Multi-objective Optimization Research Articles

Exploring Evolutionary Algorithms for Multi-Objective Optimization in Seismic Structural Design

The seismic design of structures is an emerging practice in earthquake-resistant construction. Therefore, using energy-dissipation devices and optimizing these devices for various purposes are important. Evolutionary computation, nature-inspired, and meta-heuristic algorithms have been studied more in recent years for the optimization of these devices. In this study, the development of evolutionary algorithms for seismic design in the context of multi-objective optimization is examined through bibliometric analysis. In particular, evolutionary algorithms such as genetic algorithms and particle swarm optimization are used to optimize the performance of structures to meet seismic loads. While genetic algorithms are used to improve both the cost and seismic performance of the structure, particle swarm optimization is used to optimize the vibration and displacement performance of structures. In this study, a bibliometric analysis of 661 publications is performed on the Web of Science and Scopus databases and on how the research in this field has developed since 1986. The R-studio program with the biblioshiny package is used for the analyses. The increase in studies on the optimization of energy dissipation devices in recent years reveals the effectiveness of evolutionary algorithms in this field.

Sistem Pendukung Keputusan Seleksi Peserta Lomba Karnaval Murid TK Di Kabupaten Pidie Menggunakan Metode Multi Objective Optimization On The Basic Of Ratio Analysis (MOORA) Berbasis Web

Kindergarten is an example of an educational sector that has been impacted by advances in computer technology. One of the most important parts of a kindergarten is student assessment and the creativity of school children. In one kindergarten there are dozens of students and each has different creativity values. However, there are problems at the Pidie Regency Education Office in assessing the process of determining the selection as the best participant to take part in the kindergarten student carnival competition in Pidie Regency. This writing will discuss the design of a decision support system using the Multi-Objective Optimization On The Basis Of Ratio Analysis (MOORA) method to select participants in the kindergarten student carnival competition in Pidie Regency. The aim of this research is to assist the Pidie District Education Office in making decisions by evaluating and ranking existing alternatives so that it is easier to determine which kindergarten student participants can take part in the carnival competition. The programming language used in designing this application is PHP using the CodeIgniter framework and HTML. For display using CSS3, namely using the Bootstrap and Jquery framework. The database uses MySQL. The tools and editors used are XAMPP for Windows, and Microsoft Visual Studio Code. The final result of this system is to provide a recommendation output ranking participants from the largest alternative value to the smallest. With this system, the Education Department will be helped and made easier in determining competition participants.

Optimization and synthesis on the dynamics performance of the tensioning and relaxing wearable system in a novel knee exoskeleton using co-simulation

Abstract In this paper, a novel tensioning and relaxing wearable system is introduced to improve the wearing comfort and load-bearing capabilities of knee exoskeletons. The research prototype of the novel system, which features a distinctive overrunning clutch drive, is presented. Through co-simulation with ANSYS, MATLAB, and SOLIDWORKS software, a comprehensive multi-objective optimization is performed to enhance the dynamics performance of the prototype. Firstly, the wearing contact stiffness of the prototype and the mechanical parameters of the relevant materials are simulated and fitted based on the principle of functional equivalence. And then, its equivalent nonlinear circumferential stiffness model is obtained. Secondly, to enhance the wearing comfort of the exoskeleton, a novel comprehensive performance evaluation index, termed wearing comfort, is introduced. The index considers multiple factors such as the duration of vibration transition, the acceleration encountered during wear, and the average pressure applied. Finally, through the utilization of this indicator, the system’s dynamics performance is optimized via multi-platform co-simulation, and the simulation results validate the effectiveness of the research method and the proposed wearable comfort index. The theoretical basis for the subsequent research on the effectiveness of prototype weight-bearing is provided.

Deep reinforcement learning-based multi-objective optimization for electricity–gas–heat integrated energy systems

