Research On Evolutionary Optimization And Learning For Complex Continuous Optimization Problems

Whether in the field of science or engineering,continuous optimization problems are a very important research topic.Since complex continuous optimization problems usually present nonlinear,non-differentiable,multi-modal and other mathematical characteristics,this brings huge challenges to traditional mathematical programming methods.Population-based evolutionary algorithms have been favored by more and more researchers due to their simple principles and low requirements on the mathematical properties of the objective function.However,how to effectively balance the exploration and development of evolutionary algorithms has become a bottleneck in the field of numerical optimization.With this in mind,this thesis focuses on three different types of complex continuous optimization problems and studies the balance between exploration and exploitation of evolutionary algorithms.The research work is as follows:First,in this paper,a new mutation strategy called Level-Based Learning(LLDE)for Differential Evolution is proposed to improve the exploration capabilities without losing local search capability.This mutation strategy is based on the promising Level-Based Learning Swarm Optimizer.LLDE divides the population into levels according to the individuals'fitness value.Then,LLDE generates mutant vectors based on superior levels than the target vectors' levels.Hence,LLDE encourages learning in a more controlled way than the most popular mutation strategies.Experimental tests are performed on the CEC 2014 benchmark functions,and three original versions of state-of-the-art algorithms are compared with their LL-based version.From the obtained results,it is concluded that LLDE is competitive with commonly used mutation strategies and performs better in some complex hybrid functions,indicating an improvement in exploration when dealing with this kind of landscape.Second,this paper presents an improved stochastic-ranking-based differential evolution algorithm(ISRDE)for solving constrained numerical optimization problems.In ISRDE,some inferior solutions with lower objective values stored in an external archive are used to conditionally replace some individuals in the population by a cheap niche technique.This replacement process helps maintain effectively the balance between the constraints and objective function.Moreover,the proposed algorithm introduces a new mutation rule by utilizing the good information in the DE population and bad information in the external archive,which can secure a balance in the exploration and exploitation abilities.Besides,a bimodal distribution parameter setting is introduced to update the values of the mutation scaling and crossover rate.To verify and analyze the performance of ISRDE,experimental studies are conducted on CEC'06 benchmark test functions.The experimental results indicate that the performance of ISR has better or at least comparable to those of stochastic ranking and helps base algorithms to achieve better consistency towards finding feasible and optimal solutions.Third,this paper presents HMMOGA,a Hybrid algorithm for multimodal multiobjective numerical optimization.HMMOGA encourages the balance between exploration and exploration to effectively optimize problems with local Pareto sets.The exploration is achieved by using a multimodal optimization algorithm to direct individuals towards the promising regions with local optima.Later,HMMOGA uses clustering algorithms to identify the different separate regions and evolves each region independently to encourage convergence towards each Pareto set.To verify the performance of HMMOGA,experimental studies are conducted on CEC 2020 benchmark test functions.The experimental results indicate that HMMOGA has better convergence capabilities towards multimodal Pareto sets than other state-of-the-art algorithms while maintaining a competitive convergence towards optimal values in the objective space.