On nonsmooth and discontinuous problems of stochastic systems optimization

Article Abstract:

A group of nonsmooth stochastic optimization problems, such as risk-control, optimization of stochastic networks, and discrete event systems, were analyzed to demonstrate the pertinence of random search models in resolving such problems. The solutions to nonsmooth optimization problems cannot be found through deterministic and standard stochastic computation methods. Results show that the use of the stochastic mollifier gradient can produce approximation methods for systems with Lipschitz and discontinuous objective functions.

Research and Development in the Physical, Engineering, and Life Sciences, Mathematics, Chaos theory, Chaotic systems, Stochastic approximation

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Exact solutions for constrained two-dimensional cutting problems

Article Abstract:

An extension to P.Y. Wang's 1983 algorithm for solving the constrained two-dimensional cutting problem is introduced. The problem involves the minimum-waste derivation of guillotine-cut rectangular pieces from a rectangular plate. Wang's algorithm, which allows the incremental development of rectangles, is generalized to developed the AAO* algorithm, an informed search procedure, for solving such problems using And/Or graphs as solution-space representatives.

Cutting

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Coordinated search for an object hidden on the line

Article Abstract:

The coordinated search problem with the objective function of minimizing the time consumed to meet again at the starting point after finding a hidden object is considered. The problem, which assumes that the hidden object is symmetrically distributed on a line, is illustrated using an example characterized by a negative exponential distribution for the case of a continuous and decreasing target density.

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