76,699 research outputs found
A Bayesian approach to constrained single- and multi-objective optimization
This article addresses the problem of derivative-free (single- or
multi-objective) optimization subject to multiple inequality constraints. Both
the objective and constraint functions are assumed to be smooth, non-linear and
expensive to evaluate. As a consequence, the number of evaluations that can be
used to carry out the optimization is very limited, as in complex industrial
design optimization problems. The method we propose to overcome this difficulty
has its roots in both the Bayesian and the multi-objective optimization
literatures. More specifically, an extended domination rule is used to handle
objectives and constraints in a unified way, and a corresponding expected
hyper-volume improvement sampling criterion is proposed. This new criterion is
naturally adapted to the search of a feasible point when none is available, and
reduces to existing Bayesian sampling criteria---the classical Expected
Improvement (EI) criterion and some of its constrained/multi-objective
extensions---as soon as at least one feasible point is available. The
calculation and optimization of the criterion are performed using Sequential
Monte Carlo techniques. In particular, an algorithm similar to the subset
simulation method, which is well known in the field of structural reliability,
is used to estimate the criterion. The method, which we call BMOO (for Bayesian
Multi-Objective Optimization), is compared to state-of-the-art algorithms for
single- and multi-objective constrained optimization
Closed-loop automatic gradient design for liquid chromatography using Bayesian optimization
Contemporary complex samples require sophisticated methods for full analysis. This work describes the development of a Bayesian optimization algorithm for automated and unsupervised development of gradient programs. The algorithm was tailored to LC using a Gaussian process model with a novel covariance kernel. To facilitate unsupervised learning, the algorithm was designed to interface directly with the chromatographic system. Single-objective and multi-objective Bayesian optimization strategies were investigated for the separation of two complex (n>18, and n>80) dye mixtures. Both approaches found satisfactory optima in under 35 measurements. The multi-objective strategy was found to be powerful and flexible in terms of exploring the Pareto front. The performance difference between the single-objective and multi-objective strategy was further investigated using a retention modeling example. One additional advantage of the multi-objective approach was that it allows for a trade-off to be made between multiple objectives without prior knowledge. In general, the Bayesian optimization strategy was found to be particularly suitable, but not limited to, cases where retention modelling is not possible, although its scalability might be limited in terms of the number of parameters that can be simultaneously optimized
Adaptive and Safe Bayesian Optimization in High Dimensions via One-Dimensional Subspaces
Bayesian optimization is known to be difficult to scale to high dimensions,
because the acquisition step requires solving a non-convex optimization problem
in the same search space. In order to scale the method and keep its benefits,
we propose an algorithm (LineBO) that restricts the problem to a sequence of
iteratively chosen one-dimensional sub-problems that can be solved efficiently.
We show that our algorithm converges globally and obtains a fast local rate
when the function is strongly convex. Further, if the objective has an
invariant subspace, our method automatically adapts to the effective dimension
without changing the algorithm. When combined with the SafeOpt algorithm to
solve the sub-problems, we obtain the first safe Bayesian optimization
algorithm with theoretical guarantees applicable in high-dimensional settings.
We evaluate our method on multiple synthetic benchmarks, where we obtain
competitive performance. Further, we deploy our algorithm to optimize the beam
intensity of the Swiss Free Electron Laser with up to 40 parameters while
satisfying safe operation constraints
Multi-objective and multi-fidelity Bayesian optimization of laser-plasma acceleration
Beam parameter optimization in accelerators involves multiple, sometimes
competing objectives. Condensing these multiple objectives into a single
objective unavoidably results in bias towards particular outcomes that do not
necessarily represent the best possible outcome for the operator in terms of
parameter optimization. A more versatile approach is multi-objective
optimization, which establishes the trade-off curve or Pareto front between
objectives. Here we present first results on multi-objective Bayesian
optimization of a simulated laser-plasma accelerator. We find that
multi-objective optimization is equal or even superior in performance to its
single-objective counterparts, and that it is more resilient to different
statistical descriptions of objectives.
