Stochastic mixed integer nonlinear programming using rank filter and ordinal optimization

A rank filter algorithm is developed to cope with the computational-difficulty in solving stochastic mixed integer nonlinear programming (SMINLP) problems. The proposed approximation method estimates the expected performance values, whose relative rankforms a subset of good solutions with high probability. Suboptimal solutions are obtained by searching the subset using the accurate performances. High-computational efficiency is achieved, because the accurate performance is limited to a small subset of the search space. Three benchmark problems show that the rank filter algorithm can reduce computational expense by several orders of magnitude without signify icant loss of precision. The rank filter algorithm presents an efficient approach for solving the large-scale SMINLP problems that are nonconvex, highly combinatorial, and strongly nonlinear. (C) 2009 American Institute of Chemical Engineers AIChE J, 55: 2873-2882, 2009