1 /* Copyright (c) 2007-2017. 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"
20 XBT_LOG_NEW_DEFAULT_SUBCATEGORY(surf_lagrange, surf, "Logging specific to SURF (lagrange)");
21 XBT_LOG_NEW_SUBCATEGORY(surf_lagrange_dichotomy, surf_lagrange, "Logging specific to SURF (lagrange dichotomy)");
23 #define SHOW_EXPR(expr) XBT_CDEBUG(surf_lagrange, #expr " = %g", expr);
24 #define VEGAS_SCALING 1000.0
25 #define RENO_SCALING 1.0
26 #define RENO2_SCALING 1.0
32 double (*func_f_def)(const Variable&, double);
33 double (*func_fp_def)(const Variable&, double);
34 double (*func_fpi_def)(const Variable&, double);
37 * Local prototypes to implement the Lagrangian optimization with optimal step, also called dichotomy.
39 // solves the proportional fairness using a Lagrangian optimization with dichotomy step
40 void lagrange_solve(lmm_system_t sys);
41 // computes the value of the dichotomy using a initial values, init, with a specific variable or constraint
42 static double dichotomy(double init, double diff(double, const Constraint&), const Constraint& cnst, double min_error);
43 // computes the value of the differential of constraint cnst applied to lambda
44 static double partial_diff_lambda(double lambda, const Constraint& cnst);
46 template <class CnstList, class VarList>
47 static int __check_feasible(const CnstList& cnst_list, const VarList& var_list, int warn)
49 for (Constraint const& cnst : cnst_list) {
51 for (Element const& elem : cnst.enabled_element_set) {
52 Variable* var = elem.variable;
53 xbt_assert(var->sharing_weight > 0);
57 if (double_positive(tmp - cnst.bound, sg_maxmin_precision)) {
59 XBT_WARN("The link (%p) is over-used. Expected less than %f and got %f", &cnst, cnst.bound, tmp);
62 XBT_DEBUG("Checking feasability for constraint (%p): sat = %f, lambda = %f ", &cnst, tmp - cnst.bound, cnst.lambda);
65 for (Variable const& var : var_list) {
66 if (not var.sharing_weight)
70 XBT_DEBUG("Checking feasability for variable (%p): sat = %f mu = %f", &var, var.value - var.bound, var.mu);
72 if (double_positive(var.value - var.bound, sg_maxmin_precision)) {
74 XBT_WARN("The variable (%p) is too large. Expected less than %f and got %f", &var, var.bound, var.value);
81 static double new_value(const Variable& var)
85 for (Element const& elem : var.cnsts) {
86 tmp += elem.constraint->lambda;
90 XBT_DEBUG("\t Working on var (%p). cost = %e; Weight = %e", &var, tmp, var.sharing_weight);
91 // uses the partial differential inverse function
92 return var.func_fpi(var, tmp);
95 static double new_mu(const Variable& var)
100 for (Element const& elem : var.cnsts) {
101 sigma_i += elem.constraint->lambda;
103 mu_i = var.func_fp(var, var.bound) - sigma_i;
109 template <class VarList, class CnstList>
110 static double dual_objective(const VarList& var_list, const CnstList& cnst_list)
114 for (Variable const& var : var_list) {
115 double sigma_i = 0.0;
117 if (not var.sharing_weight)
120 for (Element const& elem : var.cnsts)
121 sigma_i += elem.constraint->lambda;
126 XBT_DEBUG("var %p : sigma_i = %1.20f", &var, sigma_i);
128 obj += var.func_f(var, var.func_fpi(var, sigma_i)) - sigma_i * var.func_fpi(var, sigma_i);
131 obj += var.mu * var.bound;
134 for (Constraint const& cnst : cnst_list)
135 obj += cnst.lambda * cnst.bound;
140 void lagrange_solve(lmm_system_t sys)
142 /* Lagrange Variables. */
143 int max_iterations = 100;
144 double epsilon_min_error = 0.00001; /* this is the precision on the objective function so it's none of the
145 configurable values and this value is the legacy one */
146 double dichotomy_min_error = 1e-14;
147 double overall_modification = 1;
149 XBT_DEBUG("Iterative method configuration snapshot =====>");
150 XBT_DEBUG("#### Maximum number of iterations : %d", max_iterations);
151 XBT_DEBUG("#### Minimum error tolerated : %e", epsilon_min_error);
152 XBT_DEBUG("#### Minimum error tolerated (dichotomy) : %e", dichotomy_min_error);
154 if (XBT_LOG_ISENABLED(surf_lagrange, xbt_log_priority_debug)) {
158 if (not sys->modified)
161 /* Initialize lambda. */
162 auto& cnst_list = sys->active_constraint_set;
163 for (Constraint& cnst : cnst_list) {
165 cnst.new_lambda = 2.0;
166 XBT_DEBUG("#### cnst(%p)->lambda : %e", &cnst, cnst.lambda);
170 * Initialize the var_list variable with only the active variables. Initialize mu.
