3 /* Copyright (c) 2007 Arnaud Legrand, Pedro Velho. All rights reserved. */
5 /* This program is free software; you can redistribute it and/or modify it
6 * under the terms of the license (GNU LGPL) which comes with this package. */
9 * Modelling the proportional fairness using the Lagrange Optimization
10 * Approach. For a detailed description see:
11 * "ssh://username@scm.gforge.inria.fr/svn/memo/people/pvelho/lagrange/ppf.ps".
14 #include "xbt/sysdep.h"
15 #include "xbt/mallocator.h"
16 #include "maxmin_private.h"
24 XBT_LOG_NEW_DEFAULT_SUBCATEGORY(surf_lagrangedico, surf,
25 "Logging specific to SURF (lagrange)");
28 void lagrange_dicotomi_solve(lmm_system_t sys);
30 double partial_diff_mu(double mu, lmm_variable_t var1);
31 double partial_diff_lambda(double lambda, lmm_constraint_t cnst1);
33 void lagrange_dicotomi_solve(lmm_system_t sys)
38 int max_iterations= 10;
39 double epsilon_min_error = 1e-10;
40 double overall_error = 1;
41 double min, max, middle;
45 * Variables to manipulate the data structure proposed to model the maxmin
46 * fairness. See docummentation for more details.
48 xbt_swag_t elem_list = NULL;
49 lmm_element_t elem1 = NULL;
52 xbt_swag_t cnst_list = NULL;
53 lmm_constraint_t cnst1 = NULL;
55 xbt_swag_t var_list = NULL;
56 _variable_t var1 = NULL;
67 DEBUG0("Iterative method configuration snapshot =====>");
68 DEBUG1("#### Maximum number of iterations : %d", max_iterations);
69 DEBUG1("#### Minimum error tolerated : %e", epsilon_min_error);
72 if ( !(sys->modified))
76 * Initialize the var list variable with only the active variables.
77 * Associate an index in the swag variables. Initialize mu.
79 var_list = &(sys->variable_set);
81 xbt_swag_foreach(var1, var_list) {
82 if((var1->bound > 0.0) || (var1->weight <= 0.0)){
83 DEBUG1("#### NOTE var1(%d) is a boundless variable", i);
89 DEBUG2("#### var1(%d)->mu : %e", i, var1->mu);
90 DEBUG2("#### var1(%d)->weight: %e", i, var1->weight);
97 cnst_list=&(sys->active_constraint_set);
98 xbt_swag_foreach(cnst1, cnst_list) {
100 cnst1->new_lambda = 2.0;
101 DEBUG2("#### cnst1(%p)->lambda : %e", cnst1, cnst1->lambda);
107 * While doesn't reach a minimun error or a number maximum of iterations.
109 while(overall_error > epsilon_min_error && iteration < max_iterations){
115 * Compute the value of ----------- (\lambda^k, \mu^k) this portion
117 * of code depends on function f(x).
119 var_list = &(sys->variable_set);
120 //forall mu_i in mu_1, mu_2, ..., mu_n
121 xbt_swag_foreach(var1, var_list) {
122 if((var1->bound >= 0) && (var1->weight > 0) ){
123 //for each link with capacity cnsts[i] that uses flow of variable var1 do
125 min = max = var1->mu;
127 while(overall_error < epsilon_min_error){
128 if( partial_diff_mu(min, var1)>0 && partial_diff_mu(max, var1)>0 ){
134 }else if( partial_diff_mu(min, var1)<0 && partial_diff_mu(max, var1)<0 ){
140 }else if( partial_diff_mu(min,var1)<0 && partial_diff_mu(max,var1) > 0 ){
142 middle = partial_diff_mu((fabs(min - max)/2), var1);
144 max = (fabs(min - max)/2);
145 }else if( middle < 0 ){
146 min = (fabs(min - max)/2);
148 WARN0("Found an optimal solution with 0 error!");
151 overall_error = fabs(min - max);
154 WARN0("The impossible happened, partial_diff(min) >0 && partial_diff(max) < 0");
168 * Compute the value of ------------- (\lambda^k, \mu^k) this portion
170 * of code depends on function f(x).
