Optimal networks for mass transportation problems

Alessio Brancolini, Giuseppe Buttazzo
2004 E S A I M: Control, Optimisation and Calculus of Variations  
Given the probability measure ν over the given region Ω⊂^n, we consider the optimal location of a set Σ composed by n points in order to minimize the average distance Σ∫_(x,Σ) dν (the classical optimal facility location problem). The paper compares two strategies to find optimal configurations: the long-term one which consists in placing all n points at once in an optimal position, and the short-term one which consists in placing the points one by one adding at each step at most one point and
more » ... eserving the configuration built at previous steps. We show that the respective optimization problems exhibit qualitatively different asymptotic behavior as n→∞, although the optimization costs in both cases have the same asymptotic orders of vanishing.
doi:10.1051/cocv:2004032 fatcat:ukrp3noyuzd5rbfofp7c3rrgga