Chapter 3: Optimization methods in CAMD-I

Abstract

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 (P MD ) 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.