A Bi-population Cooperative Optimization Algorithm Assisted by an Autoencoder for Medium-scale Expensive Problems

This study presents an autoencoder-embedded optimization(AEO)algorithm which involves a bi-population cooperative strategy for medium-scale expensive problems(MEPs).A huge search space can be compressed to an informative lowdimensional space by using an autoencoder as a dimension reduction tool.The search operation conducted in this low space facilitates the population with fast convergence towards the optima.To strike the balance between exploration and exploitation during optimization,two phases of a tailored teaching-learning-based optimization(TTLBO)are adopted to coevolve solutions in a distributed fashion,wherein one is assisted by an autoencoder and the other undergoes a regular evolutionary process.Also,a dynamic size adjustment scheme according to problem dimension and evolutionary progress is proposed to promote information exchange between these two phases and accelerate evolutionary convergence speed.The proposed algorithm is validated by testing benchmark functions with dimensions varying from 50 to 200.As indicated in our experiments,TTLBO is suitable for dealing with medium-scale problems and thus incorporated into the AEO framework as a base optimizer.Compared with the state-of-the-art algorithms for MEPs,AEO shows extraordinarily high efficiency for these challenging problems,t hus opening new directions for various evolutionary algorithms under AEO to tackle MEPs and greatly advancing the field of medium-scale computationally expensive optimization.

Hybrid Meta-Model Based Design Space Differentiation Method for Expensive Problems

In this work,a hybrid meta-model based design space differentiation（HMDSD）method is proposed for practical problems.In the proposed method,an iteratively reduced promising region is constructed using the expensive points,with two different search strategies respectively applied inside and outside the promising region.Besides,the hybrid meta-model strategy applied in the search process makes it possible to solve the complex practical problems.Tested upon a serial of benchmark math functions,the HMDSD method shows great efficiency and search accuracy.On top of that,a practical lightweight design demonstrates its superior performance.

Classification- and Regression-Assisted Differential Evolution for Computationally Expensive Problems

Differential Evolution （DE） has been well accepted ever, it usually involves a large number of fitness evaluations to as an effective evolutionary optimization technique. Howobtain a satisfactory solution. This disadvantage severely restricts its application to computationally expensive problems, for which a single fitness evaluation can be highly timeconsuming. In the past decade, a lot of investigations have been conducted to incorporate a surrogate model into an evolutionary algorithm （EA） to alleviate its computational burden in this scenario. However, only limited work was devoted to DE. More importantly, although various types of surrogate models, such as regression, ranking, and classification models, have been investigated separately, none of them consistently outperforms others. In this paper, we propose to construct a surrogate model by combining both regression and classification techniques. It is shown that due to the specific selection strategy of DE, a synergy can be established between these two types of models, and leads to a surrogate model that is more appropriate for DE. A novel surrogate model-assisted DE, named Classification- and Regression-Assisted DE （CRADE） is proposed on this basis. Experimental studies are carried out on a set of 16 benchmark functions, and CRADE has shown significant superiority over DE-assisted with only regression or classification models. Further comparison to three state-of-the-art DE variants, i.e., DE with global and local neighborhoods （DECL）, JADE, and composite DE （CODE）, also demonstrates the superiority of CRADE.

Large-Scale Expensive Optimization with a Switching Strategy

Some optimization problems in scientific research,such as the robustness optimization for the Internet of Things and the neural architecture search,are large-scale in decision space and expensive for objective evaluation.In order to get a good solution in a limited budget for the large-scale expensive optimization,a random grouping strategy is adopted to divide the problem into some low-dimensional sub-problems.A surrogate model is then trained for each sub-problem using different strategies to select training data adaptively.After that,a dynamic infill criterion is proposed corresponding to the models currently used in the surrogate-assisted sub-problem optimization.Furthermore,an escape mechanism is proposed to keep the diversity of the population.The performance of the method is evaluated on CEC’2013 benchmark functions.Experimental results show that the algorithm has better performance in solving expensive large-scale optimization problems.

Evolutionary Computation for Expensive Optimization:A Survey

Expensive optimization problem(EOP) widely exists in various significant real-world applications. However, EOP requires expensive or even unaffordable costs for evaluating candidate solutions, which is expensive for the algorithm to find a satisfactory solution. Moreover, due to the fast-growing application demands in the economy and society, such as the emergence of the smart cities, the internet of things, and the big data era, solving EOP more efficiently has become increasingly essential in various fields, which poses great challenges on the problem-solving ability of optimization approach for EOP. Among various optimization approaches, evolutionary computation(EC) is a promising global optimization tool widely used for solving EOP efficiently in the past decades. Given the fruitful advancements of EC for EOP, it is essential to review these advancements in order to synthesize and give previous research experiences and references to aid the development of relevant research fields and real-world applications. Motivated by this, this paper aims to provide a comprehensive survey to show why and how EC can solve EOP efficiently. For this aim, this paper firstly analyzes the total optimization cost of EC in solving EOP. Then, based on the analysis, three promising research directions are pointed out for solving EOP, which are problem approximation and substitution, algorithm design and enhancement, and parallel and distributed computation. Note that, to the best of our knowledge, this paper is the first that outlines the possible directions for efficiently solving EOP by analyzing the total expensive cost. Based on this, existing works are reviewed comprehensively via a taxonomy with four parts, including the above three research directions and the real-world application part. Moreover, some future research directions are also discussed in this paper. It is believed that such a survey can attract attention, encourage discussions, and stimulate new EC research ideas for solving EOP and related real-world applications more efficiently.

Metamodel-based multidisciplinary design optimization methods for aerospace system

The design of complex aerospace systems is a multidisciplinary design optimization(MDO)problem involving the interaction of multiple disciplines.However,because of the necessity of evaluating expensive black-box simulations,the enormous computational cost of solving MDO problems in aerospace systems has also become a problem in practice.To resolve this,metamodel-based design optimization techniques have been applied to MDO.With these methods,system models can be rapidly predicted using approximate metamodels to improve the optimization efficiency.This paper presents an overall survey of metamodel-based MDO for aerospace systems.From the perspective of aerospace system design,this paper introduces the fundamental methodology and technology of metamodel-based MDO,including aerospace system MDO problem formulation,metamodeling techniques,state-of-the-art metamodel-based multidisciplinary optimization strategies,and expensive black-box constraint-handling mechanisms.Moreover,various aerospace system examples are presented to illustrate the application of metamodel-based MDOs to practical engineering.The conclusions derived from this work are summarized in the final section of the paper.The survey results are expected to serve as guide and reference for designers involved in metamodel-based MDO in the field of aerospace engineering.

An Optimization Algorithm Employing Multiple Metamodels and Optimizers

Modern engineering design optimization often relies on computer simulations to evaluate candidate designs, a setup which results in expensive black-box optimization problems. Such problems introduce unique challenges, which has motivated the application of metamodel-assisted computational intelligence algorithms to solve them. Such algorithms combine a computational intelligence optimizer which employs a population of candidate solutions, with a metamodel which is a computationally cheaper approximation of the expensive computer simulation. However, although a variety of metamodels and optimizers have been proposed, the optimal types to employ are problem dependant. Therefore, a priori prescribing the type of metamodel and optimizer to be used may degrade its effectiveness. Leveraging on this issue, this study proposes a new computational intelligence algorithm which autonomously adapts the type of the metamodel and optimizer during the search by selecting the most suitable types out of a family of candidates at each stage. Performance analysis using a set of test functions demonstrates the effectiveness of the proposed algorithm, and highlights the merit of the proposed adaptation approach.