Objective Function Research Articles

Longitudinal analysis of objective and self-reported cognitive functions in individuals with subjective cognitive decline

Introduction: Subjective cognitive decline (SCD) is considered a preclinical manifestation of Alzheimer’s disease (AD). Recent research suggests that subtle cognitive changes in SCD are linked to an increased risk of clinical decline. This study investigates the longitudinal trajectories of both objective and self-reported cognitive functions in individuals with SCD, with a focus on the impact of subtle cognitive impairment (SCI). Methods: A total of 107 individuals with SCD, with at least two annual follow-ups, were included in this study. We analyzed the trajectories of both objective and subjective cognitive functions, assessed changes in medial temporal lobe regional volumes, and compared baseline AD biomarkers between SCD individuals with SCI (n = 22, SCI group) and without SCI (n = 85). Results: SCD individuals with SCI showed a faster decline in objective cognitive function over time compared to those without SCI, who exhibited cognitive improvement. Self-reported cognitive complaints showed no differences between groups at baseline or in annual changes over time. The SCI group had lower baseline entorhinal cortical volumes and greater volume reductions over time, and also exhibited more abnormalities in AD biomarkers, including higher amyloid PET positivity, a lower Aβ 42/40 ratio, and elevated p-tau181. Conclusion: SCI status in SCD individuals is associated with significant cognitive decline, along with more abnormal AD biomarkers. These findings suggest that early identification of SCI status in individuals with SCD may improve the prediction of cognitive decline. However, self-reported cognitive complaints may have a limited role in monitoring clinical changes in SCD.

Beam collimation and filtration optimization for a novel orthovoltage radiotherapy system.

The inaccessibility of clinical linear accelerators in low- and middle-income countries creates a need for low-cost alternatives. Kilovoltage (kV)x-ray tubes have shown promise as a source that could meet this need. However, performing radiotherapy with a kV x-ray tube has numerous difficulties, including high skin dose, rapid dose fall-off, and low dose rates. These limitations create a need for highly effective beam collimation andfiltration. To improve the treatment potential of a novel kV x-ray system by optimizing an iris collimator and beam filtration using Bayesian techniques and Monte Carlo (MC)simulations. The Kilovoltage Optimized AcceLerated Adaptive therapy system's current beam configuration consists of a 225kVp x-ray tube, a 12-leaflet tungsten iris collimator, and a 0.1mm copper filter. A Bayesian optimization was performed for the large and small focal spot sizes of the kV x-ray tube source at 220kVp using TopasOpt, an open-source library for optimization in TOPAS. Collimator thickness, copper filter thickness, source-to-collimator distance (SCD), and source-to-surface distance (SSD) were the variables considered in the optimization. The objective function was designed to maximize the dose rate and the dose at a depth of 5 cm while minimizing the beam penumbra width and the out-of-field dose (OFD), all evaluated in a water phantom. Post-optimization, the optimal beam configuration was simulated and compared to the existingconfiguration. The optimal collimation setup consisted of 2.5mm thick tungsten leaflets for the iris collimator and a 350mm SSD for both focal spot sizes. The optimal copper filtration was 0.22mm for the large focal spot and 0.15mm for the small focal spot, with a SCD of 148.5mm for the large focal spot and 125.8mm for the small focal spot. For the large focal spot, the surface dose rate decreased by 9.4%, while the PDD at 5cm depth ( ) increased by 7.7% compared to the existing iris collimator. Additionally, the surface beam penumbra width was reduced by 31.3%, and no significant changes in the OFD were observed. For the small focal spot, the surface dose rate for the new collimator increased by 3.7% and the increased by 5.3%, with no statistically significant changes in the beam penumbra width orOFD. The optimal beam collimation and filtration for both x-ray tube focal spot sizes of a kV radiotherapy system was determined using Bayesian optimization and MC simulations and resulted in improved dosedistributions.

