On the solution of mixed-integer nonlinear programming models for computer aided molecular design

Area of Science:

• Chemical Engineering
• Computational Chemistry
• Optimization

Background:

• Computer-aided molecular design (CAMD) problems are often formulated as mixed-integer nonlinear programming (MINLP) models.
• These models frequently feature a high number of linear constraints and nonconvex terms, necessitating global optimization methods.
• Efficiently solving these complex MINLP models is crucial for advancing molecular design.

Purpose of the Study:

• To develop an efficient global optimization algorithm for CAMD problems.
• To address the computational challenges posed by MINLP models with numerous linear constraints and nonconvex variables.
• To specifically tackle the problem of designing optimal solvents for lithographic printing applications.

Main Methods:

• A tailored branch-and-bound (BB) algorithm is proposed for solving CAMD problems.
• A novel branching strategy is introduced, utilizing linear branching functions to reduce search space dimensionality.
• Linear underestimators are constructed for a class of functions relevant to CAMD.

Main Results:

• The proposed BB algorithm significantly reduces the number of node traversals compared to conventional methods.
• The new branching strategy effectively decreases the dimensionality of the search space.
• The method demonstrates efficiency in solving the specific CAMD problem of optimal solvent design.

Conclusions:

• The developed branch-and-bound algorithm offers an efficient solution for complex CAMD problems.
• The novel branching strategy is key to overcoming the computational burden of traditional BB methods.
• This approach provides a valuable tool for the design of optimal solvents in industrial applications like lithographic printing.