With the increasing global attention on energy efficiency and carbon emissions, the optimization of integrated energy systems (IES) has become the key to improve energy efficiency and reduce pollution emissions. However, most of the existing optimization methods cannot effectively deal with the complexity of high dimensional continuous action space. Therefore, this paper focuses on a novel multi-objective optimization strategy for the electricity–gas–heat integrated energy systems (EGH-IES). Firstly, considering the absorption capacity of wind power and the emission of pollutant gases, a multi-objective optimization model is constructed based on the mechanism model and operation constraints of each device in EGH-IES, in which the integrated operation cost and the environmental factors are taken as optimization objectives. Then, the multi-objective optimization problem is designed as the optimal strategy of interaction learning between agent and environment in reinforcement learning, and the output power of the devices constitutes the action of reinforcement learning. Additionally, the Ornstein–Uhlenbeck process is introduced to enhance the training efficiency and exploration performance of the agent, and the deep deterministic policy gradients (DDPG) algorithm is employed to optimize the action, thus the output power of the appliances could be obtained. Finally, the simulation results show that compared with deep Q network (DQN) method and proximal policy optimization (PPO) method, the reward function value of the proposed method increases by 2.43% and 6.09%, respectively, which represents a reduction in economic cost and pollutant emissions. These verify the effectiveness and superiority of the proposed multi-objective optimization scheme in cost reduction and benefit improvement for the EGH-IES.

An Adaptive Unmixing Method Based on Iterative Multi-Objective Optimization for Surface Water Fraction Mapping (IMOSWFM) Using Zhuhai-1 Hyperspectral Images

Surface water fraction mapping is an essential preprocessing step for the subpixel mapping (SPM) of surface water, providing valuable prior knowledge about surface water distribution at the subpixel level. In recent years, spectral mixture analysis (SMA) has been extensively applied to estimate surface water fractions in multispectral images by decomposing each mixed pixel into endmembers and their corresponding fractions using linear or nonlinear spectral mixture models. However, challenges emerge when introducing existing surface water fraction mapping methods to hyperspectral images (HSIs) due to insufficient exploration of spectral information. Additionally, inaccurate extraction of endmembers can result in unsatisfactory water fraction estimations. To address these issues, this paper proposes an adaptive unmixing method based on iterative multi-objective optimization for surface water fraction mapping (IMOSWFM) using Zhuhai-1 HSIs. In IMOSWFM, a modified normalized difference water fraction index (MNDWFI) was developed to fully exploit the spectral information. Furthermore, an iterative unmixing framework was adopted to dynamically extract high-quality endmembers and estimate their corresponding water fractions. Experimental results on the Zhuhai-1 HSIs from three test sites around Nanyi Lake indicate that water fraction maps obtained by IMOSWFM are closest to the reference maps compared with the other three SMA-based surface water fraction estimation methods, with the highest overall accuracy (OA) of 91.74%, 93.12%, and 89.73% in terms of pure water extraction and the lowest root-mean-square errors (RMSE) of 0.2506, 0.2403, and 0.2265 in terms of water fraction estimation. This research provides a reference for adapting existing surface water fraction mapping methods to HSIs.

A Multi-Objective Optimization Business Model for Non-Commercial Port Sustainability

A Multi-Objective Optimization Business Model for Non-Commercial Port Sustainability

Design and Testing of a Branched Air-Chamber Type Pneumatic Seed Metering Device for Rice

To meet the diverse seeding requirements of super hybrid rice, common hybrid rice, and conventional rice—which vary from 1 to 3 seeds, 2 to 4 seeds, and 5 to 8 seeds per hole, respectively—this study developed a branched air-chamber type pneumatic seed metering device for rice. The device utilizes an air chamber control board to manage the branched air chamber casing, enabling precise adjustments to the seeding quantity. This study presents a theoretical analysis of the seed metering device’s operation and its critical components. Structural parameter optimization was conducted using Ansys-Fluent (2021 R1) software, followed by multi-objective optimization of operational parameters through bench testing. Simulation results indicated that optimal vacuum pressure in the seed metering disc pores reached a maximum of 857 Pa with a chamber depth of 22 mm, an angle of 100°, and a cavity depth of 25 mm, achieving a minimal coefficient of variation of 0.86%. Bench test results showed that for seeding targets of 1 to 3 rice seeds per hole, the optimal operational parameters were: two openings, a working vacuum of 1355 Pa, and a rotor speed of 32.78 r/min, resulting in a missed seeding rate of 4.70%, a qualification rate of 85.81%, and a re-seeding rate of 9.49%. For targets of 2 to 4 seeds per hole, the best parameters included three openings, a working vacuum of 1357 Pa, and a speed of 32.87 r/min, with a missed seeding rate of 4.60%, a qualification rate of 85.59%, and a re-seeding rate of 9.81%. For 5 to 8 seeds per hole, optimal parameters were six openings, a vacuum of 1339 Pa, and a rotor speed of 31.07 r/min, yielding a missed seeding rate of 4.09%, a qualification rate of 87.27%, and a re-seeding rate of 8.64%. These findings demonstrate that the branched air-chamber type pneumatic seed metering device effectively meets the varied direct seeding requirements of rice, enhancing the adaptability of pneumatic seed metering devices to different seeding quantities in rice and potentially informing the design of pneumatic seeders for other crops.

