Extremal circular permutations with concave functions

Let {a1,a2,…,an} be a set of n distinct real numbers and let α1,α2,…,αn be a permutation of the numbers. We construct the permutation to maximise Lf=∑i=1nf(|αi+1−αi|), for any increasing concave function f, where we denote αn+1≡α1. The optimal permutation depends on the particular numbers {a1,a2,…,an} and the function f, contrary to a postulate by Chao and Liang (European J. Combin. 13 (1992) 325).