Virtual Machine Placement in Edge Computing Based on Multi-Objective Reinforcement Learning

With the popularization of internet of things (IoT), the energy consumption of mobile edge computing (MEC) servers is also on the rise. Some important IoT applications, such as autonomous driving, smart manufacturing, and smart wearables, have high real-time requirements, making it imperative for edge computing to reduce task response latency. Virtual machine (VM) placement can effectively reduce the response latency of VM requests and the energy consumption of MEC servers. However, the existing work does not consider the selection of weighting coefficients for the optimization objectives and the feasibility of the solution. Besides, these algorithms scalarize the objective functions without considering the order-of-magnitude difference between objectives. To overcome the above problems, the article proposes an algorithm called EVMPRL for VM placement in edge computing based on reinforcement learning (RL). Our aim is to find the Pareto approximate solution set that achieves the trade-off between the response latency of VM requests and the energy consumption of MEC servers. EVMPRL is based on the Chebyshev scalarization function, which is able to efficiently solve the problem of selecting weighting coefficients for objectives. EVMPRL can always search for solutions in the feasible domain, which can be guaranteed by selecting the servers that can satisfy the current VM request as the next action. Furthermore, EVMPRL scalarizes the Q-values instead of the objective functions, thus avoiding the problem in previous work where the order-of-magnitude difference between the optimization objectives makes the impact of an objective function on the final result too small. Finally, we conduct experiments to prove that EVMPRL is superior to the state-of-the-art algorithm in terms of objectives and the solution set quality.

Identification of Dynamic Recrystallization Model Parameters for 40CrMnMoA Alloy Steel Using the Inverse Optimization Method

The microstructure of 40CrMnMoA during hot forging determines its macroscopic mechanical properties. Dynamic recrystallization (DRX) behavior is commonly used to refine grains and improve the microstructure of materials; therefore, it is important to be able to predict mechanical behavior during hot forging and the microstructure evolution during dynamic recrystallization. In order to accurately determine the DRX model parameters of 40CrMnMoA steel, an inverse optimization method is proposed in this work. The uniaxial isothermal compression experiment of 40CrMnMoA steel was carried out on a Gleeble-1500D thermal simulation tester (Dynamic Systems Inc. (DSI), Poestenkill, NY, USA) under the temperature range of 900~1200 °C and the strain rate range of 0.005 to 5 s−1. Based on the true stress–strain data obtained by a compression test, the DRX model of 40CrMnMoA was initially established using the traditional averaging method. Subsequently, the DRX model parameters calculated by the conventional averaging method were used as the initial values, the mean-square error between the experimental and calculated values of the DRX volume fraction was set as the objective function, and the DRX model parameters were optimized by the adaptive simulated annealing (ASA) algorithm. By comparing the correlation coefficient R, average absolute relative error (AARE), and the root mean square error (RMSE) of the predicted DRX percentage with the experimental values before and after optimization, it was found that the optimized model achieved an R-value of 0.992, with AARE and RMSE decreased by 34% and 2%, respectively, which verified the accuracy of the optimized DRX model. Through the program’s secondary development, the optimized DRX model of 40CrMnMoA was integrated into finite element software Forge® 3.2 to simulate the isothermal compression process. The comparison between grain size from the central region of simulation results and actual samples revealed that the relative error is less than 3%. This result demonstrated that the inverse optimization method can accurately identify the DRX model parameters of 40CrMnMoA alloy steel.

Calibrar: An R package for fitting complex ecological models

Abstract The fitting or parameter estimation of complex ecological models is a challenging optimisation task, with a notable lack of tools for fitting complex, long runtime or stochastic models. calibrar is an R package that is dedicated to the fitting of complex models to data. It is a generic tool that can be used for any type of model, especially those with non‐differentiable objective functions and long runtime, including individual or agent based models. calibrar supports multiple phases and constrained optimisation, includes 20 optimisation algorithms, including derivative‐based and heuristic ones. It supports any type of parallelisation, the capability to restart interrupted optimisations for long runtime models and the combination of different optimisation methods during the multiple phases of a calibration. User‐level expertise in R is necessary to handle calibration experiments with calibrar, but there is no need to modify the model's code, which can be programmed in any language. It implements maximum likelihood estimation methods and automated construction of the objective function from simulated model outputs. For more experienced users, calibrar allows the implementation of user‐defined objective functions. The package source code is fully accessible and can be installed directly from CRAN.

