Surrogate-based Multi-objective Optimization Research Articles

Multi-Objective Surrogate-Based Optimization Method for the Scaling of Combustion Chambers

Abstract In this study, we developed an efficient computer-aided design tool for scaling combustor designs. From a limited number of fluid simulations, an original design is scaled while preserving most of the flow properties, using a multi-objective optimization method and deep neural network or kriging surrogate models. The accuracy and robustness of the method were first tested with a simple geometry. Investigations have shown a strong sensitivity of the surrogate models to the sample distribution, which can be reduced using a strategic sampling method. Subsequently, the geometry was scaled down to a factor of two using both surrogate models while preserving most of the flow features.

Surrogate-Based Multiobjective Optimization of Detention Pond Volume in Sponge City

Detention ponds are effective structures for stormwater management in the urban drainage system of sponge cities. The pond size is taken as the decision variable, while the cost, total suspended solids (TSS), and catchment peak outflow (CPO) serve as the objectives for optimizing the detention pond volume. First, we randomly generated 10,000 pond areas and input them into the stormwater management model to simulate the time series of outflow and suspended solids concentration, thereby generating samples by combining the set of pond area, corresponding cost, TSS, and CPO. Then, two backpropagation neural network models (i.e., BPNN-TSS and BPNN-CPO) were trained, tested, and evaluated for predicting TSS and CPO, respectively. We employed them as surrogates and used the non-dominated sorting genetic algorithm-II to solve the optimization problem. The results showed: (1) The BPNN models accurately predicted TSS and CPO (determination coefficient 0.988~0.996, Nash–Sutcliffe efficiency 0.988~0.997), and efficiently substituted stormwater management model simulations for optimization purposes (residuals −18.49~28.10 kg and −0.45~0.29 m3/s). (2) For the Pareto solutions, the detention pond reduced TSS by 0~8.33% and CPO by 0~72.44% and delayed their peaks by 4~52 min; the reduction in TSS and CPO tends to grow as pond size increases, and CPO reduction exhibits a minor marginal effect. (3) The surrogate-based approach saves 90.03% runtime while preserving the quality of the Pareto solutions, verifying reliability.

Probability-based visual comfort assessment and optimization in national fitness halls under sports behavior uncertainty

Sports behavior uncertainty is a main cause of mismatch between simulated and actual visual comfort in sports spaces, which has not been properly addressed in existing studies. This study proposes a multi-phase and multi-objective optimization approach to improve visual comfort in national fitness halls by better considering sports behavior uncertainty. Specifically, a surrogate-based multi-objective optimization workflow is developed for fast optimization of visual comfort. Then, a probabilistic behavior model is created to predict player's occupancy probability in all possible view scenes during sports, and based on which the probabilistic visual comfort is introduced to assess player's realistic visual comfort taking account of the occupancy probability. The sport of tennis in a parametric national fitness hall is selected as the case study scenario. Results indicated that the proposed response surface model outperformed artificial neural network model in predicting visual comfort, while this approach saved 35.43% of total computational time versus the traditional simulation-based multi-objective optimization approach in this case study; 296 Pareto solutions out of 1758 design alternatives were quickly identified, among which the final optimum solution indicated an approximately 200% better visual comfort against the worst one; Sports behavior uncertainty was found to affect player's visual comfort assessment in tennis sports, presenting variances on different court locations under two court layouts. This study contributes new insights of probabilistic visual comfort assessment under sports scenarios and explores the potential of court location and layout arrangement for multi-purpose usage consideration in national fitness halls.

