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Benchmark experiments are required to test, compare, tune, and understand optimization algorithms. Ideally, benchmark problems closely reflect real-world problem behavior. Yet, real-world problems are not always readily available for benchmarking. For example, evaluation costs may be too high, or resources are unavailable (e.g., software or equipment). As a solution, data from previous evaluations can be used to train surrogate models which are then used for benchmarking. The goal is to generate test functions on which the performance of an algorithm is similar to that on the real-world objective function. However, predictions from data-driven models tend to be smoother than the ground-truth from which the training data is derived. This is especially problematic when the training data becomes sparse. The resulting benchmarks may not reflect the landscape features of the ground-truth, are too easy, and may lead to biased conclusions.
To resolve this, we use simulation of Gaussian processes instead of estimation (or prediction). This retains the covariance properties estimated during model training. While previous research suggested a decomposition-based approach for a small-scale, discrete problem, we show that the spectral simulation method enables simulation for continuous optimization problems. In a set of experiments with an artificial ground-truth, we demonstrate that this yields more accurate benchmarks than simply predicting with the Gaussian process model.
An important class of black-box optimization problems relies on using simulations to assess the quality of a given candidate solution. Solving such problems can be computationally expensive because each simulation is very time-consuming. We present an approach to mitigate this problem by distinguishing two factors of computational cost: the number of trials and the time needed to execute the trials. Our approach tries to keep down the number of trials by using Bayesian optimization (BO) –known to be sample efficient– and reducing wall-clock times by parallel execution of trials. We compare the performance of four parallelization methods and two model-free alternatives. Each method is evaluated on all 24 objective functions of the Black-Box-Optimization- Benchmarking (BBOB) test suite in their five, ten, and 20-dimensional versions. Additionally, their performance is investigated on six test cases in robot learning. The results show that parallelized BO outperforms the state-of-the-art CMA-ES on the BBOB test functions, especially for higher dimensions. On the robot learning tasks, the differences are less clear, but the data do support parallelized BO as the ‘best guess’, winning on some cases and never losing.
This survey compiles ideas and recommendations from more than a dozen researchers with different backgrounds and from different institutes around the world. Promoting best practice in benchmarking is its main goal. The article discusses eight essential topics in benchmarking: clearly stated goals, well- specified problems, suitable algorithms, adequate performance measures, thoughtful analysis, effective and efficient designs, comprehensible presentations, and guaranteed reproducibility. The final goal is to provide well-accepted guidelines (rules) that might be useful for authors and reviewers. As benchmarking in optimization is an active and evolving field of research this manuscript is meant to co-evolve over time by means of periodic updates.
When researchers and practitioners in the field of
computational intelligence are confronted with real-world
problems, the question arises which method is the best to
apply. Nowadays, there are several, well established test
suites and well known artificial benchmark functions
available.
However, relevance and applicability of these methods to
real-world problems remains an open question in many
situations. Furthermore, the generalizability of these
methods cannot be taken for granted.
This paper describes a data-driven approach for the
generation of test instances, which is based on
real-world data. The test instance generation uses
data-preprocessing, feature extraction, modeling, and
parameterization. We apply this methodology on a classical
design of experiment real-world project and generate test
instances for benchmarking, e.g. design methods, surrogate
techniques, and optimization algorithms. While most
available results of methods applied on real-world
problems lack availability of the data for comparison,
our future goal is to create a toolbox covering multiple
data sets of real-world projects to provide a test
function generator to the research community.