An Adaptive Framework to Tune the Coordinate Systems in Evolutionary Algorithms

In the evolutionary computation research community, the performance of most evolutionary algorithms (EAs) depends strongly on their implemented coordinate system. However, the commonly used coordinate system is fixed and not well suited for different function landscapes, EAs 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 EAs. 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, EAs 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 EA paradigms, i.e., particle swarm optimization (PSO) and differential evolution (DE), for solving 30 test functions with 30 and 50 dimensions at the 2014 IEEE Congress on Evolutionary Computation. The experimental studies demonstrate its effectiveness.