Expensive Optimization with Production-Graph Resource Constraints: A First Look at a New Problem Class Stefan Pricopie Alliance Manchester Business School, University of Manchester stefan.pricopie@manchester.ac.uk Richard Allmendinger Alliance Manchester Business School, University of Manchester richard.allmendinger@manchester.ac.uk Manuel López-Ibáñez Alliance Manchester Business School, University of Manchester manuel.lopez-ibanez@manchester.ac.uk Clyde Fare IBM clyde.fare@ibm.com Matt Benatan Sonos mattbenatan@gmail.com Joshua Knowles Alliance Manchester Business School, University of Manchester knowles.joshua@gmail.com ABSTRACT We consider a new class of expensive, resource-constrained opti- mization problems (here arising from molecular discovery) where costs are associated with the experiments (or evaluations) to be carried out during the optimization process. In the molecular dis- covery problem, candidate compounds to be optimized must be synthesized in an iterative process that starts from a set of pur- chasable items and builds up to larger molecules. To produce target molecules, their required resources are either used from already- synthesized items in storage or produced themselves on-demand at an additional cost. Any remaining resources from the production process are stored for reuse for the next evaluations. We model these resource dependencies with a directed acyclic production graph describing the development process from granular purchasable items to evaluable target compounds. Moreover, we develop several resource-efcient algorithms to address this problem. In particular, we develop resource-aware variants of Random Search heuristics and of Bayesian Optimization and analyze their performance in terms of anytime behavior. The experimental results were obtained from a real-world molecular optimization problem. Our results sug- gest that algorithms that encourage exploitation by reusing existing resources achieve satisfactory results while using fewer resources overall. CCS CONCEPTS · Theory of computation → Random search heuristics;· Mathe- matics of computing → Probabilistic algorithms. KEYWORDS molecular discovery, production costs, resource constraints, expen- sive optimization Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for proft or commercial advantage and that copies bear this notice and the full citation on the frst page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specifc permission and/or a fee. Request permissions from permissions@acm.org. GECCO ’22, July 9ś13, 2022, Boston, MA, USA © 2022 Association for Computing Machinery. ACM ISBN 978-1-4503-9237-2/22/07. . . $15.00 https://doi.org/10.1145/3512290.3528741 ACM Reference Format: Stefan Pricopie, Richard Allmendinger, Manuel López-Ibáñez, Clyde Fare, Matt Benatan, and Joshua Knowles. 2022. Expensive Optimization with Production-Graph Resource Constraints: A First Look at a New Problem Class. In Genetic and Evolutionary Computation Conference (GECCO ’22), July 9ś13, 2022, Boston, MA, USA. ACM, New York, NY, USA, 9 pages. https: //doi.org/10.1145/3512290.3528741 1 INTRODUCTION In a standard iterative optimization approach, we usually wish to attain the best possible value of the function at minimal efort or cost. In black-box optimization [15, 34], the only optimization efort that is counted is the number of calls to the function, i.e. the number of candidate solutions evaluated. This setting makes sense when candidate evaluations dominate optimization cost, as is the case in what is increasingly referred to as expensive optimization problems. Another useful concept for real-world expensive optimization prob- lems is that of an anytime algorithm [25, 37]. Here, it is intended that the algorithm is set up such that whenever it is stopped, it would always achieve close to the best possible solution value (in distribution) that could be achieved by an algorithm running for that long. This is useful because in practice we cannot always plan ahead how long an algorithm should or will be run for, especially in a scenario where an optimizer is limited resource-wise with re- source utilization varying across evaluations. In this paper, we are looking for a good anytime algorithm for an expensive problem, but we consider here a problem (class) in which candidate solutions are not all equally costly, but instead vary in cost. Related optimization problem settings to the one we work on have been considered previously by Allmendinger and Knowles [1ś4]. The key idea is that candidate solutions are built from re- sources, and it is the resources that have associated costs (or impose associated dynamic constraints). Allmendinger and Knowles [2] proposed the concept of ephemeral resource constraints (ERCs) to model this scenario; more specifcally, ERCs model temporary non-availability of resources needed to carry out evaluations (i.e. physical experiments or time-consuming computer simulations). To the best of our knowledge, in this paper we address for the frst time this problem which occurs in molecular discovery, where candidate solutions (molecules) are built from resources newly purchased or already in storage. This forces the optimizer to trade-of between using already stored resources and exploiting solutions at a lower cost, or purchasing additional resources to explore new solutions 840