Investigating the Local-Meta-Model CMA-ES for Large Population Sizes

3rd European Event on Bio-inspired Algorithms for Continuous Parameter Optimisation (EvoNum 2010)International audienceFor many real-life engineering optimization problems, the cost of one objective function evaluation can take several minutes or hours. In this context, a popular approach to reduce the number of function evaluations consists in building a (meta-)model of the function to be optimized using the points explored during the optimization process and replacing some (true) function evaluations by the function values given by the meta-model. In this paper, the local-meta-model CMA-ES (lmm-CMA) proposed by Kern et al. in 2006 coupling local quadratic meta-models with the Covariance Matrix Adaptation Evolution Strategy is investigated. The scaling of the algorithm with respect to the population size is analyzed and limitations of the approach for population sizes larger than the default one are shown. A new variant for deciding when the meta-model is accepted is proposed. The choice of the recombination type is also investigated to conclude that the weighted recombination is the most appropriate. Finally, this paper illustrates the influence of the different initial parameters on the convergence of the algorithm, for multimodal 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

Black-box optimization benchmarking of IPOP-saACM-ES on the BBOB-2012 noisy testbed

In this paper, we study the performance of IPOP-saACM-ES, recently proposed self-adaptive surrogate-assisted Covariance Matrix Adaptation Evolution Strategy. The algorithm was tested using restarts till a total number of function evaluations of $10^6D$ was reached, where $D$ is the dimension of the function search space. The experiments show that the surrogate model control allows IPOP-saACM-ES to be as robust as the original IPOP-aCMA-ES and outperforms the latter by a factor from 2 to 3 on 6 benchmark problems with moderate noise. On 15 out of 30 benchmark problems in dimension 20, IPOP-saACM-ES exceeds the records observed during BBOB-2009 and BBOB-2010.Comment: Genetic and Evolutionary Computation Conference (GECCO 2012) (2012

Quantifying the Impact of Parameter Tuning on Nature-Inspired Algorithms

The problem of parameterization is often central to the effective deployment of nature-inspired algorithms. However, finding the optimal set of parameter values for a combination of problem instance and solution method is highly challenging, and few concrete guidelines exist on how and when such tuning may be performed. Previous work tends to either focus on a specific algorithm or use benchmark problems, and both of these restrictions limit the applicability of any findings. Here, we examine a number of different algorithms, and study them in a "problem agnostic" fashion (i.e., one that is not tied to specific instances) by considering their performance on fitness landscapes with varying characteristics. Using this approach, we make a number of observations on which algorithms may (or may not) benefit from tuning, and in which specific circumstances.Comment: 8 pages, 7 figures. Accepted at the European Conference on Artificial Life (ECAL) 2013, Taormina, Ital

An Investigation of Factors Influencing Algorithm Selection for High Dimensional Continuous Optimisation Problems

The problem of algorithm selection is of great importance to the optimisation community, with a number of publications present in the Body-of-Knowledge. This importance stems from the consequences of the No-Free-Lunch Theorem which states that there cannot exist a single algorithm capable of solving all possible problems. However, despite this importance, the algorithm selection problem has of yet failed to gain widespread attention . In particular, little to no work in this area has been carried out with a focus on large-scale optimisation; a field quickly gaining momentum in line with advancements and influence of big data processing. As such, it is not as yet clear as to what factors, if any, influence the selection of algorithms for very high-dimensional problems (> 1000) - and it is entirely possible that algorithms that may not work well in lower dimensions may in fact work well in much higher dimensional spaces and vice-versa. This work therefore aims to begin addressing this knowledge gap by investigating some of these influencing factors for some common metaheuristic variants. To this end, typical parameters native to several metaheuristic algorithms are firstly tuned using the state-of-the-art automatic parameter tuner, SMAC. Tuning produces separate parameter configurations of each metaheuristic for each of a set of continuous benchmark functions; specifically, for every algorithm-function pairing, configurations are found for each dimensionality of the function from a geometrically increasing scale (from 2 to 1500 dimensions). The nature of this tuning is therefore highly computationally expensive necessitating the use of SMAC. Using these sets of parameter configurations, a vast amount of performance data relating to the large-scale optimisation of our benchmark suite by each metaheuristic was subsequently generated. From the generated data and its analysis, several behaviours presented by the metaheuristics as applied to large-scale optimisation have been identified and discussed. Further, this thesis provides a concise review of the relevant literature for the consumption of other researchers looking to progress in this area in addition to the large volume of data produced, relevant to the large-scale optimisation of our benchmark suite by the applied set of common metaheuristics. All work presented in this thesis was funded by EPSRC grant: EP/J017515/1 through the DAASE project