Theoretical foundations and practical implementation of supply chain optimization a metal fabrication business model

In the dynamic landscape of modern business, effective management of supply chains stands as a cornerstone of organizational success and competitive edge. This study investigates the theoretical principles and practical implementations of optimization models aimed at refining supply chain operations in the metal fabrication business, giving the maximum profit. It begins with a comprehensive survey of optimization theory, encompassing linear programming, integer programming, and stochastic optimization. It proceeds to their application in addressing diverse challenges encountered in supply chain management. The discussion includes deterministic models, such as those optimizing facility location under capacity constraints and transportation logistics, alongside stochastic models designed to manage uncertainties inherent in demand forecasting and inventory control. Advanced methodologies like metaheuristic algorithms and multi-objective optimization techniques are examined for their capacity to navigate the intricate and often conflicting objectives within supply chain networks. Through comprehensive theoretical analysis and a study of the supply chain model developed for the metal fabrication business, this paper contributes to advancing knowledge in mechanical engineering and supply chain management, offering insights pertinent to practitioners and researchers alike. Ultimately, it emphasizes the critical role of optimization models in optimizing efficiency, reducing costs, improving profit margin, reducing CO2 emission, and enhancing competitiveness in modern supply chain operations.

Energy-efficient resource allocation for UAV-aided full-duplex OFDMA wireless powered IoT communication networks

The rapid development of wireless-powered Internet of Things (IoT) networks, supported by multiple unmanned aerial vehicles (UAVs) and full-duplex technologies, has opened new avenues for simultaneous data transmission and energy harvesting. In this context, optimizing energy efficiency (EE) is crucial for ensuring sustainable and efficient network operation. This paper proposes a novel approach to EE optimization in multi-UAV-aided wireless-powered IoT networks, focusing on balancing the uplink data transmission rates and total system energy consumption within an orthogonal frequency-division multiple access (OFDMA) framework. This involves formulating the EE optimization problem as a Multi-Objective Optimization Problem (MOOP), consisting of the maximization of the uplink total rate and the minimization of the total system energy consumption, which is then transformed into a Single-Objective Optimization Problem (SOOP) using the Tchebycheff method. To address the non-convex nature of the resulting SOOP, characterized by combinatorial variables and coupled constraints, we developed an iterative algorithm that combines Block Coordinate Descent (BCD) with Successive Convex Approximation (SCA). This algorithm decouples the subcarrier assignment and power control subproblems, incorporates a penalty term to relax integer constraints, and alternates between solving each subproblem until convergence is reached. Simulation results demonstrate that our proposed method outperforms baseline approaches in key performance metrics, highlighting the practical applicability and robustness of our framework for enhancing the efficiency and sustainability of real-world UAV-assisted wireless networks. Our findings provide insights for future research on extending the proposed framework to scenarios involving dynamic UAV mobility, multi-hop communication, and enhanced energy management, thereby supporting the development of next-generation sustainable communication systems.

Multi-objective optimization design of a battery pack system for crashworthiness and lightweight based on a submodel and hybrid weighting method

The research focuses on optimizing battery pack systems (BPSs) for crashworthiness and lightweight design in electric vehicles. Traditional methods have high computing costs and do not account for the battery cell's failure criterion. This study uses a submodel and hybrid weighting for multi-objective design. It starts with the finite element model of a single cell, validates it and then builds a BPS model with a submodel for key areas. The optimal Latin hypercube sampling technique is used to sample the design space, and a kriging surrogate model and multi-objective particle swarm algorithm are used to find the Pareto solution. The compromise solution is selected using the analytic hierarchy process–Entropy–VIKOR method, considering the maximum principal strain of the cell. This approach cuts the computation time by 56.2% and offers a practical solution for BPS design by utilizing the load-bearing ability of the BPS.

