This paper presents results of the BBOB-2009 benchmarking 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 single convergence graph and the runtime distribution is uncovered. Performance is investigated for different dimensions up to 40-D, for different target precision values, and in different 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.

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Four methods for global numerical black box optimization with origins in the mathematical programming community are described and experimentally compared with the state of the art evolutionary method, BIPOP-CMA-ES. The methods chosen for the comparison exhibit various features that are potentially interesting for the evolutionary computation community: systematic sampling of the search space (DIRECT, MCS) possibly combined with a local search method (MCS), or a multi-start approach (NEWUOA, GLOBAL) possibly equipped with a careful selection of points to run a local optimizer from (GLOBAL). The recently proposed “comparing continuous optimizers” (COCO) methodology was adopted as the basis for the comparison. Based on the results, we draw suggestions about which algorithm should be used depending on the available budget of function evaluations, and we propose several possibilities for hybridizing evolutionary algorithms (EAs) with features of the other compared algorithms.

An evolutionary algorithm for the optimization of a function with real parameters is described in this paper. It uses a cooperative co-evolution to breed and reproduce successful mutation steps. The algorithm described herein is then tested on a suite of 10D and 30D reference optimization problems collected for the Special Session on Real-Parameter Optimization of the IEEE Congress on Evolutionary Computation 2005. The results are of mixed quality (as expected), but reveal several interesting aspects of this simple algorithm.

JADE, an adaptive version of the differential evolution (DE) algorithm, is benchmarked on the testbed of 24 noiseless functions chosen for the Black-Box Optimization Benchmarking workshop. The results of full-featured JADE are then compared with the results of 3 other DE variants ("downgraded" JADE variants) to reveal the contributions of the algorithm components. Another adaptive DE variant benchmarked during BBOB 2010 is used as a reference algorithm. The results confirm that the original JADE outperforms the other (JA)DE versions, while the comparison with the other adaptive DE shows that the different sources of adaptivity make the algorithms suitable for different functions.

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Abstract. When a simple real-valued estimation of distribution algorithm (EDA) with Gaussian model and maximum likelihood estimation of parameters is used, it converges prematurely even on the slope of the fitness function. The simplest way of preventing premature convergence by multiplying the variance estimate by a constant factor k each generation is studied. Recent works have shown that when increasing the dimensionality of the search space, such an algorithm becomes very quickly unable to traverse the slope and focus to the optimum at the same time. In this paper it is shown that when isotropic distributions with Gaussian or Cauchy distributed norms are used, the simple constant setting of k is able to ensure a reasonable behaviour of the EDA on the slope and in the valley of the fitness function at the same time.

We propose a novel hybrid algorithm "Brent-STEP" for univariate global function minimization, based on the global line search method STEP and accelerated by Brent's method, a local optimizer that combines quadratic interpolation and golden section steps. We analyze the performance of the hybrid algorithm on various one-dimensional functions and experimentally demonstrate a significant improvement relative to its constituent algorithms in most cases. We then generalize the algorithm to multivariate functions, adopting the recently proposed [8] scheme to interleave evaluations across dimensions to achieve smoother and more efficient convergence. We experimentally demonstrate the highly competitive performance of the proposed multivariate algorithm on separable functions of the BBOB benchmark. The combination of good performance and smooth convergence on separable functions makes the algorithm an interesting candidate for inclusion in algorithmic portfolios or hybrid algorithms that aim to provide good performance on a wide range of problems.