Lagrange Variables. */
130 int max_iterations = 100;
131 double epsilon_min_error = 0.00001; /* this is the precision on the objective function so it's none of the
132 configurable values and this value is the legacy one */
133 double dichotomy_min_error = 1e-14;
134 double overall_modification = 1;
136 XBT_DEBUG("Iterative method configuration snapshot =====>");
137 XBT_DEBUG("#### Maximum number of iterations : %d", max_iterations);
138 XBT_DEBUG("#### Minimum error tolerated : %e", epsilon_min_error);
139 XBT_DEBUG("#### Minimum error tolerated (dichotomy) : %e", dichotomy_min_error);
141 if (XBT_LOG_ISENABLED(surf_lagrange, xbt_log_priority_debug)) {
148 /* Initialize lambda. */
149 auto& cnst_list = active_constraint_set;
150 for (Constraint& cnst : cnst_list) {
152 cnst.new_lambda = 2.0;
153 XBT_DEBUG("#### cnst(%p)->lambda : %e", &cnst, cnst.lambda);
157 * Initialize the var_list variable with only the active variables. Initialize mu.
159 auto& var_list = variable_set;
160 for (Variable& var : var_list) {
161 if (not var.sharing_weight)
164 if (var.bound < 0.0) {
165 XBT_DEBUG("#### NOTE var(%p) is a boundless variable", &var);
171 var.value = new_value(var);
172 XBT_DEBUG("#### var(%p) ->weight : %e", &var, var.sharing_weight);
173 XBT_DEBUG("#### var(%p) ->mu : %e", &var, var.mu);
174 XBT_DEBUG("#### var(%p) ->weight: %e", &var, var.sharing_weight);
175 XBT_DEBUG("#### var(%p) ->bound: %e", &var, var.bound);
177 std::find_if(begin(var.cnsts), end(var.cnsts), [](Element const& x) { return x.consumption_weight != 0.0; });
178 if (weighted == end(var.cnsts))
183 /* Compute dual objective. */
184 double obj = dual_objective();
186 /* While doesn't reach a minimum error or a number maximum of iterations. */
188 while (overall_modification > epsilon_min_error && iteration < max_iterations) {
190 XBT_DEBUG("************** ITERATION %d **************", iteration);
191 XBT_DEBUG("-------------- Gradient Descent ----------");
193 /* Improve the value of mu_i */
194 for (Variable& var : var_list) {
195 if (var.sharing_weight && var.bound >= 0) {
196 XBT_DEBUG("Working on var (%p)", &var);
197 var.new_mu = new_mu(var);
198 XBT_DEBUG("Updating mu : var->mu (%p) : %1.20f -> %1.20f", &var, var.mu, var.new_mu);
201 double new_obj = dual_objective();
202 XBT_DEBUG("Improvement for Objective (%g -> %g) : %g", obj, new_obj, obj - new_obj);
203 xbt_assert(obj - new_obj >= -epsilon_min_error, "Our gradient sucks! (%1.20f)", obj - new_obj);
208 /* Improve the value of lambda_i */
209 for (Constraint& cnst : cnst_list) {
210 XBT_DEBUG("Working on cnst (%p)", &cnst);
211 cnst.new_lambda = dichotomy(cnst.lambda, partial_diff_lambda, cnst, dichotomy_min_error);
212 XBT_DEBUG("Updating lambda : cnst->lambda (%p) : %1.20f -> %1.20f", &cnst, cnst.lambda, cnst.new_lambda);
213 cnst.lambda = cnst.new_lambda;
215 double new_obj = dual_objective();
216 XBT_DEBUG("Improvement for Objective (%g -> %g) : %g", obj, new_obj, obj - new_obj);
217 xbt_assert(obj - new_obj >= -epsilon_min_error, "Our gradient sucks! (%1.20f)", obj - new_obj);
221 /* Now computes the values of each variable (\rho) based on the values of \lambda and \mu. */
222 XBT_DEBUG("-------------- Check convergence ----------");
223 overall_modification = 0;
224 for (Variable& var : var_list) {
225 if (var.sharing_weight <= 0)
228 double tmp = new_value(var);
230 overall_modification = std::max(overall_modification, fabs(var.value - tmp));
233 XBT_DEBUG("New value of var (%p) = %e, overall_modification = %e", &var, var.value, overall_modification);
237 XBT_DEBUG("-------------- Check feasability ----------");
238 if (not check_feasible(false))
239 overall_modification = 1.0;
240 XBT_DEBUG("Iteration %d: overall_modification : %f", iteration, overall_modification);
243 check_feasible(true);
245 if (overall_modification <= epsilon_min_error) {
246 XBT_DEBUG("The method converges in %d iterations.", iteration);
248 if (iteration >= max_iterations) {
249 XBT_DEBUG("Method reach %d iterations, which is the maximum number of iterations allowed.", iteration);
252 if (XBT_LOG_ISENABLED(surf_lagrange, xbt_log_priority_debug)) {
258 * Returns a double value corresponding to the result of a dichotomy process with respect to a given
259 * variable/constraint (\mu in the case of a variable or \lambda in case of a constraint) and a initial value init.
