Analysis of evolutionary algorithms on fitness function with time-linkage property (hot-off-the-press track at GECCO 2021)
Weijie Zheng, Huanhuan Chen, Xin Yao · Proceedings of the Genetic and Evolutionary Computation Conference Companion · 2021
In real-world applications, many optimization problems have the time-linkage property, that is, the objective function value relies on the current solution as well as the historical solutions. Although the rigorous theoretical analysis on evolutionary algorithms has rapidly developed in the last two decades, it remains an open problem to theoretically understand the behaviors of evolutionary algorithms on time-linkage problems. This paper takes the first step towards the rigorous analyses of evolutionary algorithms for time-linkage functions. Based on the basic OneMax function, we propose a time-linkage function where the first bit value of the last time step is integrated but has a different preference from the current first bit. We prove that with probability 1 - o(1), randomized local search and (1 + 1) EA cannot find the optimum, and with probability 1 - o(1), (μ + 1) EA is able to reach the optimum.