9,027 research outputs found
Deterministic Annealing and Nonlinear Assignment
For combinatorial optimization problems that can be formulated as Ising or
Potts spin systems, the Mean Field (MF) approximation yields a versatile and
simple ANN heuristic, Deterministic Annealing. For assignment problems the
situation is more complex -- the natural analog of the MF approximation lacks
the simplicity present in the Potts and Ising cases. In this article the
difficulties associated with this issue are investigated, and the options for
solving them discussed. Improvements to existing Potts-based MF-inspired
heuristics are suggested, and the possibilities for defining a proper
variational approach are scrutinized.Comment: 15 pages, 3 figure
Adiabatic evolution on a spatial-photonic Ising machine
Combinatorial optimization problems are crucial for widespread applications
but remain difficult to solve on a large scale with conventional hardware.
Novel optical platforms, known as coherent or photonic Ising machines, are
attracting considerable attention as accelerators on optimization tasks
formulable as Ising models. Annealing is a well-known technique based on
adiabatic evolution for finding optimal solutions in classical and quantum
systems made by atoms, electrons, or photons. Although various Ising machines
employ annealing in some form, adiabatic computing on optical settings has been
only partially investigated. Here, we realize the adiabatic evolution of
frustrated Ising models with 100 spins programmed by spatial light modulation.
We use holographic and optical control to change the spin couplings
adiabatically, and exploit experimental noise to explore the energy landscape.
Annealing enhances the convergence to the Ising ground state and allows to find
the problem solution with probability close to unity. Our results demonstrate a
photonic scheme for combinatorial optimization in analogy with adiabatic
quantum algorithms and enforced by optical vector-matrix multiplications and
scalable photonic technology.Comment: 9 pages, 4 figure
Portfolio selection using neural networks
In this paper we apply a heuristic method based on artificial neural networks
in order to trace out the efficient frontier associated to the portfolio
selection problem. We consider a generalization of the standard Markowitz
mean-variance model which includes cardinality and bounding constraints. These
constraints ensure the investment in a given number of different assets and
limit the amount of capital to be invested in each asset. We present some
experimental results obtained with the neural network heuristic and we compare
them to those obtained with three previous heuristic methods.Comment: 12 pages; submitted to "Computers & Operations Research
Asymptotic behavior of memristive circuits
The interest in memristors has risen due to their possible application both
as memory units and as computational devices in combination with CMOS. This is
in part due to their nonlinear dynamics, and a strong dependence on the circuit
topology. We provide evidence that also purely memristive circuits can be
employed for computational purposes. In the present paper we show that a
polynomial Lyapunov function in the memory parameters exists for the case of DC
controlled memristors. Such Lyapunov function can be asymptotically
approximated with binary variables, and mapped to quadratic combinatorial
optimization problems. This also shows a direct parallel between memristive
circuits and the Hopfield-Little model. In the case of Erdos-Renyi random
circuits, we show numerically that the distribution of the matrix elements of
the projectors can be roughly approximated with a Gaussian distribution, and
that it scales with the inverse square root of the number of elements. This
provides an approximated but direct connection with the physics of disordered
system and, in particular, of mean field spin glasses. Using this and the fact
that the interaction is controlled by a projector operator on the loop space of
the circuit. We estimate the number of stationary points of the approximate
Lyapunov function and provide a scaling formula as an upper bound in terms of
the circuit topology only.Comment: 20 pages, 8 figures; proofs corrected, figures changed; results
substantially unchanged; to appear in Entrop
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