A Multi-level Surrogate-assisted Algorithm for Expensive Optimization Problems

In this paper, a surrogate-assisted differential evolution (DE) algorithm is proposed to solve the computationally expensive optimization problems. In it, the Kriging model is used to approximate the objective function, while DE employs a mechanism to dynamically select the best performing combinations of parameters (amplification factor, crossover rate and population size). The performance of the algorithm is tested on the WCCI2014 competition on expensive single objective optimization problems. The experimental results demonstrate that the proposed algorithm has the ability to obtain good solutions.

Running climate model on a commercial cloud computing environment: A case study using Community Earth System Model (CESM) on Amazon AWS

The applications of Differential Evolution (DE) and the attraction of researchers towards it, shows that it is a simple, powerful, efficient as well as reliable evolutionary algorithm to solve optimization problems. In this study an improved DE called aesthetic DE algorithm (ADEA) is introduced to solve Computationally Expensive Optimization (CEO) problems discussed in competition of congress of evolutionary computation (CEC) 2014. ADEA uses the concept of mirror images to produce new decorative positions. The mirror is placed near the most beautiful (global best) individual to accentuate its attractiveness (significance). Simulated statistical results demonstrate the efficiency and ability of the proposal to obtain good results.

Surrogate-assisted evolutionary algorithms (SAEAs) have shown great potential to solve computationally expensive optimization problems (EOPs). Their two key components, i.e., the optimizer and the surrogate model, both need to select solutions to promote further evolution and to update the model, respectively. However, the corresponding selection strategies are designed independently and mainly consider the predicted fitness of candidate solutions. Consequently, they can hardly complement each other well and are much likely to mislead the population evolution since the surrogate model necessarily has some prediction errors. Directing against this issue, this study proposes a unified dual-space-driven selection (DSDS) strategy and develops a new SAEA by taking differential evolution and radial basis function as the optimizer and the surrogate model, respectively. Besides the predicted fitness in objective space of candidate solutions, DSDS also considers their distribution in decision space by measuring how close they are to the geometric centers of their respective neighborhoods with a new indicator called neighborhood centrality (NC). It tries to select the solutions with good fitness and small NC values under a multi-objective sample selection framework and thus helps the resulting SAEA steadily search in multiple neighborhoods of excellent solutions. The performance of the new SAEA was extensively tested on six commonly used benchmark functions with five different dimensions from 20 to 200 as well as two typical real-word traffic signal optimization cases. Experimental results demonstrate that it possesses more competitive performance and stronger robustness than state-of-the-art SAEAs.

Efficient hierarchical surrogate-assisted differential evolution for high-dimensional expensive optimization

Characterizing the elements of Earth's radiative budget: Applying uncertainty quantification to the CESM

Many real-world applications can be formulated as expensive multimodal optimization problems (EMMOPs). When surrogate-assisted evolutionary algorithms (SAEAs) are employed to tackle these problems, they not only face the problem of selecting surrogate models but also need to tackle the problem of discovering and updating multiple modalities. Different optimization problems and different stages of evolutionary algorithms (EAs) generally require different types of surrogate models. To address this issue, in this article, we present a multisurrogate-assisted multitasking particle swarm optimization algorithm to seek multiple optimal solutions of EMMOPs at a low computational cost. The proposed algorithm first transforms an EMMOP into a multitasking optimization problem by integrating various surrogate models, and designs a multitasking niche particle swarm algorithm to solve it. Following that, a surrogate model management strategy based on the skill factor and clustering is developed to effectively balance the number of real function evaluations and the prediction accuracy of candidate optimal solutions. In addition, an adaptive local search strategy based on the trust region is proposed to enhance the capability of swarm in exploiting potential optimal modalities. We compare the proposed algorithm with five state-of-the-art SAEAs and seven multimodal EAs on 19 benchmark functions and the building energy conservation problem and experimental results show that the proposed algorithm can obtain multiple highly competitive optimal solutions.

