Pareto-optimal Designs Research Articles

Decomposition based estimation of distribution algorithm for high-level synthesis design space exploration

High-Level Synthesis (HLS) has evolved significantly due to the increasing complexity of integrated circuit design and the demand for efficient design methodologies. HLS, which raises the abstraction level of design specification, allows designers to focus on hardware functionality, thus enhancing productivity and reducing verification efforts. However, a key challenge in HLS is efficiently exploring the vast design space to find the Pareto-optimal designs. In this paper, we introduce a novel approach for multi-objective design space exploration in HLS. Our methodology decomposes the design space exploration problem into simpler sub-problems using the Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) framework and utilizes the Estimation of Distribution Algorithm (EDA) to build a probabilistic model for generating candidate solutions, thereby reducing the required number of expensive synthesis runs. Experimental results show that the proposed method has a faster convergence speed and reduces the number of syntheses by 24.34% to 32.01%, which significantly outperforms state-of-the-art works. Our approach achieves superior Pareto fronts with the lowest average ADRS value, outperforming Lattice-expl, ϵ -Constraint GA, and NSGA-II by 85.64%, 39.90%, and 33.31% respectively.

Multi-armed Bandit Experimental Design: Online Decision-Making and Adaptive Inference

Multi-armed bandit has been well known for its efficiency in online decision-making in terms of minimizing the loss of the participants’ welfare during experiments (i.e., the regret). In clinical trials and many other scenarios, the statistical power of inferring the treatment effects (i.e., the gaps between the mean outcomes of different arms) is also crucial. Nevertheless, minimizing the regret entails harming the statistical power of estimating the treatment effect because the observations from some arms can be limited. In this paper, we investigate the trade-off between efficiency and statistical power by casting the multi-armed bandit experimental design into a minimax multi-objective optimization problem. We introduce the concept of Pareto optimality to mathematically characterize the situation in which neither the statistical power nor the efficiency can be improved without degrading the other. We derive a useful sufficient and necessary condition for the Pareto optimal solutions to the minimax multi-objective optimization problem. Additionally, we design an effective Pareto optimal multi-armed bandit experiment that can be tailored to different levels of the trade-off between the two objectives. Moreover, we extend the design and analysis to the setting where the outcome of each arm consists of an adversarial baseline reward and a stochastic treatment effect, demonstrating the robustness of our design. Finally, motivated by clinical trials, we examine the setting where the employed experiment must split the experimental units into a small number of batches, and we propose a flexible Pareto optimal design. This paper was accepted by George Shanthikumar, data science. Funding: The authors thank the Massachusetts Institute of Technology (MIT)-IBM partnership in Artificial Intelligence and the MIT Data Science Laboratory for support. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2023.00492 .

Experimental, numerical simulation and genetic algorithm as a hybrid method for the design of hydrogen peroxide separation via non-dispersive solvent extraction

This work employed a hybrid approach combining experiments, numerical simulation, and genetic algorithm (GA) to optimize the non-dispersive solvent extraction (NDSX) process of H2O2. A numerical simulation model with high accuracy was developed. The relative error between the simulation results and experimental data was controlled within 2.2 %. The results indicated the velocity of lumen side and temperature are the key factors affecting the extraction efficiency. The non-dominated sorting GA-II algorithm coupled with the numerical simulation was used to optimize the NDSX process. The Pareto optimal design of the NDSX process can be achieved within the water outlet concentration range of 13.44 to 550.2 kg m-3. Intensification factors of NDSX versus extraction towers are evaluated to be 17.9 and 13.2. In summary, this work provides a design framework for NDSX of H2O2, which is expected to simultaneously promote the mass transfer efficiency and safety of the H2O2 separation process.

