Cooperative co-evolution with differential grouping for large scale optimization

Cooperative co-evolution has been introduced into evolutionary algorithms with the aim of solving increasingly complex optimization problems through a divide-and-conquer paradigm. In theory, the idea of co-adapted subcomponents is desirable for solving large-scale optimization problems. However, in practice, without prior knowledge about the problem, it is not clear how the problem should be decomposed. In this paper, we propose an automatic decomposition strategy called differential grouping that can uncover the underlying interaction structure of the decision variables and form subcomponents such that the interdependence between them is kept to a minimum. We show mathematically how such a decomposition strategy can be derived from a definition of partial separability. The empirical studies show that such near-optimal decomposition can greatly improve the solution quality on large-scale global optimization problems. Finally, we show how such an automated decomposition allows for a better approximation of the contribution of various subcomponents, leading to a more efficient assignment of the computational budget to various subcomponents

A Parallel Divide-and-Conquer based Evolutionary Algorithm for Large-scale Optimization

Large-scale optimization problems that involve thousands of decision variables have extensively arisen from various industrial areas. As a powerful optimization tool for many real-world applications, evolutionary algorithms (EAs) fail to solve the emerging large-scale problems both effectively and efficiently. In this paper, we propose a novel Divide-and-Conquer (DC) based EA that can not only produce high-quality solution by solving sub-problems separately, but also highly utilizes the power of parallel computing by solving the sub-problems simultaneously. Existing DC-based EAs that were deemed to enjoy the same advantages of the proposed algorithm, are shown to be practically incompatible with the parallel computing scheme, unless some trade-offs are made by compromising the solution quality.Comment: 12 pages, 0 figure

A similarity-based cooperative co-evolutionary algorithm for dynamic interval multi-objective optimization problems

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Dynamic interval multi-objective optimization problems (DI-MOPs) are very common in real-world applications. However, there are few evolutionary algorithms that are suitable for tackling DI-MOPs up to date. A framework of dynamic interval multi-objective cooperative co-evolutionary optimization based on the interval similarity is presented in this paper to handle DI-MOPs. In the framework, a strategy for decomposing decision variables is first proposed, through which all the decision variables are divided into two groups according to the interval similarity between each decision variable and interval parameters. Following that, two sub-populations are utilized to cooperatively optimize decision variables in the two groups. Furthermore, two response strategies, rgb0.00,0.00,0.00i.e., a strategy based on the change intensity and a random mutation strategy, are employed to rapidly track the changing Pareto front of the optimization problem. The proposed algorithm is applied to eight benchmark optimization instances rgb0.00,0.00,0.00as well as a multi-period portfolio selection problem and compared with five state-of-the-art evolutionary algorithms. The experimental results reveal that the proposed algorithm is very competitive on most optimization instances

Limited Evaluation Cooperative Co-evolutionary Differential Evolution for Large-scale Neuroevolution

Many real-world control and classification tasks involve a large number of features. When artificial neural networks (ANNs) are used for modeling these tasks, the network architectures tend to be large. Neuroevolution is an effective approach for optimizing ANNs; however, there are two bottlenecks that make their application challenging in case of high-dimensional networks using direct encoding. First, classic evolutionary algorithms tend not to scale well for searching large parameter spaces; second, the network evaluation over a large number of training instances is in general time-consuming. In this work, we propose an approach called the Limited Evaluation Cooperative Co-evolutionary Differential Evolution algorithm (LECCDE) to optimize high-dimensional ANNs. The proposed method aims to optimize the pre-synaptic weights of each post-synaptic neuron in different subpopulations using a Cooperative Co-evolutionary Differential Evolution algorithm, and employs a limited evaluation scheme where fitness evaluation is performed on a relatively small number of training instances based on fitness inheritance. We test LECCDE on three datasets with various sizes, and our results show that cooperative co-evolution significantly improves the test error comparing to standard Differential Evolution, while the limited evaluation scheme facilitates a significant reduction in computing time

Large-scale optimization : combining co-operative coevolution and fitness inheritance

Large-scale optimization, here referring mainly to problems with many design parameters remains a serious challenge for optimization algorithms. When the problem at hand does not succumb to analytical treatment (an overwhelmingly common place situation), the engineering and adaptation of stochastic black box optimization methods tends to be a favoured approach, particularly the use of Evolutionary Algorithms (EAs). In this context, many approaches are currently under investigation for accelerating performance on large-scale problems, and we focus on two of those in this research. The first is co-operative co-evolution (CC), where the strategy is to successively optimize only subsets of the design parameters at a time, keeping the remainder fixed, with an organized approach to managing and reconciling these subspace optimization. The second is fitness inheritance (FI), which is essentially a very simple surrogate model strategy, in which, with some probability, the fitness of a solution is simply guessed to be a simple function of the finesses of that solution’s parents. Both CC and FI have been found successful on nontrivial and multiple test cases, and they use fundamentally distinct strategies. In this thesis, we explored the extent to which both of these strategies can be used to provide additional benefits. In addition to combining CC and FI, this thesis also introduces a new FI scheme which further improves the performance of CC-FI. We show that the new algorithm CC-FI is highly effective for solving problems, especially when the new FI scheme is used. In the thesis, we also explored two basic adaptive parameter setting strategies for the FI component. We found that engineering FI (and CC, where it was otherwise not present) into these algorithms led to good performance and results

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