Title

The SDNBI algorithm for bi-objective optimisation of mixed-integer nonlinear programs: development and applications

Abstract

Multi-objective optimisation (MOO) techniques have been applied to design problems across a wide range of engineering fields to identify trade-offs between conflicting decision criteria which cannot be easily placed on the same quantitative footing. Some of the most widely used approaches to solving MOO problems are based on scalarisation methods and include the weighted sum method [Marler and Arora, 2004], the normal boundary intersection (NBI) method [Das and Dennis, 1998] and the sandwich algorithm [Rennen et al., 2011]. However, these methods cannot reliably produce optimal solutions along nonconvex or discrete regions of a Pareto front. As a result, the application of these methods to the solution of many practical problems is limited when nonconvexities arise to the use of discrete decision variables and nonlinear model equations.

In this work, we present a robust bi-objective optimisation approach that combines the sandwich algorithm and NBI method in order to overcome difficulties in both converging to the true Pareto front and maintaining a well-distributed set of solutions. The main improvements we introduce are the identification of regions where no further optimal solution exists, i.e., disconnected sections of the Pareto front, and the exploration of nonconvex parts of the Pareto front. The proposed approach is evaluated using three published benchmark models with different levels of complexity in terms of problem size and numerical difficulty. The performance of the algorithm is compared with that of the sandwich algorithm and the modified version of the NBI (mNBI) method [Shukla, 2007], based on the accuracy of the approximate the Pareto front generated. The efficiency of the proposed algorithm is further investigated through a computer-aided molecular design problem [Lee et al., 2020] by examining its applicability and reliability in the mixed-integer nonlinear problem domain. The initial results indicate that the algorithm presented outperforms the mNBI method and sandwich algorithm in convex, nonconvex-continuous, combinatorial problems, both in terms of computational cost and the overall quality of the Pareto-optimal set.

Bio

Claire Adjiman is Professor of Chemical Engineering at Imperial College London. She holds an MEng from Imperial College and a PhD from Princeton University, both in Chemical Engineering. Her research is focused on multiscale process and molecular/materials design, including the development of design methods, property prediction techniques and optimisation algorithms. She works extensively with industry, especially the oil and gas, pharmaceuticals and agrochemicals sectors and has licensed thermodynamic modelling software.
She is a Fellow of the Royal Academy of Engineering (2015), an International Honorary Member of the American Academy of Arts and Sciences (2022) and of the US National Academy of Engineering (2023). She is also a Fellow of the Institution of Chemical Engineers and the Royal Society of Chemistry. She has received awards that include a RAEng-ICI Fellowship (1998-2003), the Philip Leverhulme Prize for Engineering (2009), the SCI Armstrong Lecture (2011), an EPSRC Leadership Fellowship (2012-2017), and the RSC Elizabeth Colbourn Memorial Lecture (2020), the American Institute of Chemical Engineers’ Computing in Chemical Engineering Award (2021). She is Editor-in-Chief of Molecular Systems Design and Engineering and she is a member of the editorial boards of Computers and Chemical Engineering and Fluid Phase Equilibria. At Imperial, she was a Founding Co-Director of the Institute for Molecular Science and Engineering (2015-2020) and she is Director of the Sargent Centre for Process Systems Engineering. She is a Trustee of Future Innovation in Process Systems Engineering (FIPSE). She is/has been a member of several advisory bodies, in the UK (EPSRC Strategic Advisory Network) and Singapore (CARES-C4T), and chairs the Scientific Advisory Board of the Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg (Germany).