Informatica

Recent publications on multidimensional scaling express contradicting opinion on multimodality of STRESS criterion. An example has been published with rigorously provable multimodality of STRESS. We present an example of data and the rigorous proof of multimodality of SSTRESS for this data. Some comments are included on widely accepted opinion that minimization of SSTRESS is easier than minimization of STRESS.

In this paper we are concerned with global optimization, which can be defined as the problem of finding points on a bounded subset of R^m, in which some real-valued function f(x) assumes its optimal value. We consider here a global optimization algorithm. We present a stochastic approach, which is based on the simulated annealing algorithm. The optimization function f(x) here is discrete and with noise.

A random walk dan be used to model various types of discrete random processes. It may be of interest at some point to find the peak of this function. A direct method of doing so involves evaluating the function at every point and recording the highest value. However, it may be desirable to find the peak without having, to evaluate the function at every point. A search technique was developed to find the peak of a random walk with a minimal number of function evaluations using probabilistic means to guess at where the peak will most likely occur given the parameters of a specific function. A computer program was written to implement the search strategy and a series-of random walk functions of varying lengths were generated to test its performance. Data was compiled and the results show that the search is capable of finding the peak with a significant reduction in the number of function evaluations needed for a point by point search, especially for functions of greater walk length.

In well-known statistical models of global optimization only values of objective functions are taken into consideration. However, efficient algorithms of local optimization are also based on the use of gradients of objective functions. Thus, we are interested in a possibility of the use of gradients in statistical models of multimodal functions, aiming to create productive algorithms of global optimization.

In this paper the problem of optimization of multivariate multimodal functions observed with random error is considered. Using the random function for a statistical model of the objective function the minimization procedure is suggested. This algorithm is convergent on a discrete set. To avoid computational difficulties, the modified algorithm is defined by substituting the parameters of minimization procedure by their estimates.