Research On Constrained Multi-objective Optimization Problems Based On Evolutionary Algorithms

Recently,constrained multi-objective optimization problems are widely occurring in many fields of production and scientific research,and they have become a hot spot and difficult research area in the field of intelligent optimization.Research on constrained optimization based on multi-objective evolutionary algorithms has become a mainstream research direction because of their outstanding processing effect.However,there are still many drawbacks,such as being easy to fall into a local optimum,an uneven distribution of Pareto solution set,and low convergence accuracy.In particular,for constrained many-objective optimization problems,the difficulty of solving the problem increases significantly with the increase of the number of objectives.Moreover,to improve the convergence accuracy,the existing algorithms sacrifice the convergence speed,which limits its application in practical problems.Therefore,it is of great theoretical and practical significance to study effective constrained multi-objective evolutionary algorithms.In this thesis,a series of improvements are proposed to improve the performance of the algorithms for solving various types of constrained multi-objective optimization problems.In a practical application,the proposed improved algorithms were used to improve the optimization effectiveness of the existing methods for the optimization problems in the hydrodynamic performance of ships.The main work of the paper can be summarized in the following four aspects.Firstly,an adaptive ?-constrained bi-objective and tri-objective evolutionary algorithm based on decomposition and differential is proposed.Firstly,to balance the distributivity and convergence of the algorithm,the selection operation is improved by making full use of infeasible individuals with smaller objective function values in the population.Then,to improve the population diversity and further balance the distributivity and convergence of the algorithm,an adaptive ?-constrained level value calculation method is proposed.Finally,to improve the search efficiency and avoid falling into local optimum,a crossover strategy based on differential evolution is designed to balance the exploration ability and exploitation ability through the effective use of excellent infeasible individuals.Through the above series of improvements,the problem of low convergence accuracy of the constrained bi-objective and tri-objective evolutionary algorithms is effectively solved.Secondly,an angle information-based constrained many-objective evolutionary algorithm is proposed.To improve the convergence speed of the algorithm,an angle violation function-based selection operation is designed to directly select the better individuals from the combined population based on the dynamic convergence and distributivity.However,the above improvements reduce the convergence accuracy,for which a crossover strategy based on the differential evolution algorithm is proposed,and a proportionality factor is set,which can select infeasible individuals to participate in the crossover operation at different evolutionary stages.Through the above two improvements,the convergence speed of the algorithm is substantially improved while ensuring that the convergence accuracy meets the requirements and effectively solves the slow convergence speed problem of the current constrained many-objective evolutionary algorithms.Thirdly,a coevolutionary-based equality constrained multi-objective evolutionary algorithm is proposed.Through weak coevolution,the main population is responsible for guiding the whole population to approach the feasible region and get close to the Pareto front by considering the constraints,while the auxiliary population is only responsible for exploring the whole search space without considering the constraints.Furthermore,different crossover strategies are respectively designed for the two coevolutionary populations.Finally,a repair operation is added to the individuals obtained from the crossover operation to make it more individuals approach the feasible region.Through the above three improvements,the problem of low convergence accuracy of the equality-constrained multi-objective evolutionary algorithm is effectively solved.Finally,the proposed constrained bi-objective and tri-objective evolutionary algorithm was applied to the optimal design of ship maneuverability,which makes the ship has greater linear stability and smaller relative slew diameter.The proposed constrained many-objective evolutionary algorithm was applied to the comprehensive optimal design of green ship hydrodynamic performance by constructing a constrained many-objective optimization model with fast,wave resistant,maneuverable,and energy-efficient design indices as the objective functions to achieve a comprehensive design process for environment protection,energy efficiency index,and hydrodynamic performance.