Jens Viggo Clausen

Solving Large Quadratic Assignment Problems in Parallel

Quadratic Assignment problems are in practice among the mostdifficult to solve in the class of NP-complete problems. Theonly successful approach hitherto has been Branch-and-Bound-basedalgorithms, but such algorithms are crucially dependent on good boundfunctions to limit the size of the space searched. Much work hasbeen done to identify such functions for the QAP, but with limitedsuccess.Parallel processing has also been used in order to increase the sizeof problems solvable to optimality. The systems used have, however, oftenbeen systems with relatively few, but very powerful vector processors, andhave hence not been ideally suited for computations essentially involving non-vectorizable computations on integers.In this paper we investigate the combination of one of the best bound functions for a Branch-and-Bound algorithm (the Gilmore-Lawler bound) and various testing, variable binding and recalculation of bounds between branchings when used in aparallel Branch-and-Bound algorithm. The algorithm has been implemented on a 16-processor MEIKO Computing Surface with Intel i860processors. Computational results from the solution of a number of large QAPs, including the classical Nugent 20 are reported.

Solving Graph Bisection Problems with Semidefinite Programming

An exact solution method for the graph bisection problem is presented. We describe a branch-and-bound algorithm which is based on a cutting plane approach combining semidefinite programming and polyhedral relaxations. We report on extensive numerical experiments which were performed for various classes of graphs. The results indicate that the present approach solves general problem instances with 80--90 vertices exactly in reasonable time and provides tight approximations for larger instances. Our approach is particularly well suited for special classes of graphs as planar graphs and graphs based on grid structures.

A new standard: age and distance for the open cluster NGC 6791 from the eclipsing binary member V20

Context. We wish to determine accurate ages for open clusters and use this, in conjunction with colour-magnitude diagrams, to constrain models of stellar structure and evolution. Aims. The detached eclipsing binary V20 in the old, metal-rich ((Fe/H) =+ 0.40) open cluster NGC 6791 is studied in order to determine highly accurate masses and radii of its components. This allows the cluster age to be established with high precision, using isochrones in the mass-radius diagram. Methods. We employ high-resolution UVES spectroscopy of V20 to determine the spectroscopic orbit and time-series V,I photometry to obtain the photometric elements. Results. The masses and radii of the V20 components are found to be 1.074 ± 0.008 Mand 1.399 ± 0.016 R� (primary) and 0.827 ± 0.004 Mand 0.768 ± 0.006 R� (secondary). The primary is located almost exactly at the hottest point along the cluster isochrone, and the secondary is a ∼7 times fainter main-sequence star. We determine an apparent cluster distance-modulus of (m − M)V = 13.46 ± 0.10 (average of primary and secondary). The cluster age is obtained from comparisons with theoretical isochrones in the mass-radius diagram. Using the isochrones from Victoria-Regina with (Fe/H) =+ 0.37 we find 7.7 ± 0.5 Gyr, whereas the Yonsei-Yale (Y 2 ) isochrones lead to 8.2 ± 0.5 Gyr, and BaSTI isochrones to 9.0 ± 0.5 Gyr. In a mass-radius diagram, the 7.7 Gyr VRSS and 9.0 Gyr BaSTI isochrones overlap nearly perfectly despite the age-difference. This model dependence, which is significantly larger than the precision determined from mass, radius, and abundance uncertainties, prevents a definitive age-determination of the cluster. Conclusions. Using detached eclipsing binaries for determination of cluster ages, the dominant error is due to differences among stellar models and no longer to observational errors in cluster reddening and distance. By observing a suitable number of detached eclipsing binaries in several open clusters it should be possible to calibrate the age-scale and provide firm constraints which stellar models must reproduce.

New strong evidence for the importance of convective overshooting in intermediate-mass stars

Major differences between current series of stellar evolution calculations concern their opacities and treatment of convection. Accurate mass, radius, luminosity, and abundance data from eclipsing binaries now allow significant conclusions on these differences: binary stars with small convective cores are very well fitted by standard models using Los Alamos (but not Cox-Stewart) opacities. However, at just slightly larger masses, the moderately evolved binaries clearly require convective overshooting for a satisfactory fit. Precise radial velocities for F-type turnoff stars in IC 4651 and NGC 3680 not only confirm the signatures of overshooting observed in these clusters but also show that any such firm conclusions require proper identification of binaries and nonmembers. It is concluded that standard (and some overshooting) models are inconsistent with current precise data for intermediate-mass stars. Among the consequences of rejecting the older models, it is pointed out that ages for stars younger than roughly 4 Gyr will increase by up to 50-100 percent. 27 refs.

