STK_DOMINATEHV computes the hypervolume dominated by a set of points CALL: HV = stk_dominatedhv (Y, Y_REF) CALL: HV = stk_dominatedhv (Y, Y_REF, 0) computes the hypervolume dominated by the rows of Y, with respect to the reference point Y_REF (a row vector with the same number of columns as Y). It is expected that all the rows of Y are smaller than Y_REF (multi-objective minimization framework). CALL: HV = stk_dominatedhv (Y) CALL: HV = stk_dominatedhv (Y, [], 0) uses [0 0 ... 0] as a reference point. CALL: DECOMP = stk_dominatedhv (Y, Y_REF, 1) computes a signed decomposition of the dominated hyper-region delimited by the reference point Y_REF into overlapping rectangles. Assuming that Y is of size N x D, the result DECOMP is a structure with field .sign (N x 1), .xmin (N x D) and .xmax (N x D). The hypervolume can be recovered from this decomposition using HV = sum (DECOMP.sign .* prod (DECOMP.xmax - DECOMP.xmin, 2)) provided that the resulting decomposition is not empty. CALL: HV = stk_dominatedhv (Y, [], 1) computed a signed decomposition using [0 0 ... 0] as a reference point. NOTE: This function relies internally on the WFG algorithm [1, 2]. REFERENCES: [1] Lyndon While, Lucas Bradstreet and Luigi Barone, "A Fast Way of Calculating Exact Hypervolumes", IEEE Transactions on Evolutionary Computation, 16(1):86-95, 2012 http://dx.doi.org/10.1109/TEVC.2010.2077298 [2] WFG 1.10, released under the GPLv2 licence, available online from: http://www.wfg.csse.uwa.edu.au/hypervolume/ See also: sortrows, stk_isdominated, stk_paretofind
Package: stk