Long-term sustainability and resilience enhancement of building portfolios

The role of community building portfolios in socioeconomic development and the growth of the built environment cannot be overstated. Damage to these structures can have far-reaching consequences on socioeconomic and environmental aspects, requiring a long-term perspective for recovery. As communities aim to enhance their resilience and sustainability, there is a cost burden that needs to be considered. To address this issue, this paper proposes a community-level performance enhancement approach that focuses on optimizing the long-term resilience and sustainability of community building portfolios, taking into account recurrent seismic hazards. A Gaussian process surrogate-based multi-objective optimization framework is utilized to optimize the cost objective while considering performance indicators for resilience and sustainability. The proposed framework involves using performance-based assessment methods to evaluate the socioeconomic and environmental consequences under stochastic and recurrent seismic hazard scenarios. These evaluated indicators are then used to efficiently optimize the community resilience and sustainability, taking into account the retrofit costs. Finally, approximate Pareto-optimal solutions are extracted and utilized for decision-making. In summary, this paper presents a novel approach for optimizing the long-term resilience and sustainability of community building portfolios by considering recurrent seismic hazards. The proposed framework incorporates performance-based assessment methods and multi-objective optimization techniques to achieve an optimal balance between cost, resilience, and sustainability, with the ultimate goal of enhancing community well-being and decision-making in the face of seismic hazards.

Expensive Multiobjective Optimization Based on Information Transfer Surrogate

Objective value estimation based on computationally efficient surrogate models is widely used to reduce the computational cost in solving expensive multiobjective optimization problems (MOPs). However, due to the scarcity of training data and the lack of data sharing between training tasks in a surrogate-based system, the estimation effectiveness of the surrogate models might not be satisfactory. In this study, we present a novel surrogate methodology based on information transfer to deal with this problem. Particularly, in the proposed framework, the objectives of an MOP that may have little apparent similarity or correlation are linearly mapped to a number of related tasks. Afterward, the related tasks are used to train a multitask Gaussian process (MTGP). MTGP expands the training data leading to more confident learning of the parameters of the model. The predicted values of the objective functions can be obtained by a reverse mapping from the learned MTGP model. In this way, the computational burden of the expensive objective functions of an MOP can be substantially reduced while maintaining good estimation accuracy. MTGP facilitates mutual information transfer across tasks, avoids learning from scratch for new tasks, and captures the underlying structural information between tasks. The proposed surrogate approach is merged into MOEA/D to address MOPs. Experimental tests under various scenarios indicate that the resultant algorithm outperforms other state-of-the-art surrogate-based multiobjective optimization algorithms.

The blade shape optimization of a low-pressure axial fan using the surrogate-based multi-objective optimization method

The blade shape optimization of a low-pressure axial fan using the surrogate-based multi-objective optimization method

Surrogate-based multiobjective optimization to rapidly size low impact development practices for outflow capture

The optimal implementation of low impact development (LID) practices remains an open research issue. Multiobjective optimization (MOO) based on physically-based models facilitates LID sizing but requires large computational budgets. We developed and validated a surrogate MOO framework based on machine learning (ML) models to obtain satisfactory optimal solutions with an affordable computational cost. First, a calibrated and validated storm water management model (SWMM) was driven by a 2-year, 120 min Chicago pattern storm with random LID areas for generating 10,000 samples. Second, ML models, including multiple linear regression (MLR), generalized regression neural network (GRNN), and backpropagation neural network (BPNN), were trained and validated to predict catchment total outflow (CTO) and catchment peak outflow (CPO). Third, using the outperformed ML models as surrogates, the LID areas were optimized by non-dominated sorting genetic algorithm-II to minimize construction costs, CTO, and CPO. The results obtained for an urban catchment in Fengxi, China, demonstrated that: (1) BPNN outperformed MLR and GRNN in terms of accuracy, while the training time (∼40 min) was ∼6857 times and ∼706 times that of MLR (∼0.35 s) and GRNN (3.4 s) models, respectively. (2) The optimization process using BPNN models as surrogates converged well, indicating the efficiency of the proposed framework. (3) Under the marginal effect, the permeable pavement was identified as the leading practice for most Pareto solutions, followed by bioretention cell and green roof. Moreover, a subcatchment with a higher runoff coefficient was deemed preferable for LID implementation. (4) Outflow reduction by the LIDs was significant (CTO and CPO were reduced by 28.6–56.9 % and 27.5–48.3 %, respectively) but negligible for retarding the time of CPO. (5) The optimization time was reduced by ∼95.82 % using the surrogate-based MOO instead of the SWMM-based model when the training time of the BPNN models was ignored. This study provides insights into the efficient optimization of LIDs.