Age and Distance for the Old Open Cluster NGC 188 from the Eclipsing Binary Member V 12

We present time series radial velocity, and photometric observations of a solar-type double-lined eclipsing binary star (V 12) in the old open cluster NGC?188. We use these data to determine the spectroscopic orbit and the photometric elements for V 12. From our analysis, we determine accurate masses (Mp = 1.103 ? 0.007 M ?, Ms = 1.081 ? 0.007 M ?) and radii (Rp = 1.424 ? 0.019 R ?, Rs = 1.373 ? 0.019 R ?) for the primary (p) and secondary (s) binary components. We adopt a reddening of E B?V = 0.087 for NGC?188, and derive component effective temperatures of 5900 ? 100 K and 5875 ? 100 K, respectively, for the primary and secondary stars. From their absolute dimensions, the two components of V 12 yield identical distance moduli of V 0 ? MV = 1124 ? 009, corresponding to 1770 ? 75 pc. Both stars are near the end of their main-sequence evolutionary phase, and are located at the cluster turnoff in the color-magnitude diagram. We determine an age of 6.2 ? 0.2 Gyr for V 12 and NGC?188, from a comparison with theoretical isochrones in the mass-radius diagram. This age is independent of distance, reddening, and color-temperature transformations. We use isochrones from Victoria-Regina (VRSS) and Yonsei-Yale (Y 2) with [Fe/H] = ?0.1 and [Fe/H] = 0.0. From the solar metallicity isochrones, an age of 6.4 Gyr provides the best fit to the binary components for both sets of models. For the isochrones with [Fe/H] = ?0.1, ages of 6.0 Gyr and 5.9 Gyr provide the best fits for the (VRSS) and (Y 2) models, respectively. We use the distance and age estimates for V 12, together with best estimates for the metallicity and reddening of NGC?188, to investigate the locations of the corresponding VRSS and Y 2 isochrones relative to cluster members in the color-magnitude diagram. Plausible changes in the model metallicity and distance to better match the isochrones to the cluster sequences, result in a range of ages for NGC?188 that is more than 3 times that resulting from our analysis of V 12.

On the best search strategy in parallel branch‐and‐bound:Best‐First Search versus Lazy Depth‐First Search

The Best‐First Search strategy (BeFS) and the Depth‐First Search strategy (DFS) areregarded as the prime strategies when solving combinatorial optimization problems by parallelBranch‐and‐Bound (B&B) ‐ BeFS because of efficiency with respect to the number of nodesexplored, and DFS for reasons of space efficiency.We investigate the efficiency of both strategies experimentally, and two versions of eachstrategy are tested: In the first, a B&B iteration for a node consists of bounding followed bybranching on the node if necessary. For the second, the order is reversed ‐ first branchingtakes place, and then each child of the node is bounded and possibly fathomed. The first iscalled lazy, the second eager.The strategies are tested on the Quadratic Assignment Problem and the Job Shop SchedulingProblem. We use parallel codes developed specifically for the solution of the problem inquestion, and hence containing different heuristic rules and tests to speed up computation.In both cases, we start with an initial solution close to but not equal to the optimal solution.Surprisingly, the BeFS‐based strategies turn out to be inferior to the DFS‐based strategies,both in terms of running times and in terms of bound calculations performed. Furthermore,when tested in a sequential setting, DFS turns out to be still superior because pruning andevaluation tests are more effective in DFS due to the presence of better incumbents.

A dual framework for lower bounds of the quadratic assignment problem based on linearization

Abstract.A dual framework allowing the comparison of various bounds for the quadratic assignment problem (QAP) based on linearization, e.g. the bounds of Adams and Johnson, Carraresi and Malucelli, and Hahn and Grant, is presented. We discuss the differences of these bounds and propose a new and more general bounding procedure based on the dual of the linearization of Adams and Johnson. The new procedure has been applied to problems of dimension up to

Parallel branch-and-bound methods for thejob-shop scheduling problem

n=72

Implementation of parallel branch-and-bound algorithms – experiences with the graph partitioning problem

, and the computational results indicate that the new bound competes well with existing linearization bounds and yields a good trade off between computation time and bound quality.

Eclipsing binaries observed with the WIRE satellite - I. Discovery and photometric analysis of the new bright A0 IV eclipsing binary ψ Centauri

Job-Shop Scheduling (JSS) problems are among the more difficult to solve in the class of NP-complete problems. The only successful approach has been branch-and-bound based algorithms, but such algorithms depend heavily on good bound functions. Much work has been done to identify such functions for the JSS problem, but with limited success. Even with recent methods, it is still not possible to solve problems substantially larger than 10machines and 10 jobs. In the current study, we focus on parallel methods for solving JSS problems. We implement two different parallel branch-and-bound algorithms for JSS on a16-processor MEIKO Computing Surface with Intel i860 processors and perform extensive computational testing using classical publicly available benchmark problems. The parallel part of one of the implementations is based on a similar parallel code for Quadratic Assignment Problems. Results are reported for different branching rules proposed in the literature.