The surrogate-assisted optimization algorithms (SAOAs) are very promising for solving computationally expensive optimization problems (EOPs). Generally, the performance of a SAOA is determined by the quality of its surrogate model and the infill sampling criterion. In this paper, we propose a radial basis function (RBF) assisted optimization algorithm with batch infill sampling criterion for solving EOPs (short for RBFBS). In RBFBS, the quality of RBF model is adjusted by choosing a good shape parameter via solving a sub-expensive hyperparameter optimization problem. Moreover, a batch infill sampling criterion that includes a bi-objective-based sampling approach and a single-objective-based sampling approach is proposed to get a batch of samples for expensive evaluation. The experimental results on various benchmark problems show that RBFBS is very promising for expensive optimization.

Surface longwave emissivity can be less than unity and vary significantly with frequency. However, most climate models still assume a blackbody surface in the longwave (LW) radiation scheme of their atmosphere models. This study incorporates realistic surface spectral emissivity into the atmospheric component of the Community Earth System Model (CESM), version 1.1.1, and evaluates its impact on simulated climate. By ensuring consistency of the broadband surface longwave flux across different components of the CESM, the top-of-the-atmosphere (TOA) energy balance in the modified model can be attained without retuning the model. Inclusion of surface spectral emissivity, however, leads to a decrease of net upward longwave flux at the surface and a comparable increase of latent heat flux. Global-mean surface temperature difference between the modified and standard CESM simulation is 0.20 K for the fully coupled run and 0.45 K for the slab-ocean run. Noticeable surface temperature differences between the modified and standard CESM simulations are seen over the Sahara Desert and polar regions. Accordingly, the climatological mean sea ice fraction in the modified CESM simulation can be less than that in the standard CESM simulation by as much as 0.1 in some regions. When spectral emissivities of sea ice and open ocean surfaces are considered, the broadband LW sea ice emissivity feedback is estimated to be −0.003 W m−2 K−1, assuming flat ice emissivity as sea ice emissivity, and 0.002 W m−2 K−1, assuming coarse snow emissivity as sea ice emissivity, which are two orders of magnitude smaller than the surface albedo feedback.

Surrogate-assisted evolutionary framework with an ensemble of teaching-learning and differential evolution for expensive optimization

Practitioners often encounter computationally expensive multiobjective optimization problems to be solved in a variety of real-world applications. On the purpose of challenging these problems, we propose a new surrogate-based multiobjective optimization algorithm that does not require a large evaluation budget. It is called Multiobjective Tree-structured Parzen Estimator (MOTPE) and is an extension of the tree-structured Parzen estimator widely used to solve expensive single-objective optimization problems. Our empirical evidences reveal that MOTPE can approximate Pareto fronts of many benchmark problems better than existing methods with a limited budget. In this paper, we discuss furthermore the influence of MOTPE configurations to understand its behavior.

Surrogate modeling techniques are widely employed in solving constrained expensive black-box optimization problems. Therein, Kriging is among the most popular surrogates in which the trend function is considered as a constant mean. However, it also encounters several challenges related to capturing the overall trend with a relatively limited number of function evaluations as well as searching feasible points with complex or discontinuous feasible regions. To address this above issue, this paper presents an improved surrogate blind Kriging (IBK) and a combined infill strategy to find the optimal solution. According to enhancing the prediction accuracy of metamodels of objective and constraints, the high-order effects of regression function in the blind Kriging are identified by promising a variable selection technique. In addition, an infill strategy is developed based on the probability of feasibility, penalization, and constrained expected improvement for updating blind Kriging metamodels of the objective and constraints. At each iteration, two infill sample points are allocated at the positions to achieve improvement in optimality and feasibility. The IBK metamodels are updated by the newly-added infill sample points, which leads the proposed framework search to rapidly converge to the optimal solution. The performance and applicability of the proposed model are tested on several numerical benchmark problems via comparing with other metamodel-based constrained optimization methods. The obtained results indicate that IBK generally has a greater efficiency performance and outperforms the competitors in terms of a limited number of function evaluations. Finally, IBK is successfully applied to structural design optimization. The optimization results show that IBK is able to find the best feasible design with fewer evaluation functions compared with other studies, and this demonstrates the effectiveness and practicality of the proposed model for solving the constrained expensive black-box engineering design optimization problems.