Surrogate-based multi-objective design optimization of tree-shaped fins with uniform branch end distribution for latent heat thermal energy storage

The enhancement of latent heat thermal energy storage (LHTES) systems through fin geometry optimization remains a critical challenge for leveraging the full potential of renewable energy sources. This study focuses on optimizing the geometries of tree-shaped fins to enhance power and energy densities in LHTES systems. The goal is to find branch designs with high energy and power density through a novel surrogate model-based optimization strategy that explores a broad design space. The surrogate models applied, including linear regression, principal component analysis-based linear regression, artificial neural networks, and random forest, are evaluated for their predictive performance. The random forest model demonstrates superior accuracy in predicting targets. The optimization process results in a Pareto-optimal design with a volume fraction of 33.9%. This optimal design substantially enhances the system's power density by 61.6% compared to conventional plate fins at an equivalent energy density. This optimized design improves energy and power density, achieving a uniform end-to-branch distribution, which is a pivotal factor for consistent temperature distribution and improved thermal efficiency. By integrating surrogate-based optimization with broad ranges of the tree-shaped fin design, this research has significantly improved the operational efficiency of LHTES systems. This research promises more effective thermal management and provides a methodological framework for design innovation in thermal energy storage.

On Single-Objective Sub-Graph-Based Mutation for Solving the Bi-Objective Minimum Spanning Tree Problem.

We contribute to the efficient approximation of the Pareto-set for the classical NP-hard multiobjective minimum spanning tree problem (moMST) adopting evolutionary computation. More precisely, by building upon preliminary work, we analyze the neighborhood structure of Pareto-optimal spanning trees and design several highly biased sub-graph-based mutation operators founded on the gained insights. In a nutshell, these operators replace (un)connected sub-trees of candidate solutions with locally optimal sub-trees. The latter (biased) step is realized by applying Kruskal's single-objective MST algorithm to a weighted sum scalarization of a sub-graph. We prove runtime complexity results for the introduced operators and investigate the desirable Pareto-beneficial property. This property states that mutants cannot be dominated by their parent. Moreover, we perform an extensive experimental benchmark study to showcase the operator's practical suitability. Our results confirm that the sub-graph-based operators beat baseline algorithms from the literature even with severely restricted computational budget in terms of function evaluations on four different classes of complete graphs with different shapes of the Pareto-front.

Multiobjective Optimization of Rotodynamic Blood Pumps: The Use Case of a Cavopulmonary Assist Device.

Comprehensive optimization of rotodynamic blood pumps (RBPs) requires the consideration of three partially conflicting objectives: size, hemocompatibility, and motor efficiency. Optimizing these individual objectives independently, the potential of multiobjective optimizations often remains untapped. This study aimed at the multiobjective optimization of an RBP for cavopulmonary support accounting for all three objectives simultaneously. Hydraulic and electromagnetic design spaces were characterized using computational fluid dynamics and computational electromagnetics, respectively. Design variables included secondary flow gap widths, impeller diameters, and stator heights. The size objective encompassed the RBP widths and heights, the hemocompatibility objective was a weighted composite measure of well-established metrics, and the motor objective was determined by motor losses. Multiobjective optimization was performed through Pareto analysis. 81 designs were considered, and 21 Pareto-optimal designs were identified. The Pareto analysis indicated that hemocompatibility performance could be improved by 72.4% with a concomitant 1.5% reduction in the baseline pump volume. This, however, entailed an increase in motor losses by 0.2 W, while still meeting design requirements, with maximum local temperature rises remaining below 0.4 K. The multiobjective optimization led to a Pareto front, demonstrating the feasibility to improve hemocompatibility at reduced pump volume, however, at the cost of a diminished yet still acceptable motor performance.

CFD-based multi-objective Bayesian optimization approach for compact and efficient hydrogen production in steam reforming reactor

This paper introduces a multi-objective Bayesian optimization approach for concurrently optimizing the size and productivity of a steam methane reforming reactor. Seven design variables, resulting in a total of 3,929,310 possible combinations, were explored, leading to three Pareto optimal designs after 100 iterations. Parametric studies were conducted first, and the results of Bayesian optimization were suggested with initial samples obtained via Latin Hypercube Sampling. The Pareto optimal designs revealed significant reduction in size and improvement in productivity. Furthermore, adjusting operating conditions, specifically the steam-to-carbon ratio, showed additional improvements of productivity. This study can contribute to efficiently proposing Pareto optimal designs with potential applications in hydrogen supply for compact and highly efficient systems.

