Comparing Results of 31 Algorithms from the Black-Box Optimization Benchmarking BBOB-2009

pp. 1689-1696This paper presents results of the BBOB-2009 benchmark- ing of 31 search algorithms on 24 noiseless functions in a black-box optimization scenario in continuous domain. The runtime of the algorithms, measured in number of function evaluations, is investigated and a connection between a sin- gle convergence graph and the runtime distribution is uncov- ered. Performance is investigated for different dimensions up to 40-D, for different target precision values, and in dif- ferent subgroups of functions. Searching in larger dimension and multi-modal functions appears to be more difficult. The choice of the best algorithm also depends remarkably on the available budget of function evaluations

COCO: A Platform for Comparing Continuous Optimizers in a Black-Box Setting

We introduce COCO, an open source platform for Comparing Continuous Optimizers in a black-box setting. COCO aims at automatizing the tedious and repetitive task of benchmarking numerical optimization algorithms to the greatest possible extent. The platform and the underlying methodology allow to benchmark in the same framework deterministic and stochastic solvers for both single and multiobjective optimization. We present the rationales behind the (decade-long) development of the platform as a general proposition for guidelines towards better benchmarking. We detail underlying fundamental concepts of COCO such as the definition of a problem as a function instance, the underlying idea of instances, the use of target values, and runtime defined by the number of function calls as the central performance measure. Finally, we give a quick overview of the basic code structure and the currently available test suites.Comment: Optimization Methods and Software, Taylor & Francis, In press, pp.1-3

KL-based Control of the Learning Schedule for Surrogate Black-Box Optimization

This paper investigates the control of an ML component within the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) devoted to black-box optimization. The known CMA-ES weakness is its sample complexity, the number of evaluations of the objective function needed to approximate the global optimum. This weakness is commonly addressed through surrogate optimization, learning an estimate of the objective function a.k.a. surrogate model, and replacing most evaluations of the true objective function with the (inexpensive) evaluation of the surrogate model. This paper presents a principled control of the learning schedule (when to relearn the surrogate model), based on the Kullback-Leibler divergence of the current search distribution and the training distribution of the former surrogate model. The experimental validation of the proposed approach shows significant performance gains on a comprehensive set of ill-conditioned benchmark problems, compared to the best state of the art including the quasi-Newton high-precision BFGS method

COCO: Performance Assessment

We present an any-time performance assessment for benchmarking numerical optimization algorithms in a black-box scenario, applied within the COCO benchmarking platform. The performance assessment is based on runtimes measured in number of objective function evaluations to reach one or several quality indicator target values. We argue that runtime is the only available measure with a generic, meaningful, and quantitative interpretation. We discuss the choice of the target values, runlength-based targets, and the aggregation of results by using simulated restarts, averages, and empirical distribution functions

Self-Adaptive Surrogate-Assisted Covariance Matrix Adaptation Evolution Strategy

This paper presents a novel mechanism to adapt surrogate-assisted population-based algorithms. This mechanism is applied to ACM-ES, a recently proposed surrogate-assisted variant of CMA-ES. The resulting algorithm, saACM-ES, adjusts online the lifelength of the current surrogate model (the number of CMA-ES generations before learning a new surrogate) and the surrogate hyper-parameters. Both heuristics significantly improve the quality of the surrogate model, yielding a significant speed-up of saACM-ES compared to the ACM-ES and CMA-ES baselines. The empirical validation of saACM-ES on the BBOB-2012 noiseless testbed demonstrates the efficiency and the scalability w.r.t the problem dimension and the population size of the proposed approach, that reaches new best results on some of the benchmark problems.Comment: Genetic and Evolutionary Computation Conference (GECCO 2012) (2012

Benchmarking Evolutionary Algorithms For Single Objective Real-valued Constrained Optimization - A Critical Review

Benchmarking plays an important role in the development of novel search algorithms as well as for the assessment and comparison of contemporary algorithmic ideas. This paper presents common principles that need to be taken into account when considering benchmarking problems for constrained optimization. Current benchmark environments for testing Evolutionary Algorithms are reviewed in the light of these principles. Along with this line, the reader is provided with an overview of the available problem domains in the field of constrained benchmarking. Hence, the review supports algorithms developers with information about the merits and demerits of the available frameworks.Comment: This manuscript is a preprint version of an article published in Swarm and Evolutionary Computation, Elsevier, 2018. Number of pages: 4

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

Online Selection of CMA-ES Variants

In the field of evolutionary computation, one of the most challenging topics is algorithm selection. Knowing which heuristics to use for which optimization problem is key to obtaining high-quality solutions. We aim to extend this research topic by taking a first step towards a selection method for adaptive CMA-ES algorithms. We build upon the theoretical work done by van Rijn \textit{et al.} [PPSN'18], in which the potential of switching between different CMA-ES variants was quantified in the context of a modular CMA-ES framework. We demonstrate in this work that their proposed approach is not very reliable, in that implementing the suggested adaptive configurations does not yield the predicted performance gains. We propose a revised approach, which results in a more robust fit between predicted and actual performance. The adaptive CMA-ES approach obtains performance gains on 18 out of 24 tested functions of the BBOB benchmark, with stable advantages of up to 23\%. An analysis of module activation indicates which modules are most crucial for the different phases of optimizing each of the 24 benchmark problems. The module activation also suggests that additional gains are possible when including the (B)IPOP modules, which we have excluded for this present work.Comment: To appear at Genetic and Evolutionary Computation Conference (GECCO'19) Appendix will be added in due tim