A solution to common fixed point problems using a hybrid method of invasive weed optimization and jaya algorithm

Common fixed point problems (CFPs) arise in many practical engineering applications and are challenging problems since they can be non-convex, nonlinear and non-smooth. Solving nonlinear and non-smooth problems is difficult due to their intricate nature and the lack of well-established methods for addressing them. Furthermore, achieving convergence to a common fixed point can be challenging, especially when dealing with non-convex problems. The convergence rate and stability of the common fixed point can be affected by various factors, such as the choice of initialization, the optimization algorithm used, and the optimized function properties. To address the above difficulties, an efficient and robust hybrid algorithm method is proposed, merging the Jaya Algorithm (JAYA) with Invasive Weed Optimization (IWO). It is abbreviated as JAIWO. In the IWO, each weed, (i.e. a solution), reproduces new seeds (offspring) based on their own knowledge. In other words, there is no information-sharing among weeds in the reproduction process. It may cause premature convergence, trapping by local optima, and slow convergence. To get rid of the inherited drawbacks of IWO, it is hybridized with JAYA since it has good exploration and exploitation abilities in the search space. To demonstrate the performance of the proposed JAIWO, four CFPs are taken into account for experimentation and the experimental results are compared with eight well-known and state-of-the-art algorithms. The comparisons reveal that JAIWO outperforms the competitors for all considered CFPs.