Informatica

In this paper, we consider the multi-Weber problem with polyhedral barriers. For this problem, a set of obstacles are introduced where travelling or placement is prohibited, which makes the distance metric non-convex and requires constructing a special graph for calculating the distances between pairs of points. For obtaining the global solution of the problem, we build a branch and bound algorithm with pruning criteria based on dividing clients into groups and analysing them separately. We have managed to obtain global solutions to several multi-Weber with polyhedral barriers problem size instances which to our knowledge have not been reported before.

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.

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 the paper the global optimization is described from the point of an interactive software design. The interactive software that implements numeric methods and other techniques to solve global optimization problems is presented. Some problems of such a software design are formulated and discussed.

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.