(212f) Multi-Objective Optimisation for Mixed-Integer Nonlinear Optimization Problems: Algorithms and Applications to Molecular Modelling and Design

A significant fraction of Chris Floudas’ work was at the interface between optimisation and molecular modelling. In this talk, we discuss some of the particular challenges that molecular modelling and design pose for optimisation. Amongst the many classes of optimisation problems that are relevant to this broad field, we identify multi-objective optimisation (MOO) as an increasingly valuable tool, whether for the parameterization of new models (typically, nonlinear MOO) or the solution of computer-aided molecular design problems (mixed-integer nonlinear MOO).

Chris Floudas took an interest in MOO early in his career, focusing on the interaction between design and control [1] and proposing a cutting plane algorithm for MOO. Given the nonlinear nature of physical property models and phase equilibrium calculations and the mixed-integer nature of molecular design problems, many MOO problems in molecular modelling and design are characterized by a nonconvex Pareto front. Finding a good approximation to such a Pareto front can be challenging [2]. There is therefore much scope for the development of global optimisation algorithms for MOO.

To explore the state-of-the-art in MOO and identify open challenges, we investigate the application of a set of MOO algorithms to several molecular modelling and design problems [3]. We review their performance using metrics that indicate: (i) whether points on the Pareto front are identified correctly, (ii) whether a well-distributed finite representation of the true (usually infinite) Pareto front is achieved, (iii) how computationally efficient the approach is.

Unfortunately, many MOO algorithms do not allow the identification of nonconvex parts of the Pareto front. Focusing specifically on bi-objective mixed-integer MOO problems, we propose a new algorithm to overcome this. We study the performance of the algorithm on several convex and nonconvex problems and find that it often results in a reliable and well-distributed Pareto front.

[1] M. L. Luyben, C. A. Floudas, "A Multiobjective Optimization Approach for Analyzing the Interaction of Design and Control”, IFAC Proceedings Volumes, 1992, 25:101-106.

[2] B. Beykal, F. Boukouvala, C. A. Floudas, E. N. Pistikopoulos, "Optimal design of energy systems using constrained grey-box multi-objective optimization", Computers & Chemical Engineering, 2018, 116:488-502.

[3] Y. S. Lee, E. J. Graham, A. Galindo, G. Jackson, C. S. Adjiman, "A comparative study of multi-objective optimization methodologies for molecular and process design", Computers & Chemical Engineering, 2020, 136:106802.