I encounter the following optimization problem, but I can't solve it.

Given N variables satisfying 0 <= x_1 < x_2 < x_3 < ... < x_N <= 1 and an integer K no large than N, solve the following problem.

maximize \sum_{S \subset {1,2,..., N}, |S| = K} \prod_{i,j \in S} (x_i - x_j)^2.

This problem is somehow related to Vandermonde matrix. Each additional term in the above target function is just the square of the determinate of Vandermonde matrix generated by the K selected variables belonging set S.