int ios_driver(glp_tree *T) { int p, curr_p, p_stat, d_stat, ret; #if 1 /* carry out to glp_tree */ int pred_p = 0; /* if the current subproblem has been just created due to branching, pred_p is the reference number of its parent subproblem, otherwise pred_p is zero */ #endif glp_long ttt = T->tm_beg; #if 0 ((glp_iocp *)T->parm)->msg_lev = GLP_MSG_DBG; #endif /* on entry to the B&B driver it is assumed that the active list contains the only active (i.e. root) subproblem, which is the original MIP problem to be solved */ loop: /* main loop starts here */ /* at this point the current subproblem does not exist */ xassert(T->curr == NULL); /* if the active list is empty, the search is finished */ if (T->head == NULL) { if (T->parm->msg_lev >= GLP_MSG_DBG) xprintf("Active list is empty!\n"); xassert(dmp_in_use(T->pool).lo == 0); ret = 0; goto done; } /* select some active subproblem to continue the search */ xassert(T->next_p == 0); /* let the application program select subproblem */ if (T->parm->cb_func != NULL) { xassert(T->reason == 0); T->reason = GLP_ISELECT; T->parm->cb_func(T, T->parm->cb_info); T->reason = 0; if (T->stop) { ret = GLP_ESTOP; goto done; } } if (T->next_p != 0) { /* the application program has selected something */ ; } else if (T->a_cnt == 1) { /* the only active subproblem exists, so select it */ xassert(T->head->next == NULL); T->next_p = T->head->p; } else if (T->child != 0) { /* select one of branching childs suggested by the branching heuristic */ T->next_p = T->child; } else { /* select active subproblem as specified by the backtracking technique option */ T->next_p = ios_choose_node(T); } /* the active subproblem just selected becomes current */ ios_revive_node(T, T->next_p); T->next_p = T->child = 0; /* invalidate pred_p, if it is not the reference number of the parent of the current subproblem */ if (T->curr->up != NULL && T->curr->up->p != pred_p) pred_p = 0; /* determine the reference number of the current subproblem */ p = T->curr->p; if (T->parm->msg_lev >= GLP_MSG_DBG) { xprintf("-----------------------------------------------------" "-------------------\n"); xprintf("Processing node %d at level %d\n", p, T->curr->level); } /* if it is the root subproblem, initialize cut generators */ if (p == 1) { if (T->parm->gmi_cuts == GLP_ON) { if (T->parm->msg_lev >= GLP_MSG_ALL) xprintf("Gomory's cuts enabled\n"); } if (T->parm->mir_cuts == GLP_ON) { if (T->parm->msg_lev >= GLP_MSG_ALL) xprintf("MIR cuts enabled\n"); xassert(T->mir_gen == NULL); T->mir_gen = ios_mir_init(T); } if (T->parm->cov_cuts == GLP_ON) { if (T->parm->msg_lev >= GLP_MSG_ALL) xprintf("Cover cuts enabled\n"); } if (T->parm->clq_cuts == GLP_ON) { xassert(T->clq_gen == NULL); if (T->parm->msg_lev >= GLP_MSG_ALL) xprintf("Clique cuts enabled\n"); T->clq_gen = ios_clq_init(T); } } more: /* minor loop starts here */ /* at this point the current subproblem needs either to be solved for the first time or re-optimized due to reformulation */ /* display current progress of the search */ if (T->parm->msg_lev >= GLP_MSG_DBG || T->parm->msg_lev >= GLP_MSG_ON && (double)(T->parm->out_frq - 1) <= 1000.0 * xdifftime(xtime(), T->tm_lag)) show_progress(T, 0); if (T->parm->msg_lev >= GLP_MSG_ALL && xdifftime(xtime(), ttt) >= 60.0) #if 0 /* 16/II-2012 */ { glp_long total; glp_mem_usage(NULL, NULL, &total, NULL); xprintf("Time used: %.1f secs. Memory used: %.1f Mb.