As a second major result of our paper, we significantly reduce the
computational costs of the optimization by choosing the resolution and box size
of the simulations dynamically. This is relevant since even with the use of
Bayesian statistics, performing such optimizations on a multi-dimensional
search space may require hundreds or thousands of simulations. Our algorithm
translates information gained from fast, low-resolution runs with lower
fidelity to high-resolution data, thus requiring fewer actual simulations at
highest computational cost.
The techniques demonstrated in this paper can be translated to many different
use cases, both computational and experimental
Computer-Aided Multi-Objective Optimization in Small Molecule Discovery
Molecular discovery is a multi-objective optimization problem that requires
identifying a molecule or set of molecules that balance multiple, often
competing, properties. Multi-objective molecular design is commonly addressed
by combining properties of interest into a single objective function using
scalarization, which imposes assumptions about relative importance and uncovers
little about the trade-offs between objectives. In contrast to scalarization,
Pareto optimization does not require knowledge of relative importance and
reveals the trade-offs between objectives. However, it introduces additional
considerations in algorithm design. In this review, we describe pool-based and
de novo generative approaches to multi-objective molecular discovery with a
focus on Pareto optimization algorithms. We show how pool-based molecular
discovery is a relatively direct extension of multi-objective Bayesian
optimization and how the plethora of different generative models extend from
single-objective to multi-objective optimization in similar ways using
non-dominated sorting in the reward function (reinforcement learning) or to
select molecules for retraining (distribution learning) or propagation (genetic
algorithms). Finally, we discuss some remaining challenges and opportunities in
the field, emphasizing the opportunity to adopt Bayesian optimization
techniques into multi-objective de novo design
Multi-objective constrained Bayesian optimization for structural design
The planning and design of buildings and civil engineering concrete structures constitutes a complex problem subject to constraints, for instance, limit state constraints from design codes, evaluated by expensive computations such as finite element (FE) simulations. Traditionally, the focus has been on minimizing costs exclusively, while the current trend calls for good trade-offs of multiple criteria such as sustainability, buildability, and performance, which can typically be computed cheaply from the design parameters. Multi-objective methods can provide more relevant design strategies to find such trade-offs. However, the potential of multi-objective optimization methods remains unexploited in structural concrete design practice, as the expensiveness of structural design problems severely limits the scope of applicable algorithms. Bayesian optimization has emerged as an efficient approach to optimizing expensive functions, but it has not been, to the best of our knowledge, applied to constrained multi-objective optimization of structural concrete design problems. In this work, we develop a Bayesian optimization framework explicitly exploiting the features inherent to structural design problems, that is, expensive constraints and cheap objectives. The framework is evaluated on a generic case of structural design of a reinforced concrete (RC) beam, taking into account sustainability, buildability, and performance objectives, and is benchmarked against the well-known Non-dominated Sorting Genetic Algorithm II (NSGA-II) and a random search procedure. The results show that the Bayesian algorithm performs considerably better in terms of rate-of-improvement, final solution quality, and variance across repeated runs, which suggests it is well-suited for multi-objective constrained optimization problems in structural design
Bayesian Gait Optimization for Bipedal Locomotion
One of the key challenges in robotic bipedal locomotion is finding gait parameters that optimize a desired performance criterion, such as speed, robustness or energy efficiency. Typically, gait optimization requires extensive robot experiments and specific expert knowledge. We propose to apply data-driven machine learning to automate and speed up the process of gait optimization. In particular, we use Bayesian optimization to efficiently find gait parameters that optimize the desired performance metric. As a proof of concept we demonstrate that Bayesian optimization is near-optimal in a classical stochastic optimal control framework. Moreover, we validate our approach to Bayesian gait optimization on a low-cost and fragile real bipedal walker and show that good walking gaits can be efficiently found by Bayesian optimization. © 2014 Springer International Publishing
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