| The optimization problem has been widely researched and applied in many fields such as manufacturing,agriculture,transportation,finance.With the rapid development of network and sensor technologies,human society has entered a new data-intensive era,namely the era of big data.In this context,the scale of the optimization problem expands naturally,and accordingly the large-scale optimization problem arises.As a result of exponential growth of search space and increasing complexity among decision variables,traditional optimization algorithms are difficult to find satisfactory solutions of large-scale problems within a reasonable time range.This thesis mainly focuses on the innovative research of complex large-scale optimization problems under three different characteristics of single-objective,computationally expensive and multi-objective.This thesis proposes evolutionary algorithms to deal with this kind of complex optimization problems,including a large-scale single-objective optimization algorithm considering computational resource allocation;a bi-population cooperative optimization algorithm assisted by an autoencoder for large-scale expensive problems;a surrogate-assisted autoencoder-embedded evolutionary optimization algorithm;an improved competitive particle swarm optimization algorithm based on generalized Pareto dominance for solving large-scale multi-objective optimization problems.The specific contents as listed follows:(1)For large-scale single-objective optimization problems,the search space increases exponentially with the increase of decision variable dimensions,therefore it is difficult to search in such a huge space.The "divide-and-conquer" framework provides a direction for solving this kind of problems,which decomposes large-scale problems into several low-dimensional sub-problems and then optimizes the subproblems separately.Existing works mainly focus on exploring different decomposition methods.However,efficient optimizer is the core of improving the solution accuracy,and how to allocate computational resources to each subproblem more effectively is the key to improve solution efficiency as well.In view of this,we propose a selevtive biogeography-based optimization algorithm considering computational resource allocation,depicted as follows: We design a selective migration operator which can not only improve the exploration ability,but also maintain better exploitation ability.Computational resource allocation method based on contribution uses the relative performance improvement to evaluate the contribution of each sub-population,which can reflect the contribution of each sub-population in time.At the same time,the threshold strategy is used as an additional constraint to measure whether a sub-population is in a stagnant condition.Once a sub-population is considered as a stagnant one,computational resources will not be allocated to it in this generation of evolution.Therefore,the proposed algorithm can effectively improve the accuracy and efficiency of dealing with large-scale problems.(2)Many practical optimization problems not only have high dimensional decision variables but also have computationally expensive evaluation models,thus requiring to find satisfactory solutions with limited computational resources.Surrogate-assisted evolutionary optimization is a mainstream method for solving computationally expensive problems.However,with the increase of the dimension of decision variables,it is difficult to build high-quality surrogate models based on limited data samples,therefore its optimization performance degrades sharply.If high-quality solutions can be produced,the number of real evaluation models consumed before finding satisfactory solutions can be greatly reduced,which is an alternative method to solve this kind of problems.Nevertheless,high-dimensional decision variables lead to huge and complex search space,which makes it difficult to traverse the whole search space within a limited number of search steps.Therefore,we intuitively consider an autoencoder as a dimension reduction technology to compress high-dimensional space into low-dimensional one,and then carry out reproduction operation in this significantly compressed space.In order to improve population diversity,we adopt a bi-population cooperative strategy,which is more conducive to a distributed evolution manner.In addition,we propose a dynamic size adjustment strategy based on problem dimension and evolutionary process,which can effectively enhance the diversity of sub-population and accelerate the convergence rate.As seen from experimental results,this framework provides a new direction for solving computationally expensive optimization problems.(3)Compared with other algorithms,the autoencoder-embedded optimization algorithm has some advantages when dealing with high-dimensional computationally expensive problems.However,if more evaluations are available,it can converge further to find better solutions.Therefore,we intend to incorporate surrogate models into the autoencoder-embedded optimization framework,which uses the cheap surrogate models to replace part of the real models for offspring evaluation,with the aim to effectively reduce the use of expensive models.In order to ensure the high-quality of surrogate models,we propose a surrogate activation condition considering problem dimension,which means that surroagete models are not trained and activated until enough data samples are collected.Moreover,we propose a novel model management strategy that only individuals whose predicted values are better than the historical values are reevaluated by the true model,because these solutions have higher possibility to help find the global optimum.In order to reduce the use of unnecessary real model evaluations,we also set a maximum number of reevaluated candidates each generation.It can be seen from the experimental results that the incorporation of surrogate models into the autoencoder-embedded optimization framework can significantly improve the convergence speed of the algorithm as well as reduce the time consumption under the condition of limited number of evaluation models.(4)Large-scale multi-objective and many-objective problems are extremely challenging to deal with as a result of exponentially expanded search space as well as complicated conflicting objectives.Most existing algorithms focus either on large-scale decision variables or multiple objectives solely while few algorithms consider both of them.Therefore,we propose an improved competitive swarm optimizer based on generalized Pareto dominance.Firstly,we propose an improved competitive swarm optimization(ICSO)which adopts a tri-competition mechanism and a novel updating strategy with the aim to strike the balance between convergence and diversity.Moreover,MultiGPO takes advantages of environmental selection strategy to enhance selection pressure and diversity.Therefore,we incorporate ICSO into MultiGPO framework to solve large-scale many-objective problems and name it as MultiGPO＿ICSO.The experimental results indicate that MultiGPO＿ICSO shows competitive performance on most problems with limited computational resources.Therefore,MultiGPO＿ICSO is suitable to deal with large-scale multi-objective and many-objective problems. |
