Is CC-(1+1) EA More Efficient than (1+1) EA on Separable and Inseparable Problems?

Per Kristian Lehre, Shishen Lin

Abstract: Many Real-world optimisation tasks are increasingly large-scale optimisation (LSO) problems. Cooperative co-evolutionary algorithms (CoEAs), which involve more than two populations and utilise the divide-and-conquer approach, have been introduced to solve LSO problems more efficiently. However, the behaviour of cooperative CoEAs is not fully understood because the interactions between two or more populations make analysis challenging. Runtime analysis has improved the under-standing of traditional EAs. We argue that using runtime analysis of CoEAs could provide helpful insights, e.g., how their expected runtime depends on alaorithmic design decisions. In this paper, we show that the expected optimisation time of the basic cooperative co-evolutionary (1+1) EA (CC-(1+1) EA) on linear functions is $\Theta(n\log n)$. This solves an open conjecture by (Jansen and Wiegand, 2004). Moreover, empirical analysis is conducted on two more complicated problems: NK − LANDSCAPE and $k$-MAXSAT problems. Our results show that the CC-(1+1) EA perform similarly to the (1+1) EA on these problems. However, adjusting block length allows us to optimise its performance on the NK − LANDSCAPE problem. Our results provide a more precise bound for the expected runtime of CC-(1+1) EA and a more detailed empirical analysis of its behaviour on more complicated inseparable problems.