Research And Application Of Heuristic Arithmetic Optimization Algorithm

The arithmetic optimization algorithm(AOA)is a heuristic optimization algorithm to simulate the operator’s functions of the add(+),subtract(-),multiply(×)and division(÷)in mathematical operations.The algorithm has a simple structure and easy to understand and implement.It is widely used in many fields such as scientific calculation,engineering optimization,etc.However,with the deepening of research for the algorithm,the researchers have found some shortcomings,such as low accuracy for solving problems and can only to deal with the single objective problems.In this paper,the defects of arithmetic optimization algorithm are studied and improved,and then the improved algorithm is applied to solve numerical optimization,multi-root problems of nonlinear equations and polygon approximation problems,expanding the application scope of the algorithm.The research achievements of this paper are as follows:(1)The AOA based on population control strategy is proposed,which not only improves the population diversity,the convergence speed and the solution prediction,but also balances the exploration and exploitation capabilities of the algorithm.The improved arithmetic optimization algorithm is applied to solve CEC2019 test function,numerical solution of complex nonlinear problems and singular integrals,and the minimum joint rotation angle of the manipulator.The results of numerical experiments prove that there is significant improvement for the convergence speed and accuracy of the improved arithmetic optimization algorithm.(2)A hybrid AOA algorithm is proposed by combining the mechanism of moths updating around the light source in moth-fighting algorithm,and introducing the repulsion mechanism,archiving mechanism and reinitialization mechanism.The hybrid AOA algorithm is applied to solve 30 groups of nonlinear equation systems,and the results show that the AOA is better than other algorithms in solving multiple roots compared with relevant literatures.(3)An integer coded IAOA algorithm is proposed and applied to the polygon approximation problem.The experimental results show that the IAOA algorithm has better approximation ability compared with six algorithms by testing the approximation polygons of six groups of graphs and can find the key points in the original graph to approximate the ideal polygon.A new method for the approximation of curve graphs is proposed.