Covariance-based hardware selection part IV: Solution using the generalized benders decomposition

• Published in: AIChE journal Vol. 62; no. 10; pp. 3628 - 3638
• Main Authors: Zhang, Jin, Wang, Xiaoxi, Chmielewski, Donald J.
• Format: Journal Article
• Language: English
• Published: New York Blackwell Publishing Ltd 01.10.2016; American Institute of Chemical Engineers
• Subjects: Algorithms; Benders decomposition; Chemical engineering; Computation; Decomposition; generalized benders decomposition; Hardware; linear matrix inequalities; Mixed integer; Optimization; Reduction; Searching; sensor placement
• ISSN: 0001-1541; 1547-5905
• DOI: 10.1002/aic.15285

Recently the covariance based hardware selection problem has been shown to be of the mixed integer convex programming (MICP) class. While such a formulation provides a route to global optimality, use of the branch and bound search procedure has limited application to fairly small systems. The particular bottleneck is that during each iteration of the branch and bound search, a fairly slow semi‐definite programming (SDP) problem must be solved to its global optimum. In this work, we illustrate that a simple reformulation of the MICP and subsequent application of the generalized Benders decomposition algorithm will result in massive reductions in computational effort. While the resulting algorithm must solve multiple mixed integer linear programs, this increase in computational effort is significantly outweighed by the reduction in the number of SDP problems that must be solved. © 2016 American Institute of Chemical Engineers AIChE J, 62: 3628–3638, 2016