Realtime optimization and management system (ROAM): A decision support system for digital agriculture systems

The growing disparity between food supply and demand requires innovative Digital Agriculture (DA) systems to increase farm sustainability and profitability. However, current systems suffer from problems of complexity stemming from the challenge of integrating diverse, often non-interoperable hardware and software components. In order to tackle these complexities to increase farm efficiency and understand the tradeoffs of these new DA innovations we developed Realtime Optimization and Management System (ROAM), which is a decision-support system developed to find a Pareto optimal architectural design to build DA systems. To find the Pareto optimal solution, we employed the Rhodium Multi-Objective Evolutionary Algorithm (MOEA), which systematically evaluates the trade-offs in DA system designs. Based on data from five live deployments at Cornell University, each DA design can be analyzed based on user defined objectives and evaluated under uncertain farming environments with ROAM. Paired with this, we develop a web interface that allows users to define personalized decision spaces and visualize decision tradeoffs. To help validate ROAM, it was deployed to a commercial farm where the user was recommended a DA architecture design method to increase farm efficiency. ROAM allows users to quickly make key decisions in designing their DA systems to increase farm profitability.

Neural networks as effective surrogate models of radio-frequency quadrupole particle accelerator simulations

Radio-frequency quadrupoles (RFQs) are multi-purpose linear particle accelerators that simultaneously bunch and accelerate charged particle beams. They are ubiquitous in accelerator physics, especially as injectors to higher-energy machines, owing to their impressive efficiency. The design and optimization of these devices can be lengthy due to the need to repeatedly perform high-fidelity simulations. Several recent papers have demonstrated that machine learning can be used to build surrogate models (fast-executing replacements of computationally costly beam simulations) for order-of-magnitude computing time speedups. However, while these pilot studies are encouraging, there is room to improve their predictive accuracy. Particularly, beam summary statistics such as emittances (an important figure of merit in particle accelerator physics) have historically been challenging to predict. For the first time, we present a surrogate model trained on 200 000 samples that yields < 6% mean average percent error for the predictions of all relevant beam output parameters from defining RFQ design parameters, solving the problem of poor emittance predictions by identifying and including hidden variables which were not accounted for previously. These surrogate models were made possible by using the Julia language and GPU computing; we briefly discuss both. We demonstrate the utility of surrogate modeling by performing a multi-objective optimization using our best model as a callback in the objective function to select an optimal RFQ design. We consider trade-offs in RFQ performance for various choices of Pareto-optimal design variables—common issues for any multi-objective optimization scheme. Lastly, we make recommendations for input data preparation, selection, and neural network architectures that pave the way for future development of production-capable surrogate models for RFQs and other particle accelerators.

FlexiBO: A Decoupled Cost-Aware Multi-objective Optimization Approach for Deep Neural Networks (Abstract Reprint)

The design of machine learning systems often requires trading off different objectives, for example, prediction error and energy consumption for deep neural networks (DNNs). Typically, no single design performs well in all objectives; therefore, finding Pareto-optimal designs is of interest. The search for Pareto-optimal designs involves evaluating designs in an iterative process, and the measurements are used to evaluate an acquisition function that guides the search process. However, measuring different objectives incurs different costs. For example, the cost of measuring the prediction error of DNNs is orders of magnitude higher than that of measuring the energy consumption of a pre-trained DNN as it requires re-training the DNN. Current state-of-the-art methods do not consider this difference in objective evaluation cost, potentially incurring expensive evaluations of objective functions in the optimization process. In this paper, we develop a novel decoupled and cost-aware multi-objective optimization algorithm, which we call Flexible Multi-Objective Bayesian Optimization (FlexiBO) to address this issue. For evaluating each design, FlexiBO selects the objective with higher relative gain by weighting the improvement of the hypervolume of the Pareto region with the measurement cost of each objective. This strategy, therefore, balances the expense of collecting new information with the knowledge gained through objective evaluations, preventing FlexiBO from performing expensive measurements for little to no gain. We evaluate FlexiBO on seven state-of-the-art DNNs for image recognition, natural language processing (NLP), and speech-to-text translation. Our results indicate that, given the same total experimental budget, FlexiBO discovers designs with 4.8% to 12.4% lower hypervolume error than the best method in state-of-the-art multi-objective optimization.