172 auto& var_list = sys->variable_set;
173 for (Variable& var : var_list) {
174 if (not var.sharing_weight)
177 if (var.bound < 0.0) {
178 XBT_DEBUG("#### NOTE var(%p) is a boundless variable", &var);
184 var.value = new_value(var);
185 XBT_DEBUG("#### var(%p) ->weight : %e", &var, var.sharing_weight);
186 XBT_DEBUG("#### var(%p) ->mu : %e", &var, var.mu);
187 XBT_DEBUG("#### var(%p) ->weight: %e", &var, var.sharing_weight);
188 XBT_DEBUG("#### var(%p) ->bound: %e", &var, var.bound);
190 std::find_if(begin(var.cnsts), end(var.cnsts), [](Element const& x) { return x.consumption_weight != 0.0; });
191 if (weighted == end(var.cnsts))
196 /* Compute dual objective. */
197 double obj = dual_objective(var_list, cnst_list);
199 /* While doesn't reach a minimum error or a number maximum of iterations. */
201 while (overall_modification > epsilon_min_error && iteration < max_iterations) {
203 XBT_DEBUG("************** ITERATION %d **************", iteration);
204 XBT_DEBUG("-------------- Gradient Descent ----------");
206 /* Improve the value of mu_i */
207 for (Variable& var : var_list) {
208 if (var.sharing_weight && var.bound >= 0) {
209 XBT_DEBUG("Working on var (%p)", &var);
210 var.new_mu = new_mu(var);
211 XBT_DEBUG("Updating mu : var->mu (%p) : %1.20f -> %1.20f", &var, var.mu, var.new_mu);
214 double new_obj = dual_objective(var_list, cnst_list);
215 XBT_DEBUG("Improvement for Objective (%g -> %g) : %g", obj, new_obj, obj - new_obj);
216 xbt_assert(obj - new_obj >= -epsilon_min_error, "Our gradient sucks! (%1.20f)", obj - new_obj);
221 /* Improve the value of lambda_i */
222 for (Constraint& cnst : cnst_list) {
223 XBT_DEBUG("Working on cnst (%p)", &cnst);
224 cnst.new_lambda = dichotomy(cnst.lambda, partial_diff_lambda, cnst, dichotomy_min_error);
225 XBT_DEBUG("Updating lambda : cnst->lambda (%p) : %1.20f -> %1.20f", &cnst, cnst.lambda, cnst.new_lambda);
226 cnst.lambda = cnst.new_lambda;
228 double new_obj = dual_objective(var_list, cnst_list);
229 XBT_DEBUG("Improvement for Objective (%g -> %g) : %g", obj, new_obj, obj - new_obj);
230 xbt_assert(obj - new_obj >= -epsilon_min_error, "Our gradient sucks! (%1.20f)", obj - new_obj);
234 /* Now computes the values of each variable (\rho) based on the values of \lambda and \mu. */
235 XBT_DEBUG("-------------- Check convergence ----------");
236 overall_modification = 0;
237 for (Variable& var : var_list) {
238 if (var.sharing_weight <= 0)
241 double tmp = new_value(var);
243 overall_modification = std::max(overall_modification, fabs(var.value - tmp));
246 XBT_DEBUG("New value of var (%p) = %e, overall_modification = %e", &var, var.value, overall_modification);
250 XBT_DEBUG("-------------- Check feasability ----------");
251 if (not __check_feasible(cnst_list, var_list, 0))
252 overall_modification = 1.0;
253 XBT_DEBUG("Iteration %d: overall_modification : %f", iteration, overall_modification);
256 __check_feasible(cnst_list, var_list, 1);
258 if (overall_modification <= epsilon_min_error) {
259 XBT_DEBUG("The method converges in %d iterations.", iteration);
261 if (iteration >= max_iterations) {
262 XBT_DEBUG("Method reach %d iterations, which is the maximum number of iterations allowed.", iteration);
265 if (XBT_LOG_ISENABLED(surf_lagrange, xbt_log_priority_debug)) {
271 * Returns a double value corresponding to the result of a dichotomy process with respect to a given
272 * variable/constraint (\mu in the case of a variable or \lambda in case of a constraint) and a initial value init.
