The user interface and performance of commercial mixed integer programming software

Summary Today's mixed integer programming software packages are still not sophisticated enough to be treated as black boxes. Their efficiency can be augmented considerably by a deep knowledge of their functioning and the degrees of freedom they offer to the user. This paper describes at first the choices of the underlying branch and bound method in seven representative MIP-systems and demonstrates their usage, their profitability and their catches at illustrative examples. An account follows of the procedures and administrative facilities of commercial MIP-modules as far as they are submitted to user influence. An outlook is given on future developments, which can further improve the acceptance and the performance of MIP-software. Finally, some effort assessment criteria are proposed, which help judging the amount of work ahead before and at different stages during the solution process.

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Zusammenfassung Heute verfügbare Softwarepakete der gemischt-ganzzahligen Programmierung sind noch nicht fortgeschritten genug, um als Black Boxes behandelt zu werden. Ihre Effizienz kann durch eine gründliche Kenntnis ihrer Funktionsweise und der dem Benutzer angebotenen Freiheitsgrade beträchtlich gesteigert werden. Diese Veröffentlichung beschreibt zuerst die Auswahlmöglichkeiten der zugrundeliegenden Branch und Bound Methode in sieben repräsentativen MIP-Systemen und demonstriert anhand illustrativer Beispiele deren Anwendung, deren Nutzen und deren Fußangeln. Im Anschluß werden Proceduren und administrative Funktionen in kommerziellen MIP-Modulen, soweit sie dem Benutzereinfluß unterliegen, dargestellt. Ein Ausblick auf zukünftige Entwicklungen zeigt, wie sich Akzeptanz und Leistungvon MIP-Software steigern können. Schließlich werden einige Kriterien zur Aufwandsabschätzung vor und in verschiedenen Stadien während des Lösungsprozesses vorgeschlagen.

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List of Symbols c vector of objective function coefficients of continuous variables - C matrix of coefficients of continuous variables - d vector of objective function coefficients of integer variables - D matrix of coefficients of integer variables - d ₁ distance betweenF _as and X ₀ ^* - d ₂ distance betweenF _as andF _bk - d _j ^– estimated functional value degradation when lowering the value ofy _j by one unit - d _j ⁺ estimated functional value degradation when rising the value ofy _j by one unit - E _k estimation of best functional value of any integer solution contained in waiting nodek - F _as aspiration level; nodes with functional value worse thanF _as are postponed - F _ase aspiration level; nodes with estimationE _k worse thanF _ase are postponed - F _bI functional value of best integer solution known so far - F _bk best functional value of all waiting nodes - F _IT0 functional value of integer optimum - F _k functional value of waiting nodek - F ₀ functional value of continuous optimum - M big positiv real number - p maximum percentage deviation ofF _ITO fromF _bI - skj successor nodej - u distance by whichX ₀ ^* is lower thanF _bI - X ₀ ^* cutoff value; nodes with functional value beyondX ₀ ^* are finally discarded - x vector of integer variables - y vector of integer variables - y _j integer variablej - y _j ^(k) value of integer variablej at nodek - w _j associated weight of integer variabley _j in a Special Ordered Set - ¯w average weight of a Special Ordered Set - [ ] greatest integer smaller than or equal to the argument     

Electrodeposition of copper into high aspect ratio PCB micro-via using megasonic agitation

This paper presents the use of micro-particle imaging velocimetry (micro-PIV) to analyse fluid flow and hence ion replenishment in PCB micro-via during the electroplating process. The cross section of a PCB via is fabricated in PMMA to allow optical access to the sample. Fluid flow within two 1:1 aspect ratio blind micro-vias, one with straight side walls and the other with tapered side walls were compared. Flow is also analysed in a 1:1 aspect ratio through via. Flow rates measured using micro-PIV are used to validate simulated flow models. The results show that there are increased flow rates within the blind via with tapered side walls. This goes some way to explaining the improved electroplating results obtained in industry when tapered vias are used. Initial experimental results using megasonic streaming to remove bubbles from blind micro-via and promote ion transportation within high aspect ratio PCB micro-via to enhance electrodeposition are also reported.     

