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Hybrid search for optimum in a small implicitly defined region

100%

Zilinskas A.

Control and Cybernetics

2004

tom Vol. 33, no 4

599-609

We consider optimization problems with a small implicitly denned feasible region, and with an objective function corrupted by irregularities, e.g. small noise added to the function values. Known mathematical programming methods with high convergence rate can not, lie applied to such problems. A hybrid technique is developed combining random search for the feasible region of a considered problem, and evolutionary search for the minimum over the found region. The solution results of two test problems and of a difficult real world problem are presented.

On probabilistic bounds inspired by interval arithmetic

63%

Zilinskas A. , Zilinskas J.

tom Vol. 39, no 2

507-525

A randomized method aimed at evaluation of probabilistic bounds for function values is considered. Stochastic intervals tightly covering ranges of function values with probability close to one are modelled by a randomized method inspired by interval arithmetic. Statistical properties of the modelled intervals are investigated experimentally. The experimental results are discussed with respect to application of this method in the construction of a branch and bound type randomized algorithm for global optimization.

On the choice of statistical model for one-dimensional P-algorithms

63%

Calvin J. , Zilinskas A.

Control and Cybernetics

2000

tom Vol. 29, no 2

555-565

Algorithms based on statistical models compete favorably with other global optimization algorithms as proved by extensive testing results. Recently, techniques were developed for theoretically estimating the rate of convergence of global optimization algorithms with respect to the underlying statistical models. In the present paper these technictues are extended for theoretical investigation of P-algorithms without respect to a statistical model. Theoretical estimates may eliminate the need for lengthy experimental investigation which previously was the only method for comparison of the algorithms. The rcaults obtained give new insight into the role of the mnderlying statistical model with respect to the asymptotic properties of the algorithm which will be useful for the implementation of new versions of the algoritlmns.