\n", xdifftime(xtime(), T->tm_beg), xltod(total) / 1048576.0); ttt = xtime(); } #else { size_t total; glp_mem_usage(NULL, NULL, &total, NULL); xprintf("Time used: %.1f secs. Memory used: %.1f Mb.\n", xdifftime(xtime(), T->tm_beg), (double)total / 1048576.0); ttt = xtime(); } #endif /* check the mip gap */ if (T->parm->mip_gap > 0.0 && ios_relative_gap(T) <= T->parm->mip_gap) { if (T->parm->msg_lev >= GLP_MSG_DBG) xprintf("Relative gap tolerance reached; search terminated " "\n"); ret = GLP_EMIPGAP; goto done; } /* check if the time limit has been exhausted */ if (T->parm->tm_lim < INT_MAX && (double)(T->parm->tm_lim - 1) <= 1000.0 * xdifftime(xtime(), T->tm_beg)) { if (T->parm->msg_lev >= GLP_MSG_DBG) xprintf("Time limit exhausted; search terminated\n"); ret = GLP_ETMLIM; goto done; } /* let the application program preprocess the subproblem */ if (T->parm->cb_func != NULL) { xassert(T->reason == 0); T->reason = GLP_IPREPRO; T->parm->cb_func(T, T->parm->cb_info); T->reason = 0; if (T->stop) { ret = GLP_ESTOP; goto done; } } /* perform basic preprocessing */ if (T->parm->pp_tech == GLP_PP_NONE) ; else if (T->parm->pp_tech == GLP_PP_ROOT) { if (T->curr->level == 0) { if (ios_preprocess_node(T, 100)) goto fath; } } else if (T->parm->pp_tech == GLP_PP_ALL) { if (ios_preprocess_node(T, T->curr->level == 0 ? 100 : 10)) goto fath; } else xassert(T != T); /* preprocessing may improve the global bound */ if (!is_branch_hopeful(T, p)) { xprintf("*** not tested yet ***\n"); goto fath; } /* solve LP relaxation of the current subproblem */ if (T->parm->msg_lev >= GLP_MSG_DBG) xprintf("Solving LP relaxation...\n"); ret = ios_solve_node(T); if (!(ret == 0 || ret == GLP_EOBJLL || ret == GLP_EOBJUL)) { if (T->parm->msg_lev >= GLP_MSG_ERR) xprintf("ios_driver: unable to solve current LP relaxation;" " glp_simplex returned %d\n", ret); ret = GLP_EFAIL; goto done; } /* analyze status of the basic solution to LP relaxation found */ p_stat = T->mip->pbs_stat; d_stat = T->mip->dbs_stat; if (p_stat == GLP_FEAS && d_stat == GLP_FEAS) { /* LP relaxation has optimal solution */ if (T->parm->msg_lev >= GLP_MSG_DBG) xprintf("Found optimal solution to LP relaxation\n"); } else if (d_stat == GLP_NOFEAS) { /* LP relaxation has no dual feasible solution */ /* since the current subproblem cannot have a larger feasible region than its parent, there is something wrong */ if (T->parm->msg_lev >= GLP_MSG_ERR) xprintf("ios_driver: current LP relaxation has no dual feas" "ible solution\n"); ret = GLP_EFAIL; goto done; } else if (p_stat == GLP_INFEAS && d_stat == GLP_FEAS) { /* LP relaxation has no primal solution which is better than the incumbent objective value */ xassert(T->mip->mip_stat == GLP_FEAS); if (T->parm->msg_lev >= GLP_MSG_DBG) xprintf("LP relaxation has no solution better than incumben" "t objective value\n"); /* prune the branch */ goto fath; } else if (p_stat == GLP_NOFEAS) { /* LP relaxation has no primal feasible solution */ if (T->parm->msg_lev >= GLP_MSG_DBG) xprintf("LP relaxation has no feasible solution\n"); /* prune the branch */ goto fath; } else { /* other cases cannot appear */ xassert(T->mip != T->mip); } /* at this point basic solution to LP relaxation of the current subproblem is optimal */ xassert(p_stat == GLP_FEAS && d_stat == GLP_FEAS); xassert(T->curr != NULL); T->curr->lp_obj = T->mip->obj_val; /* thus, it defines a local bound to integer optimal solution of the current subproblem */ { double bound = T->mip->obj_val; /* some local bound to the current subproblem could be already set before, so we should only improve it */ bound = ios_round_bound(T, bound); if (T->mip->dir == GLP_MIN) { if (T->curr->bound < bound) T->curr->bound = bound; } else if (T->mip->dir == GLP_MAX) { if (T->curr->bound > bound) T->curr->bound = bound; } else xassert(T->mip != T->mip); if (T->parm->msg_lev >= GLP_MSG_DBG) xprintf("Local bound is %.9e\n", bound); } /* if the local bound indicates that integer optimal solution of the current subproblem cannot be better than the global bound, prune the branch */ if (!is_branch_hopeful(T, p)) { if (T->parm->msg_lev >= GLP_MSG_DBG) xprintf("Current branch is hopeless and can be pruned\n"); goto fath; } /* let the application program generate additional rows ("lazy" constraints) */ xassert(T->reopt == 0); xassert(T->reinv == 0); if (T->parm->cb_func != NULL) { xassert(T->reason == 0); T->reason = GLP_IROWGEN; T->parm->cb_func(T, T->parm->cb_info); T->reason = 0; if (T->stop) { ret = GLP_ESTOP; goto done; } if (T->reopt) { /* some rows were added; re-optimization is needed */ T->reopt = T->reinv = 0; goto more; } if (T->reinv) { /* no rows were added, however, some inactive rows were removed */ T->reinv = 0; xassert(glp_factorize(T->mip) == 0); } } /* check if the basic solution is integer feasible */ check_integrality(T); /* if the basic solution satisfies to all integrality conditions, it is a new, better integer feasible solution */ if (T->curr->ii_cnt == 0) { if (T->parm->msg_lev >= GLP_MSG_DBG) xprintf("New integer feasible solution found\n"); if (T->parm->msg_lev >= GLP_MSG_ALL) display_cut_info(T); record_solution(T); if (T->parm->msg_lev >= GLP_MSG_ON) show_progress(T, 1); /* make the application program happy */ if (T->parm->cb_func != NULL) { xassert(T->reason == 0); T->reason = GLP_IBINGO; T->parm->cb_func(T, T->parm->cb_info); T->reason = 0; if (T->stop) { ret = GLP_ESTOP; goto done; } } /* since the current subproblem has been fathomed, prune its branch */ goto fath; } /* at this point basic solution to LP relaxation of the current subproblem is optimal, but integer infeasible */ /* try to fix some non-basic structural variables of integer kind on their current bounds due to reduced costs */ if (T->mip->mip_stat == GLP_FEAS) fix_by_red_cost(T); /* let the application program try to find some solution to the original MIP with a primal heuristic */ if (T->parm->cb_func != NULL) { xassert(T->reason == 0); T->reason = GLP_IHEUR; T->parm->cb_func(T, T->parm->cb_info); T->reason = 0; if (T->stop) { ret = GLP_ESTOP; goto done; } /* check if the current branch became hopeless */ if (!is_branch_hopeful(T, p)) { if (T->parm->msg_lev >= GLP_MSG_DBG) xprintf("Current branch became hopeless and can be prune" "d\n"); goto fath; } } /* try to find solution with the feasibility pump heuristic */ if (T->parm->fp_heur) { xassert(T->reason == 0); T->reason = GLP_IHEUR; ios_feas_pump(T); T->reason = 0; /* check if the current branch became hopeless */ if (!is_branch_hopeful(T, p)) { if (T->parm->msg_lev >= GLP_MSG_DBG) xprintf("Current branch became hopeless and can be prune" "d\n"); goto fath; } } /* it's time to generate cutting planes */ xassert(T->local != NULL); xassert(T->local->size == 0); /* let the application program generate some cuts; note that it can add cuts either to the local cut pool or directly to the current subproblem */ if (T->parm->cb_func != NULL) { xassert(T->reason == 0); T->reason = GLP_ICUTGEN; T->parm->cb_func(T, T->parm->cb_info); T->reason = 0; if (T->stop) { ret = GLP_ESTOP; goto done; } } /* try to generate generic cuts with built-in generators (as suggested by Matteo Fischetti et al. the built-in cuts are not generated at each branching node; an intense attempt of generating new cuts is only made at the root node, and then a moderate effort is spent after each backtracking step) */ if (T->curr->level == 0 || pred_p == 0) { xassert(T->reason == 0); T->reason = GLP_ICUTGEN; generate_cuts(T); T->reason = 0; } /* if the local cut pool is not empty, select useful cuts and add them to the current subproblem */ if (T->local->size > 0) { xassert(T->reason == 0); T->reason = GLP_ICUTGEN; ios_process_cuts(T); T->reason = 0; } /* clear the local cut pool */ ios_clear_pool(T, T->local); /* perform re-optimization, if necessary */ if (T->reopt) { T->reopt = 0; T->curr->changed++; goto more; } /* no cuts were generated; remove inactive cuts */ remove_cuts(T); if (T->parm->msg_lev >= GLP_MSG_ALL && T->curr->level == 0) display_cut_info(T); /* update history information used on pseudocost branching */ if (T->pcost != NULL) ios_pcost_update(T); /* it's time to perform branching */ xassert(T->br_var == 0); xassert(T->br_sel == 0); /* let the application program choose variable to branch on */ if (T->parm->cb_func != NULL) { xassert(T->reason == 0); xassert(T->br_var == 0); xassert(T->br_sel == 0); T->reason = GLP_IBRANCH; T->parm->cb_func(T, T->parm->cb_info); T->reason = 0; if (T->stop) { ret = GLP_ESTOP; goto done; } } /* if nothing has been chosen, choose some variable as specified by the branching technique option */ if (T->br_var == 0) T->br_var = ios_choose_var(T, &T->br_sel); /* perform actual branching */ curr_p = T->curr->p; ret = branch_on(T, T->br_var, T->br_sel); T->br_var = T->br_sel = 0; if (ret == 0) { /* both branches have been created */ pred_p = curr_p; goto loop; } else if (ret == 1) { /* one branch is hopeless and has been pruned, so now the current subproblem is other branch */ /* the current subproblem should be considered as a new one, since one bound of the branching variable was changed */ T->curr->solved = T->curr->changed = 0; goto more; } else if (ret == 2) { /* both branches are hopeless and have been pruned; new subproblem selection is needed to continue the search */ goto fath; } else xassert(ret != ret); fath: /* the current subproblem has been fathomed */ if (T->parm->msg_lev >= GLP_MSG_DBG) xprintf("Node %d fathomed\n", p); /* freeze the current subproblem */ ios_freeze_node(T); /* and prune the corresponding branch of the tree */ ios_delete_node(T, p); /* if a new integer feasible solution has just been found, other branches may become hopeless and therefore must be pruned */ if (T->mip->mip_stat == GLP_FEAS) cleanup_the_tree(T); /* new subproblem selection is needed due to backtracking */ pred_p = 0; goto loop; done: /* display progress of the search on exit from the solver */ if (T->parm->msg_lev >= GLP_MSG_ON) show_progress(T, 0); if (T->mir_gen != NULL) ios_mir_term(T->mir_gen), T->mir_gen = NULL; if (T->clq_gen != NULL) ios_clq_term(T->clq_gen), T->clq_gen = NULL; /* return to the calling program */ return ret; }
