Cooperative Coevolution for Non-Separable Large-Scale Black-Box Optimization: Convergence Analyses and Distributed Accelerations

Given the ubiquity of non-separable optimization problems in real worlds, in this paper we analyze and extend the large-scale version of the well-known cooperative coevolution (CC), a divide-and-conquer optimization framework, on non-separable functions. First, we reveal empirical reasons of why decomposition-based methods are preferred or not in practice on some non-separable large-scale problems, which have not been clearly pointed out in many previous CC papers. Then, we formalize CC to a continuous game model via simplification, but without losing its essential property. Different from previous evolutionary game theory for CC, our new model provides a much simpler but useful viewpoint to analyze its convergence, since only the pure Nash equilibrium concept is needed and more general fitness landscapes can be explicitly considered. Based on convergence analyses, we propose a hierarchical decomposition strategy for better generalization, as for any decomposition there is a risk of getting trapped into a suboptimal Nash equilibrium. Finally, we use powerful distributed computing to accelerate it under the multi-level learning framework, which combines the fine-tuning ability from decomposition with the invariance property of CMA-ES. Experiments on a set of high-dimensional functions validate both its search performance and scalability (w.r.t. CPU cores) on a clustering computing platform with 400 CPU cores

Symbol: Generating Flexible Black-Box Optimizers through Symbolic Equation Learning

Recent Meta-learning for Black-Box Optimization (MetaBBO) methods harness neural networks to meta-learn configurations of traditional black-box optimizers. Despite their success, they are inevitably restricted by the limitations of predefined hand-crafted optimizers. In this paper, we present \textsc{Symbol}, a novel framework that promotes the automated discovery of black-box optimizers through symbolic equation learning. Specifically, we propose a Symbolic Equation Generator (SEG) that allows closed-form optimization rules to be dynamically generated for specific tasks and optimization steps. Within \textsc{Symbol}, we then develop three distinct strategies based on reinforcement learning, so as to meta-learn the SEG efficiently. Extensive experiments reveal that the optimizers generated by \textsc{Symbol} not only surpass the state-of-the-art BBO and MetaBBO baselines, but also exhibit exceptional zero-shot generalization abilities across entirely unseen tasks with different problem dimensions, population sizes, and optimization horizons. Furthermore, we conduct in-depth analyses of our \textsc{Symbol} framework and the optimization rules that it generates, underscoring its desirable flexibility and interpretability.Comment: Published as a conference paper at ICLR 202

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

Towards large scale continuous EDA: a random matrix theory perspective

Estimation of distribution algorithms (EDA) are a major branch of evolutionary algorithms (EA) with some unique advantages in principle. They are able to take advantage of correlation structure to drive the search more efficiently, and they are able to provide insights about the structure of the search space. However, model building in high dimensions is extremely challenging and as a result existing EDAs lose their strengths in large scale problems. Large scale continuous global optimisation is key to many real world problems of modern days. Scaling up EAs to large scale problems has become one of the biggest challenges of the field. This paper pins down some fundamental roots of the problem and makes a start at developing a new and generic framework to yield effective EDA-type algorithms for large scale continuous global optimisation problems. Our concept is to introduce an ensemble of random projections of the set of fittest search points to low dimensions as a basis for developing a new and generic divide-and-conquer methodology. This is rooted in the theory of random projections developed in theoretical computer science, and will exploit recent advances of non-asymptotic random matrix theory

Discovering Attention-Based Genetic Algorithms via Meta-Black-Box Optimization

Genetic algorithms constitute a family of black-box optimization algorithms, which take inspiration from the principles of biological evolution. While they provide a general-purpose tool for optimization, their particular instantiations can be heuristic and motivated by loose biological intuition. In this work we explore a fundamentally different approach: Given a sufficiently flexible parametrization of the genetic operators, we discover entirely new genetic algorithms in a data-driven fashion. More specifically, we parametrize selection and mutation rate adaptation as cross- and self-attention modules and use Meta-Black-Box-Optimization to evolve their parameters on a set of diverse optimization tasks. The resulting Learned Genetic Algorithm outperforms state-of-the-art adaptive baseline genetic algorithms and generalizes far beyond its meta-training settings. The learned algorithm can be applied to previously unseen optimization problems, search dimensions & evaluation budgets. We conduct extensive analysis of the discovered operators and provide ablation experiments, which highlight the benefits of flexible module parametrization and the ability to transfer (`plug-in') the learned operators to conventional genetic algorithms.Comment: 14 pages, 31 figure

A New Optimization Algorithm Based on Search and Rescue Operations

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Also, in order to evaluate the application of SAR on real-world optimization problems, it was applied to three engineering design problems, and the results revealed that SAR is able to find more accurate solutions with fewer function evaluations in comparison with the other existing algorithms. Thus, the proposed algorithm can be considered an efficient optimization method for real-world optimization problems.This study was partially supported by the Spanish Research Project (nos. TIN2016-80856-R and TIN2015-65515-C4-1-R).Shabani, A.; Asgarian, B.; Gharebaghi, SA.; Salido Gregorio, MA.; Giret Boggino, AS. (2019). A New Optimization Algorithm Based on Search and Rescue Operations. Mathematical Problems in Engineering. 2019:1-23. https://doi.org/10.1155/2019/2482543S1232019Bianchi, L., Dorigo, M., Gambardella, L. M., & Gutjahr, W. J. (2008). A survey on metaheuristics for stochastic combinatorial optimization. Natural Computing, 8(2), 239-287. doi:10.1007/s11047-008-9098-4Holland, J. H. 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Weed/Plant Classification Using Evolutionary Optimised Ensemble Based On Local Binary Patterns

This thesis presents a novel pixel-level weed classification through rotation-invariant uniform local binary pattern (LBP) features for precision weed control. Based on two-level optimisation structure; First, Genetic Algorithm (GA) optimisation to select the best rotation-invariant uniform LBP configurations; Second, Covariance Matrix Adaptation Evolution Strategy (CMA-ES) in the Neural Network (NN) ensemble to select the best combinations of voting weights of the predicted outcome for each classifier. The model obtained 87.9% accuracy in CWFID public benchmark