  Molecule optimization is a fundamental task for accelerating drug discovery,
with the goal of generating new valid molecules that maximize multiple drug
properties while maintaining similarity to the input molecule. Existing
generative models and reinforcement learning approaches made initial success,
but still face difficulties in simultaneously optimizing multiple drug
properties. To address such challenges, we propose the MultI-constraint
MOlecule SAmpling (MIMOSA) approach, a sampling framework to use input molecule
as an initial guess and sample molecules from the target distribution. MIMOSA
first pretrains two property agnostic graph neural networks (GNNs) for molecule
topology and substructure-type prediction, where a substructure can be either
atom or single ring. For each iteration, MIMOSA uses the GNNs' prediction and
employs three basic substructure operations (add, replace, delete) to generate
new molecules and associated weights. The weights can encode multiple
constraints including similarity and drug property constraints, upon which we
select promising molecules for next iteration. MIMOSA enables flexible encoding
of multiple property- and similarity-constraints and can efficiently generate
new molecules that satisfy various property constraints and achieved up to
49.6% relative improvement over the best baseline in terms of success rate. The
code repository (including readme file, data preprocessing and model
construction, evaluation) is available https://github.com/futianfan/MIMOSA.