261 * @param init initial value for \mu or \lambda
262 * @param diff a function that computes the differential of with respect a \mu or \lambda
263 * @param var_cnst a pointer to a variable or constraint
264 * @param min_erro a minimum error tolerated
266 * @return a double corresponding to the result of the dichotomy process
268 double Lagrange::dichotomy(double init, double diff(double, const Constraint&), const Constraint& cnst,
273 double overall_error;
280 if (fabs(init) < 1e-20) {
287 diff_0 = diff(1e-16, cnst);
289 XBT_CDEBUG(surf_lagrange_dichotomy, "returning 0.0 (diff = %e)", diff_0);
294 double min_diff = diff(min, cnst);
295 double max_diff = diff(max, cnst);
297 while (overall_error > min_error) {
298 XBT_CDEBUG(surf_lagrange_dichotomy, "[min, max] = [%1.20f, %1.20f] || diffmin, diffmax = %1.20f, %1.20f", min, max,
301 if (min_diff > 0 && max_diff > 0) {
303 XBT_CDEBUG(surf_lagrange_dichotomy, "Decreasing min");
305 min_diff = diff(min, cnst);
307 XBT_CDEBUG(surf_lagrange_dichotomy, "Decreasing max");
311 } else if (min_diff < 0 && max_diff < 0) {
313 XBT_CDEBUG(surf_lagrange_dichotomy, "Increasing max");
315 max_diff = diff(max, cnst);
317 XBT_CDEBUG(surf_lagrange_dichotomy, "Increasing min");
321 } else if (min_diff < 0 && max_diff > 0) {
322 middle = (max + min) / 2.0;
323 XBT_CDEBUG(surf_lagrange_dichotomy, "Trying (max+min)/2 : %1.20f", middle);
325 if ((fabs(min - middle) < 1e-20) || (fabs(max - middle) < 1e-20)) {
326 XBT_CWARN(surf_lagrange_dichotomy,
327 "Cannot improve the convergence! min=max=middle=%1.20f, diff = %1.20f."
328 " Reaching the 'double' limits. Maybe scaling your function would help ([%1.20f,%1.20f]).",
329 min, max - min, min_diff, max_diff);
332 middle_diff = diff(middle, cnst);
334 if (middle_diff < 0) {
335 XBT_CDEBUG(surf_lagrange_dichotomy, "Increasing min");
337 overall_error = max_diff - middle_diff;
338 min_diff = middle_diff;
339 } else if (middle_diff > 0) {
340 XBT_CDEBUG(surf_lagrange_dichotomy, "Decreasing max");
342 overall_error = max_diff - middle_diff;
343 max_diff = middle_diff;
347 } else if (fabs(min_diff) < 1e-20) {
350 } else if (fabs(max_diff) < 1e-20) {
353 } else if (min_diff > 0 && max_diff < 0) {
354 XBT_CWARN(surf_lagrange_dichotomy, "The impossible happened, partial_diff(min) > 0 && partial_diff(max) < 0");
357 XBT_CWARN(surf_lagrange_dichotomy,
358 "diffmin (%1.20f) or diffmax (%1.20f) are something I don't know, taking no action.", min_diff,
364 XBT_CDEBUG(surf_lagrange_dichotomy, "returning %e", (min + max) / 2.0);
366 return ((min + max) / 2.0);
369 double Lagrange::partial_diff_lambda(double lambda, const Constraint& cnst)
375 XBT_CDEBUG(surf_lagrange_dichotomy, "Computing diff of cnst (%p)", &cnst);
377 for (Element const& elem : cnst.enabled_element_set) {
378 Variable& var = *elem.variable;
379 xbt_assert(var.sharing_weight > 0);
380 XBT_CDEBUG(surf_lagrange_dichotomy, "Computing sigma_i for var (%p)", &var);
381 // Initialize the summation variable
382 double sigma_i = 0.0;
385 for (Element const& elem2 : var.cnsts)
386 sigma_i += elem2.constraint->lambda;
388 // add mu_i if this flow has a RTT constraint associated
392 // replace value of cnst.lambda by the value of parameter lambda
393 sigma_i = (sigma_i - cnst.lambda) + lambda;
395 diff += -func_fpi(var, sigma_i);
400 XBT_CDEBUG(surf_lagrange_dichotomy, "d D/d lambda for cnst (%p) at %1.20f = %1.20f", &cnst, lambda, diff);
405 /** \brief Attribute the value bound to var->bound.