Multi-objective simulation–optimization via kriging surrogate models applied to natural gas liquefaction process design

A surrogate-based multi-objective optimization framework is employed in the design of natural gas liquefaction processes using reliable, black-box process simulation. The conflicting objectives are minimizing both power consumption and heat exchanger area utilization. The Pareto solutions of the single-mixed refrigerant (SMR) and propane-precooled mixed refrigerant (C3MR) processes are compared to determine the suitability of each process in terms of energy consumption and heat exchanger area. Kriging models and the ɛ-constraint methodology are used to sequentially provide simple surrogate optimization subproblems, whose minimizers are promising feasible and non-dominated solutions to the original black-box problem. The surrogate-based ɛ-constrained optimization subproblems are solved in GAMS using CONOPT. The Pareto Fronts achieved with the surrogate-based framework dominate the results from the NSGA-II, a well-established meta-heuristics of multi-objective optimization. The objective functions of non-dominated solutions go as low as 1045 and 980.3 kJ/kg-LNG and specific UA values of 212.2 and 266.9 kJ/(°C kg-LNG) for SMR and C3MR, respectively. The trade-off solutions that present the minimum sum of relative objectives are analyzed as well as the dominance of C3MR over SMR at low power consumption values and conversely at low heat exchanger area utilization.

Robust optimal operation of continuous catalytic reforming process under feedstock uncertainty

The continuous catalytic regenerative (CCR) reforming process is one of the most significant sources of hydrogen production in the petroleum refining process. However, the fluctuations in feedstock composition and flow rate could significantly affect both product distribution and energy consumption. In this study, a robust deviation criterion based multi-objective optimization approach is proposed to perform the optimal operation of CCR reformer under feedstock uncertainty, with simultaneous maximization of product yields and minimization of energy consumption. Minimax approach is adopted to handle these uncertain objectives, and the Latin hypercube sampling method is then used to calculate these robust deviation criteria. Multi-objective surrogate-based optimization methods are next introduced to effectively solve the robust operational problem with high computational cost. The level diagram method is finally utilized to assist in multi-criteria decision-making. Two robust operational optimization problems with different objectives are solved to demonstrate the effectiveness of the proposed method for robust optimal operation of the CCR reforming process under feedstock uncertainty.

Surrogate-based decision-making of community building portfolios under uncertain consequences and risk attitudes

The performance of community building portfolios under extreme events is increasingly been assessed in terms of socioeconomic and environmental consequences. These multiple consequences are expensive to be evaluated, uncertain in nature, and it requires an efficient optimization and decision-making tool for performance enhancements on a community level. In this paper, an efficient multi-objective performance-based optimization and decision-making framework is proposed to assess and enhance the performance of community building portfolios under uncertain consequences. The proposed approach includes (1) performance-based black-box to evaluate the socioeconomic and environmental consequences given community building portfolios by considering all the possible hazard scenarios, (2) surrogate-based multi-objective optimization to efficiently approximate the Pareto-optimal solutions by exploiting Gaussian process models, spectral sampling, non-dominated crowding and sorting, and hyper improvements, among others, and (3) utility theory-based decision-making of a community building portfolios considering multiple performance-objectives over an entire hazard curve and under different risk attitudes. The proposed methodology is illustrated on community building portfolio under seismic hazards of varying intensities and occurrence probabilities. A performance-based black box is utilized along with a proposed optimization technique to assess community-level consequences. Finally, the utility for Pareto-optimal solutions is assessed and discussed for possible performance enhancements and decision-making.

