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

A hybrid swarm-based algorithm for single-objective optimization problems involving high-cost analyses

In many technical fields, single-objective optimization procedures in continuous domains involve expensive numerical simulations. In this context, an improvement of the Artificial Bee Colony (ABC) algorithm, called the Artificial super-Bee enhanced Colony (AsBeC), is presented. AsBeC is designed to provide fast convergence speed, high solution accuracy and robust performance over a wide range of problems. It implements enhancements of the ABC structure and hybridizations with interpolation strategies. The latter are inspired by the quadratic trust region approach for local investigation and by an efficient global optimizer for separable problems. Each modification and their combined effects are studied with appropriate metrics on a numerical benchmark, which is also used for comparing AsBeC with some effective ABC variants and other derivative-free algorithms. In addition, the presented algorithm is validated on two recent benchmarks adopted for competitions in international conferences. Results show remarkable competitiveness and robustness for AsBeC.Comment: 19 pages, 4 figures, Springer Swarm Intelligenc

Alternative Restart Strategies for CMA-ES

This paper focuses on the restart strategy of CMA-ES on multi-modal functions. A first alternative strategy proceeds by decreasing the initial step-size of the mutation while doubling the population size at each restart. A second strategy adaptively allocates the computational budget among the restart settings in the BIPOP scheme. Both restart strategies are validated on the BBOB benchmark; their generality is also demonstrated on an independent real-world problem suite related to spacecraft trajectory optimization

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

Sequential vs. Integrated Algorithm Selection and Configuration: A Case Study for the Modular CMA-ES

When faced with a specific optimization problem, choosing which algorithm to use is always a tough task. Not only is there a vast variety of algorithms to select from, but these algorithms often are controlled by many hyperparameters, which need to be tuned in order to achieve the best performance possible. Usually, this problem is separated into two parts: algorithm selection and algorithm configuration. With the significant advances made in Machine Learning, however, these problems can be integrated into a combined algorithm selection and hyperparameter optimization task, commonly known as the CASH problem. In this work we compare sequential and integrated algorithm selection and configuration approaches for the case of selecting and tuning the best out of 4608 variants of the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) tested on the Black Box Optimization Benchmark (BBOB) suite. We first show that the ranking of the modular CMA-ES variants depends to a large extent on the quality of the hyperparameters. This implies that even a sequential approach based on complete enumeration of the algorithm space will likely result in sub-optimal solutions. In fact, we show that the integrated approach manages to provide competitive results at a much smaller computational cost. We also compare two different mixed-integer algorithm configuration techniques, called irace and Mixed-Integer Parallel Efficient Global Optimization (MIP-EGO). While we show that the two methods differ significantly in their treatment of the exploration-exploitation balance, their overall performances are very similar

A Computationally Efficient Limited Memory CMA-ES for Large Scale Optimization

We propose a computationally efficient limited memory Covariance Matrix Adaptation Evolution Strategy for large scale optimization, which we call the LM-CMA-ES. The LM-CMA-ES is a stochastic, derivative-free algorithm for numerical optimization of non-linear, non-convex optimization problems in continuous domain. Inspired by the limited memory BFGS method of Liu and Nocedal (1989), the LM-CMA-ES samples candidate solutions according to a covariance matrix reproduced from $m$ direction vectors selected during the optimization process. The decomposition of the covariance matrix into Cholesky factors allows to reduce the time and memory complexity of the sampling to $O(mn)$, where $n$ is the number of decision variables. When $n$ is large (e.g., $n$ > 1000), even relatively small values of $m$ (e.g., $m=20,30$) are sufficient to efficiently solve fully non-separable problems and to reduce the overall run-time.Comment: Genetic and Evolutionary Computation Conference (GECCO'2014) (2014

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