Multi-objective Optimization Research Articles

Hybrid wind speed optimization forecasting system based on linear and nonlinear deep neural network structure and data preprocessing fusion

Wind speed time series forecasting has been widely used in wind power generation. However, the nonlinear and non-stationary characteristics of wind speed make accurate wind speed forecasting a difficult task. In recent years, the rapid development of artificial intelligence and machine learning technology provides a new solution to the problem of wind speed forecasting. Combining the advance of artificial intelligence and data analysis strategy, this paper proposes a wind speed forecasting system based on multi-model fusion and integrated learning. Considering the differences in data observation and training principles of various algorithms and exploiting the advantages of each model, a wind speed forecasting system with multiple machine learning algorithms embedded in integrated learning is constructed, which includes three modules: data preprocessing, optimization and forecasting. The data preprocessing module can conduct quantitative analysis through input data decomposition and feature extraction, and the combination of multi-objective intelligent optimization algorithm and combined forecasting method can effectively forecast the wind speed time series. The validity of the algorithm is verified using the data of Shandong wind farm in China. The forecasting results show that compared with the traditional single model forecasting, the proposed integrated wind speed forecasting system based on the fusion of multiple models has higher forecasting accuracy.

Optimized Resource Allocation for Sustainable Development in Beijing: Integrating Water, Land, Energy, and Carbon Nexus

Chinese megacities face significant challenges in reducing carbon emissions while balancing economic growth and social welfare. This study constructs an innovative multi-objective optimization model, the SD-NSGA-III model, integrated with a System Dynamics (SD) model and using the Non-dominated Sorting Genetic Algorithm III (NSGA-III) to optimize resource allocation in Beijing. The model targets environmental, economic, and social goals by establishing a water–land–energy–carbon (WLEC) nexus for analyzing resource allocation strategies and carbon reduction pathways under various constraints. Scenario simulations under the efficiency-oriented scenario indicated a potential reduction in energy carbon emissions of 81.4% by 2030. The fairness-oriented scenario revealed significant trade-offs between equity and emission reductions, emphasizing the need for balanced strategies. Introducing constraints on resources and economic growth significantly reduced median energy carbon emissions to 80 million tons by 2030. These findings demonstrate the effectiveness of the SD-NSGA-III model in providing actionable strategies for achieving carbon neutrality and sustainable development in cities.

Determining method of optimal process parameters using Taguchi method and technique for order preference by similarity to ideal solution in plastic injection molding

Many plastic injection molding (PIM) process optimization problems are multi-objective optimization problems that optimize multiple mechanical properties. This paper proposed a determining method of optimal process parameters and their effect ranks using Taguchi method and TOPSIS in the PIM. TOPSIS was used to convert multiple mechanical properties into single comprehensive response. It was selected as a reasonable multi-attribute decision-making (MADM) method from among some well-known MADM methods based on mean rank correlation coefficient and mean absolute rank deviation. Taguchi method was used to design experiment and find the optimal process parameters. The proposed method was applied to determine the optimal values of the process parameters: melt temperature (MT), packing pressure (PP), cooling time (CT), and injection pressure (IP) for improving tensile strength, elasticity module, flexural modulus, and impact strength in the PIM with Acrylonitrile-Butadiene-Styrene compound as plastic materials and AISI 1020 as mold materials. The optimal values of the process parameters were MT of 280°C, PP of 28 MPa, CT of 22 s, and IP of 50 MPa, and their effect ranking was IP (51.941%), PP (32.280%), CT (9.045%), and MT (6.734%). The method could be widely applied to not only the PIM process optimization but also various manufacturing process optimization problems.

Optimization study on circadian tunability and Rec. 2020 of RGB-LED-based displays considering the users with different ages

