Benchmarking the BFGS Algorithm on the BBOB-2009 Noisy Testbed

International audienceThe BFGS quasi-Newton method is benchmarked on the noisy BBOB-2009 testbed. A multistart strategy is applied with a maximum number of function evaluations of about 10^4 times the search space dimension

Benchmarking the NEWUOA on the BBOB-2009 Noisy Testbed

International audienceThe NEWUOA which belongs to the class of Derivative-Free optimization algorithms is benchmarked on the BBOB-2009 noisy testbed. A multistart strategy is applied with a maximum number of function evaluations of 10^4 times the search space dimension

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

Real-Parameter Black-Box Optimization Benchmarking 2009: Noisy Functions Definitions

Quantifying and comparing performance of optimization algorithms is one important aspect of research in search and optimization. However, this task turns out to be tedious and difficult to realize even in the single-objective case - at least if one is willing to accomplish it in a scientifically decent and rigorous way. The BBOB 2009 workshop will furnish most of this tedious task for its participants: (1) choice and implementation of a well-motivated real-parameter benchmark function testbed, (2) design of an experimental set-up, (3) generation of data output for (4) post-processing and presentation of the results in graphs and tables. What remains to be done for the participants is to allocate CPU-time, run their favorite black-box real-parameter optimizer in a few dimensions a few hundreds of times and execute the provided post-processing script afterwards. In this report, the testbed of noisy functions is defined and motivated

Implementing Parallel Differential Evolution on Spark

[Abstract] Metaheuristics are gaining increased attention as an efficient way of solving hard global optimization problems. Differential Evolution (DE) is one of the most popular algorithms in that class. However, its application to realistic problems results in excessive computation times. Therefore, several parallel DE schemes have been proposed, most of them focused on traditional parallel programming interfaces and infrastruc- tures. However, with the emergence of Cloud Computing, new program- ming models, like Spark, have appeared to suit with large-scale data processing on clouds. In this paper we investigate the applicability of Spark to develop parallel DE schemes to be executed in a distributed environment. Both the master-slave and the island-based DE schemes usually found in the literature have been implemented using Spark. The speedup and efficiency of all the implementations were evaluated on the Amazon Web Services (AWS) public cloud, concluding that the island- based solution is the best suited to the distributed nature of Spark. It achieves a good speedup versus the serial implementation, and shows a decent scalability when the number of nodes grows.[Resumen] Las metaheurísticas están recibiendo una atención creciente como técnica eficiente en la resolución de problemas difíciles de optimización global. Differential Evolution (DE) es una de las metaheurísticas más populares, sin embargo su aplicación en problemas reales deriva en tiempos de cómputo excesivos. Por ello se han realizado diferentes propuestas para la paralelización del DE, en su mayoría utilizando infraestructuras e interfaces de programación paralela tradicionales. Con la aparición de la computación en la nube también se han propuesto nuevos modelos de programación, como Spark, que permiten manejar el procesamiento de datos a gran escala en la nube. En este artículo investigamos la aplicabilidad de Spark en el desarrollo de implementaciones paralelas del DE para su ejecución en entornos distribuidos. Se han implementado tanto la aproximación master-slave como la basada en islas, que son las más comunes. También se han evaluado la aceleración y la eficiencia de todas las implementaciones usando el cloud público de Amazon (AWS, Amazon Web Services), concluyéndose que la implementación basada en islas es la más adecuada para el esquema de distribución usado por Spark. Esta implementación obtiene una buena aceleración en relación a la implementación serie y muestra una escalabilidad bastante buena cuando el número de nodos aumenta.[Resume] As metaheurísticas están recibindo unha atención a cada vez maior como técnica eficiente na resolución de problemas difíciles de optimización global. Differential Evolution (DE) é unha das metaheurísticas mais populares, ainda que a sua aplicación a problemas reais deriva en tempos de cómputo excesivos. É por iso que se propuxeron diferentes esquemas para a paralelización do DE, na sua maioría utilizando infraestruturas e interfaces de programación paralela tradicionais. Coa aparición da computación na nube tamén se propuxeron novos modelos de programación, como Spark, que permiten manexar o procesamento de datos a grande escala na nube. Neste artigo investigamos a aplicabilidade de Spark no desenvolvimento de implementacións paralelas do DE para a sua execución en contornas distribuidas. Implementáronse tanto a aproximación master-slave como a baseada en illas, que son as mais comúns. Tamén se avaliaron a aceleración e a eficiencia de todas as implementacións usando o cloud público de Amazon (AWS, Amazon Web Services), tirando como conclusión que a implementación baseada en illas é a mais acaida para o esquema de distribución usado por Spark. Esta implementación obtén unha boa aceleración en relación á implementación serie e amosa unha escalabilidade bastante boa cando o número de nos aumenta.Ministerio de Economía y Competitividad; DPI2014-55276-C5-2-RXunta de Galicia; GRC2013/055Xunta de Galicia; R2014/04

Features for Exploiting Black-Box Optimization Problem Structure.

