A Study Of Evolutionary Algorithms For Solving Complex Multiobjective Optimization Problems

Many optimization problems in the real world may contain multiple objectives to be optimized.Such a class of problems is defined as multiobjective optimization problems.Since multiple objectives usually conflict with each other,the solutions of multiobjective optimization problems are referred to as a set of trade-off solutions.Evolutionary algorithms,such as genetic algorithm,differential evolution,and particle swarm optimization,are considered as an effective class of methods to deal with multiobjective optimization problems,drawing much attention in the last decades.However,existing multiobjective evolutionary algorithms often suffer from performance degradation when solving some complex multiobjective optimization problems,such as those with expensive evaluation,with many decision variables,and with irregular Pareto fronts.They cannot obtain a set of trade-off solutions with well convergence and spread.This thesis focuses on solving the most common complex multiobjective optimization problems and proposes a series of new multiobjective evolutionary algorithms,aiming to improve the theoretical framework and application scenarios of evolutionary algorithms.The main research contents are summarized as follows.(1)A two-stage optimization-based multiobjective evolutionary algorithm.To address a class of large-scale multiobjective optimization problems with many decision variables and sparse Pareto optimal solutions,i.e.,large-scale sparse multiobjective optimization problems,this thesis proposes a two-stage optimization-based multiobjective evolutionary algorithm(TSSparse EA).TS-Sparse EA first adopts a binary weight optimization framework in the first stage.Through a set of low-dimensional binary weights,TS-Sparse EA transforms the original largescale optimization problem into a low-dimensional one.In the second stage,TS-Sparse EA employs an evolutionary algorithm with a hybrid encoding and matching mechanism.The binary weight optimization and hybrid encoding couple the prior information that Pareto optimal solutions are sparse to the evolution process,while the matching integrates the offspring solutions formed by different types of encodings after crossover and mutation.All three steps help the population move toward the Pareto front.Experimental results on benchmark test problems such as SMOP show that TS-Sparse EA can effectively generate more sparse Pareto optimal solutions than existing multiobjective evolutionary algorithms,which confirms its advantages in solving large-scale sparse multiobjective optimization problems.(2)A multiobjective evolutionary algorithm based on a hierarchical surrogate model.To address a class of multi-objective optimization problems with many decision variables and expensive objective evaluations(i.e.,high-dimensional expensive multiobjective optimization problems),this thesis proposes a multiobjective evolutionary algorithm based on a hierarchical surrogate model(HS-MOEA).On one hand,HS-MOEA utilizes the dynamic grouping in each generation,aiming to divide the decision variables into several groups and optimize these groups one by one.On the other hand,the local surrogate learns the mapping between a group and objective functions,while the global surrogate approximates the mapping between all the variables and objective functions and finally selects a promising solution for real objective evaluation.In addition,HS-MOEA adopts a strategy for managing training samples based on K-means clustering,aiming to weaken the influence of decision variables in other groups on the local surrogate.Experimental results on benchmark test problems such as DTLZ show that compared with existing multiobjective evolutionary algorithms,HS-MOEA can generate a set of Pareto optimal solutions that are closer to the true Pareto front within a limited number of objective function evaluations and is competitive in solving high-dimensional expensive multiobjective optimization problems.(3)A decomposition-based multiobjective evolutionary algorithm with local reference point-aided search.To address a class of multiobjective optimization problems with irregular Pareto front shapes,this thesis proposes a novel decomposition-based multiobjective evolutionary algorithm with local reference point-aided search(MOEA/D-LRAS).Firstly,MOEA/D-LRAS defines two novel concepts,including a global reference point and a local reference point.The global reference point is applied to all the weight vectors,and it guides a global search in the objective space.In contrast,the local reference point is only applied to some of the weight vectors,and it guides a local search in some regions of the objective space.Secondly,MOEA/D-LRAS adopts an adaptive local reference point assignment strategy.It decides whether to assign a local reference point to a weight vector member by analyzing the impact of the solution jointly selected by the local reference point and the weight vector on the current population quality.Experimental results show that MOEA/D-LRAS can well address various shapes of Pareto fronts.It also has a superiority compared with existing multiobjective evolutionary algorithms on solving multiobjective optimization problems with regular or irregular Pareto front shapes.(4)A decomposition-based multiobjective particle swarm optimization for automating convolutional neural networks.Convolutional neural network architecture search,as a class of complex multi-objective optimization problems in deep learning,is characterized as a problem with implicitly-defined search space and expensive computation cost.To address the issue,this thesis proposes a decomposition-based multiobjective particle swarm optimization for automating convolutional neural networks(MOPSO/D-NAS).MOPSO/D-NAS utilizes a hybrid binary encoding representation to express the topology and operator types of neural networks.Then,it adopts an adaptive penalty to refine the search of decision preference regions in the objective space.Experimental results on both MNIST and CIFAR-10 datasets confirm that MOPSO/D-NAS can obtain convolutional neural network architectures with better generalization performance and fewer params than the other neural architecture search methods.