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 (IOPs) 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 IOPs. In this paper, we study how to adopt cooperative coevolution to efficiently solve a specific type of IOPs, namely, those with increasing decision variables. First, we present a benchmark function generator on the basis of some basic formulations of IOPs 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. © 1997-2012 IEEE.
Bibliographical noteThis work was supported in part by the National Key Research and Development Program of China under Grant 2017YFC0804003, in part by EPSRC under Grant EP/J017515/1 and Grant EP/P005578/1, in part by the Program for Guangdong Introducing Innovative and Enterpreneurial Teams under Grant 2017ZT07X386, in part by the Shenzhen Peacock Plan under Grant KQTD2016112514355531, in part by the Science and Technology Innovation Committee Foundation of Shenzhen under Grant ZDSYS201703031748284, and in part by the Program for University Key Laboratory of Guangdong Province under Grant 2017KSYS008. The work of X. Yao was supported in part by the Royal Society Wolfson Research Merit Award and in part by Honda Research Institute Europe. (Ran Cheng and Mohammad Nabi Omidvar contributed equally to this work.)
- Cooperative coevolution (CC)
- experience-based optimization
- incremental optimization problem (IOP)
- variable grouping