14,225 research outputs found
Random Neural Networks and Optimisation
In this thesis we introduce new models and learning algorithms for the Random
Neural Network (RNN), and we develop RNN-based and other approaches for the
solution of emergency management optimisation problems.
With respect to RNN developments, two novel supervised learning algorithms are
proposed. The first, is a gradient descent algorithm for an RNN extension model
that we have introduced, the RNN with synchronised interactions (RNNSI), which
was inspired from the synchronised firing activity observed in brain neural circuits.
The second algorithm is based on modelling the signal-flow equations in RNN as a
nonnegative least squares (NNLS) problem. NNLS is solved using a limited-memory
quasi-Newton algorithm specifically designed for the RNN case.
Regarding the investigation of emergency management optimisation problems,
we examine combinatorial assignment problems that require fast, distributed and
close to optimal solution, under information uncertainty. We consider three different
problems with the above characteristics associated with the assignment of
emergency units to incidents with injured civilians (AEUI), the assignment of assets
to tasks under execution uncertainty (ATAU), and the deployment of a robotic
network to establish communication with trapped civilians (DRNCTC).
AEUI is solved by training an RNN tool with instances of the optimisation problem
and then using the trained RNN for decision making; training is achieved using
the developed learning algorithms. For the solution of ATAU problem, we introduce
two different approaches. The first is based on mapping parameters of the
optimisation problem to RNN parameters, and the second on solving a sequence of
minimum cost flow problems on appropriately constructed networks with estimated
arc costs. For the exact solution of DRNCTC problem, we develop a mixed-integer
linear programming formulation, which is based on network flows. Finally, we design
and implement distributed heuristic algorithms for the deployment of robots
when the civilian locations are known or uncertain
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
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