A pairwise comparison based surrogate-assisted evolutionary algorithm for expensive multi-objective optimization

Evolutionary computation is a rapidly evolving field and the related algorithms have been successfully used to solve various real-world optimization problems. The past decade has also witnessed their fast progress to solve a class of challenging optimization problems called high-dimensional expensive problems (HEPs). The evaluation of their objective fitness requires expensive resource due to their use of time-consuming physical experiments or computer simulations. Moreover, it is hard to traverse the huge search space within reasonable resource as problem dimension increases. Traditional evolutionary algorithms (EAs) tend to fail to solve HEPs competently because they need to conduct many such expensive evaluations before achieving satisfactory results. To reduce such evaluations, many novel surrogate-assisted algorithms emerge to cope with HEPs in recent years. Yet there lacks a thorough review of the state of the art in this specific and important area. This paper provides a comprehensive survey of these evolutionary algorithms for HEPs. We start with a brief introduction to the research status and the basic concepts of HEPs. Then, we present surrogate-assisted evolutionary algorithms for HEPs from four main aspects. We also give comparative results of some representative algorithms and application examples. Finally, we indicate open challenges and several promising directions to advance the progress in evolutionary optimization algorithms for HEPs.

Evolutionary Optimization Methods for High-Dimensional Expensive Problems: A Survey

Expensive dynamic multi-objective optimization problems (EXDMOPs) involve multiple objective functions changing over time steps. In this kind of problems, only a small number of function evaluations can be allowed in each time step. The challenge of EXDMOP is how to quickly and accurately track the changing optimal solutions with only a small number of function evaluations. Although EXDMOP can be solved as a series of independent expensive multi-objective optimization problems or as an ordinary dynamic multi-objective optimization problems, these two methods either ignore the connection between different time steps or degrade the performance significantly due to the requirement for a large number of function evaluations. In this paper, we incorporate two proposed strategies named training data augmentation and sampling pool expansion to the Kriging-assisted reference vector guided evolutionary algorithm to construct a novel algorithm for solving EXDMOPs. The training data augmentation strategy tries to look for the previous similar time step, and adds the solutions evaluated by the objective functions at that time step to current time step. The accuracies of the Kriging models are improved in this way. The sampling pool expansion strategy sends the predicted optimal solutions to the competition of the function evaluations assignment at each time step, where the predicted optimal solutions are generated by the improved population prediction strategy. We set the ablation experiment for the proposed algorithm and compare it with four dynamic multi-objective evolutionary algorithms on various of problems. The experiment results validate the effectiveness of the proposed two strategies. It also indicates that the proposed algorithm is promising for solving EXDMOPs. 

A data augmentation based Kriging-assisted reference vector guided evolutionary algorithm for expensive dynamic multi-objective optimization

In preference-based multi-objective optimization, knee solutions are termed as the implicit preferred promising solution, particularly when users have trouble in articulating any sensible preferences. However, finding knee solutions by existing posteriori knee identification methods is hard when the function evaluations are expensive, because the computational budget wastes on non-knee solutions. Although a number of knee-oriented multi-objective evolutionary algorithms have been proposed to overcome this issue, they still demand massive function evaluations. Therefore, we propose a surrogate-assisted evolutionary multi-objective optimization algorithm via knee-oriented Pareto front estimation, which employs surrogate models to replace most of the expensive evaluations. The proposed algorithm uses a Pareto front estimation method and a cooperative knee point identification method to predict the potential knee vector. Then, based on the potential knee vector, the aggregated function with an error-tolerant assignment converts the original problem into a single-objective optimization problem for an efficient optimizer. We perform the proposed algorithm on 2-/3-objective problems and experimental results demonstrate that the proposed algorithm outperforms the state-of-the-art knee identification evolutionary algorithms on most test problems within a limited computational budget. 

Surrogate-assisted multi-objective optimization via knee-oriented Pareto front estimation

An adaptive Gaussian process based manifold transfer learning to expensive dynamic multi-objective optimization

Surrogate-assisted multi-objective evolutionary algorithms have become increasingly popular for solving computationally expensive problems, profiting from surrogate modeling and infill approaches to reduce the time cost of optimization. Most existing algorithms have specified the type of surrogate model before a run and keep the type static during the optimization process. However, a sole surrogate model may not consistently perform well for all problems without any prior knowledge. In this context, this paper proposes an adaptive technique for surrogate models with multiple radial basis functions (RBFs), as the technique can dynamically establish the most promising RBF for each objective, thereby enhancing the reliability of surrogate prediction. Moreover, multi-objective evolutionary algorithms (MOEAs) that are employed as optimizers for infilling criteria can highly affect the search behavior of a surrogate-assisted evolutionary algorithm. The proposed infill technique develops a crowding distance-based prescreening operator to embed various MOEAs. Two techniques collaboratively promote the convergence, coverage, and diversity of the predicted Pareto front. Representative benchmark problems and a structural optimization problem are given to show the effectiveness of the algorithm that employs these techniques. Empirical experiments demonstrate that the proposed algorithm significantly outperforms other state-of-the-art algorithms in most cases. 