Multiple solutions of tungsten carbide-cobalt cutting tool turning performance optimization results by Taguchi's combined multiobjective approach analysis an exponentiated exponential Weibull Dagum distribution model

Manufacturers employ various techniques to enhance tool life and influence both production costs and surface finish quality. Recently, cryogenic treatment has gained attention for improving machining performance. In this study, tungsten carbide-cobalt (WC–Co) cutting tools underwent cryogenic treatment at −196 °C for 24 h followed by tempering at 200 °C for 2 h. Machinability characteristics including Tool Wear Rate and Surface Roughness (Ra) were assed for Cryo Treated (CT) cutting tool during spinning operations on Al6063 alloy. This evaluation was compared with an untreated tool. Results demonstrate that the CT tool significantly enhances tool longevity while ensuring a satisfactory surface finish. To optimize the performance of the CT tool in turning processes, multiobjective optimization techniques, namely Taguchi's Grey Relational Analysis and Technique for Order Preference by Similarity to Ideal Solution, were utilized. In this research exponentiated exponential Weibull Dagum (EEWD) model has been utilized with the goal of increasing the tractability of the DGM (Dagum) in modeling the real-world data. The main object of this work, an innovative generalization of the EEWD distribution of Quantile Function (QntFEEWD) has been derived with six parameters. This QntFEEWD is significantly influent in driving measures of position such as the Qutl (quartiles), Octl (octiles), Decl (deciles), Pecl (percentiles), and median of EEWD distribution. The T-R{.} framework has been recently used to generalize different distributions; however, the DGM distribution's viability has not been examined. The T-R{.} combines three distributions, with one acting as a standard distribution. Each distribution's combined potency, which is a weighted hazard function of the baseline distribution, would have more parameters but be able to handle dataset bimodality with great flexibility. In order to generalize the DGM distribution, this paper used the quantile function of the Weibull distribution. The current study presents the EEWD, a novel generalized six parameter (6P) model.

A theoretical framework for predicting the heterogeneous stiffness map of brain white matter tissue

Finding the stiffness map of biological tissues is of great importance in evaluating their healthy or pathological conditions. However, due to the heterogeneity and anisotropy of biological fibrous tissues, this task presents challenges and significant uncertainty when characterized only by single-mode loading experiments. In this study, we propose a new theoretical framework to map the stiffness landscape of fibrous tissues, specifically focusing on brain white matter tissue. Initially, a finite element (FE) model of the fibrous tissue was subjected to six loading cases, and their corresponding stress-strain curves were characterized. By employing multiobjective optimization, the material constants of an equivalent anisotropic material model were inversely extracted to best fit all six loading modes simultaneously. Subsequently, large-scale FE simulations were conducted, incorporating various fiber volume fractions and orientations, to train a convolutional neural network capable of predicting the equivalent anisotropic material properties solely based on the fibrous architecture of any given tissue. The proposed method, leveraging brain fiber tractography, was applied to a localized volume of white matter, demonstrating its effectiveness in precisely mapping the anisotropic behavior of fibrous tissue. In the long-term, the proposed method may find applications in traumatic brain injury, brain folding studies, and neurodegenerative diseases, where accurately capturing the material behavior of the tissue is crucial for simulations and experiments.

OPTIMIZATION ALGORITHM OF PUBLIC SERVICE FACILITIES LAYOUT IN EARTHQUAKE-STRICKEN AREAS BASED ON SA ALGORITHM

The environment in earthquake-stricken areas is complex and changeable. The optimization of public service facility layout usually involves multiple objectives, such as maximizing coverage, minimizing service distance, optimizing resource allocation, etc. The coupling conflict between these objectives weakens the functions of public service facilities in earthquake-stricken areas. To improve the emergency response speed of the earthquake-stricken regions and reduce disaster losses, a simulated annealing (SA) based optimization algorithm for the layout of public service facilities in earthquake-stricken areas is proposed. Considering the public service demand in different stages of the earthquake-stricken area, set the minimum maximum weighted distance, the minimum number of facility points, and the minimum total weighted distance of the service demand point area within the service area of the public service facility point as the objective function, and set constraints such as each demand point is covered by at least one facility point, and the minimum number of public service facility points, build a multi-objective optimization model of public service facilities layout to avoid coupling conflicts between multiple objectives. The SA algorithm is used to solve the multi-objective optimization model of public service facility layout. SA algorithm adopts temperature update function and sets heuristic cooling criteria. Combining the success-failure method and the variable scale method, a new solution is generated using the effective offset. The improved Metropolis algorithm is used to set the acceptance criteria for the solution to obtain the optimal layout result for public service facilities in earthquake-stricken areas. The experimental results show that the algorithm can effectively optimize the layout of public service facilities in earthquake-stricken areas, and improve facility coverage and resource utilization.