Calibration of cloud and aerosol related parameters for solar irradiance forecasts in WRF-solar

Model parameters are one of the sources of uncertainties in numerical weather prediction. Recently, the Weather Research and Forecasting model with Solar extensions (WRF-Solar) has been upgraded by enhancing the treatment of sub-grid scale cloud and aerosols with augmentations of a sub-grid scale cloud scheme (CLD3) and an upgraded aerosol-aware Thompson-Eidhammer scheme (TE14). However, the value of model parameters associated with these parameterizations are assigned based on limited measurements or theoretical calculations. Calibrating the sensitive parameters has the potential to improve solar irradiance predictions. In this work, we adopted a multi-objective surrogate-based optimization (SBO) framework to calibrate nine parameters used in CLD3 and TE14 that lead to the largest sensitivity in simulated irradiance. The normalized mean-absolute-error (NMAE) of global horizontal irradiance (GHI) and direct normal irradiance (DNI) are minimized by calibrating WRF-Solar over two regions including the Southern Great Plains (SGP) and Central California. We selected two cloudy cases, one over less-polluted SGP and another over Central California with high aerosol loading associated with wildfire events. The results show that generalized linear model (GLM)-based surrogate models approximate physical models well, particularly when the third order and three-way interaction terms are considered. The SBO framework efficiently searches the parameter space for optimal solutions with less computational costs than directly calibrating the physical model. We first calibrate CLD3 parameters over the less-polluted SGP region. Optimized CLD3 parameters alone result in NMAE reduction by 14% for the site-mean and up to 33% for individual cases over the SGP region. With further calibration of TE14 parameters over the Central California during active fire periods, the optimized parameters lead to over 20% reductions of NMAE.

Surrogate model-based multiobjective design optimization for air-cooled battery thermal management systems

ABSTRACT A well-designed battery thermal management system (BTMS) can achieve optimal cooling performance with less power consumption than a poorly-designed system. However, it is difficult to use the computational fluid dynamics (CFD) method to perform an effective and optimal design of BTMSs when there are several structural design parameters and multiple evaluation criteria. In this paper, instead of CFD, a compound surrogate model based on the mixture of experts (MoE) method is developed to accurately approximate the BTMS performance of different structural configurations. Then, the multiple criteria evaluation of the structural design is transformed into a multiobjective optimization (MOO) problem, which is solved by the nondominated sorting genetic algorithm II (NSGA-II). To address the nonuniqueness of the optimal solutions and the contradiction between evaluation criteria, the entropy weight method (EWM) and criteria importance through the intercriteria correlation (CRITIC) method are applied to analyze the weight of each evaluation criterion. Finally, the optimal structural parameters are obtained for the corresponding weights. The results show that the surrogate-based MOO can find a structural design that meets expectations, and this approach can provide guidelines for the design of BTMSs.

Joint Dual-Input Digital Predistortion of Supply-Modulated RF PA by Surrogate-Based Multi-Objective Optimization

A generalized dual-input digital predistortion (DPD) methodology for supply-modulated (SM) power amplifiers (PAs) is proposed. Contrary to classical approaches, the SM and the radio frequency (RF) signals are treated as separate digital inputs to be jointly predistorted. A multi-objective optimization (MOO) strategy allows to explore the inherent PA performance tradeoffs to jointly optimize the DPD coefficients for improved power-added efficiency (PAE) and higher RF output power, yet guaranteeing a prescribed linearity performance. To avoid dealing with an unbearably high number of experimental acquisitions, MOO is here made feasible by fast simulation of an empirical surrogate model of the PA, which is progressively refined from a reduced set of iterative acquisitions. The proposed technique enables the adoption of a dynamic supply shaping function, and it automatically accounts for the signals’ statistics. Eventually, the method outperforms classical SM approaches, yet using a DPD of the same order, as demonstrated by the experimental results on a gallium nitride (GaN) SM PA operating at 3.5 GHz in the presence of orthogonal-frequency-division-multiplexing (OFDM)-like high-peak-to-average power ratio (PAPR) modulated signals with 10- and 20-MHz bandwidths (BWs).