The reasonable design of spectral power distribution (SPD) of GaN-based light-emitting diode (LED) display becomes more and more important and popular. In this work, we perform an investigation on the circadian effects of three-primary (red R, green G, and blue B, also denoted as RGB) LED based self-luminous displays (such as emerging mini-LED or micro-LED based displays) considering the users with different ages. With the increment of peoples’ ages from 1 year to 100 years, the optical transmittance of humans’ eyes may decrease due to the aging of their body functions. Therefore, it is important and meaningful for performing a spectral optimization study on the circadian effects of light that is emitting from self-luminous LED-based displays for the users with different ages. Here, the melanopic efficacy of luminous radiation (MELR) is mainly used to evaluate the circadian effects of white light coming from RGB-LED displays. With the aid of multi-objective optimization genetic algorithm (MOGA), the maximum MELR and the minimum MELR value are separately obtained for the standard observers at the age of 32, while maintaining at a certain high color gamut of Rec. 2020 standard (i.e., 60 %, 70 %, 80 %, and 90 % Rec. 2020, respectively) for these LED-based displays. Then, an extrapolation of optimal SPD at the age of 32 is done to other ages. Another parameter that can be denoted as circadian stimulus (CS) is also calculated and discussed for different ages. It is believable that this work is helpful for guiding the design and fabrication of future RGB-LED-based displays in consideration of the users with different ages, meeting large requirements of human-centric lighting (HCL) in the future.

On formal modeling, analysis and optimization of reconfigurable manufacturing systems

ABSTRACT This paper deals with the formal specification and multi-objective optimization of reconfigurable manufacturing systems (RMSs). RMSs are characterized by their dynamic structure, crucial for responding to functional variations, adjusting production capacity and overcoming operational dysfuntions promptly and cos-effectively. The effective utilization of this dynamic capability depends on thorough study and optimization of RMS configurations. To tackle this challenge, a novel formalism called genetic reconfigurable object nets (Gen-RONs) is introduced. Gen-RONs formalism integrates the modeling, verification and reconfiguration capabilities of reconfigurable object nets with advanced multi-objective techniques from genetic algorithms. Within Gen-RONs, Petri nets serve to: (i) encode RMS configurations, (ii) manage RMS scheduling and (iii) employ graph transformation theory rules as genetic algorithm operators for real-time system reconfiguration. Thus, Gen-RONs formalism provides a robust framework for optimizing RMSs using genetic algorithms. To ensure deadlock-free RMS configurations, Gen-RONs incorporate a binary tree-based technique. Furthermore, Taguchi’s method is employed to fine-tune genetic algorithm parameters. The contribution of this paper is demonstrated through a case study involving an RMS and the widely used genetic algorithm NSGA-II. Significant gains in terms of the number of solutions (i.e. configurations) and the criteria values are achieved.

Multi-objective optimization towards cooling performance of teardrop section Kagome trusses array jet impingement composite cooling structure with cross-flow

Teardrop Section Kagome trusses array can be a spoiler for a new generation of advanced combustion chambers. In this study, multi-objective optimizations are applied to optimize a jet impingement composite cooling structure with cross-flow. Four structural parameters with five levels and three performance parameters are calculated in design of experiment and fitted by response surface methodology. The database is expanded by non-dominated sorting genetic algorithm-II, and then technique for order preference by similarity to an ideal solution is used to calculate the optimal structures under different operating conditions by different weights of the performance parameter. The conclusions are as follows: The minimal Equality of variances and fitting accuracy are 35.4371 and 93.6%. Diameter of the cross-section has the largest positive main effect on average Nusselt number and pressure loss coefficient, while angle between the rod and the horizontal plane has the largest positive effect on temperature uniformity coefficient. The interaction of trailing edge angle with angle between the front rod and the back rod in the horizontal plane is large. Case15 is chosen, where the weight ratio is 1:5:5, improvement of the corresponding optimized performance parameters of the simulation results with respect to the Origin of three performance parameters are 26.72%, −2.93%, 91.59% respectively. It provides a feasible reference for future advanced combustion chambers and accelerates their development process.

Pore-Scale multi-objective shape optimization of triply periodic minimal surface cellular architectures: Volumetric Nusselt number versus friction factor

