GloMPO (Globally Managed Parallel Optimization): a tool for expensive, black-box optimizations, application to ReaxFF reparameterizations

Abstract

In this work we explore the properties which make many real-life global optimization problems extremely difficult to handle, and some of the common techniques used in literature to address them. We then introduce a general optimization management tool called GloMPO (Globally Managed Parallel Optimization) to help address some of the challenges faced by practitioners. GloMPO manages and shares information between traditional optimization algorithms run in parallel. We hope that GloMPO will be a flexible framework which allows for customization and hybridization of various optimization ideas, while also providing a substitute for human interventions and decisions which are a common feature of optimization processes of hard problems. GloMPO is shown to produce lower minima than traditional optimization approaches on global optimization test functions, the Lennard-Jones cluster problem, and ReaxFF reparameterizations. The novel feature of forced optimizer termination was shown to find better minima than normal optimization. GloMPO is also shown to provide qualitative benefits such a identifying degenerate minima, and providing a standardized interface and workflow manager.

Sensitivity Analysis for ReaxFF Reparametrization Using the Hilbert–Schmidt Independence Criterion

“…An initial set of 16 reparametrizations were performed using the covariance matrix adaptation–evolutionary strategy (CMA-ES), which has been shown to work well on ReaxFF reparametrizations. , All of the optimizers were started from the initial force field values described in Section with a wide initial sampling distribution (σ 0 = 0.5). All parameters were scaled between 0 and 1 according to their bounds, which are automatically suggested by ParAMS.…”

“…This makes the task of fixing the parameters quite difficult. The procedure typically used to do this is the minimization of some cost function which measures the deviations between predictions made by ReaxFF and some training set of values the user would like to replicate. − However, the question of which parameters should be optimized has always been a difficult one. Optimizing all potentially relevant parameters simultaneously is prone to producing overfitted results, and very high dimensional optimizations are costly and insufficiently exploratory .…”

“…The procedure typically used to do this is the minimization of some cost function which measures the deviations between predictions made by ReaxFF and some training set of values the user would like to replicate. − However, the question of which parameters should be optimized has always been a difficult one. Optimizing all potentially relevant parameters simultaneously is prone to producing overfitted results, and very high dimensional optimizations are costly and insufficiently exploratory . A key conclusion from our previous work , is that the careful conditioning of the error function (in terms of parameter selection and training set items) is crucial to obtaining reasonable results.…”

“…Aside from the real, practical issues related to their use, the assumptions made by variance-based techniques are inappropriate in the context of identifying parameter sensitivities in the ReaxFF error function. This is because it can produce extremely large values and minima which are often located in narrow valleys and are unlikely to be captured during a sampling procedure . Cheaper approximation methods are typically insufficiently space-filling or rely on strong assumptions about the structure of the inputs or outputs. , The main criticism of variance-based techniques, however, is the fact that they limit the amount of information extracted from distributions to a single metric.…”

“…Optimizing all potentially relevant parameters simultaneously is prone to producing overfitted results, and very high dimensional optimizations are costly and insufficiently exploratory . A key conclusion from our previous work , is that the careful conditioning of the error function (in terms of parameter selection and training set items) is crucial to obtaining reasonable results.…”