A recipe for finding good solutions to MINLPs

Finding good (or even just feasible) solutions for Mixed-Integer Nonlinear Programming problems independently of the specific problem structure is a very hard but practically important task, especially when the objective and/or the constraints are nonconvex. With this goal in mind, we present a general-purpose heuristic based on Variable Neighborhood Search, Local Branching, a local Nonlinear Programming algorithm and Branch-and-Bound. We test the proposed approach on MINLPLib, comparing with several existing heuristic and exact methods. An implementation of the proposed heuristic is freely available and can employ all NLP/MINLP solvers with an AMPL interface as the main search tools.     

Boundary crisis and transient in a dissipative relativistic standard map

Some dynamical properties for a problem concerning the acceleration of particles in a wave packet are studied. The model is described in terms of a two-dimensional nonlinear map obtained from a Hamiltonian which describes the motion of a relativistic standard map. The phase space is mixed in the sense that there are regular and chaotic regions coexisting. When dissipation is introduced, the property of area preservation is broken and attractors emerge. We have shown that a tiny increase of the dissipation causes a change in the phase space. A chaotic attractor as well as its basin of attraction are destroyed thereby leading the system to experience a boundary crisis. We have characterized such a boundary crisis via a collision of the chaotic attractor with the stable manifold of a saddle fixed point. Once the chaotic attractor is destroyed, a chaotic transient described by a power law with exponent −1 is observed.     

A heuristic algorithm based on multi-assignment procedures for nurse scheduling

This paper tackles a Nurse Scheduling Problem which consists of generating work schedules for a set of nurses while considering their shift preferences and other requirements. The objective is to maximize the satisfaction of nurses’ preferences and minimize the violation of soft constraints. This paper presents a new deterministic heuristic algorithm, called MAPA (multi-assignment problem-based algorithm), which is based on successive resolutions of the assignment problem. The algorithm has two phases: a constructive phase and an improvement phase. The constructive phase builds a full schedule by solving successive assignment problems, one for each day in the planning period. The improvement phase uses a couple of procedures that re-solve assignment problems to produce a better schedule. Given the deterministic nature of this algorithm, the same schedule is obtained each time that the algorithm is applied to the same problem instance. The performance of MAPA is benchmarked against published results for almost 250,000 instances from the NSPLib dataset. In most cases, particularly on large instances of the problem, the results produced by MAPA are better when compared to best-known solutions from the literature. The experiments reported here also show that the MAPA algorithm finds more feasible solutions compared with other algorithms in the literature, which suggest that this proposed approach is effective and robust.     

Towards higher topology

We categorify the adjunction between locales and topological spaces, this amounts to an adjunction between (generalized) bounded ionads and topoi. We show that the adjunction is idempotent. We relate this adjunction to the Scott adjunction, which was discussed from a more categorical point of view in [21]. We hint that 0-dimensional adjunction inhabits the categorified one.     

Modeling triplet flavin-indole electron transfer and interradical dipolar interaction: a perturbative approach

A benchmark biochemical reaction is here theoretically investigated by means of a perturbative approach in order to model each reaction step. The reaction is the flavin-indole electron transfer, involving also a spin-state relaxation of the ionic complex. The whole reaction path is modeled and the kinetics of the process is studied. The dipolar interaction between the two radicals is explicitly considered during the dynamic evolution of the system in order to investigate the proper conditions for the triplet-to-singlet transition to occur.     

Auslander–Reiten Components with Sectional Bypasses

In this work, we will prove that the modules lying in a sectional bypass of an arrow in the Auslander–Reiten quiver of an artin algebra, are either all left stable or all right stable, but not τ-periodic. Moreover, if such a bypass exists, then the Auslander–Reiten quiver has an infinite left or right stable component which contains a section with a bypass.     

