Chapter 3: Optimization methods in CAMD-I

• Published in: Computer Aided Chemical Engineering Vol. 12; pp. 43 - 61
• Main Authors: Sinha, M., Achenie, L.E.K., Ostrovsky, G.M.
• Format: Book Chapter
• Language: English
• Published: 2003
• ISBN: 9780444512833; 0444512837
• ISSN: 1570-7946
• DOI: 10.1016/S1570-7946(03)80005-6

The computer-aided molecular design (CAMD) problem can often be posed as a mathematical program, in which a number of binary and continuous variables define the search space. A binary variable is an integer variable that can have one of the two possible values, for example 0 and 1. This chapter discusses a branch and bound approach to solving the resulting mathematical program. A typical molecular design problem may be modeled as a single objective minimization or maximization subject to the structural and performance constraints. The group contribution model is a structure–property correlation that has found wide use in the chemical process industry. The constraints involve the following: (1) structural feasibility, (2) physical property targets, and (3) process constraints. The nonlinear mathematical programming model for the CAMD problem (PMD) has the following features: (1) it is a nonconvex mixed integer nonlinear problem (MINLP), involving a large number of binary variables, (2) the number of linear constrains is larger than the number of nonlinear constraints, and (3) most of the components of the design vector (u) participate in the nonlinear terms. The chapter presents the CAMD design procedure, using the branch and bound (BB) method, and presents a simple example.