Research On Gradient-free Algorithm For Solving Multiobjective Optimization Problems

Multiobjective optimization problems are a class of problems that are common in engineering application and scientific research.Such problems have multiple conflicting objectives,and there is usually no single optimal solution that achieves optimality on all objectives.The evolutionary multiobjective optimization algorithms have no requirements on the nature of the objective function and have the ability of global optimization,so they have become the current mainstream algorithms for solving multiobjective optimization problems.However,they suffer from slow convergence speed and low search efficiency.The traditional gradient-free algorithms have fast convergence speed,which are expected to improve the efficiency of the evolutionary multiobjective optimization algorithms.The main research goal of this paper is to integrate the gradient-free algorithms into the evolutionary multiobjective optimization algorithms,design a more efficient algorithm,and apply it to the nonlinear equation systems.The main innovations of this paper are as follows:1.To balance the local exploitation and global exploration capabilities of the algorithms,a multiobjective optimization algorithm based on direct multisearch location is proposed.The algorithm utilizes the decision variable control property recognition technology to analyze a given problem.According to the analysis results,a direct multisearch location strategy is designed,which adopts two different search methods to quickly locate promising areas and improves the algorithm’s ability to solve different types of problems.The improved NSGAII is used to update the solutions of promising areas,effectively balancing the diversity and convergence of the population.Comparative experimental results on three standard test suits demonstrate that the algorithm has great competitiveness.2.Aiming at the problem that the Pareto solution set is inconsistent with the direction vector distribution after the nonlinear equation system is transformed into a multiobjective optimization problem,a weighted biobjective optimization algorithm based on decomposition is proposed.The algorithm first proposes a modified weighted biobjective transformation method,which ensures the consistency of the Pareto solution set of the optimization problem and the distribution of the direction vector and makes the neighborhood information of the solutions can be effectively utilized.Second,the K-means clustering algorithm divides the population into several subpopulations to locate promising regions of roots.The designed population control strategy enables individuals in each subpopulation to exchange information with a certain probability.Comparative experimental results on standard test problems demonstrate that the algorithm has better performance.