Consensus, error estimates and applications of first- and second-order consensus-based optimization algorithms

摘要

Swarm-intelligence has received a lot of attention in relation to the modeling of cooperative control of drones, unmanned vehicles and robots from engineering, and meta-heuristic optimizers are often used by researchers from diverse disciplines from sociology to engineering. To name a few, ant-colony algorithm, artificial bee colony algorithm, genetic algorithm and particle swarm optimization correspond to such meta-heuristic optimizers driven by biology. Despite their handy implementations and broad coverage to diverse optimization problems, their rigorous theoretical analysis such as convergence, stability and error estimates are not well understood. Recently, consensus-based optimization (CBO) algorithm was proposed in the realm of applied mathematics and its theoretical analysis has been done, e.g. consensus and error estimates of CBO. In this paper, we provide a survey on the state-of-the-art results on the quantitative estimates and applications of first-order and second-order CBOs which are derivative-free optimization method that employs a multi-point aggregation model. Although it was motivated by the particle swarm optimization algorithm, CBO admits theoretical analysis such as convergence and error estimates under suitable frameworks. This paper offers a comprehensive summary of recent achievement concerning consensus, convergence, and performance results in first- and second-order time-discrete CBO algorithms. We provide numerical experiments, illustrating operations on various random networks and examining the effects on computation time and minimization performance under different parameters. Furthermore, we also discuss several applications in finance and real-world optimization problems.