This study investigates the interaction of the quasi-biennial oscillation (QBO) and the El Niño–Southern Oscillation (ENSO) in the troposphere separately for the North Pacific and North Atlantic region. Three 145-yr model simulations with NCAR’s Community Earth System Model Whole Atmosphere Community Climate Model (CESM-WACCM) are analyzed where only natural (no anthropogenic) forcings are considered. These long simulations allow the authors to obtain statistically reliable results from an exceptional large number of cases for each combination of the QBO (westerly and easterly) and ENSO phases (El Niño and La Niña). Two different analysis methods were applied to investigate where nonlinearity might play a role in QBO–ENSO interactions. The analyses reveal that the stratospheric equatorial QBO anomalies extend down to the troposphere over the North Pacific during Northern Hemisphere winter only during La Niña and not during El Niño events. The Aleutian low is deepened during QBO westerly (QBOW) as compared to QBO easterly (QBOE) conditions, and the North Pacific subtropical jet is shifted northward during La Niña. In the North Atlantic, the interaction of QBOW with La Niña conditions (QBOE with El Niño) results in a positive (negative) North Atlantic Oscillation (NAO) pattern. For both regions, nonlinear interactions between the QBO and ENSO might play a role. The results provide the potential to enhance the skill of tropospheric seasonal predictions in the North Atlantic and North Pacific region.

This paper investigates the suitability of the Particle Swarm Optimization (PSO) and the Differential Evolution (DE) algorithms in solving expensive optimization problems. Eight PSO variants, and eight DE variants are experimentally compared among each other. The Comparing Continuous Optimizers (COCO) methodology was adopted in comparing these variants on the noiseless BBOB test bed. Based on the results, we provide useful insights regarding the algorithms' relative efficiency and effectiveness under an expensive budget of function evaluations, and draw suggestions about which algorithm should be used depending on what we know about our optimization problem in terms of evaluation budget, dimensionality, and function structure. Furthermore, we propose possible future research directions addressing the algorithms limitations. Overall, DE variants perform well in low dimensions, whereas in higher dimensions, several PSO variants surpass DE algorithms. Among the top performers, JADE and χPSO are the robust algorithms for solving expensive budget problems.

<p>Sudden and strong positive sea surface temperatures (SST) anomalies in the far eastern Pacific that are tied to the rather narrow NINO1+2 (0-10°S, 90°W-80°W) region are known as coastal El Niño events. In contrast to the well-studied features of typical basin-scale ENSO events, the frequency, origin and relevant processes of coastal El Niños are largely unknown. Here, we analyze their characteristics and future behavior using observational data and simulations with the Community Earth System Model (CESM), which exhibits skill in simulating precipitation, wind and SST fields associated with coastal El Niños. We find that tropical Pacific basin-scale ocean dynamics – in sharp contrast to a typical El Niño event  – play no major role in the evolution of a coastal El Niño. On the other hand, we find that atmospheric circulation anomalies from the Southern Hemisphere lead the evolution of coastal El Niño events, by causing warm SST anomalies that then propagate into the NINO1+2 region. Once initiated, local thermodynamical feedback processes such as cloud radiation feedbacks are responsible for the growth and decay of the events. Greenhouse gas forcing leads to an increase in the frequency of coastal El Niño events and a shift of their peak month in CESM simulations, related to a shallowing of the thermocline and changes in Rossby wave forcing from the Southern Hemisphere. In conclusion, based on our results, we will demonstrate the potential for increased predictability of coastal El Niño events, whose intense coastal SST warming and associated extreme precipitation poses a serious threat for local communities via loss of life and severe economic damage.</p>