Triply Periodic Minimal Surface (TPMS) cellular architectures, i.e., minimal surfaces that are periodic in three independent directions, have attracted interest in the engineering community for their potential in heat transfer applications with severe volume constraints due to their high surface-to-volume ratio, unique geometrical properties and smooth porous structure. Such performance can be conveniently controlled by tuning the TPMS unit type, relative density, and structural parameters. In this study, a multi-objective optimization process is carried out to investigate how pore-scale geometric characteristics affect the heat transfer performance of TPMS, and which combinations result in an optimal trade-off between heat dissipation capability and associated pressure drop in terms of the Nusselt number and friction factor. The analysis is performed using an in-house Genetic Algorithm routine that generates the structure, allowing for a wider and denser range of investigation, and incorporates a commercial finite element CFD software as a black box fitness function. Over 14,000 unique combinations between two heat transfer boundary conditions (constant wall heat flux, fixed wall temperature) and several flow inlet conditions are investigated. The optimization achieved an increase in performance of up to 245 % in terms of volumetric Nusselt number, which was accompanied, however, by a significant, although reasonable, increase in friction factor values. The results also show specific trends among the geometric characteristics studied, which are then contextualized through the use of CFD analysis. Finally, empirical correlations are derived to cluster the non-dominated solutions obtained, enabling the reader to choose the best cellular TPMS structure by selecting the desired level of trade-off between convection heat transfer and flow resistance.

Multi-objective spectral range optimization for different heat source temperatures to maximize thermophotovoltaic performance using NSGA-II

The energy conversion efficiency (ECE) and output power density of thermophotovoltaic (TPV) cells are mutually constraining. To better utilize this relationship, a framework was proposed to integrate the internal quantum efficiency (IQE) of TPV cells with a multi-objective genetic algorithm (NSGA-II) to optimize both efficiency and power density across diverse operating conditions. A spectrally selective emitter with a temperature of 1000–3000 K was selected as the radiation source for the studied TPV devices, capable of emitting a spectrum between 0.4 and 2.0 μm. The gallium antimonide (GaSb) cell was selected as the exploration cell, operating within a temperature range of 0–200 °C. Through theoretical calculation, the changes in physical parameters and IQE curves of GaSb cells at various temperatures were determined. The optimal spectral range for varying cell and emitter temperatures was determined using the NSGA-II algorithm. It was found that the IQE curve decreases with increasing temperature. Due to the spectral mismatch, the TPV conversion efficiency is much less than 20 % when the spectral range of the cell is 0.4–2.0 μm at room temperature. By incorporating IQE into the multi-objective optimization, the efficiency and power density distribution curves can be divided into three regions. In practical applications, the corresponding regions can be selected based on different efficiency and output power requirements.

Enhancing disaster management through multi-objective water wave optimization for medical supplies storage and distribution

This paper conducts a comparative analysis of advanced methodologies aimed at addressing the intricate task of scheduling medical supplies in both civilian and military sectors for epidemic prevention and control. This study introduces a multi-objective water wave optimization (MOWWO) algorithm and enhance its efficacy by incorporating a dynamically adjusted component to the metaheuristic approach (DAMOWWO). The primary goal of this research is to assess the proposed approach in contrast to established state of the art methods with similar objectives. The aim of this study is to optimize multiple aspects simultaneously, including the overall satisfaction rates of medical supply delivery and the reduction of scheduling costs, while ensuring a minimum military supply reservation ratio. This paper offers a comprehensive evaluation of the MOOW algorithm, emphasizing its potential applications in emergency response scenarios.

Driving Control Strategy and Specification Optimization for All-Wheel-Drive Electric Vehicle System with a Two-Speed Transmission

Equipping electric vehicles with a two-speed gearbox allows for achieving high torque and maximum speed through appropriate gear ratio adjustments. Additionally, tuning motor operating points to efficient zones, considering energy efficiency, significantly enhances the vehicle’s overall performance. This paper presents an AWD system configuration method, integrating a two-speed transmission to improve energy efficiency and driving performance through front and rear motor torque distribution and powertrain specification optimization. Based on vehicle simulations conducted using MATLAB/Simulink, a strategy for torque distribution between the front/rear axles was established using fuzzy logic, considering energy efficiency and driving stability. Furthermore, a multi-objective optimization was performed using a surrogate model trained through MATLAB parallel simulations. When the optimization results were applied to various vehicle specifications, it was observed that energy efficiency was improved, and acceleration performance was increased compared to a baseline vehicle without optimization.

Optimizing the Scheduling of Teaching Activities in a Faculty

To maximize resource usage, minimize disputes, and improve academic experience, professors must schedule teaching activities efficiently. This study provides an optimized automated schedule creation technique. The system generates schedules that aim to be conflict-free and efficient, utilizing evolutionary algorithms along with multi-objective optimization. Resource usage, scheduling problems, and faculty/student satisfaction are the goals of the research. The system optimizes scheduling based on room limitations, instructor availability, and student preferences. The project uses system design, model creation, algorithm implementation, and performance analysis to solve the difficult timetable-generating problem. This research should save administrators time, improve academic operations, and improve staff and student academic experiences. Scalability and flexibility allow the system to be used in multiple faculties and incorporate new limits and requirements. This paper presents a complete approach to faculty scheduling, including insights and recommendations for future study and application in educational institutions.

