### Table 2 Problems to solve and a solution for each within the proposed framework

"... In PAGE 7: ... However, the above mentioned co- evolutionary theme would be most effective if we keep this very ordering in the levels or at least let the innermost level stay where it is as it makes more sense to have a hybrid set of predictors and then let the subsets compete with each other than to enforce competition without having a mix. Essentially, there is a range of problems the framework tries to solve and these are enumerated in Table2 together with the ways these have been addressed. help traverse the search space and we have borrowed the idea of negative correlation in the formulation of our multi-objective problem as well.... ..."

### Table 3: The number of PCG iterations during the interior point method iterations.

2007

"... In PAGE 20: ... For one problem, chr22b, using the mixed approach leads to significantly fewer IPM iterations being required. In order to give an insight into the behaviour of the preconditioned conjugate gradients, in Table3 we report the number of PCG iterations needed to solve a particular linear system. First, we report separately this number for the last interior point iteration when our preconditioner is supposed to behave best.... ..."

### Table 3: The number of PCG iterations during the interior point method iterations.

2006

"... In PAGE 20: ... For one problem, chr22b, using the mixed approach leads to signi cantly fewer IPM iterations being required. In order to give an insight into the behaviour of the preconditioned conjugate gradients, in Table3 we report the number of PCG iterations needed to solve a particular linear system. First, we report separately this number for the last interior point iteration when our preconditioner is supposed to behave best.... ..."

### Table 2. Implementations obtained as Pareto-points in a single run of the Evolutionary Algorithm.

1997

"... In PAGE 5: ... The tness value directly gives the number of implementations that dominate an individual J. With a population size of N = 100, the Pareto-set found in a single optimization run after 200 generations is shown in Table2 and depicted in Fig. 7.... In PAGE 5: ...hown in Table 2 and depicted in Fig. 7. In general, there is no evidence that the Pareto-points obtained above are the true Pareto-points of the problem. Surprisingly, all points in Table2 turn out to be true Pareto-points of the problem. Fig.... ..."

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### Table 2. Implementations obtained as Pareto-points in a single run of the Evolutionary Algorithm.

1997

"... In PAGE 5: ... The tness value directly gives the number of implementations that dominate an individual J. With a population size of N = 100, the Pareto-set found in a single optimization run after 200 generations is shown in Table2 and depicted in Fig. 7.... In PAGE 5: ...hown in Table 2 and depicted in Fig. 7. In general, there is no evidence that the Pareto-points obtained above are the true Pareto-points of the problem. Surprisingly, all points in Table2 turn out to be true Pareto-points of the problem. Fig.... ..."

Cited by 32

### Table 5.13: Problems solved in different evolutionary algorithms Method Unimodal Basic Multimodal Expanded Hybrid Composition

2006

### TABLE 5. Efficiency on inductive inference problems: interior point and combinatorial approaches

1998

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### Table 3: SAT: Comparison of Simplex and interior point methods

"... In PAGE 9: ... Instances with up to 1000 variables and 32,000 clauses were solved. Compared with the Simplex Method approach on small problems #28 Table3 #29, speedups of over two orders of magnitude were observed. Furthermore, the in- terior point approachwas successful in proving satis#0Cabilityinover 250 instances that the Simplex Method approach failed.... ..."

### Table 3: E ciency of ACCPM. 7 Conclusions We have given in this paper a systematic discussion of the way of treating relaxed master program with an interior point algorithm. We have not imposed any condition on the decomposition scheme used (it may be either the \optimal point strategy quot; or the \central point strategy quot;). We have concentrated on the exploitation of the special structure of the relaxed master problem within a single iteration of any interior point method to make it the most e cient. The techniques presented in this paper have been incorporated into the implementation of the Analytic Center Cutting Plane Method. We have demonstrated its advantages when applying ACCPM to the solution of the large scale nonlinear multicommodity network ow problems. The use of the structure exploiting techniques presented in this paper has allowed us to solve signi cantly larger problems than [13]. Their sizes have been pushed from 1000 arcs and 5000 commodities in the old version to 5000 arcs and 10000 commodities, respectively in the new one.

1997

"... In PAGE 14: ...actorization would in such a case cost 13(5000)3 = 4:17 1010, i.e., it would be, roughly speaking, 10 times more expensive. Table3 collects data on the solution of our collection of large scale problems. We report in it: the number of outer iterations, NITER, the number of inner iterations, Newton, the total number of cuts (subgradients) added through the whole solution process, the number of shortest path type cuts and the CPU time (to reach a 6-digit accurate solution on a POWER PC computer).... In PAGE 14: ... We report in it: the number of outer iterations, NITER, the number of inner iterations, Newton, the total number of cuts (subgradients) added through the whole solution process, the number of shortest path type cuts and the CPU time (to reach a 6-digit accurate solution on a POWER PC computer). To give a bit of an insight into the ACCPM apos;s behavior, Table3 additionally reports the time spent in the factorizations of S (dominating term in the master), tF , and the time spent to solve subproblems, tS. The reader may note that the solution times for these problems are considerable.... ..."

Cited by 12

### Table 2: Number of function evaluations, number of CG iterations and CPU time for the new primal-dual interior point method (NITRO) and LANCELOT (LAN). A * indicates that the method did not meet the stopping test in 10,000 iterations.

1999

"... In PAGE 20: ... constraint types objective CORKSCRW 456 350 free, bounded, xed linear eq, nonlinear ineq nonlinear COSHFUN 61 20 free nonlinear ineq linear DIXCHLNV 100 50 bounded nonlinear eq nonlinear GAUSSELM 14 11 free, bounded, xed linear ineq, nonlinear eq linear HAGER4 2001 1000 free, bounded, xed linear eq nonlinear HIMMELBK 24 14 bounded linear eq, nonlinear eq linear NGONE 100 1273 bounded, xed linear ineq, nonlinear ineq nonlinear OBSTCLAE 1024 0 bounded, xed nonlinear OPTCNTRL 32 20 free, bounded, xed linear eq, nonlinear eq nonlinear OPTMASS 1210 1005 free, xed linear eq, nonlinear ineq nonlinear ORTHREGF 1205 400 free, bounded nonlinear eq nonlinear READING1 202 100 bounded, xed nonlinear eq nonlinear SVANBERG 500 500 bounded nonlinear ineq nonlinear TORSION1 484 0 bounded, xed nonlinear Table 1: The main test problem set. In Table2 we present the results for the primal-dual version of our new algorithm, NITRO. For comparison we also solved the problems with LANCELOT [16] using sec- ond derivatives and all its default settings.... In PAGE 20: ... The runs of NITRO were terminated when E(xk; sk; 0) 10?7, and LANCELOT was stopped when the projected gradient and con- straint violations were less than 10?7; the termination criteria for these two methods are therefore very similar. Since both algorithms use the conjugate gradient method to compute the step, we also report in Table2 the total number of CG iterations needed for conver- gence. All runs were performed on a Sparcstation 20 with 32 MG of main memory, using a FORTRAN 77 compiler and double precision; the CPU time reported is in seconds.... In PAGE 21: ...of NITRO reported in Table2 are highly encouraging, particularly the number of function... ..."

Cited by 61