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Multi-criteria optimization has gained increasing attention during the last decades. This article exemplifies multi-criteria features, which are implemented in the statistical software package SPOT. It describes related software packages such as mco and emoa and gives a comprehensive introduction to simple multi criteria optimization tasks. Several hands-on examples are used for illustration. The article is well-suited as a starting point for performing multi-criteria optimization tasks with SPOT.
When designing or developing optimization algorithms, test functions are crucial to evaluate
performance. Often, test functions are not sufficiently difficult, diverse, flexible or relevant to real-world
applications. Previously,
test functions with real-world relevance were generated by training a machine learning model based on
real-world data. The model estimation is used as a test function.
We propose a more principled approach using simulation instead of estimation.
Thus, relevant and varied test functions
are created which represent the behavior of real-world fitness landscapes.
Importantly, estimation can lead to excessively smooth test functions
while simulation may avoid this pitfall. Moreover, the simulation
can be conditioned by the data, so that the simulation reproduces the training data
but features diverse behavior in unobserved regions of the search space.
The proposed test function generator is illustrated with an intuitive, one-dimensional
example. To demonstrate the utility of this approach it
is applied to a protein sequence optimization problem.
This application demonstrates the advantages as well as practical limits of simulation-based
test functions.
Formerly, multi-criteria optimization algorithms were often tested using tens of thousands function evaluations. In many real-world settings function evaluations are very costly or the available budget is very limited. Several methods were developed to solve these cost-extensive multi-criteria optimization problems by reducing the number of function evaluations by means of surrogate optimization. In this study, we apply different multi-criteria surrogate optimization methods to improve (tune) an event-detection software for water-quality monitoring. For tuning two important parameters of this software, four state-of-the-art methods are compared: S-Metric-Selection Efficient Global Optimization (SMS-EGO), S-Metric-Expected Improvement for Efficient Global Optimization SExI-EGO, Euclidean Distance based Expected Improvement Euclid-EI (here referred to as MEI-SPOT due to its implementation in the Sequential Parameter Optimization Toolbox SPOT) and a multi-criteria approach based on SPO (MSPOT). Analyzing the performance of the different methods provides insight into the working-mechanisms of cutting-edge multi-criteria solvers. As one of the approaches, namely MSPOT, does not consider the prediction variance of the surrogate model, it is of interest whether this can lead to premature convergence on the practical tuning problem. Furthermore, all four approaches will be compared to a simple SMS-EMOA to validate that the use of surrogate models is justified on this problem.
Surrogate-based optimization relies on so-called infill criteria (acquisition functions) to decide which point to evaluate next. When Kriging is used as the surrogate model of choice (also called Bayesian optimization), one of the most frequently chosen criteria is expected improvement. We argue that the popularity of expected improvement largely relies on its theoretical properties rather than empirically validated performance. Few results from the literature show evidence, that under certain conditions, expected improvement may perform worse than something as simple as the predicted value of the surrogate model. We benchmark both infill criteria in an extensive empirical study on the ‘BBOB’ function set. This investigation includes a detailed study of the impact of problem dimensionality on algorithm performance. The results support the hypothesis that exploration loses importance with increasing problem dimensionality. A statistical analysis reveals that the purely exploitative search with the predicted value criterion performs better on most problems of five or higher dimensions. Possible reasons for these results are discussed. In addition, we give an in-depth guide for choosing the infill criteria based on prior knowledge about the problem at hand, its dimensionality, and the available budget.
Cyclone Dust Separators are devices often used to filter solid particles from flue gas. Such cyclones are supposed to filter as much solid particles from the carrying gas as possible. At the same time, they should only introduce a minimal pressure loss to the system. Hence, collection efficiency has to be maximized and pressure loss minimized. Both the collection efficiency and pressure loss are heavily influenced by the cyclones geometry. In this paper, we optimize seven geometrical parameters of an analytical cyclone model. Furthermore, noise variables are introduced to the model, representing the non-deterministic structure of the real-world problem. This is used to investigate robustness and sensitivity of solutions. Both the deterministic as well as the stochastic model are optimized with an SMS-EMOA. The SMS-EMOA is compared to a single objective optimization algorithm. For the harder, stochastic optimization problem, a surrogate-model-supported SMS-EMOA is compared against the model-free SMS-EMOA. The model supported approach yields better solutions with the same run-time budget.
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.