Adaptive surrogate-assisted multi-objective evolutionary algorithm using an efficient infill technique

The simulation-optimization method, integrating the numerical model and the evolutionary algorithm, is increasingly popular for identifying the release history of groundwater contaminant sources. However, due to the usage of computationally intensive evolutionary algorithms, traditional simulation-optimization methods always require thousands of simulations to find appropriate solutions. Such methods yield a prohibitive computational burden if the simulation involved is time-consuming. To reduce general computation, this study proposes a novel simulation-optimization method for solving the inverse contaminant source identification problems, which uses surrogate models to approximate the numerical model. Unlike many existing surrogate-assisted methods using the pre-determined surrogate model, this paper presents an adaptive surrogate technique to construct the most appropriate surrogate model for the current numerical model. Two representative cases about identifying the release history of contaminant sources are used to investigate the accuracy and robustness of the proposed method. The results indicate that the proposed adaptive surrogate-assisted method effectively identifies the release history of groundwater contaminant sources with a higher degree of accuracy and shorter computation time than traditional methods.

/pdf/an-adaptive-surrogate-assisted-simulation-optimization-1k26ta5z.pdf

An Adaptive Surrogate-Assisted Simulation-Optimization Method for Identifying Release History of Groundwater Contaminant Sources

Three-Dimensional Hydrodynamics and Morpho-dynamics at a Tidal River Junction

Understanding variations in contaminant concentrations and exploring their driving factors are essential for pollution control and water environment improvement. The Huaihe River Basin, as an important region in the eastern region of China, has attracted much attention to its water environment issues in recent years. Therefore, an in-depth analysis of spatiotemporal patterns of water quality parameters was carried out on the Huaihe River–Hongze Lake system, for the period 1998–2018, using the Mann–Kendall test (MKT) and wavelet transforms (WTs). Significant decrease trends of ammonia nitrogen (AN) and chemical oxygen demand (COD) concentrations were detected in the Huaihe River (HR) before 2008 using the MKT. High concentration in the contaminant load was a result of the effect of increased construction and decreased forest on increasing input of pollutants during this period. The results of the WT showed how factors (e.g., streamflow and water temperature), except land use, affect the variations in AN and COD concentrations. The comparison of spatiotemporal patterns of AN and COD between the HR and Hongze Lake (HL) showed their differences in contaminant transport regimes. The contaminants were rapidly transported downstream along the HR with high streamflow during the wet season, while these in the HL were less responsive due to the long residence time of the water body. In addition, rebounds of contaminant concentrations occurred many times at the confluence between the HR and the HL due to strong river–lake interactions, especially in the flood season. These results have implications for future water environment management in the Huaihe River Basin and in similar settings worldwide.

/pdf/spatiotemporal-patterns-of-ammonia-nitrogen-and-chemical-2himy2ar.pdf

Spatiotemporal Patterns of Ammonia Nitrogen and Chemical Oxygen Demand in the Huaihe River–Hongze Lake System (Eastern China)


 Understanding the transport of point source solutes across the sediment–water interface (SWI) is important for the protection of river environments. Conventional coupled models assume the porous media layer as Darcy's laminar flow and therefore cannot accurately capture the transport processes within the porous media. Furthermore, the effect of the porous structure of the riverbed on the transport process is largely unknown. In this study, we performed pore-scale numerical simulations of point source solutes transport across the SWI to investigate the effects of different porous structures in the riverbed on flow and point source dispersion. By solving the Reynolds-averaged Navier–Stokes equations with the k–ω shear stress transport turbulence closure model, we determine the complex flow field information and the spatial distribution of point source solutes for the coupled model. The results indicate that the presence of porous structures creates recirculation zones in the coupled model, which preventing turbulent structures to reach deeper layers. Random porous structures induce more preferential flow, inhibit the formation of recirculation zones, and exhibit higher solute dispersion, which is directly related to turbulent solute fluxes. Furthermore, our study reveals that the release position of point sources significantly influences the distribution of solute concentrations within the porous bed.

Effects of porous structures on point source dispersion across the sediment–water interface

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