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= 1000000;
39 double epsilon_min_error = 0.00001;
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 lmm_variable_t var1 = NULL;
65 FILE *gnuplot_file=NULL;
68 DEBUG0("Iterative method configuration snapshot =====>");
69 DEBUG1("#### Maximum number of iterations : %d", max_iterations);
70 DEBUG1("#### Minimum error tolerated : %e", epsilon_min_error);
73 if ( !(sys->modified))
77 * Initialize the var list variable with only the active variables.
78 * Associate an index in the swag variables. Initialize mu.
80 var_list = &(sys->variable_set);
82 xbt_swag_foreach(var1, var_list) {
83 if((var1->bound > 0.0) || (var1->weight <= 0.0)){
84 DEBUG1("#### NOTE var1(%d) is a boundless variable", i);
90 DEBUG2("#### var1(%d)->mu : %e", i, var1->mu);
91 DEBUG2("#### var1(%d)->weight: %e", i, var1->weight);
98 cnst_list=&(sys->active_constraint_set);
99 xbt_swag_foreach(cnst1, cnst_list) {
101 cnst1->new_lambda = 2.0;
102 DEBUG2("#### cnst1(%p)->lambda : %e", cnst1, cnst1->lambda);
108 * While doesn't reach a minimun error or a number maximum of iterations.
110 while(overall_error > epsilon_min_error && iteration < max_iterations){
116 * Compute the value of ----------- (\lambda^k, \mu^k) this portion
118 * of code depends on function f(x).
120 var_list = &(sys->variable_set);
121 //forall mu_i in mu_1, mu_2, ..., mu_n
122 xbt_swag_foreach(var1, var_list) {
123 if((var1->bound >= 0) && (var1->weight > 0) ){
124 //for each link with capacity cnsts[i] that uses flow of variable var1 do
128 while(overall_error < epsilon_min_error){
129 if( partial_diff_mu(min, var1)>0 && partial_diff_mu(max, var1)>0 ){
135 }else if( partial_diff_mu(min, var1)<0 && partial_diff_mu(max, var1)<0 ){
141 }else if( partial_diff_mu(min,var1)<0 && partial_diff_mu(max,var1) > 0 ){
143 middle = partial_diff_mu((fabs(min - max)/2), var1);
145 max = (fabs(min - max)/2);
146 }else if( middle < 0 ){
147 min = (fabs(min - max)/2);
149 WARN0("Found an optimal solution with 0 error!");
152 overall_error = fabs(min - max);
155 WARN0("The impossible happened, partial_diff(min) >0 && partial_diff(max) < 0");
161 if(var1->new_mu < 0){
169 * Compute the value of ------------- (\lambda^k, \mu^k) this portion
171 * of code depends on function f(x).
173 xbt_swag_foreach(cnst1, cnst_list) {
178 while(overall_error < epsilon_min_error){
179 if( partial_diff_lambda(min, cnst1) > 0 && partial_diff_lambda(max, cnst1) > 0 ){
185 }else if( partial_diff_lambda(min, cnst1) < 0 && partial_diff_lambda(max, cnst1) < 0 ){
191 }else if( partial_diff_lambda(min,cnst1) < 0 && partial_diff_lambda(max,cnst1) > 0 ){
193 middle = partial_diff_lambda((fabs(min - max)/2), cnst1);
195 max = (fabs(min - max)/2);
196 }else if( middle < 0 ){
197 min = (fabs(min - max)/2);
199 WARN0("Found an optimal solution with 0 error!");
202 overall_error = fabs(min - max);
205 WARN0("The impossible happened, partial_diff(min) >0 && partial_diff(max) < 0");
211 cnst1->new_lambda = cnst1->lambda;
213 if(cnst1->new_lambda < 0){
214 cnst1->new_lambda = 0;
220 * Now computes the values of each variable (\rho) based on
221 * the values of \lambda and \mu.
224 xbt_swag_foreach(var1, var_list) {
229 for(i=0; i<var1->cnsts_number; i++){
230 tmp += (var1->cnsts[i].constraint)->lambda;
235 //computes de overall_error
236 if(overall_error < fabs(var1->value - 1.0/tmp)){
237 overall_error = fabs(var1->value - 1.0/tmp);
240 var1->value = 1.0 / tmp;
246 /* Updating lambda's and mu's */
247 xbt_swag_foreach(var1, var_list)
248 if(!((var1->bound > 0.0) || (var1->weight <= 0.0)))
249 var1->mu = var1->new_mu;
252 xbt_swag_foreach(cnst1, cnst_list)
253 cnst1->lambda = cnst1->new_lambda;
257 //verify the KKT property
258 xbt_swag_foreach(cnst1, cnst_list){
260 elem_list = &(cnst1->element_set);
261 xbt_swag_foreach(elem1, elem_list) {
262 var1 = elem1->variable;
263 if(var1->weight<=0) continue;
267 tmp = tmp - cnst1->bound;
270 if(tmp != 0 || cnst1->lambda != 0){
271 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);
277 xbt_swag_foreach(var1, var_list){
278 if(var1->bound <= 0 || var1->weight <= 0) continue;
280 tmp = (var1->value - var1->bound);
283 if(tmp != 0 || var1->mu != 0){
284 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);
290 if(overall_error <= epsilon_min_error){
291 DEBUG1("The method converge in %d iterations.", iteration);
293 WARN1("Method reach %d iterations, which is the maxmimun number of iterations allowed.", iteration);
297 if(XBT_LOG_ISENABLED(surf_writelambda, xbt_log_priority_debug)) {
298 fclose(gnuplot_file);
306 double partial_diff_mu(double mu, lmm_variable_t var1){
307 double mu_partial=0.0;
310 //for each link with capacity cnsts[i] that uses flow of variable var1 do
311 for(i=0; i<var1->cnsts_number; i++)
312 mu_partial += (var1->cnsts[i].constraint)->lambda + mu;
314 mu_partial = (-1.0/mu_partial) + var1->bound;
320 double partial_diff_lambda(double lambda, lmm_constraint_t cnst1){
324 double lambda_partial=0.0;
325 xbt_swag_t elem_list = NULL;
326 lmm_element_t elem1 = NULL;
327 lmm_variable_t var1 = NULL;
330 elem_list = &(cnst1->element_set);
332 xbt_swag_foreach(elem1, elem_list) {
333 var1 = elem1->variable;
334 if(var1->weight<=0) continue;
337 for(i=0; i<var1->cnsts_number; i++){
338 tmp += (var1->cnsts[i].constraint)->lambda;
344 if(tmp==0) lambda_partial = 10e-8;
345 lambda_partial += (-1.0 / (tmp - 3*cnst1->lambda + 3*cnst1->lambda));
348 return lambda_partial;