274 * @param init initial value for \mu or \lambda
275 * @param diff a function that computes the differential of with respect a \mu or \lambda
276 * @param var_cnst a pointer to a variable or constraint
277 * @param min_erro a minimum error tolerated
279 * @return a double corresponding to the result of the dichotomy process
281 static double dichotomy(double init, double diff(double, const Constraint&), const Constraint& cnst, double min_error)
285 double overall_error;
292 if (fabs(init) < 1e-20) {
299 diff_0 = diff(1e-16, cnst);
301 XBT_CDEBUG(surf_lagrange_dichotomy, "returning 0.0 (diff = %e)", diff_0);
306 double min_diff = diff(min, cnst);
307 double max_diff = diff(max, cnst);
309 while (overall_error > min_error) {
310 XBT_CDEBUG(surf_lagrange_dichotomy, "[min, max] = [%1.20f, %1.20f] || diffmin, diffmax = %1.20f, %1.20f", min, max,
313 if (min_diff > 0 && max_diff > 0) {
315 XBT_CDEBUG(surf_lagrange_dichotomy, "Decreasing min");
317 min_diff = diff(min, cnst);
319 XBT_CDEBUG(surf_lagrange_dichotomy, "Decreasing max");
323 } else if (min_diff < 0 && max_diff < 0) {
325 XBT_CDEBUG(surf_lagrange_dichotomy, "Increasing max");
327 max_diff = diff(max, cnst);
329 XBT_CDEBUG(surf_lagrange_dichotomy, "Increasing min");
333 } else if (min_diff < 0 && max_diff > 0) {
334 middle = (max + min) / 2.0;
335 XBT_CDEBUG(surf_lagrange_dichotomy, "Trying (max+min)/2 : %1.20f", middle);
337 if ((fabs(min - middle) < 1e-20) || (fabs(max - middle) < 1e-20)) {
338 XBT_CWARN(surf_lagrange_dichotomy,
339 "Cannot improve the convergence! min=max=middle=%1.20f, diff = %1.20f."
340 " Reaching the 'double' limits. Maybe scaling your function would help ([%1.20f,%1.20f]).",
341 min, max - min, min_diff, max_diff);
344 middle_diff = diff(middle, cnst);
346 if (middle_diff < 0) {
347 XBT_CDEBUG(surf_lagrange_dichotomy, "Increasing min");
349 overall_error = max_diff - middle_diff;
350 min_diff = middle_diff;
351 } else if (middle_diff > 0) {
352 XBT_CDEBUG(surf_lagrange_dichotomy, "Decreasing max");
354 overall_error = max_diff - middle_diff;
355 max_diff = middle_diff;
359 } else if (fabs(min_diff) < 1e-20) {
362 } else if (fabs(max_diff) < 1e-20) {
365 } else if (min_diff > 0 && max_diff < 0) {
366 XBT_CWARN(surf_lagrange_dichotomy, "The impossible happened, partial_diff(min) > 0 && partial_diff(max) < 0");
369 XBT_CWARN(surf_lagrange_dichotomy,
370 "diffmin (%1.20f) or diffmax (%1.20f) are something I don't know, taking no action.", min_diff,
376 XBT_CDEBUG(surf_lagrange_dichotomy, "returning %e", (min + max) / 2.0);
378 return ((min + max) / 2.0);
381 static double partial_diff_lambda(double lambda, const Constraint& cnst)
387 XBT_CDEBUG(surf_lagrange_dichotomy, "Computing diff of cnst (%p)", &cnst);
389 for (Element const& elem : cnst.enabled_element_set) {
390 Variable& var = *elem.variable;
391 xbt_assert(var.sharing_weight > 0);
392 XBT_CDEBUG(surf_lagrange_dichotomy, "Computing sigma_i for var (%p)", &var);
393 // Initialize the summation variable
394 double sigma_i = 0.0;
397 for (Element const& elem2 : var.cnsts)
398 sigma_i += elem2.constraint->lambda;
400 // add mu_i if this flow has a RTT constraint associated
404 // replace value of cnst.lambda by the value of parameter lambda
405 sigma_i = (sigma_i - cnst.lambda) + lambda;
407 diff += -var.func_fpi(var, sigma_i);
412 XBT_CDEBUG(surf_lagrange_dichotomy, "d D/d lambda for cnst (%p) at %1.20f = %1.20f", &cnst, lambda, diff);
417 /** \brief Attribute the value bound to var->bound.
