A Novel Free Search Algorithm

Free search(FS) is a novel swarm intelligence algorithm proposed in recentyears,which suggests to response the uncertainty with uncertainty and to reply theendlessness with endlessness.This algorithm mimics the behavior of higher gregariousanimals in nature and their daily exploration for water sources.The free and uncertainsearch behavior of the animals is abstracted and modelled in FS to optimize theobjective function,and the results showed better performance. Meantime,there are alsoproblems in the algorithm and bringing forward efficient improvement against theseproblems are becoming a hot topic among the researchers. A new improved algorithmThis paper improves the basic FS algorithm based on the diversities of individuals insearch capability, and applies the improved algorithm in solving nonlinear equations.The contributions are as following：1. First of all, the biological background, search mechanism, mathematical modelof the FS algorithm are introduced in this paper. And its existing problems are alsosummarized through parametric analysis and convergence analysis. At the same time,the ideological principle of several improved FS algorithm are briefly illustrated, andthe advantages and potential problems that may exist of these improvement strategiesare pointed out.2. For the problems that existed in the FS algorithm and its improved algorithm, anew adapted neighbourhood and step free search(ANSFS) algorithm is presented in thispaper. Its biological principles,search mechanism, mathematical model and performanceanalysis are also described in detail.3. Seven typical benchmark functions are tested to validate the correctness andeffectiveness of the ANSFS algorithm. The simulation results are compared with theclassical particle swarm optimization(PSO), the basic free search(FS) and other twoimproved FS algorithm in search speed, convergence precision, and space overhead.4. ANSFS algorithm is applied to solve the problem of nonlinear equations whichexist solutions. Firstly, transform the the nonlinear equations to a objective functionwhich needs to be optimized, then use ANSFS algorithm to search the best point withthe maximum value of the objective function,and this point is precisely the solution ofnonlinear equations. In comparison with traditional solution algorithms and other swarmintelligence algorithms, the ANSFS algorithm shows better effectiveness, accuracy and comprehensiveness in the simulation experiment.