int lpx_intopt(LPX *_mip) { IPP *ipp = NULL; LPX *orig = _mip, *prob = NULL; int orig_m, orig_n, i, j, ret, i_stat; /* the problem must be of MIP class */ if (lpx_get_class(orig) != LPX_MIP) { print("lpx_intopt: problem is not of MIP class"); ret = LPX_E_FAULT; goto done; } /* the problem must have at least one row and one column */ orig_m = lpx_get_num_rows(orig); orig_n = lpx_get_num_cols(orig); if (!(orig_m > 0 && orig_n > 0)) { print("lpx_intopt: problem has no rows/columns"); ret = LPX_E_FAULT; goto done; } /* check that each double-bounded row and column has bounds */ for (i = 1; i <= orig_m; i++) { if (lpx_get_row_type(orig, i) == LPX_DB) { if (lpx_get_row_lb(orig, i) >= lpx_get_row_ub(orig, i)) { print("lpx_intopt: row %d has incorrect bounds", i); ret = LPX_E_FAULT; goto done; } } } for (j = 1; j <= orig_n; j++) { if (lpx_get_col_type(orig, j) == LPX_DB) { if (lpx_get_col_lb(orig, j) >= lpx_get_col_ub(orig, j)) { print("lpx_intopt: column %d has incorrect bounds", j); ret = LPX_E_FAULT; goto done; } } } /* bounds of all integer variables must be integral */ for (j = 1; j <= orig_n; j++) { int type; double lb, ub; if (lpx_get_col_kind(orig, j) != LPX_IV) continue; type = lpx_get_col_type(orig, j); if (type == LPX_LO || type == LPX_DB || type == LPX_FX) { lb = lpx_get_col_lb(orig, j); if (lb != floor(lb)) { print("lpx_intopt: integer column %d has non-integer low" "er bound or fixed value %g", j, lb); ret = LPX_E_FAULT; goto done; } } if (type == LPX_UP || type == LPX_DB) { ub = lpx_get_col_ub(orig, j); if (ub != floor(ub)) { print("lpx_intopt: integer column %d has non-integer upp" "er bound %g", j, ub); ret = LPX_E_FAULT; goto done; } } } /* reset the status of MIP solution */ lpx_put_mip_soln(orig, LPX_I_UNDEF, NULL, NULL); /* create MIP presolver workspace */ ipp = ipp_create_wksp(); /* load the original problem into the presolver workspace */ ipp_load_orig(ipp, orig); /* perform basic MIP presolve analysis */ switch (ipp_basic_tech(ipp)) { case 0: /* no infeasibility is detected */ break; case 1: nopfs: /* primal infeasibility is detected */ print("PROBLEM HAS NO PRIMAL FEASIBLE SOLUTION"); ret = LPX_E_NOPFS; goto done; case 2: /* dual infeasibility is detected */ nodfs: print("LP RELAXATION HAS NO DUAL FEASIBLE SOLUTION"); ret = LPX_E_NODFS; goto done; default: insist(ipp != ipp); } /* reduce column bounds */ switch (ipp_reduce_bnds(ipp)) { case 0: break; case 1: goto nopfs; default: insist(ipp != ipp); } /* perform basic MIP presolve analysis */ switch (ipp_basic_tech(ipp)) { case 0: break; case 1: goto nopfs; case 2: goto nodfs; default: insist(ipp != ipp); } /* replace general integer variables by sum of binary variables, if required */ if (lpx_get_int_parm(orig, LPX_K_BINARIZE)) ipp_binarize(ipp); /* perform coefficient reduction */ ipp_reduction(ipp); /* if the resultant problem is empty, it has an empty solution, which is optimal */ if (ipp->row_ptr == NULL || ipp->col_ptr == NULL) { insist(ipp->row_ptr == NULL); insist(ipp->col_ptr == NULL); print("Objective value = %.10g", ipp->orig_dir == LPX_MIN ? +ipp->c0 : -ipp->c0); print("INTEGER OPTIMAL SOLUTION FOUND BY MIP PRESOLVER"); /* allocate recovered solution segment */ ipp->col_stat = ucalloc(1+ipp->ncols, sizeof(int)); ipp->col_mipx = ucalloc(1+ipp->ncols, sizeof(double)); for (j = 1; j <= ipp->ncols; j++) ipp->col_stat[j] = 0; /* perform MIP postsolve processing */ ipp_postsolve(ipp); /* unload recovered MIP solution and store it in the original problem object */ ipp_unload_sol(ipp, orig, LPX_I_OPT); ret = LPX_E_OK; goto done; } /* build resultant