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

Contribution based multi-island competitive cooperative coevolution

Competition in cooperative coevolution (CC) has demonstrated success in solving global optimization problems. In a recent study, a multi-island competitive cooperative coevolution (MIC3) algorithm was introduced that featured competition and collaboration of several different problem decomposition strategies implemented as independent islands. It was shown that MIC3converges to high quality solutions without the need to find an optimal decomposition. MIC3splits the computational budget in terms of the number of function evaluations, equally amongst all the islands and evolves them in a round-robin fashion. This overlooks the difference in contributions of different islands towards improving the overall objective function value. Therefore, a considerable amount of function evaluations is wasted on the low-contributing islands as their problem decomposition strategies may not appeal to the problem at the given stage of the evolutionary process. This paper proposes contribution-based MIC3 algorithms (MIC4) that quantifies the contributions of each island and allocates the computational budget accordingly. The experimental analysis reveals that the proposed method outperforms its counterpart

High-dimensional Black-box Optimization via Divide and Approximate Conquer

Divide and Conquer (DC) is conceptually well suited to high-dimensional optimization by decomposing a problem into multiple small-scale sub-problems. However, appealing performance can be seldom observed when the sub-problems are interdependent. This paper suggests that the major difficulty of tackling interdependent sub-problems lies in the precise evaluation of a partial solution (to a sub-problem), which can be overwhelmingly costly and thus makes sub-problems non-trivial to conquer. Thus, we propose an approximation approach, named Divide and Approximate Conquer (DAC), which reduces the cost of partial solution evaluation from exponential time to polynomial time. Meanwhile, the convergence to the global optimum (of the original problem) is still guaranteed. The effectiveness of DAC is demonstrated empirically on two sets of non-separable high-dimensional problems.Comment: 7 pages, 2 figures, conferenc

Bandit-based cooperative coevolution for tackling contribution imbalance in large-scale optimization problems

This paper addresses the issue of computational resource allocation within the context of cooperative coevolution. Cooperative coevolution typically works by breaking a problem down into smaller subproblems (or components) and coevolving them in a round-robin fashion, resulting in a uniform resource allocation among its components. Despite its success on a wide range of problems, cooperative coevolution struggles to perform efficiently when its components do not contribute equally to the overall objective value. This is of crucial importance on large-scale optimization problems where such difference are further magnified. To resolve this imbalance problem, we extend the standard cooperative coevolution to a new generic framework capable of learning the contribution of each component using multi-armed bandit techniques. The new framework allocates the computational resources to each component proportional to their contributions towards improving the overall objective value. This approach results in a more economical use of the limited computational resources. We study different aspects of the proposed framework in the light of extensive experiments. Our empirical results confirm that even a simple bandit-based credit assignment scheme can significantly improve the performance of cooperative coevolution on large-scale continuous problems, leading to competitive performance as compared to the state-of-the-art algorithms

Scaling Up Dynamic Optimization Problems: A Divide-and-Conquer Approach

Scalability is a crucial aspect of designing efficient algorithms. Despite their prevalence, large-scale dynamic optimization problems are not well-studied in the literature. This paper is concerned with designing benchmarks and frameworks for the study of large-scale dynamic optimization problems. We start by a formal analysis of the moving peaks benchmark and show its nonseparable nature irrespective of its number of peaks. We then propose a composite moving peaks benchmark suite with exploitable modularity covering a wide range of scalable partially separable functions suitable for the study of large-scale dynamic optimization problems. The benchmark exhibits modularity, heterogeneity, and imbalance features to resemble real-world problems. To deal with the intricacies of large-scale dynamic optimization problems, we propose a decomposition-based coevolutionary framework which breaks a large-scale dynamic optimization problem into a set of lower dimensional components. A novel aspect of the framework is its efficient bi-level resource allocation mechanism which controls the budget assignment to components and the populations responsible for tracking multiple moving optima. Based on a comprehensive empirical study on a wide range of large-scale dynamic optimization problems with up to 200 dimensions, we show the crucial role of problem decomposition and resource allocation in dealing with these problems. The experimental results clearly show the superiority of the proposed framework over three other approaches in solving large-scale dynamic optimization problems

Solving Incremental Optimization Problems via Cooperative Coevolution

Engineering designs can involve multiple stages, where at each stage, the design models are incrementally modified and optimized. In contrast to traditional dynamic optimization problems where the changes are caused by some objective factors, the changes in such incremental optimization problems are usually caused by the modifications made by the decision makers during the design process. While existing work in the literature is mainly focused on traditional dynamic optimization, little research has been dedicated to solving such incremental optimization problems. In this work, we study how to adopt cooperative coevolution to efficiently solve a specific type of incremental optimization problems, namely, those with increasing decision variables. First, we present a benchmark function generator on the basis of some basic formulations of incremental optimization problems with increasing decision variables and exploitable modular structure. Then, we propose a contribution based cooperative coevolutionary framework coupled with an incremental grouping method for dealing with them. On one hand, the benchmark function generator is capable of generating various benchmark functions with various characteristics. On the other hand, the proposed framework is promising in solving such problems in terms of both optimization accuracy and computational efficiency. In addition, the proposed method is further assessed using a real-world application, i.e., the design optimization of a stepped cantilever beam