Recovering Beam Search: Enhancing the Beam Search Approach for Combinatorial Optimization Problems

A hybrid heuristic method for combinatorial optimization problems is proposed that combines different classical techniques such as tree search procedures, bounding schemes and local search. The proposed method enhances the classic beam search approach by applying to each partial solution corresponding to a node selected by the beam, a further test that checks whether the current partial solution is dominated by another partial solution at the same level of the search tree. If this is the case, the latter solution becomes the new current partial solution. This step allows to partially recover from previous wrong decisions of the beam search procedure and can be seen as a local search step on the partial solution. We present here the application to two well known combinatorial optimization problems: the two-machine total completion time flow shop scheduling problem and the uncapacitated p-median location problem. In both cases the method strongly improves the performances with respect to the basic beam search approach and is competitive with the state of the art heuristics.     

Combining Swaps and Node Weights in an Adaptive Greedy Approach for the Maximum Clique Problem

In this work, the NP-hard maximum clique problem on graphs is considered. Starting from basic greedy heuristics, modifications and improvements are proposed and combined in a two-phase heuristic procedure. In the first phase an improved greedy procedure is applied starting from each node of the graph; on the basis of the results of this phase a reduced subset of nodes is selected and an adaptive greedy algorithm is repeatedly started to build cliques around such nodes. In each restart the selection of nodes is biased by the maximal clique generated in the previous execution. Computational results are reported on the DIMACS benchmarks suite. Remarkably, the two-phase procedure successfully solves the difficult Brockington-Culberson instances, and is generally competitive with state-of-the-art much more complex heuristics.     

Biomagnetic measurements utilising a superparamagnetic marker: a feasibility study

Summary A preliminary study is here reported on a new potential marker for biomagnetic measurements. The marker consists of superparamagnetic polymer microspheres which were detected in the presence of external steady magnetic fields by means of an r.f.-SQUID magnetometer. The particles were prepared in samples differing in the concentration value and immersed in a homogeneous magnetic field of variable intensity. A simple model was taken into account for the distribution of the microspheres in the samples, so that the theoretical values were compared to the marker field values measured by the biomagnetic sensor. The overall sensitivity of the experimental apparatus and the minimum concentration value of the marker were then estimated.     

Weighted approximation of functions on the real line by Bernstein polynomials

The authors give error estimates, a Voronovskaya-type relation, strong converse results and saturation for the weighted approximation of functions on the real line with Freud weights by Bernstein-type operators.     

R.F. (280 MHz) EPR imaging of extended samples: Apparatus and preliminary results

This paper presents the preliminary results obtained using an Electron Paramagnetic Resonance imaging apparatus operating at 280 MHz. The acquisition technique and the procedure used to obtain the spin density spatial localization are presented and specimen images of extended samples are given. The accuracy of the images and the spatial resolution are also discussed.     

Cyano-bridged CuII-MV (M = Mo, W) bimetallic layered complexes exhibiting novel honeycomblike structures

Self-assembly of a new precursor [Cu(L)](ClO4)2 (1) (L = macrocyclic ligand) with octacyanometalates [M(CN)8]3- (M = Mo, W) produced two-dimensional cyano-bridged Cu(II)-M(V) bimetallic assemblies [Cu(L)]3n[M(CN)8]2n.6nH2O [M = Mo (2), W (3)] with novel honeycomblike structures, characterized by spectroscopic data, single-crystal X-ray diffraction studies, and magnetic measurements. The crystallographic determination reveals that compounds 2 and 3 are isostructural and crystallize in the triclinic system (P). The Cu atom in a distorted octahedral environment experiences a tetragonal elongation of apical nitrogen atoms exhibiting average Cu-Nax lengths of 2.566 Angstroms for 2 and 2.593 Angstroms for 3, which accounts for the Jahn-Teller effect of a Cu(II) ion. The Cu-NC angles are magnetically important, ranging from 135.7 to 159.2 degrees. Three types of L in the crystal lattice are observed, which are dependent on the relative positions of the pendant hydroxyl groups with respect to the CuN4 basal plane. The positions are correlated with hydrogen bonding of OH groups to neighboring atoms. The magnetic data indicate that ferromagnetic and antiferromagnetic interactions between Cu(II) and M(V) through the CN linkage coexist.     

Parallel transport in the determinant line bundle: The non-zero index case

For a product family of Weyl operators of possibly non-zero index on a compact manifoldX, we express parallel transport in the determinant line bundle in terms of the spectral asymmetry of a Dirac operator on ×X. This generalizes the results of [7], where we dealt only with invertible operators.Supported in part by NSF Grant No. PHY 8605978 and the Robert A. Welch FoundationSupported in part by NSF Grant No. PHY 8215249     

Nickel-Ruthenium Mixed-Metal Carbonyl Clusters Syntheses and Solid State Structures of the Two Tetrahedral Clusters [PPh4][NiRu3(μ3 H)(CO)9(μ-CO)3] and [NEt4]2[NiRu3(CO)8(μ-CO)4]

Redox condensation of [Ru₃H(CO)₁₁]- with Ni(CO)₄, in tetrahydrofuran solution, under a nitrogen atmosphere, yields the tetranuclear anion [NiRu_H(CO)₁₁)-. Subsequent deprotonation with Bu'OK in acetonitrile solution leads to the formation of the related dianion. Both anions have been characterized by spectroscopic techniques, elemental analysis and single crystal X-ray diffraction. [PPh₄][NiRu₃H(CO)₁₂] crystallizes in the triclinic space group PI with unit cell dimensionsof a = 11.842(2) Å,b = 12.335(3) Å, c = 13.3080) Å,a = 91.89(2)°, = 93.35(1)°,y = 96.41(2)°, Z = 2, V= 1926.9(7) Å'. The NiRu₃, metal core of the molecule defines a distorted tetrahedron with nine terminal and three edge bridging carbonyl groups. The hydrido ligand was located by difference Fourier techniques and was found to bridge the NiRu₂ basal triangle at a distance of 0.88(6) A from this plane. Selected average distances and angles are: Ru-Ru = 2.839 Å, Ru-Ni = 2.640 Å, Ru-C, = 1.910 A,Ru-C _b = 2.084 Å, Ni-C _b = 2.022 Å, Ru-H = 1.77 Å, C-0, = 1.135 Å, C-O _b = 1.159 Å, M-C-O, = 176.3°,M-C--O _b = 139.3°;other distances are: Ni-C₁ = l.758(7) Å, Ni-H= 1.85(7) Å. [NEt₄]₂[NiRu₃(CO)₁₂] crystallizes in the orthorhombic space group Pnma (no. 62) with unit cell dimensions ofa=20.247(5) Å,b = 15.038(4)Å,c = 12.079(3) Å, Z=4, V=3678(2) A'. The molecule contains a tetrahedral NiRu₃ core with eight terminal and four edge bridging carbon monoxide groups which bridge the three Ni-Ru and one Ru-Ru bond. Average distances and angles are: Ru -Ru =2.3050A Ru-Ni 2.648 Å, Ru-C _t = 1.878 Å, Ru-C _b 2.045 Å, Ni-C _b = 2.055 Å, C-O _t = 1.145 Å, C-01,=1.157 Å, M-C-O,= 176.9°, M-C-O _b = 138.6°; other distance is: Ni-C _t = 1.754(10) Å,t = terminal,b = bridging.