Finding a Feasible Solution for a Simple LP Problem using Agents

In this paper we will describe a Multi-Agent System which is capable of finding a feasible solution of a specially structured linear programming problem. Emphasis is given to correctness issues and termination detection.multi-agent systems;linear programming

Asynchronous parallel branch and bound and anomalies

The parallel execution of branch and bound algorithms can result in seemingly unreasonable speedups or slowdowns. Almost never the speedup is equal to the increase in computing power. For synchronous parallel branch and bound, these effects have been studiedd extensively. For asynchronous parallelizations, only little is known. In this paper, we derive sufficient conditions to guarantee that an asynchronous parallel branch and bound algorithm (with elimination by lower bound tests and dominance) will be at least as fast as its sequential counterpart. The technique used for obtaining the results seems to be more generally applicable. The essential observations are that, under certain conditions, the parallel algorithm will always work on at least one node, that is branched from by the sequential algorithm, and that the parallel algorithm, after elimination of all such nodes, is able to conclude that the optimal solution has been found. Finally, some of the theoretical results are brought into connection with a few practical experiments

Towards an abstract parallel branch and bound machine

Many (parallel) branch and bound algorithms look very different from each other at first glance. They exploit, however, the same underlying computational model. This phenomenon can be used to define branch and bound algorithms in terms of a set of basic rules that are applied in a specific (predefined) order. In the sequential case, the specification of Mitten's rules turns out to be sufficient for the development of branch and bound algorithms. In the parallel case, the situation is a bit more complicated. We have to consider extra parameters such as work distribution and knowledge sharing. Here, the implementation of parallel branch and bound algorithms can be seen as a tuning of the parameters combined with the specification of Mitten's rules. These observations lead to generic systems, where the user provides the specifications of the problem to be solved, and the system generates a branch and bound algorithm running on a specific architecture. We will discuss some proposals that appeared in the literature. Next, we raise the question whether the proposed models are flexible enough. We analyze the design decisions to be taken when implementing a parallel branch and bound algorithm. It results in a classification model, which is validated by checking whether it captures existing branch and bound implementations. Finally, we return to the issue of flexibility of existing systems, and propose to add an abstract machine model to the generic framework. The model defines a virtual parallel branch and bound machine, within which the design decisions can be expressed in terms of the abstract machine. We will outline some ideas on which the machine may be based, and present directions of future work

An object oriented approach to generic branch and bound

Branch and bound algorithms can be characterized by a small set of basic rules that are applied in a divide-and-conquer-like framework. The framework is about the same in all applications, whereas the specification of the rules is problem dependent. Building a framework is a rather simple task in sequential implementations, but must not be underestimated in the parallel case, especially if an efficient branch and bound algorithm is required. In generic branch and bound models, the basic rules can be clearly identified within the framework, and, hence, it can be developed independently from the application. Furthermore, it gives the user the opportunity to concentrate on the actual problem to be solved, without being distracted by user-irrelevant issues like the properties of the underlying architecture. In this paper, we will discuss an object oriented approach to generic branch and bound. We will show how object orientation can help us to build a flexible branch and bound framework, that is able to perform like any branch and bound algorithm that fits into some powerful taxonomies known from the literature. We will define an interface for the specification of the problem dependent parts, and we will give a first indication of how the user can tune the framework if a non-default behavior is desired

Kinetic small angle neutron scattering of the skyrmion lattice in MnSi

We report a kinetic small angle neutron scattering study of the skyrmion lattice (SL) in MnSi. Induced by an oscillatory tilting of the magnetic field direction, the elasticity and relaxation of the SL along the magnetic field direction have been measured with microsecond resolution. For the excitation frequency of 325 Hz the SL begins to track the tilting motion of the applied magnetic field under tilting angles exceeding $\alpha_c$ > 0.4{\deg}. Empirically the associated angular velocity of the tilting connects quantitatively with the critical charge carrier velocity of approx. 0.1mm/s under current driven spin transfer torques, for which the SL unpins. In addition, a pronounced temperature dependence of the skyrmion motion is attributed to the variation of the skyrmion stiffness. Taken together our study highlights the power of kinetic small angle neutron scattering as a new experimental tool to explore, in a rather general manner, the elasticity and impurity pinning of magnetic textures across a wide parameter space without parasitic signal interferences due to ohmic heating or Oersted magnetic fields

Monopolar and dipolar relaxation in spin ice Ho2_2Ti2_2O7_7

When degenerate states are separated by large energy barriers, the approach to thermal equilibrium can be slow enough that physical properties are defined by the thermalization process rather than the equilibrium. The exploration of thermalization pushes experimental boundaries and provides refreshing insights into atomic scale correlations and processes that impact steady state dynamics and prospects for realizing solid state quantum entanglement. We present a comprehensive study of magnetic relaxation in Ho$_2$Ti$_2$O$_7$ based on frequency-dependent susceptibility measurements and neutron diffraction studies of the real-time atomic-scale response to field quenches. Covering nearly ten decades in time scales, these experiments uncover two distinct relaxation processes that dominate in different temperature regimes. At low temperatures (0.6K<T<1K) magnetic relaxation is associated with monopole motion along the applied field direction through the spin-ice vacuum. The increase of the relaxation time upon cooling indicates reduced monopole conductivity driven by decreasing monopole concentration and mobility as in a semiconductor. At higher temperatures (1K<T<2K) magnetic relaxation is associated with the reorientation of monopolar bound states as the system approaches the single-spin tunneling regime. Spin fractionalization is thus directly exposed in the relaxation dynamics