Landscape-Aware Fixed-Budget Performance Regression and Algorithm Selection for Modular CMA-ES Variants

Automated algorithm selection promises to support the user in the decisive task of selecting a most suitable algorithm for a given problem. A common component of these machine-trained techniques are regression models which predict the performance of a given algorithm on a previously unseen problem instance. In the context of numerical black-box optimization, such regression models typically build on exploratory landscape analysis (ELA), which quantifies several characteristics of the problem. These measures can be used to train a supervised performance regression model. First steps towards ELA-based performance regression have been made in the context of a fixed-target setting. In many applications, however, the user needs to select an algorithm that performs best within a given budget of function evaluations. Adopting this fixed-budget setting, we demonstrate that it is possible to achieve high-quality performance predictions with off-the-shelf supervised learning approaches, by suitably combining two differently trained regression models. We test this approach on a very challenging problem: algorithm selection on a portfolio of very similar algorithms, which we choose from the family of modular CMA-ES algorithms.Comment: To appear in Proc. of Genetic and Evolutionary Computation Conference (GECCO'20

Challenges of ELA-guided Function Evolution using Genetic Programming

Within the optimization community, the question of how to generate new optimization problems has been gaining traction in recent years. Within topics such as instance space analysis (ISA), the generation of new problems can provide new benchmarks which are not yet explored in existing research. Beyond that, this function generation can also be exploited for solving complex real-world optimization problems. By generating functions with similar properties to the target problem, we can create a robust test set for algorithm selection and configuration. However, the generation of functions with specific target properties remains challenging. While features exist to capture low-level landscape properties, they might not always capture the intended high-level features. We show that a genetic programming (GP) approach guided by these exploratory landscape analysis (ELA) properties is not always able to find satisfying functions. Our results suggest that careful considerations of the weighting of landscape properties, as well as the distance measure used, might be required to evolve functions that are sufficiently representative to the target landscape

Tools for Landscape Analysis of Optimisation Problems in Procedural Content Generation for Games

The term Procedural Content Generation (PCG) refers to the (semi-)automatic generation of game content by algorithmic means, and its methods are becoming increasingly popular in game-oriented research and industry. A special class of these methods, which is commonly known as search-based PCG, treats the given task as an optimisation problem. Such problems are predominantly tackled by evolutionary algorithms. We will demonstrate in this paper that obtaining more information about the defined optimisation problem can substantially improve our understanding of how to approach the generation of content. To do so, we present and discuss three efficient analysis tools, namely diagonal walks, the estimation of high-level properties, as well as problem similarity measures. We discuss the purpose of each of the considered methods in the context of PCG and provide guidelines for the interpretation of the results received. This way we aim to provide methods for the comparison of PCG approaches and eventually, increase the quality and practicality of generated content in industry.Comment: 30 pages, 8 figures, accepted for publication in Applied Soft Computin

Towards Dynamic Algorithm Selection for Numerical Black-Box Optimization: Investigating BBOB as a Use Case

One of the most challenging problems in evolutionary computation is to select from its family of diverse solvers one that performs well on a given problem. This algorithm selection problem is complicated by the fact that different phases of the optimization process require different search behavior. While this can partly be controlled by the algorithm itself, there exist large differences between algorithm performance. It can therefore be beneficial to swap the configuration or even the entire algorithm during the run. Long deemed impractical, recent advances in Machine Learning and in exploratory landscape analysis give hope that this dynamic algorithm configuration~(dynAC) can eventually be solved by automatically trained configuration schedules. With this work we aim at promoting research on dynAC, by introducing a simpler variant that focuses only on switching between different algorithms, not configurations. Using the rich data from the Black Box Optimization Benchmark~(BBOB) platform, we show that even single-switch dynamic Algorithm selection (dynAS) can potentially result in significant performance gains. We also discuss key challenges in dynAS, and argue that the BBOB-framework can become a useful tool in overcoming these

Algorithm Instance Footprint: Separating Easily Solvable and Challenging Problem Instances

In black-box optimization, it is essential to understand why an algorithm instance works on a set of problem instances while failing on others and provide explanations of its behavior. We propose a methodology for formulating an algorithm instance footprint that consists of a set of problem instances that are easy to be solved and a set of problem instances that are difficult to be solved, for an algorithm instance. This behavior of the algorithm instance is further linked to the landscape properties of the problem instances to provide explanations of which properties make some problem instances easy or challenging. The proposed methodology uses meta-representations that embed the landscape properties of the problem instances and the performance of the algorithm into the same vector space. These meta-representations are obtained by training a supervised machine learning regression model for algorithm performance prediction and applying model explainability techniques to assess the importance of the landscape features to the performance predictions. Next, deterministic clustering of the meta-representations demonstrates that using them captures algorithm performance across the space and detects regions of poor and good algorithm performance, together with an explanation of which landscape properties are leading to it.Comment: To appear at GECCO 202