On the global minimum ot the objective function in a balanced circular packing problem - Stetsyuk, P. I.; Romanova, Т. Е.; Schiethauer, G. (Reports of the National Academy of Sciences of Ukraine, 2014)
The paper considers the balanced packing problem of a given family of circles into a larger circle of the minimal radius as a multiextremal nonlinear programming problem. We reduce the problem to an unconstrained minimization problem of a non-smooth function by means of nonsmooth penalty functions. We propose an efficient algorithm to search for local extrema, as well as an algorithm of improvement of a lower estimate of the global minimum of the objective function. The algorithms use non-differentiable optimization methods based on Shor's r-algorithm. Computational test results are given.