Patient-specific prostate tumour growth simulation: a first step towards the digital twin

Prostate cancer (PCa) is a major world-wide health concern. Current diagnostic methods involve Prostate-Specific Antigen (PSA) blood tests, biopsies, and Magnetic Resonance Imaging (MRI) to assess cancer aggressiveness and guide treatment decisions. MRI aligns with in silico medicine, as patient-specific image biomarkers can be obtained, contributing towards the development of digital twins for clinical practice. This work presents a novel framework to create a personalized PCa model by integrating clinical MRI data, such as the prostate and tumour geometry, the initial distribution of cells and the vasculature, so a full representation of the whole prostate is obtained. On top of the personalized model construction, our approach simulates and predicts temporal tumour growth in the prostate through the Finite Element Method, coupling the dynamics of tumour growth and the transport of oxygen, and incorporating cellular processes such as proliferation, differentiation, and apoptosis. In addition, our approach includes the simulation of the PSA dynamics, which allows to evaluate tumour growth through the PSA patient’s levels. To obtain the model parameters, a multi-objective optimization process is performed to adjust the best parameters for two patients simultaneously. This framework is validated by means of data from four patients with several MRI follow-ups. The diagnosis MRI allows the model creation and initialization, while subsequent MRI-based data provide additional information to validate computational predictions. The model predicts prostate and tumour volumes growth, along with serum PSA levels. This work represents a preliminary step towards the creation of digital twins for PCa patients, providing personalized insights into tumour growth.

Reliability design involving optimization with multiple objectives by means of probabilistic multi-objective optimization

AbstractAlthough there have been many achievements on single—objective models, the reliability research involving multi-objective optimization problems has not obtained satisfactory research results. In this paper, the reliability design involving optimization with multiple objectives is developed by means of probabilistic multi-objective optimization (PMOO), which considers the simultaneity of optimization of multiple objectives and treats both beneficial type of utility indexes and unbeneficial type of utility indexes of performance indicators equivalently and conformably. Three cases of reliability design concerning multi—objective optimization, i.e., reliability requirement as the additional constraint condition, reliability assessment as an additional optimized objective, and the mixture of these two cases, are formulated by means of PMOO, respectively. Furthermore, a typical example is given to show the procedure of the approach for reliability assessment involving multiple objectives by means of PMOO, which exhibits the validity of the present approach. The approach is objective without any subjective factors.

Multiobjective optimization of magnetic abrasive finishing process with periodic re-distribution of magnetic abrasive particles on 17-4PH stainless steel

Magnetic abrasive finishing (MAF) exhibits considerable potential as a promising process for enhancing surface finish quality for softer as well as harder materials. This work proposes a novel approach to harness the potential of MAF for obtaining superior surface quality of precipitation-hardening martensitic steel (17-4PH steel) while performing periodic re-distribution of magnetic abrasive particles. The experiments were conducted using the Box-Behnken design of experiments and response surface methodology (RSM). RSM-based desirability function approach and genetic algorithms were used for multiobjective optimization. The set of pareto-optimal solutions obtained through multiobjective optimization were ranked using the Technique for Order of Preference by Similarity to an Ideal Solution (TOPSIS) by assigning equal importance to the selected performance parameters (percentage change in surface roughness (PCSR) and material removal rate (MRR)). The optimized values of PCSR and MRR obtained through the desirability function of RSM and genetic algorithm were validated experimentally and compared with the predicted values obtained through the regression model. Results showed that the desirability function of RSM provided better results than the genetic algorithm for the selected conditions and confirmed the effectiveness of the proposed approach.

Multi-objective optimization of non-fossil energy structure in China towards the carbon peaking and carbon neutrality goals

Numerous nations and regions are earnestly dedicated to propelling energy transition. China accounts for 31.78 % of the total global carbon emissions, and China's energy structure holds paramount significance in the broader context of global initiatives. China has officially proposed to achieve the target of carbon peak by 2030 and carbon neutrality by 2060, imposing substantial pressure on the transformation of the energy structure. In this study, we propose a multi-objective optimization model for the non-fossil energy structure, encompassing three primary optimization objectives: maximizing power generation, minimizing economic costs, and reducing CO₂ emissions. The optimization involves determining the proportion of seven key non-fossil energy sources—hydropower, onshore wind, offshore wind, photovoltaic (PV), bioenergy, geothermal, and nuclear power—while adhering to constraints related to power demand, nuclear safety, and other factors. The analysis explores the installed capacity, power generation, power generation costs, and CO₂ emission reductions of non-fossil energy under distinct scenarios in 2025, 2030, and 2060. The findings reveal that by 2030, the optimal share of power generation should be sequenced as onshore wind, hydropower, nuclear power, offshore wind, PV, bioenergy, and geothermal. Subsequently, by 2060, the top three developed power should be onshore wind, nuclear power, and hydropower.