Multi-Fidelity Design of Porous Microstructures for Thermofluidic Applications

Abstract As modern electronic devices are increasingly miniaturized and integrated, their performance relies more heavily on effective thermal management. In this regard, two-phase cooling methods which capitalize on thin-film evaporation atop structured porous surfaces are emerging as potential solutions. In such porous structures, the optimum heat dissipation capacity relies on two competing objectives that depend on mass and heat transfer. Optimizing these objectives for effective thermal management is challenging due to the simulation costs and the high dimensionality of the design space which is often a voxelated microstructure representation that must also be manufacturable. We address these challenges by developing a data-driven framework for designing optimal porous microstructures for cooling applications. In our framework, we leverage spectral density functions to encode the design space via a handful of interpretable variables and, in turn, efficiently search it. We develop physics-based formulas to simulate the thermofluidic properties and assess the feasibility of candidate designs based on offline image-based analyses. To decrease the reliance on expensive simulations, we generate multi-fidelity data and build emulators to find Pareto-optimal designs. We apply our approach to a canonical problem on evaporator wick design and obtain fin-like topologies in the optimal microstructures which are also characteristics often observed in industrial applications.

Strength Optimization of Nanocomposite Cementitious Materials Using Nanoscale Modifications

Represent Volume Element (RVE) is broadly used by investigators to control the properties of nano-cementitious materials. This paper focuses on analyzing a set of RVE data and proposes parametric equations for determining the compressive and flexural strength characteristics (σc and σf). Primarily, a parametric study is performed with RVE analysis. The essential design parameters are used to fit rational equations. The RVE data are also applied to train artificial neural networks of σc and σf. RVE, neural networks, and rational equations are correlated. Regression equations are validated with the experimental study. SEM, TEM, XRD, and FTIR results are carried out in the microscopic and mechanical analysis for carbon nanofiber cement composites, which can lift their strength, constancy, integrity, and density and reinforce the composite microstructure. Lastly, the Pareto-optimal design results are presented with a multi-objective optimization problem.

DERNA Enables Pareto Optimal RNA Design.

The design of an RNA sequence that encodes an input target protein sequence is a crucial aspect of messenger RNA (mRNA) vaccine development. There are an exponential number of possible RNA sequences for a single target protein due to codon degeneracy. These potential RNA sequences can assume various secondary structure conformations, each with distinct minimum free energy (MFE), impacting thermodynamic stability and mRNA half-life. Furthermore, the presence of species-specific codon usage bias, quantified by the codon adaptation index (CAI), plays a vital role in translation efficiency. While earlier studies focused on optimizing either MFE or CAI, recent research has underscored the advantages of simultaneously optimizing both objectives. However, optimizing one objective comes at the expense of the other. In this work, we present the Pareto Optimal RNA Design problem, aiming to identify the set of Pareto optimal solutions for which no alternative solutions exist that exhibit better MFE and CAI values. Our algorithm DEsign RNA (DERNA) uses the weighted sum method to enumerate the Pareto front by optimizing convex combinations of both objectives. We use dynamic programming to solve each convex combination in time and space. Compared with a CDSfold, previous approach that only optimizes MFE, we show on a benchmark data set that DERNA obtains solutions with identical MFE but superior CAI. Moreover, we show that DERNA matches the performance in terms of solution quality of LinearDesign, a recent approach that similarly seeks to balance MFE and CAI. We conclude by demonstrating our method's potential for mRNA vaccine design for the SARS-CoV-2 spike protein.