Surrogate‐based multi‐objective design optimization of a coronary stent: Altering geometry toward improved biomechanical performance

The main objective of this study was to solve a multi-objective optimization on a representative coronary stent platform with the goal of finding new geometric designs with improved biomechanical performance. The following set of metrics, calculated via finite element models, was used to quantify stent performance: vessel injury, radial recoil, bending resistance, longitudinal resistance, radial strength and prolapse index. The multi-objective optimization problem was solved with the aid of surrogate-based algorithms; for comparison and validation purposes, four surrogate-based multi-objective optimization algorithms (EIhv -EGO, Phv -EGO, ParEGO and SMS-EGO) with a limited sample budget were employed and their results compared. The quality of the non-dominated solution sets outputted by each algorithm was assessed against four quality indicators: hypervolume, R2, epsilon and generational distance. Results showed that Phv -EGO was the algorithm that exhibited the best performance in overall terms. Afterwards, the highest quality Pareto front was chosen for an in-depth analysis of the optimization results. The amount of correlation and conflict was quantified for each pair of objective functions. Next, through cluster analysis, one was able to identify families of solutions with similar performance behavior and to discuss the nature of the existent trade-offs between objectives, and the trends between design parameters and solutions in a biomechanical perspective. In the end, a constrained-based design selection was performed with the goal of finding solutions in the Pareto front with equal or better performance in all objectives against a baseline design.

Evaluation of novel-objective functions in the design optimization of a transonic rotor by using deep learning

Design optimization of transonic airfoils for rotary blades is a challenging subject that remarkably affects the stage and overall performance of axial-flow compressors. This paper describes a surrogate-based multi-objective optimization process over a transonic rotary blade. This blade works in the first high-pressure stage of a pre-designed industrial axial compressor. It experiences a massive separation behind an impinging shock wave over its suction side, resulting in very low efficiency of the whole stage. The key components of the current approach involve the application of novel-objective functions over the pressure distribution of airfoils, called the location of the shock wave and a flat-roof-top factor, to design supercritical airfoils. Moreover, to ensure the advantages of having an attached boundary layer and a high efficient blade, the area of separated boundary layer is also defined alongside other well-known objective functions related to the polar loss diagram. Notably, a sequential feed-forward multi-layer perceptron is designed to construct a mapping between airfoil geometrical variables and the objective functions. A numerical simulation of the whole compressor has shown an efficiency improvement of about 10% and 0.17% for the first stage and the whole compressor, respectively, and an attached boundary layer with a supercritical pressure distribution when employing the optimized rotor blade at the design stage.

A sequential surrogate-based multiobjective optimization method: effect of initial data set

Process optimization based on high-fidelity computer simulations or real experimentation is commonly expensive. Therefore, surrogate models are frequently used to reduce the computational or experimental cost. However, surrogate models need to achieve a maximum accuracy with a limited number of sampled points. Sequential sampling is a procedure in which sequentially surrogates are fitted and each surrogate defines the points that need to be sampled and used to fit the next model. For optimization purposes, points are sampled on regions of high potential for the optimal solutions. In this work, we first compared the effect of using different initial sets of points (experimental designs) in a sequential surrogate-based multiobjective optimization method. The optimization method is tested on five benchmark problems and the performance is quantified based on the total number of function evaluations and the quality of the final Pareto Front. Then an industrial applications on titanium welding is presented to show the use of the method. The case study is based on real experimental data.

Aerodynamic and Stealth Integrated Design of DSI Inlet by Surrogate-Based Multi-Objective Optimization with EHVI Infill Criterion

To deal with the problem of aerodynamic and stealth integrated optimization of DSI inlet, a multi-objective optimization study on aerodynamic and stealth of the DSI inlet is carry out which based on the deformation of the three-dimensional compression bump surface. The FFD parametric method is used to parameterize the bump surface; CFD calculation based on RANS equations is used to analyze the aerodynamic performance of the DSI inlet, large element physical optical method and uniform theory of diffraction are used to calculate RCS of the DSI inlet; And ASMOPSO algorithm with the Kriging surrogate model which based on the expect hyper-volume improvement infill criterion is adopted for integrated optimization design. The results of DSI inlet aerodynamic and stealth integrated optimization exhibit considerable improvement.

