Research On Multi-objective Optimization Algorithm Based On Game Theory

The research on multi-objective optimization problems has a long history.At present,the multi-objective evolutionary algorithm represented by NSGA-II is mainly based on the method of non-dominated sorting solution to update and iterate the population.However,it has always been accompanied by a problem that is the number of solutions in the solution set obtained by the non-dominated sorting method will not always be maintained at a brilliant value with the iterative evolution of the population.The decreasing of the value will also affect the evolutionary efficiency of the population directly,which will prone to occur two problems.One is that the convergence speed of the Pareto front decreases gradually and the convergence becomes worse due to the evolutionary power insufficient.Another one is because of the gradual deterioration of the diversity of the Pareto optimal solution set that the algorithm is apt to fall into the local optimality and the algorithm's global optimization ability weakly.Game Theory(GT)is a science that studies the individuals to make actions through observation and prediction,so as to obtain the maximum effectiveness in competition.Game theory and the multi-objective optimization are very closely related to each other in terms of basic nature,consideration of ideas,or solutions.Nowadays,the complexity of multi-objective optimization problems is increasing.Improving the efficiency of multi-objective optimization algorithms for solving problems will become a major issue.Game theory provides a new possibility for improving algorithm performance.Therefore,the combination of game theory and multi-objective optimization is destined to become a necessity.It is well-known that the inertial navigation platform system is bound to be accompanied by errors during operation.But in the practical applications,this error will not remain in a constant range.On the contrary,the error value will increase with the working of the system.The increasing of the error value will greatly reduce the measurement accuracy of the system.This problem has existed for a long time.Therefore,researchers are required to focus on the following two points now: One is to improve the stability of the inertial instrument performance;the other is to focus on the measurement and test technical problems of the inertial navigation system.And it will be a great significance for the error separation and compensation of inertial stabilized platforms.Since the continuous rolling trajectory is beneficial to obtain a better test results during the operation of the inertial navigation platform,the continuous rolling self-calibration method is generally used to test the system-level calibration of the inertial navigation platform.However,the problem of finding the optimal rotation trajectory for the calibration test of the inertial navigation platform involves the field of multi-objective optimization.Therefore,for the sake of figuring out the practical issue and obtain all the error information,we need to select a suitable multi-objective optimization algorithm to solve the practical problems efficiently.This article mainly studies how to combine the ideas of game theory to improve the multi-objective evolutionary algorithm and solve the problem of dynamic experiment design of the inertial navigation platform.Firstly,it discusses the principles and concepts related to the multi-objective optimization problems and the multi-objective optimization algorithms,mainly analyzes the principles and processes of the two algorithms of NSGA-II and SPEA-II,and studies the basic concepts of algorithm performance evaluation criteria and test functions.Secondly,a multiobjective optimization algorithm(SMSG-MOGA)combined with game theory is proposed according to the research for the multi-objective optimization and game theory.Then according to the algorithm performance evaluation criteria,the performance of the algorithm is tested and compared based on the ZDT series of test questions.And from the algorithm analysis and simulation experiments,it is concluded that the optimization performance of the new algorithm is more powerful.Then an error model of the inertial navigation platform was established based on the angle method,and the relevant content of the experimental optimization design of the multi-objective problem is studied.Finally,the algorithm is connected with actual problems to add constraints and improve the algorithm to solve the problem of multiobjective optimization experiment design based on the inertial navigation platform system.The search efficiency and global optimization performance of the above mentioned algorithms are compared and discussed through the simulation.The final simulation results show that the improved multi-objective evolutionary algorithm based on game theory(CSMSG-MOGA)has a good performance in solving this problem.