Computational discovery of microstructured composites with optimal stiffness-toughness trade-offs.

The conflict between stiffness and toughness is a fundamental problem in engineering materials design. However, the systematic discovery of microstructured composites with optimal stiffness-toughness trade-offs has never been demonstrated, hindered by the discrepancies between simulation and reality and the lack of data-efficient exploration of the entire Pareto front. We introduce a generalizable pipeline that integrates physical experiments, numerical simulations, and artificial neural networks to address both challenges. Without any prescribed expert knowledge of material design, our approach implements a nested-loop proposal-validation workflow to bridge the simulation-to-reality gap and find microstructured composites that are stiff and tough with high sample efficiency. Further analysis of Pareto-optimal designs allows us to automatically identify existing toughness enhancement mechanisms, which were previously found through trial and error or biomimicry. On a broader scale, our method provides a blueprint for computational design in various research areas beyond solid mechanics, such as polymer chemistry, fluid dynamics, meteorology, and robotics.

Purposeful co-design of OFDM signals for ranging and communications

This paper analyzes the fundamental trade-offs that occur in the co-design of pilot resource allocations in orthogonal frequency-division multiplexing signals for both ranging (via time-of-arrival estimation) and communications. These trade-offs are quantified through the Shannon capacity bound, probability of outage, and the Ziv–Zakai bound on range estimation variance. Bounds are derived for signals experiencing frequency-selective Rayleigh block fading, accounting for the impact of limited channel knowledge and multi-antenna reception. Uncompensated carrier frequency offset and phase errors are also factored into the capacity bounds. Analysis based on the derived bounds demonstrates how Pareto-optimal design choices can be made to optimize the communication throughput, probability of outage, and ranging variance. Different pilot resource allocation strategies are then analyzed, showing how Pareto-optimal design choices change depending on the channel.

Optimization of Lift-Plus-Cruise Vertical Take-Off and Landing Aircraft with Electrified Propulsion

Conventional aircraft sizing methods face challenges in analyzing all-electric or hybrid-electric novel aircraft configurations, such as those for urban air mobility applications. The vast design space containing both continuous and discrete design variables and competing design objectives necessitates searching for not necessarily a unique optimal design but rather an array of Pareto-optimal designs. This paper uses the Parametric Energy-Based Aircraft Configuration Evaluator, an aircraft sizing framework for novel aircraft and propulsion system architectures, to pursue multi-objective optimization of a lift-plus-cruise urban air mobility aircraft with all-electric, hybrid-electric, and turbo-electric propulsion system architectures using Nondominated Sorting Genetic Algorithm II. The optimization cases considered include multiple objective functions, such as maximum takeoff mass, mission time, energy and propulsion mass fraction, and energy used per unit distance per unit payload. Optimization was performed for trip distances of 80, 120, and 150 km and battery specific energy levels of 350 and 400 Wh/kg. Except when mission time was an objective function, Pareto-optimal designs occurred near the lower bound of the velocity range. Raising that bound had an impact on the architectural composition of the final generation. All-electric architectures appeared exclusively for lower trip distances, hybrid-electric designs appeared for longer trip distances, and turbo-electric designs only appeared for combinations of longer trip distances, a higher minimum cruise speed, and a lower battery specific energy level. The sizing results were sensitive to assumptions regarding the overload capacity of lift propulsor motors in postfailure conditions.

