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

Solving the G-problems in less than 500 iterations: Improved efficient constrained optimization by surrogate modeling and adaptive parameter control

Constrained optimization of high-dimensional numerical problems plays an important role in many scientific and industrial applications. Function evaluations in many industrial applications are severely limited and no analytical information about objective function and constraint functions is available. For such expensive black-box optimization tasks, the constraint optimization algorithm COBRA was proposed, making use of RBF surrogate modeling for both the objective and the constraint functions. COBRA has shown remarkable success in solving reliably complex benchmark problems in less than 500 function evaluations. Unfortunately, COBRA requires careful adjustment of parameters in order to do so. In this work we present a new self-adjusting algorithm SACOBRA, which is based on COBRA and capable to achieve high-quality results with very few function evaluations and no parameter tuning. It is shown with the help of performance profiles on a set of benchmark problems (G-problems, MOPTA08) that SACOBRA consistently outperforms any COBRA algorithm with fixed parameter setting. We analyze the importance of the several new elements in SACOBRA and find that each element of SACOBRA plays a role to boost up the overall optimization performance. We discuss the reasons behind and get in this way a better understanding of high-quality RBF surrogate modeling

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

Maximum Likelihood-based Online Adaptation of Hyper-parameters in CMA-ES

The Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is widely accepted as a robust derivative-free continuous optimization algorithm for non-linear and non-convex optimization problems. CMA-ES is well known to be almost parameterless, meaning that only one hyper-parameter, the population size, is proposed to be tuned by the user. In this paper, we propose a principled approach called self-CMA-ES to achieve the online adaptation of CMA-ES hyper-parameters in order to improve its overall performance. Experimental results show that for larger-than-default population size, the default settings of hyper-parameters of CMA-ES are far from being optimal, and that self-CMA-ES allows for dynamically approaching optimal settings.Comment: 13th International Conference on Parallel Problem Solving from Nature (PPSN 2014) (2014

State-of-the-art in aerodynamic shape optimisation methods

Aerodynamic optimisation has become an indispensable component for any aerodynamic design over the past 60 years, with applications to aircraft, cars, trains, bridges, wind turbines, internal pipe flows, and cavities, among others, and is thus relevant in many facets of technology. With advancements in computational power, automated design optimisation procedures have become more competent, however, there is an ambiguity and bias throughout the literature with regards to relative performance of optimisation architectures and employed algorithms. This paper provides a well-balanced critical review of the dominant optimisation approaches that have been integrated with aerodynamic theory for the purpose of shape optimisation. A total of 229 papers, published in more than 120 journals and conference proceedings, have been classified into 6 different optimisation algorithm approaches. The material cited includes some of the most well-established authors and publications in the field of aerodynamic optimisation. This paper aims to eliminate bias toward certain algorithms by analysing the limitations, drawbacks, and the benefits of the most utilised optimisation approaches. This review provides comprehensive but straightforward insight for non-specialists and reference detailing the current state for specialist practitioners

Surrogate-assisted multiobjective optimization based on decomposition

International audienceA number of surrogate-assisted evolutionary algorithms are being developed for tackling expensive multiobjective optimization problems. On the one hand, a relatively broad range of techniques from both machine learning and multiobjective optimization can be combined for this purpose. Diferent taxonomies exist in order to better delimit the design choices, advantages and drawbacks of existing approaches. On the other hand, assessing the relative performance of a given approach is a diicult task, since it depends on the characteristics of the problem at hand. In this paper, we focus on surrogate-assisted approaches using objective space decomposition as a core component. We propose a reined and ine-grained classiication, ranging from EGO-like approaches to iltering or pre-screening. More importantly, we provide a comprehensive comparative study of a representative selection of state-of-the-art methods , together with simple baseline algorithms. We rely on selected benchmark functions taken from the bbob-biobj benchmarking test suite, that provides a variable range of objective function diiculties. Our empirical analysis highlights the efect of the available budget on the relative performance of each approach, and the impact of the training set and of the machine learning model construction on both solution quality and runtime eiciency