Jaya Invasive Weed Optimization: An Algorithm to Solve Common Fixed Point Problems

Abstract This study makes the first attempt to find a common fixed point of a system of nonlinear mappings, namely common fixed point problems(CFPs), using meta-heuristics. Invasive Weed Optimization(IWO) mimics the colonizing behaviour of weeds in crop fields. In IWO, each weed represents a solution, reproduces new seeds (offspring) based on their 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. A recent meta-heuristic Jaya algorithm(JAYA) is a powerful optimizer. It has high exploration and exploitation abilities in the search space due to the usage of random numbers and absolute values of the solutions in the updating process. Because of this affirmative feature, each candidate solution moves towards the best candidate solution and avoid moving towards the worst candidate solution. Therefore the hybridization of IWO and JAYA, in short, JAIWO, has been proposed to balance the exploration and exploitation of the search space while solving CFPs. To demonstrate the performance of the proposed JAIWO, four CFPs, formulated from unconstrained optimization benchmark problems, are taken into account, and the results obtained are compared with the results of the conventional IWO, JAYA and six other well known algorithms. The comparisons revealed that JAIWO outperforms the competitors for all considered problems.