419 * \param func_fpi inverse of the partial differential of f (f prime inverse, (f')^{-1})
421 * Set default functions to the ones passed as parameters. This is a polymorphism in C pure, enjoy the roots of
425 void set_default_protocol_function(double (*func_f)(const Variable& var, double x),
426 double (*func_fp)(const Variable& var, double x),
427 double (*func_fpi)(const Variable& var, double x))
430 func_fp_def = func_fp;
431 func_fpi_def = func_fpi;
434 /**************** Vegas and Reno functions *************************/
435 /* NOTE for Reno: all functions consider the network coefficient (alpha) equal to 1. */
438 * For Vegas: $f(x) = \alpha D_f\ln(x)$
439 * Therefore: $fp(x) = \frac{\alpha D_f}{x}$
440 * Therefore: $fpi(x) = \frac{\alpha D_f}{x}$
442 double func_vegas_f(const Variable& var, double x)
444 xbt_assert(x > 0.0, "Don't call me with stupid values! (%1.20f)", x);
445 return VEGAS_SCALING * var.sharing_weight * log(x);
448 double func_vegas_fp(const Variable& var, double x)
450 xbt_assert(x > 0.0, "Don't call me with stupid values! (%1.20f)", x);
451 return VEGAS_SCALING * var.sharing_weight / x;
454 double func_vegas_fpi(const Variable& var, double x)
456 xbt_assert(x > 0.0, "Don't call me with stupid values! (%1.20f)", x);
457 return var.sharing_weight / (x / VEGAS_SCALING);
461 * For Reno: $f(x) = \frac{\sqrt{3/2}}{D_f} atan(\sqrt{3/2}D_f x)$
462 * Therefore: $fp(x) = \frac{3}{3 D_f^2 x^2+2}$
463 * Therefore: $fpi(x) = \sqrt{\frac{1}{{D_f}^2 x} - \frac{2}{3{D_f}^2}}$
465 double func_reno_f(const Variable& var, double x)
467 xbt_assert(var.sharing_weight > 0.0, "Don't call me with stupid values!");
469 return RENO_SCALING * sqrt(3.0 / 2.0) / var.sharing_weight * atan(sqrt(3.0 / 2.0) * var.sharing_weight * x);
472 double func_reno_fp(const Variable& var, double x)
474 return RENO_SCALING * 3.0 / (3.0 * var.sharing_weight * var.sharing_weight * x * x + 2.0);
477 double func_reno_fpi(const Variable& var, double x)
481 xbt_assert(var.sharing_weight > 0.0, "Don't call me with stupid values!");
482 xbt_assert(x > 0.0, "Don't call me with stupid values!");
484 res_fpi = 1.0 / (var.sharing_weight * var.sharing_weight * (x / RENO_SCALING)) -
485 2.0 / (3.0 * var.sharing_weight * var.sharing_weight);
488 return sqrt(res_fpi);
491 /* Implementing new Reno-2
492 * For Reno-2: $f(x) = U_f(x_f) = \frac{{2}{D_f}}*ln(2+x*D_f)$
493 * Therefore: $fp(x) = 2/(Weight*x + 2)
494 * Therefore: $fpi(x) = (2*Weight)/x - 4
496 double func_reno2_f(const Variable& var, double x)
498 xbt_assert(var.sharing_weight > 0.0, "Don't call me with stupid values!");
499 return RENO2_SCALING * (1.0 / var.sharing_weight) *
500 log((x * var.sharing_weight) / (2.0 * x * var.sharing_weight + 3.0));
503 double func_reno2_fp(const Variable& var, double x)
505 return RENO2_SCALING * 3.0 / (var.sharing_weight * x * (2.0 * var.sharing_weight * x + 3.0));
508 double func_reno2_fpi(const Variable& var, double x)
510 xbt_assert(x > 0.0, "Don't call me with stupid values!");
511 double tmp = x * var.sharing_weight * var.sharing_weight;
512 double res_fpi = tmp * (9.0 * x + 24.0);
517 res_fpi = RENO2_SCALING * (-3.0 * tmp + sqrt(res_fpi)) / (4.0 * tmp);