An Adaptive Framework to Tune the Coordinate Systems in Nature-Inspired Optimization Algorithms

The performance of many nature-inspired optimization algorithms (NIOAs) depends strongly on their implemented coordinate system. However, the commonly used coordinate system is fixed and not well suited for different function landscapes, NIOAs thus might not search efficiently. To overcome this shortcoming, in this paper we propose a framework, named ACoS, to adaptively tune the coordinate systems in NIOAs. In ACoS, an Eigen coordinate system is established by making use of the cumulative population distribution information, which can be obtained based on a covariance matrix adaptation strategy and an additional archiving mechanism. Since the population distribution information can reflect the features of the function landscape to some extent, NIOAs in the Eigen coordinate system have the capability to identify the modality of the function landscape. In addition, the Eigen coordinate system is coupled with the original coordinate system, and they are selected according to a probability vector. The probability vector aims to determine the selection ratio of each coordinate system for each individual, and is adaptively updated based on the collected information from the offspring. ACoS has been applied to two of the most popular paradigms of NIOAs, i.e., particle swarm optimization and differential evolution, for solving 30 test functions with 30D and 50D at the 2014 IEEE Congress on Evolutionary Computation. The experimental studies demonstrate its effectiveness.