A library of local search heuristics for the vehicle routing problem

The vehicle routing problem (VRP) is a difficult and well-studied combinatorial optimization problem. Real-world instances of the VRP can contain hundreds and even thousands of customer locations and can involve many complicating constraints, necessitating the use of heuristic methods. We present a software library of local search heuristics that allows one to quickly generate solutions to VRP instances. The code has a logical, object-oriented design and uses efficient data structures to store and modify solutions. The core of the library is the implementation of seven local search operators that share a similar interface and are designed to be extended to handle additional options with minimal code change. The code is well-documented, straightforward to compile, and is freely available online. The code contains several applications that can be used to generate solutions to the capacitated VRP. Computational results indicate that these applications are able to generate solutions that are within about one percent of the best-known solution on benchmark problems.     

On the complexity of instationary gas flows

We study a simplistic model of instationary gas flows consisting of a sequence of $k$ stationary gas flows. We present efficiently solvable cases and NP-hardness results, establishing complexity gaps between stationary and instationary gas flows (already for $k=2$) as well as between instationary gas $s$-$t$-flows and instationary gas $b$-flows.     

Methylcobaltverbindungen mit nicht chelatisierenden Liganden,IV. Monoolefinkomplexe

Methylcobalt Compounds with Non-chelating Ligands, IV. Monoolefin Complexes Tris(trimethylphosphane)cobalt(I) halides in ether solvents saturated with olefin at low temperatures from monoolefin complexes which are prone to dissociation. Upon reaction with methyl-or phenyllithium more stable compounds are formed of the composition CoR(CC)L₃ ( 1 – 4 ) (R  CH₃; CC  C₂H₄, C₃H₆, cyclo-C₅H₈; R  C₆H₅; CC  C₂H₄; L  P(CH₃)₃). In solution the fluctional molecules adopt a ground state structure containing a σ-bonded group and an olefin ligand in adjacent positions (trigonal-bipyramidal: CH₃ axial and C₂H₄ equatorial or C₆H₅ and C₂H₄ equatorial). The latter arrangement is confirmed for the crystalline state by an X-ray structure determination of (ethene)phenyltris(trimethylphosphane)cobalt ( 4 ). An equatorial plane of coordination along a Co P bond not only contains both ethene-C atoms but also all the atoms of the phenyl group. The compound is thermally decomposed to give biphenyl and (ethene)tris-(trimethylphosphane)cobalt(0). No products of an olefin insertion reaction are observed.     

pH-sensitive paramagnetic liposomes for MRI: assessment of stability in blood

The pH-dependent stability of dipalmitoyl phosphatidyl ethanolamine/palmitic acid (DPPE/PA) liposomal GdDTPA-BMA was investigated in human blood and after exposure to selected blood components. Relaxometry, visual observations and cryo-transmission electron microscopy (cryo-TEM) were employed for the assessment of stability. The liposomes were stable in buffer at physiological pH and the T(1)-relaxivity (r(1)) of the system was significantly lowered compared to that of non-liposomal GdDTPA-BMA, which could be explained by an exchange limited relaxation process. Lowering the pH, however, gave a marked increase in r(1), due to liposome aggregation and subsequent leakage of GdDTPA-BMA. After a few minutes incubation in human blood the liposomes were destabilised and leaky at both high and low pH, and blood components likely to cause the instability were studied. Physiological level of Na(+) (150 mM) did not affect the relaxometric behavior of the liposomes at pH 7.4, but shifted the pH-r(1) profile laterally to higher pH-values compared to a level of 50 mM Na(+). Increased screening of the surface charges and, concomitantly, a lowering of the energy-barrier against aggregation is a plausible explanation for this phenomenon. In contrast, both Ca(2+) and Mg(2+) (physiological level, both 2 mM) caused massive aggregation of the liposomes and leakage of contents, and were therefore much more detrimental to the stability of the liposomes than a physiological level of Na(+). This could be due to the higher screening ability of divalent cations, but aggregation could also be induced through an inter-liposomal "bridging" effect. Physiological level of both Na(+) and Ca(2+) caused less leakage than for lower Na(+) concentration (50 mM Na(+) and 2 mM Ca(2+)), probably due to competition for the negative surface charges. Albumin also destabilised the liposomes, and it was shown to be due to an interaction between albumin and PA in the liposomal membrane.     

SCF-SW-Xα Calculations on molybdenum—halogen cluster compounds

The electronic structures of the cluster cations Mo₆ X⁴⁺₈ (X = F, Cl, Br, I) have been calculated using the SCF—SW—Xα method. The eigenvalue spectra obtained are discussed and compared with results of other quantum-chemical studies of such systems. The results of population analysis are used to discuss the charge distribution in the clusters studied. A qualitative discussion of the Mo-Mo and Mo-X bond strengths is also presented. Finally, calculated bond energies are compared with adsorption energies.