172 xbt_swag_foreach(cnst1, cnst_list) {
175 DEBUG2("cnst1 (id=%s) (%p)", (char *)cnst1->id, cnst1);
180 min = max = cnst1->lambda;
181 while(overall_error > epsilon_min_error){
185 // DEBUG4("====> Dicotomi debug. [%e, %e], D(min,max) = [%e, %e]", min, max, partial_diff_lambda(min, cnst1), partial_diff_lambda(max, cnst1));
187 if( partial_diff_lambda(min, cnst1) > 0 && partial_diff_lambda(max, cnst1) > 0 ){
193 }else if( partial_diff_lambda(min, cnst1) < 0 && partial_diff_lambda(max, cnst1) < 0 ){
199 }else if( partial_diff_lambda(min,cnst1) < 0 && partial_diff_lambda(max,cnst1) > 0 ){
200 middle = (max + min)/2.0;
203 //DEBUG2("Ideal state reached middle = %e, D(fabs(min-max)/2.0) = %e", middle, partial_diff_lambda(middle, cnst1));
204 if( partial_diff_lambda(middle, cnst1) < 0 ){
206 }else if( partial_diff_lambda(middle, cnst1) > 0 ){
209 WARN0("Found an optimal solution with 0 error!");
212 overall_error = fabs(min - max);
214 WARN0("The impossible happened, partial_diff(min) >0 && partial_diff(max) < 0");
219 DEBUG1("Number of iteration in the dicotomi %d", i);
223 if(cnst1->lambda < 0){
230 * Now computes the values of each variable (\rho) based on
231 * the values of \lambda and \mu.
234 DEBUG1("Iteration %d ", iteration);
235 xbt_swag_foreach(var1, var_list) {
240 for(i=0; i<var1->cnsts_number; i++){
241 tmp += (var1->cnsts[i].constraint)->lambda;
246 //computes de overall_error
247 if(overall_error < fabs(var1->value - 1.0/tmp)){
248 overall_error = fabs(var1->value - 1.0/tmp);
251 var1->value = 1.0 / tmp;
255 DEBUG2("======> value of var1 (%p) = %e", var1, var1->value);
263 //verify the KKT property
264 xbt_swag_foreach(cnst1, cnst_list){
266 elem_list = &(cnst1->element_set);
267 xbt_swag_foreach(elem1, elem_list) {
268 var1 = elem1->variable;
269 if(var1->weight<=0) continue;
273 tmp = tmp - cnst1->bound;
276 if(tmp != 0 || cnst1->lambda != 0){
277 WARN4("The link %s(%p) doesn't match the KKT property, value expected (=0) got (lambda=%e) (sum_rho=%e)", (char *)cnst1->id, cnst1, cnst1->lambda, tmp);
283 xbt_swag_foreach(var1, var_list){
284 if(var1->bound <= 0 || var1->weight <= 0) continue;
286 tmp = (var1->value - var1->bound);
289 if(tmp != 0 || var1->mu != 0){
290 WARN4("The flow %s(%p) doesn't match the KKT property, value expected (=0) got (lambda=%e) (sum_rho=%e)", (char *)var1->id, var1, var1->mu, tmp);
296 if(overall_error <= epsilon_min_error){
297 DEBUG1("The method converge in %d iterations.", iteration);
299 WARN1("Method reach %d iterations, which is the maxmimun number of iterations allowed.", iteration);
307 double dicotomi(double init, void *diff(double, void*), void *var_cnst){
309 double overall_error;
314 while(overall_error > epsilon_min_error){
315 if( diff(min, var_cnst) > 0 && diff(max, var_cnst) > 0 ){
321 }else if( diff(min, var_cnst) < 0 && diff(max, var_cnst) < 0 ){
327 }else if( diff(min, var_cnst) < 0 && diff(max, var_cnst) > 0 ){
328 middle = (max + min)/2.0;
330 if( diff(middle, var_cnst) < 0 ){
332 }else if( diff(middle, var_cnst) > 0 ){
335 WARN0("Found an optimal solution with 0 error!");
338 overall_error = fabs(min - max);
340 WARN0("The impossible happened, partial_diff(min) >0 && partial_diff(max) < 0");
345 double partial_diff_mu(double mu, lmm_variable_t var1){
346 double mu_partial=0.0;
349 //for each link with capacity cnsts[i] that uses flow of variable var1 do
350 for(i=0; i<var1->cnsts_number; i++)
351 mu_partial += (var1->cnsts[i].constraint)->lambda + mu;
353 mu_partial = (-1.0/mu_partial) + var1->bound;
359 double partial_diff_lambda(double lambda, lmm_constraint_t cnst1){
363 double lambda_partial=0.0;
364 xbt_swag_t elem_list = NULL;
365 lmm_element_t elem1 = NULL;
366 lmm_variable_t var1 = NULL;
369 elem_list = &(cnst1->element_set);
371 xbt_swag_foreach(elem1, elem_list) {
372 var1 = elem1->variable;
373 if(var1->weight<=0) continue;
376 for(i=0; i<var1->cnsts_number; i++){
377 tmp += (var1->cnsts[i].constraint)->lambda;
383 tmp = tmp - cnst1->lambda + lambda;
385 //un peux du bricolage pour evite la catastrophe
386 if(tmp==0) lambda_partial = 10e-8;
388 lambda_partial += (-1.0 /tmp);
392 lambda_partial += cnst1->bound;
394 //DEBUG3("Partial diff lambda result cnst1 %s (%p) : %e", (char *)cnst1->id, cnst1, lambda_partial);
395 return lambda_partial;