Research On Pyramid Evolution Strategy Of Integer Programming

Integer programming(IP)is a kind of mathematical model widely used in scientific field and applied research,which belongs to NP hard problem.The current solution method is based on swarm intelligence algorithm,however,this kind of method has not been able to solve the contradiction between exploration and exploitation,competition and cooperation within the population or between the populations.The pyramid evolution strategy(PES)is a new algorithm,which adopts the hierarchical mechanism and promotion mechanism to effectively solve the above two contradictions,and has the advantage of strong ability to jump out of local optimal.However,the research of PES algorithm in the field of integer programming is still limited,and the algorithm itself still has some defects.Therefore,in this paper,PES is studied by extending it from function optimization to IP problem.The main research contents are as follows:(1)Aiming at the IP problem with constraints,this paper introduces a method to deal with constraints.(2)The basic information of PES algorithm is introduced in detail,and its mechanism,convergence and time complexity are analyzed.(3)To solve the general integer programming problems,a PES algorithm based on the optimal cooperation strategy is proposed.By introducing two extremum of particle swarm optimization algorithm,a new population updating method is designed.The convergence,stability and the best performance of the algorithm are explored by experiments and comparison.The experimental results show that PES algorithm based on optimal cooperation strategy has better performance than other 10 algorithms in solving IP problems.(4)For nonlinear IP(NLIP),an improved PES(IPES)algorithm is proposed.Firstly,the location and representation characteristics of population individuals are integrated,the potential value function is defined,and then the population is divided to make the division of labor more clear.Secondly,the guidance of the current optimal individuals to the population individuals is considered in the population renewal,a new acceleration strategy is designed to improve the global search ability of the algorithm.Simulation results show that IPES has faster convergence speed and stronger robustness than basic PES and other 10 algorithms by solving 14 integer programming problems.Through the analysis and improvement of PES algorithm,we applied it to the IP field,which enriches the theoretical knowledge of PES algorithm,and provides a new way to solve IP problem.