MIP problem object */ prob = ipp_build_prob(ipp); /* display some statistics */ { int m = lpx_get_num_rows(prob); int n = lpx_get_num_cols(prob); int nnz = lpx_get_num_nz(prob); int ni = lpx_get_num_int(prob); int nb = lpx_get_num_bin(prob); char s[50]; print("lpx_intopt: presolved MIP has %d row%s, %d column%s, %d" " non-zero%s", m, m == 1 ? "" : "s", n, n == 1 ? "" : "s", nnz, nnz == 1 ? "" : "s"); if (nb == 0) strcpy(s, "none of"); else if (ni == 1 && nb == 1) strcpy(s, ""); else if (nb == 1) strcpy(s, "one of"); else if (nb == ni) strcpy(s, "all of"); else sprintf(s, "%d of", nb); print("lpx_intopt: %d integer column%s, %s which %s binary", ni, ni == 1 ? "" : "s", s, nb == 1 ? "is" : "are"); } /* inherit some control parameters and statistics */ lpx_set_int_parm(prob, LPX_K_PRICE, lpx_get_int_parm(orig, LPX_K_PRICE)); lpx_set_real_parm(prob, LPX_K_RELAX, lpx_get_real_parm(orig, LPX_K_RELAX)); lpx_set_real_parm(prob, LPX_K_TOLBND, lpx_get_real_parm(orig, LPX_K_TOLBND)); lpx_set_real_parm(prob, LPX_K_TOLDJ, lpx_get_real_parm(orig, LPX_K_TOLDJ)); lpx_set_real_parm(prob, LPX_K_TOLPIV, lpx_get_real_parm(orig, LPX_K_TOLPIV)); lpx_set_int_parm(prob, LPX_K_ITLIM, lpx_get_int_parm(orig, LPX_K_ITLIM)); lpx_set_int_parm(prob, LPX_K_ITCNT, lpx_get_int_parm(orig, LPX_K_ITCNT)); lpx_set_real_parm(prob, LPX_K_TMLIM, lpx_get_real_parm(orig, LPX_K_TMLIM)); lpx_set_int_parm(prob, LPX_K_BRANCH, lpx_get_int_parm(orig, LPX_K_BRANCH)); lpx_set_int_parm(prob, LPX_K_BTRACK, lpx_get_int_parm(orig, LPX_K_BTRACK)); lpx_set_real_parm(prob, LPX_K_TOLINT, lpx_get_real_parm(orig, LPX_K_TOLINT)); lpx_set_real_parm(prob, LPX_K_TOLOBJ, lpx_get_real_parm(orig, LPX_K_TOLOBJ)); /* build an advanced initial basis */ lpx_adv_basis(prob); /* solve LP relaxation */ print("Solving LP relaxation..."); switch (lpx_simplex(prob)) { case LPX_E_OK: break; case LPX_E_ITLIM: ret = LPX_E_ITLIM; goto done; case LPX_E_TMLIM: ret = LPX_E_TMLIM; goto done; default: print("lpx_intopt: cannot solve LP relaxation"); ret = LPX_E_SING; goto done; } /* analyze status of the basic solution */ switch (lpx_get_status(prob)) { case LPX_OPT: break; case LPX_NOFEAS: ret = LPX_E_NOPFS; goto done; case LPX_UNBND: ret = LPX_E_NODFS; goto done; default: insist(prob != prob); } /* generate cutting planes, if necessary */ if (lpx_get_int_parm(orig, LPX_K_USECUTS)) { ret = generate_cuts(prob); if (ret != LPX_E_OK) goto done; } /* call the branch-and-bound solver */ ret = lpx_integer(prob); /* determine status of MIP solution */ i_stat = lpx_mip_status(prob); if (i_stat == LPX_I_OPT || i_stat == LPX_I_FEAS) { /* load MIP solution of the resultant problem into presolver workspace */ ipp_load_sol(ipp, prob); /* perform MIP postsolve processing */ ipp_postsolve(ipp); /* unload recovered MIP solution and store it in the original problem object */ ipp_unload_sol(ipp, orig, i_stat); } else { /* just set the status of MIP solution */ lpx_put_mip_soln(orig, i_stat, NULL, NULL); } done: /* copy back statistics about spent resources */ if (prob != NULL) { lpx_set_int_parm(orig, LPX_K_ITLIM, lpx_get_int_parm(prob, LPX_K_ITLIM)); lpx_set_int_parm(orig, LPX_K_ITCNT, lpx_get_int_parm(prob, LPX_K_ITCNT)); lpx_set_real_parm(orig, LPX_K_TMLIM, lpx_get_real_parm(prob, LPX_K_TMLIM)); } /* delete the resultant problem object */ if (prob != NULL) lpx_delete_prob(prob); /* delete MIP presolver workspace */ if (ipp != NULL) ipp_delete_wksp(ipp); return ret; }