Treatment with a nonsteroidal antiinflammatory drug after calving did not improve milk production,health, or reproduction parameters in pasture-grazed dairy cows

Previous research results have indicated an increase in pregnancy rate in pasture-grazed cows treated with a nonsteroidal antiinflammatory drug (NSAID) 3 to 4 wk postcalving, when a high proportion of nucleated cells from within the uterus were polymorphonucleated; however, no effect on milk production was detected. It was hypothesized that this lack of effect on milk production was because the administration of the NSAID was too late after calving. The aims of the current study were to evaluate the timing of administering a propionic acid-derived NSAID (i.e., carprofen) on milk production, metabolic status, uterine health, and reproductive performance. Six-hundred and thirty-nine cows (134 primiparous and 505 multiparous) calving between July 4 and September 5, 2012, in 2 herds (herd 1: n = 228; herd 2: n = 411) were enrolled. Using a randomized block design, cows were allocated to 1 of 3 treatment groups as they calved: (1) no treatment (control; n = 221), (2) NSAID administered on d 1, 3, and 5 postcalving (early; n = 214), and (3) NSAID administered on d 19, 21, and 23 postcalving (late; n = 204). Milk production and composition, and body condition were determined weekly. Blood was sampled at 4 time points (1 precalving and 3 postcalving) to determine the effects of treatment on indicators of metabolic health and energy status. Uterine health was determined by measuring the proportion of nucleated cells that were polymorphonucleated following cytobrush sampling of the uterus between d 13 to 24 and d 30 to 49 postcalving. Irrespective of timing of application, NSAID did not affect milk production, body weight, or body condition during early lactation. Treatment with an NSAID 19 to 23 d postcalving increased the proportion of cows submitted for breeding during the first 3 wk of the seasonal breeding program (control: 85%, early: 83%, and late: 92%), but did not affect conception or pregnancy rates. No detectable effect of treatment on uterine health or circulating metabolites and minerals existed, although cows in the early NSAID treatment group had marginally lower serum β-hydroxybutyrate concentrations (0.1 mmol/L) than the other groups between 2 and 26 d in milk. In conclusion, administration of this particular NSAID at either 1 or 3 wk after calving did not improve milk production, indicators of health, or reproductive performance.     

Influence of Disorder on Superconducting Correlations in Nanoparticles

We investigate how the interplay of quantum confinement and level broadening caused by disorder affects superconducting correlations in ultra-small metallic grains. We use the electron-phonon interaction-induced electron mass renormalization and the reduced static-path approximation of the BCS formalism to calculate the critical temperature as a function of the grain size. We show how the strong electron-impurity scattering additionally smears the peak structure in the electronic density of states of a metallic grain and imposes additional limits on the critical temperature under strong quantum confinement.     

Ultra-high performance concrete and fiber reinforced concrete: achieving strength and ductility without heat curing

Ultra-high performance concrete (UHPC) and ultra-high performance fiber reinforced concrete (UHP-FRC) were introduced in the mid 1990s. Special treatment, such as heat curing, pressure and/or extensive vibration, is often required in order to achieve compressive strengths in excess of 150 MPa (22 ksi). This study focuses on the development of UHP-FRCs without any special treatment and utilizing materials that are commercially available on the US market. Enhanced performance was accomplished by optimizing the packing density of the cementitious matrix, using very high strength steel fibers, tailoring the geometry of the fibers and optimizing the matrix-fiber interface properties. It is shown that addition of 1.5% deformed fibers by volume results in a direct tensile strength of 13 MPa, which is 60% higher than comparable UHP-FRC with smooth steel fibers, and a tensile strain at peak stress of 0.6%, which is about three times that for UHP-FRC with smooth fibers. Compressive strength up to 292 MPa (42 ksi), tensile strength up to 37 MPa (5.4 ksi) and strain at peak stress up to 1.1% were also attained 28 days after casting by using up to 8% volume fraction of high strength steel fibers and infiltrating them with the UHPC matrix.     

