One approach to a search for good local minimum of a packing problem of cylindrical object
Keywords:
Ф-function, local optimization, cylinders, spherocylindersAbstract
An approach which allows to improve the efficiency of the search for local minima in cylinders packing problems is proposed. In order to resolve a question of falling into “bad” non-strict local minima at the initial stage of solution process replacement of cylinders by spherocylinders (i.e. cylinders bases of which are spherical segments of a given height) is proposed. This replacement will allows to go around of points where the trajectory of the gradients of the constraints will be canceled when searching for local extrema.In addition, the properties of a mathematical model based on the form of Ф -functions allowed to offer a way of significant reduction of the runtime and computational effort when searching for local minima. The proposed approach reduce the number of constraints which describе the feasible region due to a process of search for a local minimum is reduced to the solution of sequence of mathematical programming problems on subregions of the feasible region.
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