CFD Optimization Process of a Lateral Inlet/Outlet Diffusion Part of a Pumped Hydroelectric Storage Based on Optimal Surrogate Models

The lateral inlet/outlet plays a critical role in the connecting tunnels of a water delivery system in a pumped hydroelectric storage (PHES). Therefore, the shape of the inlet/outlet was improved through computational fluid dynamics (CFD) optimization based on optimal surrogate models. The CFD method applied in this paper was validated by a physical experiment that was carefully designed to meet bidirectional flow requirements. To determine a good compromise between the generation and pump mode, reasonable weights were defined to better evaluate the overall performance. In order to find suitable surrogate models to improve the optimization process, the best suited surrogate models were identified by an optimal model selection method. The optimal configurations of the surrogate model for the head loss and the velocity distribution coefficient were the Kriging model with a Gaussian kernel and the Kriging model with an Exponential kernel, respectively. Finally, a multi-objective surrogate-based optimization method was used to determine the optimum design. The overall head loss coefficient and velocity distribution coefficients were 0.248 and 1.416. Compared with the original shape, the coefficients decrease by 6.42% and 40.28%, respectively. The methods and findings of this work may provide practical guidelines for designers and researchers.

Surrogate-based multi-objective optimization of management options for agricultural landscapes using artificial neural networks

We demonstrate the use of a surrogate-based optimization framework for large-scale and high-resolution landscape management optimization, using irrigated corn production systems in eastern Colorado, USA as a case study. An artificial neural network was employed to create a surrogate of the DayCent biogeochemical simulation model. Our optimization considered trade-offs among seven different objectives at different scales, including farm profits, irrigation water use, corn grain, corn stover, soil organic carbon (SOC), greenhouse gas (GHG) emissions, and nitrogen leaching. The results show that the surrogate captured greater than 99% of the variations in the DayCent’s simulated outputs and was 6.2 million times faster than the DayCent model for our analysis. Farm-level optimization increased farm profits by 83%–150%, SOC by 16%–53%, grain yield by 10.1–11.3%, and reduced GHG emissions by 19%–55% compared to the ‘business-as-usual’ scenario.

Simultaneous design of non-Newtonian lubricant and surface texture using surrogate-based multiobjective optimization

Surface textures decrease friction in lubricated sliding with Newtonian fluids. Viscoelastic non-Newtonian lubricants can enhance frictional performance, but the optimal rheological material properties and their coupling to the texture design are non-obvious. In this study, we present a simultaneous design of both surface texture shape and non-Newtonian properties, which can be achieved by fluid additives that introduce viscoelasticity, shear thinning, and normal stress differences. Two models with different fidelity and computational cost are used to model laminar non-Newtonian fluid flow between a rotating flat plate and a textured disk. At lower fidelity, we use the Criminale-Ericksen-Filbey (CEF) constitutive model and a thin-film approximation for conservation of momentum (Reynolds equation). At higher fidelity, we use a fully nonlinear constitutive model typically applicable to polymer solutions (multimode Giesekus model) and the full 3-D momentum equations. Fluid additive design is parameterized by two relaxation modes each having a timescale, added viscosity, and a nonlinear anisotropic drag parameter. To manage the computational complexity and constraints between design variables, we use our previously developed multiobjective adaptive surrogate modeling-based optimization (MO-ASMO) method. A new data-driven extension of MO-ASMO is introduced that constructs general boundaries to prevent attempts to evaluate designs that would lead to simulation failure. We demonstrate the efficiency of our MO-ASMO method and provide insights into co-designing the lubricant and textured surface. The Pareto-optimal solutions include fluid designs with both high and low viscoelastic additive loading. We rationalize this trade-off and discuss how the optimal design targets can be physically realized.