Improved process control of an industrial sludge centrifuge-dryer installation through binary logistic regression modeling of the fouling issues

Biological wastewater treatment generates huge amounts of waste sludge which need to be dewatered and eventually dried to minimize transportation and incineration costs. A characteristic feature of sludge in this context is that it turns into a sticky substance during its drying process inducing fouling problems in the drying installation. At the wastewater treatment plant of Monsanto in Antwerp, Belgium, one enclosed centrifuge-dryer system is used to dry the sludge. In the past, this installation had to be shut down regularly due to dryer fouling problems. To avoid these operational problems, a binary logistic regression analysis is presented in this research based on a 5-year database, resulting in an empirical model for the evaluation of the dryer fouling risk as a function of the sludge feed characteristics. The model inputs are the sludge volume index (SVI) and the dosing of clay additive and tertiary (flotation) sludge, the latter containing polyaluminumchloride (PACl), to the sludge feed of this particular system.By exploiting the knowledge captured by this model, the derived control strategy is based on the value of the SVI. Whenever the SVI is high the original high clay dosing to the feed needs to be maintained. At moderate SVI values, implying an intrinsically better sludge dewaterability, the strategy dictates a reduction in the clay dosing to the sludge feed to have a reduced sludge solids dryness after dewatering, thereby avoiding that the sludge exhibits its most sticky phase when passing the most fouling sensitive part of the dryer. When the SVI is lower than 50 mL/g the control strategy states that conditioning of the sludge with PACl is required to mask the stickiness instead of postponing it, avoiding that the stickiness of the sludge already hampers the dewatering stage of the process.     

A new thickness parameterization for Discrete Material and Thickness Optimization

In this work, a new thickness parameterization which allows for internal ply-drops without intermediate voids is introduced in the Discrete Material and Thickness Optimization (DMTO) method. With the original DMTO formulation, material had to be removed from the top in order to prevent non-physical intermediate voids in the structure. The new thickness formulation relies on a relation between density variables and ply-thicknesses rather than constitutive properties. This new formulation allows internal ply-drops which is essential for composite structures as it is common practice to cover dropped plies as to avoid delaminations. Furthermore, it is demonstrated how the new thickness formulation in some cases improves the convergence characteristics. Finally, it is also shown how solid-shell elements can be utilized within the DMTO method for structural optimization of tapered laminated composite structures.     

Scattering of Dirac electrons by a random array of magnetic flux tubes

The scattering of two-dimensional (2D) massless electrons as presented in graphene in the presence of a random array of circular magnetic flux tubes is investigated. The momentum relaxation time and the Hall factor are obtained using optical theorem techniques for scattering. Electrons with energy close to those of the Landau levels of the flux tubes exhibit resonant scattering and have a long life-time to reside inside the magnetic flux tube. These resonances appear as sharp structures in the Hall factor and the magneto-resistance.     

Lattice damage and secondary phase formation in Yttria stabilised zirconia implanted with Fe at different temperatures

In this paper we report on the lattice damage and nanocrystalline secondary phase formation in Fe implanted Yttria stabilised zirconia (YSZ) up to a peak concentration of 10%. The implantation temperature has been varied between room temperature and 1000 °C. Samples were characterized using Rutherford backscattering/channeling and X-ray diffraction. We observed that (1) YSZ remains partially crystalline even after Fe implantation at room temperature and the lattice damage can be partially recovered if implantation is performed at elevated temperatures; (2) crystalline bcc-Fe nanoparticles have formed and grown with increasing implantation temperature. The nanoscale Fe precipitates and the YSZ matrix have a crystallographic orientation relationship.