Data transmission optimization based on multi-objective deep reinforcement learning

Abstract Simultaneously reducing network energy consumption and delay is a hot topic today. This paper addresses this issue by designing a novel multi-objective data transmission optimization algorithm based on deep reinforcement learning. A three-layer back propagation (BP) neural network is designed to improve the accuracy of environmental state prediction, by learning from historical state and action sequence data, which can help the agent make better decision for routing selection in complex network environment. Based on this, we use Q-Learning to find routing for transmission demands, aggregating more traffic through less links and routers, to reduce energy consumption and delay. To enhance the efficiency and robustness of the algorithm, a new reward mechanism is designed based on the traffic demand and the link state. The algorithm divides candidate links into three levels for path selection so that a better solution can be obtained on the basis of ensuring feasible solutions are obtained. Continuous updating of the Pareto set through multiple state steps approximates the optimal solution. We leverage the Euclidean distance to the reference point to measure the optimization effect of the two objectives. The simulation results show that this algorithm outperforms existing algorithms in reducing energy consumption and network delay.

Development of PCM tile for residential buildings in hot and dry climate: design and optimization

In recent years, the building sector has become more conscious of sustainability, and the use of phase change materials (PCMs) in concrete has gained more attraction. Integration of PCM with building facades is a successful method to reduce energy consumption and improve human comfort. However, no single PCM can work in an all-weather scenario. Hence, in this research work, an attempt is made to select a suitable PCM for Chennai city, India, and this methodology can be employed at any geographical location. The PCM tile is designed by including certain features to increase the thermal conductivity of the PCM zone. The optimum design of the PCM tile is achieved through multi-objective optimization techniques. L27 orthogonal array is employed, and all the tests were conducted through validated numerical simulation. Redesigned PCM tile includes a PCM layer of 2 cm thickness with a 10% mix of copper nanoparticles covered by plaster. Redesigned PCM tile reduces the peak indoor temperature by 6.62℃ compared with conventional roof systems.

Optimizing green hydrogen strategies in Tunisia: A combined SWOT-MCDM approach

Tunisia's rapid industrial expansion and population growth have created a pressing energy deficit, despite the country's significant, yet largely untapped, renewable energy potential. This study addressed this challenge by developing a comprehensive framework to identify and evaluate strategies for promoting green hydrogen production from renewable energy sources in Tunisia. A Strength, Weakness, Opportunity, and Threat (SWOT) analysis, incorporating social, economic, and environmental dimensions, was conducted to formulate potential solutions. The Step-wise Weight Assessment Ratio Analysis (SWARA) method facilitated the weighting of SWOT factors and sub-factors. Subsequently, a multi-criteria decision-making approach, employing the gray technique for order preference by similarity to ideal solution (TOPSIS-G) method (validated by gray additive ratio assessment (ARAS-G), gray complex proportional assessment (COPRAS-G), and gray multi-objective optimization by ratio analysis (MOORA-G), was used to rank the identified strategies.The SWOT analysis revealed "Strengths" as the most influential factor with a relative weight of 47.3 %, followed by "Weaknesses" (26.5 %), "Threats" (15.6 %), and "Opportunities" (10.6 %). Specifically, experts emphasized Tunisia's renewable energy potential (21.89 %) and robust power system (12.11 %) as primary strengths. Conversely, high investment costs (11.2 %) and political instability (7.77 %) posed substantial threat. Positive socio-economic impacts represented a key opportunity with a score of 5.2 %. As for the strategies prioritizing criteria, production cost ranked first with a score of 13.5 %, followed by environmental impact (12.8 %), renewable energy potential (12.0 %), and mitigation costs (11.3 %). The gray TOPSIS analysis identified two key strategies: leveraging Tunisia's wind and solar resources and fostering regional cooperation for project implementation. The robustness of these strategies is confirmed by the strong correlation between TOPSIS-G, ARAS-G, COPRAS-G, and MOORA-G results. Overall, the study provides a comprehensive roadmap and expert-informed decision-support tools, offering valuable insights for policymakers, investors, and stakeholders in Tunisia and other emerging economies facing similar energy challenges.

