Abstract
The solution of large-scale optimization problems is the key to many decision-making processes in practice. However, it is a challenging research topic when considered both the quality of solutions and the required computational time. One of the popular approaches for these problems is to divide the problems into a number of smaller sub-problems, that are then solved separately with an exchange of some information using the cooperative co-evolution (CC) concept. However, the characteristics of sub-components could be different, and their contributions to the overall performance can also be different while solving the problem. In the CC approach, it usually applies one optimizer and allocates equal computational budget to all sub-components. In this article, a new algorithm is proposed with the use of multiple optimizers, along with a need-based allocation of computational budget for the sub-components. In the proposed algorithm, a group of optimizers cooperate in an effective way to evolve the sub-components, depending on heuristic fuzzy rules. The performance of our proposed algorithm was evaluated by solving a number of large-scale global optimization benchmark functions. The empirical results show that the proposed algorithm outperforms equal allocation CC, a single selection characteristic, a single candidate optimizer and state-of-the-art algorithms.
Highlights
Optimization algorithms, such as evolutionary algorithms (EAs) [1] and swarm intelligence (SI) [2], have emerged as effective methods for solving a wide variety of optimization problems, such as single objective or multi-objective problems, with discrete and/or continuous variables, in different fields including, but not limited to, engineering and science [3], [4]
This means that all the sub-problems have equivalent computational resources, which negatively affects the performance of EAs when solving large-scale optimization problems
F3C adopted selection criteria based on: 1) fitness improvement; 2) the diversity of the population and 3) both of them, with the results shown in Table 4, which clearly illustrate the importance of merging these characteristics on evaluating the effectiveness of Ci O j pair
Summary
Optimization algorithms, such as evolutionary algorithms (EAs) [1] and swarm intelligence (SI) [2], have emerged as effective methods for solving a wide variety of optimization problems, such as single objective or multi-objective problems, with discrete and/or continuous variables, in different fields including, but not limited to, engineering and science [3], [4]. The performance of the CC algorithms is highly dependent on the number of common variables and the complexity of the sub-problems. M. Meselhi et al.: Contribution Based Co-evolutionary Algorithm for Large-scale Optimization Problems during the search process [12]. For large-scale problems, divided into a number of smaller sub-problems, the use of multiple optimizers with complementary abilities could offer significant advantages, where an optimizer can be selected for each sub-problem based on its rate of progress in the search process. Motivated by the above two aspects, in this paper, a performance-based computational budget allocation among the sub-problems, with appropriate use of multiple optimizers, called fuzzy contribution-based cooperative co-evolution (F3C), is proposed as an effective alternative to a roundrobin strategy with a single optimizer. The remainder of this paper is structured as follows: Section II highlights the related literature; Section III describes the proposed algorithm; Section IV presents the experimental results; and Section V concludes the paper with directions for future work
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