Algorithm Portfolio for Individual-based Surrogate-Assisted Evolutionary Algorithms

Surrogate-assisted evolutionary algorithms (SAEAs) are powerful optimisation tools for computationally expensive problems (CEPs). However, a randomly selected algorithm may fail in solving unknown problems due to no free lunch theorems, and it will cause more computational resource if we re-run the algorithm or try other algorithms to get a much solution, which is more serious in CEPs. In this paper, we consider an algorithm portfolio for SAEAs to reduce the risk of choosing an inappropriate algorithm for CEPs. We propose two portfolio frameworks for very expensive problems in which the maximal number of fitness evaluations is only 5 times of the problem's dimension. One framework named Par-IBSAEA runs all algorithm candidates in parallel and a more sophisticated framework named UCB-IBSAEA employs the Upper Confidence Bound (UCB) policy from reinforcement learning to help select the most appropriate algorithm at each iteration. An effective reward definition is proposed for the UCB policy. We consider three state-of-the-art individual-based SAEAs on different problems and compare them to the portfolios built from their instances on several benchmark problems given limited computation budgets. Our experimental studies demonstrate that our proposed portfolio frameworks significantly outperform any single algorithm on the set of benchmark problems

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

Which Surrogate Works for Empirical Performance Modelling? A Case Study with Differential Evolution

It is not uncommon that meta-heuristic algorithms contain some intrinsic parameters, the optimal configuration of which is crucial for achieving their peak performance. However, evaluating the effectiveness of a configuration is expensive, as it involves many costly runs of the target algorithm. Perhaps surprisingly, it is possible to build a cheap-to-evaluate surrogate that models the algorithm's empirical performance as a function of its parameters. Such surrogates constitute an important building block for understanding algorithm performance, algorithm portfolio/selection, and the automatic algorithm configuration. In principle, many off-the-shelf machine learning techniques can be used to build surrogates. In this paper, we take the differential evolution (DE) as the baseline algorithm for proof-of-concept study. Regression models are trained to model the DE's empirical performance given a parameter configuration. In particular, we evaluate and compare four popular regression algorithms both in terms of how well they predict the empirical performance with respect to a particular parameter configuration, and also how well they approximate the parameter versus the empirical performance landscapes

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