Multi-Objective Optimization of an Inertial Wave Energy Converter for Multi-Directional Wave Scatter

To advance wave energy devices towards commercialization, it is essential to optimize their design to enhance system performance. Additionally, a thorough economic evaluation is crucial for making these technologies competitive with other renewable energy sources. This study focuses on the techno-economic optimization of an innovative inertial system, the so-called SWINGO system, which is based on gyropendulum technology. SWINGO stands out due to its high energy efficiency in multi-directional installation sites, where wave directions vary significantly throughout the year. The study introduces the application of a multi-objective Evolutionary Algorithm (EA), specifically the Non-dominated Sorting Genetic Algorithm II (NSGA-II), to optimize the techno-economic performance of the SWINGO system. This approach aims to identify optimal design parameters that maximize energy extraction while considering economic viability. By deriving a Pareto frontier, a set of optimal devices is selected for further analysis. The performance of the SWINGO system is also compared to an alternative (mono-directional) inertial wave energy converter, the Inertial Sea Wave Energy Converter (ISWEC), to highlight the differences in techno-economic outcomes. Both systems are evaluated at two different installation sites: Pantelleria island and the North Sea in Denmark, with a focus on the directional wave scatter at each location.

Optimizing energy hub systems: A comprehensive analysis of integration, efficiency, and sustainability

This study introduces a novel application of modified particle swarm optimization (PSO) for optimizing multi-energy hub systems (EHSs) to enhance efficiency and sustainability. The proposed method leverages PSO to optimize the scheduling of various energy resources, including gas turbines, biomass units, and renewable sources such as solar and wind power. Unlike traditional optimization approaches that rely on genetic algorithm (GA) and complex encoding schemes, the PSO algorithm simplifies the process using real-valued vectors and direct communication within the swarm, which significantly reduces implementation complexity. Key contributions of this work include the development of a tailored PSO algorithm that integrates seamlessly with the multi-objective optimization of EHSs. The algorithm simultaneously targets a reduction in operational costs and carbon emissions, offering a comprehensive solution for energy hub design. The proposed PSO approach has demonstrated a 10.35 % reduction in operating costs and an 85.03 % decrease in CO2 emissions compared to traditional baseline setups. In comparative analysis, the integration of renewable sources using the PSO algorithm resulted in a 77.91 % reduction in total CO2 emissions and an 85.61 % decrease in operating costs, showcasing its effectiveness in advancing both economic and environmental objectives. Furthermore, the study provides a detailed evaluation of various scenarios, revealing that the PSO-optimized EHS configuration achieves a significant reduction in reliance on non-renewable energy sources (RES). For instance, the incorporation of photovoltaics and wind turbines in the EHS setup led to a 46.39 % increase in energy sold to the grid and a 26.82 % decrease in electricity purchased from external sources. These quantitative results underscore the robustness and practical benefits of the proposed PSO method in designing and optimizing energy systems for improved sustainability and cost-effectiveness.

Overall plan optimization of BWB UAV based on comprehensive evaluation

Based on the shape and performance characteristics of the wing-body fusion layout UAV, a multidisciplinary comprehensive analysis model, comprehensive evaluation model and optimization model suitable for the overall scheme of the UAV in the conceptual design stage are established, and the corresponding tools are developed. The geometric, weight, aerodynamic and stealth characteristics of the overall scheme of the wing-body fusion layout UAV are analyzed by combining numerical analysis and engineering methods. The improved TOPSIS method is used to establish a comprehensive evaluation model from the perspective of the loading capacity, economy and adaptability of the UAV. The rationality of the analysis model is verified by taking multiple UAV schemes as examples. Using the parallel subset simulation optimization algorithm, the traditional multi-objective optimization is completed with the maximum cruise lift-to-drag ratio and the minimum forward RCS as the goal, and the scheme optimization based on comprehensive evaluation is completed with the strongest competitiveness as the goal. Based on all the schemes generated by the multi-objective optimization process, the parameter correlation analysis is completed, and the influence of the span, sweep angle and twist angle on the aerodynamic and stealth characteristics is verified. The RCS of the final multi-objective optimization scheme is reduced 41.6%, and the cruise lift-to-drag ratio is improved 3.5% ; the competitiveness score of the comprehensive evaluation optimization scheme is improved 44.0%.