Abell T, Malitsky Y, Tierney K. Features for Exploiting Black-Box Optimization Problem Structure. In: Nicosia G, Pardalos P, eds. Learning and Intelligent Optimization: 7th International Conference, LION 7, Catania, Italy, January 7-11, 2013, Revised Selected Papers. Lecture Notes in Computer Science. Vol 7997. Berlin, Heidelberg: Springer Berlin Heidelberg; 2013: 30-36.Black-box optimization (BBO) problems arise in numerous scientific and engineering applications and are characterized by computationally intensive objective functions, which severely limit the number of evaluations that can be performed. We present a robust set of features that analyze the fitness landscape of BBO problems and show how an algorithm portfolio approach can exploit these general, problem independent, features and outperform the utilization of any single minimization search strategy. We test our methodology on data from the GECCO Workshop on BBO Benchmarking 2012, which contains 21 state-of-the-art solvers run on 24 well-established functions

Enhanced parallel Differential Evolution algorithm for problems in computational systems biology

[Abstract] Many key problems in computational systems biology and bioinformatics can be formulated and solved using a global optimization framework. The complexity of the underlying mathematical models require the use of efficient solvers in order to obtain satisfactory results in reasonable computation times. Metaheuristics are gaining recognition in this context, with Differential Evolution (DE) as one of the most popular methods. However, for most realistic applications, like those considering parameter estimation in dynamic models, DE still requires excessive computation times. Here we consider this latter class of problems and present several enhancements to DE based on the introduction of additional algorithmic steps and the exploitation of parallelism. In particular, we propose an asynchronous parallel implementation of DE which has been extended with improved heuristics to exploit the specific structure of parameter estimation problems in computational systems biology. The proposed method is evaluated with different types of benchmarks problems: (i) black-box global optimization problems and (ii) calibration of non-linear dynamic models of biological systems, obtaining excellent results both in terms of quality of the solution and regarding speedup and scalability.Ministerio de Economía y Competitividad; DPI2011-28112-C04-03Consejo Superior de Investigaciones Científicas; PIE-201170E018Ministerio de Ciencia e Innovación; TIN2013-42148-PGalicia. Consellería de Cultura, Educación e Ordenación Universitaria; GRC2013/05

Towards cloud-based parallel metaheuristics: A case study in computational biology with Differential Evolution and Spark

[Abstract] Many key problems in science and engineering can be formulated and solved using global optimization techniques. In the particular case of computational biology, the development of dynamic (kinetic) models is one of the current key issues. In this context, the problem of parameter estimation (model calibration) remains as a very challenging task. The complexity of the underlying models requires the use of efficient solvers to achieve adequate results in reasonable computation times. Metaheuristics have been the focus of great consideration as an efficient way of solving hard global optimization problems. Even so, in most realistic applications, metaheuristics require a very large computation time to obtain an acceptable result. Therefore, several parallel schemes have been proposed, most of them focused on traditional parallel programming interfaces and infrastructures. However, with the emergence of cloud computing, new programming models have been proposed to deal with large-scale data processing on clouds. In this paper we explore the applicability of these new models for global optimization problems using as a case study a set of challenging parameter estimation problems in systems biology. We have developed, using Spark, an island-based parallel version of Differential Evolution. Differential Evolution is a simple population-based metaheuristic that, at the same time, is very popular for being very efficient in real function global optimization. Several experiments were conducted both on a cluster and on the Microsoft Azure public cloud to evaluate the speedup and efficiency of the proposal, concluding that the Spark implementation achieves not only competitive speedup against the serial implementation, but also good scalability when the number of nodes grows. The results can be useful for those interested in using parallel metaheuristics for global optimization problems benefiting from the potential of new cloud programming models.Ministerio de Economía y Competitividad and FEDER; through the Project SYNBIOFACTORY; DPI2014-55276-C5-2-RMinisterio de Economía y Competitividad and FEDER; TIN2013-42148-PMinisterio de Economía y Competitividad and FEDER; TIN2016-75845-PXunta de Galicia; R2014/04

Self-adjusting Population Sizes for the (1,λ)(1, \lambda)-EA on Monotone Functions

We study the $(1,\lambda)$-EA with mutation rate $c/n$ for $c\le 1$, where the population size is adaptively controlled with the $(1:s+1)$-success rule. Recently, Hevia Fajardo and Sudholt have shown that this setup with $c=1$ is efficient on \onemax for $s<1$, but inefficient if $s \ge 18$. Surprisingly, the hardest part is not close to the optimum, but rather at linear distance. We show that this behavior is not specific to \onemax. If $s$ is small, then the algorithm is efficient on all monotone functions, and if $s$ is large, then it needs superpolynomial time on all monotone functions. In the former case, for $c<1$ we show a $O(n)$ upper bound for the number of generations and $O(n\log n)$ for the number of function evaluations, and for $c=1$ we show $O(n\log n)$ generations and $O(n^2\log\log n)$ evaluations. We also show formally that optimization is always fast, regardless of $s$, if the algorithm starts in proximity of the optimum. All results also hold in a dynamic environment where the fitness function changes in each generation