Optimisation of proprotors for tilt-wing eVTOL aircraft

Proprotors for tilt-wing advanced air mobility aircraft are often optimised without considering the transition from hover to cruise. This paper presents an optimisation method, which considers transition flight phases. Proprotors are optimised for a multi-rotor tilt-wing vehicle at nominal cruise, transition, and hover conditions. Results show that proprotors designed with transition flight conditions tend to have smaller chord distributions along the span than those designed without considering transition. The blade twist from root to tip of the transition proprotors is also more extreme, and a slight increase in pitch towards the tip section of the propeller is observed. The more significant overall twist avoids retreating blade stall during transition and transition power is the most sensitive to the pitch angle at the mid-radius to tip section of the blade. However, a proprotor that is designed taking transition into account requires a hover power that is 5.6% larger than a proprotor designed for cruise and hover only. Pareto-optimal proprotor designs from an optimisation case without transition cannot deliver enough thrust throughout all transition flight phases.

Electromagnetic-thermal co-optimization to minimize case-to-winding temperature rise in permanent magnet machines

Electrification of aerospace platforms requires efficient heat dissipation from electric machines to meet their temperature requirements while minimizing the weight and size of the onboard thermal management system. It is critical to couple available electromagnetic design optimization approaches with complementary thermal models, so that these thermal management system objectives can be considered, namely to reduce the temperature rise between the sources of heat generation and coolant. In this work, a thermal equivalent circuit model for the stator of a permanent magnet synchronous machine is developed and validated. The thermal network includes a discretization of individual conductors and considers their placement within a slot, compared to previous approaches that assumed a lumped/homogenized representation that is not versatile for robust optimization. The temperature predictions reveal that the choice of conductor sizing and packing within the stator slot significantly affects their peak temperatures. After validation, the thermal model is coupled to an electromagnetic model to perform multi-physics multi-objective design that minimizes machine mass and the temperature rise between the conductors and coolant. This approach contrasts a traditional electromagnetic design trade off between loss and mass. Design studies were performed to generate Pareto-optimal designs for comparison between these objectives. By using the co-optimization design framework with an integrated thermal objective function, the machine operating temperature can be significantly reduced while delivering the same power density at the cost of machine efficiency. The detailed machine designs are analyzed to explain the thermal advantages of the co-optimization design.

Comfort, carbon emissions, and cost of building envelope and photovoltaic arrangement optimization through a two-stage model

The design of a high-performance building necessitates tradeoffs among multiple performance objectives, and many simulation-based optimization tools have been developed for this purpose. In practice, these tools are often constrained by excessive computational load and tight project deadlines. This study aimed to develop a holistic approach to rapidly identify optimal building design schemes. A novel two-stage model was developed as a surrogate to conventional physics-based models, which were then linked to multi-objective optimization algorithms, namely, NSGA-II, NSGA-III, and C-TAEA, in search of the Pareto optimal and best design schemes. The performance of the two-stage model was further enhanced by applying the least absolute shrinkage and selection operator (LASSO) and Neural Architecture Search methods and learning from the statistical layer. The above approach was tested in the design of an apartment building for seniors in Northern China such as thermal comfort, carbon, and cost. The optimal design achieved through the compromise optimum can significantly reduce thermal discomfort, life-cycle carbon emissions, and high levels of daylighting conditions. The design scheme was visualized using a geometrical remodel module. This study contributes methodologically to complex multi-objective building optimization problems with practical implications for design.

Quantifying emission and cost reduction potentials of Corporate Mobility as a Service

Corporate Mobility as a Service (CMaaS) combines the advantages of company-exclusive and public mobility services, like carsharing, bikesharing, or taxis. Although prior research indicates that CMaaS has positive impacts on the GHG emissions and costs of corporate mobility, detailed analyses are still lacking. Against this background, we propose a methodology to quantify the potentials of CMaaS to reduce the GHG emissions and costs of corporate mobility. We apply a cost estimation, a Life Cycle Assessment, and a multi-objective optimization model to determine the pareto-optimal CMaaS designs for companies aiming to minimize GHG emissions and costs. Within the CMaaS design, we determine the fleet size and composition of company-exclusive, and the choice of price tariffs for public mobility services. By applying our methodology to a comprehensive case study that covers 428 driving profiles of 144 different companies, we deduce general insights on the potentials of CMaaS.