Scheduling optimization of continuous climb and descent operations in busy terminal airspace

Based on the current terminal airspace structure, a method for scheduling aircraft arrival and departure that integrates trajectory optimization, conflict detection and multi-objective optimization is proposed to help implement continuous climb and descent operations in busy terminal airspace. First, based on the multi-stage optimal control theory, the Gaussian pseudo-spectral method is used to propose a vertical profile optimization method for continuous climb and descent operations, and the trajectory optimization of continuous climb and descent operations based on the cost index is realized. Secondly, according to the wake turbulence interval and release interval used by the runway, and the horizontal and vertical intervals of air operations, the Mahalanobis distance is used to establish an aircraft conflict detection model. Then, considering the demands of air traffic control, airlines, airports and other operating units, a multi-objective scheduling model and method for aircraft arrival and departure that can achieve the optimization results are proposed. Finally, two sets of arrival and departure data at Guangzhou Baiyun Airport during busy periods are selected, multiple interval parameters are set, alternative paths are introduced, and case analysis and comparative studies are carried out. The results show that during the busy period dominated by departures, the terminal airspace of Guangzhou Baiyun Airport can achieve continuous climb and descent operations during busy periods; during the busy period dominated by arrivals, two aircraft could not be dispatched. The introduction of alternative paths can reduce the number of aircraft that cannot be dispatched.

Techno-economic and advanced exergy analysis and machine-learning-based multi-objective optimization of the combined supercritical CO2 and organic flash cycles

In the past few years, attention has been directed towards the advancement of renewable-driven supercritical CO2 recompression Brayton (SCRB) cycles. This highlights the impacts of sustainable and efficient power production towards transition in the electricity sector. The combination of the SCRB cycle with the organic flash cycle (OFC) is comprehensively investigated from thermodynamic, techno-economic, environmental, and advanced exergy perspectives. Conventional thermodynamic analysis alone cannot provide information on the cause of irreversibilities, the interconnections between components, and the possibility of enhancing their performance; therefore, advanced exergy analysis is implemented. Furthermore, an examination has been conducted into the effects of different decision parameters on the exergoenvironmental indicators. Multi-objective optimization based on machine learning is performed on the SCRB/OFC plant to maximize exergy efficiency, net present value, and net power output. Results from advanced exergy analysis revealed that the reactor has the worst performance, with just 2.8 % of its total exergy destruction being avoidable. Furthermore, it is feasible to decrease its total exergy destruction rate by 21.6 % through enhancements in the performances of other components. Under the optimized conditions, exergy efficiency, net present value, and net power output are found to be 70.8 %, 1347.1 M$, and 306.4 MW, respectively, representing a 21.1 %, 68.9 %, and 21.1 % enhancement compared with the base conditions, respectively.

Optimized deep learning networks for accurate identification of cancer cells in bone marrow

Radiologists utilize pictures from X-rays, magnetic resonance imaging, or computed tomography scans to diagnose bone cancer. Manual methods are labor-intensive and may need specialized knowledge. As a result, creating an automated process for distinguishing between malignant and healthy bone is essential. Bones that have cancer have a different texture than bones in unaffected areas. Diagnosing hematological illnesses relies on correct labeling and categorizing nucleated cells in the bone marrow. However, timely diagnosis and treatment are hampered by pathologists' need to identify specimens, which can be sensitive and time-consuming manually. Humanity's ability to evaluate and identify these more complicated illnesses has significantly been bolstered by the development of artificial intelligence, particularly machine, and deep learning. Conversely, much research and development is needed to enhance cancer cell identification—and lower false alarm rates. We built a deep learning model for morphological analysis to solve this problem. This paper introduces a novel deep convolutional neural network architecture in which hybrid multi-objective and category-based optimization algorithms are used to optimize the hyperparameters adaptively. Using the processed cell pictures as input, the proposed model is then trained with an optimized attention-based multi-scale convolutional neural network to identify the kind of cancer cells in the bone marrow. Extensive experiments are run on publicly available datasets, with the results being measured and evaluated using a wide range of performance indicators. In contrast to deep learning models that have already been trained, the total accuracy of 99.7% was determined to be superior.