407 * \param func_fpi inverse of the partial differential of f (f prime inverse, (f')^{-1})
409 * Set default functions to the ones passed as parameters.
411 void Lagrange::set_default_protocol_function(double (*func_f)(const Variable& var, double x),
412 double (*func_fp)(const Variable& var, double x),
413 double (*func_fpi)(const Variable& var, double x))
415 Lagrange::func_f = func_f;
416 Lagrange::func_fp = func_fp;
417 Lagrange::func_fpi = func_fpi;
420 double (*Lagrange::func_f)(const Variable&, double);
421 double (*Lagrange::func_fp)(const Variable&, double);
422 double (*Lagrange::func_fpi)(const Variable&, double);
424 /**************** Vegas and Reno functions *************************/
425 /* NOTE for Reno: all functions consider the network coefficient (alpha) equal to 1. */
428 * For Vegas: $f(x) = \alpha D_f\ln(x)$
429 * Therefore: $fp(x) = \frac{\alpha D_f}{x}$
430 * Therefore: $fpi(x) = \frac{\alpha D_f}{x}$
432 double func_vegas_f(const Variable& var, double x)
434 xbt_assert(x > 0.0, "Don't call me with stupid values! (%1.20f)", x);
435 return VEGAS_SCALING * var.sharing_weight * log(x);
438 double func_vegas_fp(const Variable& var, double x)
440 xbt_assert(x > 0.0, "Don't call me with stupid values! (%1.20f)", x);
441 return VEGAS_SCALING * var.sharing_weight / x;
444 double func_vegas_fpi(const Variable& var, double x)
446 xbt_assert(x > 0.0, "Don't call me with stupid values! (%1.20f)", x);
447 return var.sharing_weight / (x / VEGAS_SCALING);
451 * For Reno: $f(x) = \frac{\sqrt{3/2}}{D_f} atan(\sqrt{3/2}D_f x)$
452 * Therefore: $fp(x) = \frac{3}{3 D_f^2 x^2+2}$
453 * Therefore: $fpi(x) = \sqrt{\frac{1}{{D_f}^2 x} - \frac{2}{3{D_f}^2}}$
455 double func_reno_f(const Variable& var, double x)
457 xbt_assert(var.sharing_weight > 0.0, "Don't call me with stupid values!");
459 return RENO_SCALING * sqrt(3.0 / 2.0) / var.sharing_weight * atan(sqrt(3.0 / 2.0) * var.sharing_weight * x);
462 double func_reno_fp(const Variable& var, double x)
464 return RENO_SCALING * 3.0 / (3.0 * var.sharing_weight * var.sharing_weight * x * x + 2.0);
467 double func_reno_fpi(const Variable& var, double x)
471 xbt_assert(var.sharing_weight > 0.0, "Don't call me with stupid values!");
472 xbt_assert(x > 0.0, "Don't call me with stupid values!");
474 res_fpi = 1.0 / (var.sharing_weight * var.sharing_weight * (x / RENO_SCALING)) -
475 2.0 / (3.0 * var.sharing_weight * var.sharing_weight);
478 return sqrt(res_fpi);
481 /* Implementing new Reno-2
482 * For Reno-2: $f(x) = U_f(x_f) = \frac{{2}{D_f}}*ln(2+x*D_f)$
483 * Therefore: $fp(x) = 2/(Weight*x + 2)
484 * Therefore: $fpi(x) = (2*Weight)/x - 4
486 double func_reno2_f(const Variable& var, double x)
488 xbt_assert(var.sharing_weight > 0.0, "Don't call me with stupid values!");
489 return RENO2_SCALING * (1.0 / var.sharing_weight) *
490 log((x * var.sharing_weight) / (2.0 * x * var.sharing_weight + 3.0));
493 double func_reno2_fp(const Variable& var, double x)
495 return RENO2_SCALING * 3.0 / (var.sharing_weight * x * (2.0 * var.sharing_weight * x + 3.0));
498 double func_reno2_fpi(const Variable& var, double x)
500 xbt_assert(x > 0.0, "Don't call me with stupid values!");
501 double tmp = x * var.sharing_weight * var.sharing_weight;
502 double res_fpi = tmp * (9.0 * x + 24.0);
507 res_fpi = RENO2_SCALING * (-3.0 * tmp + sqrt(res_fpi)) / (4.0 * tmp);