In multiobjective optimization, the result of an optimization algorithm is a set of efficient solutions from which the decision maker selects one. It is common that not all the efficient solutions can be computed in a short time and the search algorithm has to be stopped prematurely to analyze the solutions found so far. A set of efficient solutions that are well-spread in the objective space is preferred to provide the decision maker with a great variety of solutions. However, just a few exact algorithms in the literature exist with the ability to provide such a well-spread set of solutions at any moment: we call them anytime algorithms. We propose a new exact anytime algorithm for multiobjective combinatorial optimization combining three novel ideas to enhance the anytime behavior. We compare the proposed algorithm with those in the state-of-the-art for anytime multiobjective combinatorial optimization using a set of 480 instances from different well-known benchmarks and four different performance measures: the overall non-dominated vector generation ratio, the hypervolume, the general spread and the additive epsilon indicator. A comprehensive experimental study reveals that our proposal outperforms the previous algorithms in most of the instances.

The discovery of therapeutic molecules is fundamentally a multi-objective optimization problem. One formulation of the problem is to identify molecules that simultaneously exhibit strong binding affinity for a target protein, minimal off-target interactions, and suitable pharmacokinetic properties. Inspired by prior work that uses active learning to accelerate the identification of strong binders, we implement multi-objective Bayesian optimization to reduce the computational cost of multi-property virtual screening and apply it to the identification of ligands predicted to be selective based on docking scores to on- and off-targets. We demonstrate the superiority of Pareto optimization over scalarization across three case studies. Further, we use the developed optimization tool to search a virtual library of over 4M molecules for those predicted to be selective dual inhibitors of EGFR and IGF1R, acquiring 100% of the molecules that form the library's Pareto front after exploring only 8% of the library. This workflow and associated open source software can reduce the screening burden of molecular design projects and is complementary to research aiming to improve the accuracy of binding predictions and other molecular properties.