Effect of surface square textures on the physical field of static and dynamic pressure thrust bearings and multi-objective optimization

Purpose The lubrication performance of static and dynamic pressure thrust bearings is improved by introducing texture on the sealing edge. Design/methodology/approach Through model building, meshing and boundary condition setting, the influence of square texture on oil film lubrication performance was simulated and analyzed, and an improved algorithm was applied to perform optimization of lubrication performance. Findings The findings of this study reveal that the optimum lubrication performance is attained when adjusting the parameters of the square texture to 0.12 mm, 0.1 mm, 1 mm and 34 mm. In such circumstances, the thrust bearing with square textures demonstrates an increase in loading capacity of around 19% and a temperature reduction of about 2ºC compared to a smooth thrust bearing. Originality/value The original Reynolds equation is revised, and the influence of square texture on the physical field of oil film is analyzed, considering the turbulence state and cavitation phenomenon. The multi-objective function under square texture parameters was established using BP neural network, and the improved multi-objective salp swarm algorithm was used to optimize the process parameters.

Multi-Objective Optimization and Design for Industrial Vinyl Chloride Reactor by Hybrid Model

The acetylene conversion rate and vinyl chloride production capacity are the main economic indexes for vinyl chloride synthesis, and the reaction temperature is an important operating parameter to prevent the Hg active component from being loss. These three factors have not been taken into consideration simultaneously in the traditional optimization process, making it difficult to achieve optimization targets perfectly for industrial application. To overcome this problem, an efficient strategy framework was proposed based on a hybrid model. Compared with conventional paradigms, the proposed framework could not only reduce computational expense but optimize these two economic indexes with a constrained reaction temperature simultaneously. In addition, a machine learning method was used to conduct a feature analysis, which can reveal the potential interaction between different variables so key variables of this reactor could be identified. To demonstrate and verify this framework, multi-objective optimization involving multiple variables with constrained conditions for the industrial reactor was conducted from design and operation perspectives, respectively. The proposed strategy could provide optimal operational direction for the industrial reactor from these design and operation aspects, which contribute to the sustainable and highly efficient process development in this field. For the first section of an industrial vinyl chloride reactor, this strategy could realize significant improvement in the acetylene conversion rate from 81.34% to over 95.00% and in the vinyl chloride production capacity from 2.60 to above 3.40 mol/h in the operation scenarios, which can meet production requirements. So, the second section of the traditional reactor system is not needed at all.

Optimization of Tip Seal Grooves for Aerodynamic and Durability Improvements of Small-Core Turbines

Abstract While the gap between the turbine rotor tip and the outer case in a gas turbine engine is necessary for engine function, the gap is kept as small as possible due to the detrimental effect of the flow over the turbine tip. With the increased investments in ultra-high bypass turbofans, blade tip clearances are increasing in relative size to the turbine rotor, as engines move towards smaller cores. In this work, an optimization of a rotor tip seal with discrete axisymmetric grooves was explored computationally using RANS simulations. The optimization was applied at two tip clearances representing a nominal and small-core-scaled geometry, and with both flat- and squealer-tipped blades. The multi-objective optimization was designed to maximize rotor efficiency and minimize tip heat load. Several casing designs were identified for each tip configuration that both increased efficiency and reduced the heat load into the rotor tip. However, some optimal tip seal designs were composed of grooves that were demonstrated to be detrimental in prior work. Furthermore, grooves were more effective at increasing efficiency when applied to flat tipped geometries – increasing efficiency by 0.9 points over the ungrooved baseline with flat tipped blades, as opposed to 0.25 points over the ungrooved case with squealer tipped blades. Finally, optimal seal geometries that were obtained from the small-core scaled clearance gap optimizations maintained near optimal performance when evaluated at the design tip clearance, while those geometries developed at the design clearance experienced greater tip gap sensitivity.