M?ssbauer analysis of high-energy mechanical-milled sand fraction of a magnetic soil developing on basalt

A sample of the coarse sand fraction from the soil material of the A-horizon (0?C0.2 m from the soil surface) of a dusky red magnetic Oxisol was submitted to high-energy mechanical milling for different times. This assay aimed mainly at (a) monitoring the individualization of strongly aggregated mineral particles, and (b) measuring the effect of the milling pressure on the mineralogy changes of the material. These data are also intended to experimentally subside any physical model describing the mechanical behavior of the superficial soil layer that is subjected to intensive machine management, in agriculture fields. Powder X-ray data reveal that some mineralogical phases, notably gibbsite, disappear soon after the first few hours milling. The 298 K-transmission Mössbauer spectrum for the non-milled sand sample shows a qualitatively typical pattern for the sand fraction of basalt derived soils, with magnetically ordered sextets, assignable mainly to hematite and maghemite, and an intense central (super)paramagnetic Fe^3?+? doublet. For the milled samples, spectra revealed progressive spectral reduction of the magnetic hyperfine structure, with concomitant increase of relative subspectral areas due to (super)paramagnetic phases, as the milling time increased. This result is consistent with the reduction of measured saturation magnetization, from 4.96(8) J T^???1 kg^???1, for the non-milled sample, to 3.26(7) J T^???1 kg^???1, for the sample milled for 8 hours.     

Stability of Gasless Combustion Fronts in One-Dimensional Solids

For gasless combustion in a one-dimensional solid, we show a type of nonlinear stability of the physical combustion front: if a perturbation of the front is small in both a spatially uniform norm and an exponentially weighted norm, then the perturbation stays small in the spatially uniform norm and decays in the exponentially weighted norm, provided the linearized operator has no eigenvalues in the right half-plane other than zero. Using the Evans function, we show that the zero eigenvalue must be simple. Factors that complicate the analysis are: (1) the linearized operator is not sectorial, and (2) the linearized operator has good spectral properties only when the weighted norm is used, but then the nonlinear term is not Lipschitz. The result is nevertheless physically natural. To prove it, we first show that when the weighted norm is used, the semigroup generated by the linearized operator decays on a subspace complementary to the operator’s kernel, by showing that it is a compact perturbation of the semigroup generated by a more easily analyzed triangular operator. We then use this result to help establish that solutions stay small in the spatially uniform norm, which in turn helps establish nonlinear convergence in the weighted norm.     

Effect of PBT molecular weight and reactive compatibilization on the dispersed‐phase coalescence of PBT/SAN blends

Poly(butylene terephthalate) (PBT)/styrene‐acrylonitrile copolymer (SAN) blends were investigated with respect to their phase morphology. The SAN component was kept as dispersed phase and PBT as matrix phase and the PBT/SAN viscosity ratio was changed by using different PBT molecular weights. PBT/SAN blends were also compatibilized by adding methyl methacrylate‐co‐glycidyl methacrylate‐co‐ethyl acrylate terpolymer, MGE, which is an in situ reactive compatibilizer for melt blending. In noncompatibilized blends, the dispersed phase particle size increased with SAN concentration due to coalescence effects. Static coalescence experiments showed evidence of greater coalescence in blends with higher viscosity ratios. For noncompatibilized PBT/SAN/MGE blends with high molecular weight PBT as matrix phase, the average particle size of SAN phase does not depend on the SAN concentration in the blends. However noncompatibilized blends with low molecular weight PBT showed a significant increase in SAN particle size with the SAN concentration. The effect of MGE epoxy content and MGE molecular weight on the morphology of the PBT/SAN blend was also investigated. As the MGE epoxy content increased, the average particle size of SAN initially decreased with both high and low molecular weight PBT phase, thereafter leveling off with a critical content of epoxy groups in the blend. This critical content was higher in the blends containing low molecular weight PBT than in those with high molecular weight PBT. At a fixed MGE epoxy content, a decrease in MGE molecular weight yielded PBT/SAN blends with dispersed nanoparticles with an average size of about 40 nm. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010