Induction Motor Geometric Parameter Optimization Using a Metaheuristic Optimization Method for High-Efficiency Motor Design

In this study, the optimum design for an induction motor (IM) was realized by providing details of its geometric design. The IM optimization was carried out using the Artificial Ecosystem-based Optimization (AEO) algorithm, a metaheuristic method. The AEO algorithm was used for the first time in IM optimization, and the design parameters were optimized. Ten motor design parameters were used as design variables. IM efficiency was improved, as the objective function. The genetic algorithm (GA) optimization method was used for comparison with the results obtained with the AEO method. The optimized and unoptimized results of the IM design generated with codes created in the Matlab program were verified with the Ansys RMxprt program, and it could be seen that the results are in good agreement. As a result of these studies, it was observed that the use of AEO in determining the geometric parameters of the IM had better convergence accuracy and reached the optimum result in a shorter time compared to the GA optimization method. It was observed that IM efficiency increased from 90.34% to 91.575% on average with the AEO method.

Optimal Design of Interior Permanent Magnet Synchronous Motor Considering Various Sources of Uncertainty

The automotive industry is experiencing a period of transition from traditional internal combustion engine (ICE) vehicles to electric vehicles. Although electric machines have always been used in many applications, they are generally designed neglecting the sources of uncertainty, even such uncertainty can lead to significant deterioration of the motor performance. The aim of this paper is to compare the results obtained from the multi-objective optimization of an interior permanent magnet synchronous motor (IPMSM) using a robust approach versus a deterministic one. Unlike other studies in the literature, this research simultaneously considers different sources of uncertainty, such as geometric parameters, magnet properties, and operating temperature, to assess the variability of electric motor performance. Different designs of a 48 slot–8 pole motor are simulated with finite element analysis, then the outputs are used to train artificial neural networks that are employed to find the optimal design with different approaches. The method incorporates an innovative use of the neural network-based variance estimation (NNVE) technique to efficiently calculate the standard deviation of the objective functions. Finally, the results of the robust optimization are compared with those of the deterministic optimization. Due to the small margin of improvement in robustness, both methods lead to similar results.

ROITP: Road Obstacle-Involved Trajectory Planner for Autonomous Trucks

Autonomous trucks have the potential to enhance both safety and convenience in intelligent transportation. However, their maximum speed and ability to navigate a variety of driving conditions, particularly uneven roads, are limited by a high center of gravity, which increases the risk of rollover. Road bulges, sinkholes, and unexpected debris all present additional challenges for autonomous trucks' operational design, which current perception and decision-making algorithms often overlook. To mitigate rollover risks and improve adaptability to damaged roads, this paper presents a novel Road Obstacle-Involved Trajectory Planner (ROITP). The planner categorizes road obstacles using a learning-based algorithm. A discrete optimization algorithm selects a multi-objective optimal trajectory while taking into account constraints and objective functions derived from truck dynamics. Validation across various scenarios on a hardware-in-loop platform demonstrates that the proposed planner is effective and feasible for real-time implementation.

Real-world interpatient variability in the pharmacokinetics of levetiracetam.

Levetiracetam (LEV) is an antiepileptic drug (AED) used to treat a variety of seizures in adult and pediatric populations. It is an ideal AED due to its favorable pharmacokinetic (PK) and pharmacodynamic profile and lack of interactions with other AEDs. This retrospective cohort study was designed to identify covariates that affect LEV clearance and volume of distribution and to generate a population PK model. Adults with a seizure history receiving LEV during hospital admission with a minimum of one serum LEV concentration available were included in the study. Population PK modeling and covariate testing was performed with MONOLIX Suite 2020R1 (Lixoft, France). A total of 162 serum concentrations were collected from 143 patients. Age, sex, body weight descriptors, serum creatinine, creatinine clearance (CrCL), serum albumin, liver enzymes, and total bilirubin were evaluated. Body surface area (BSA) was a significant covariate for the apparent volume of distribution (V/F). The exclusion of BSA as a covariate of V/F increased the objective function value (OFV) 5.6. CrCL was a significant covariate of apparent plasma clearance (CL/F). The exclusion of CrCL increased the OFV by 18.16 and significantly increased the root square error (RSE) % of the between-subject variabilities of the parameters. LEV clearance is an effective predictor of serum concentration. CrCL was a significant covariate influencing LEV clearance, and BSA was found to influence the volume of distribution. Further studies are needed to determine the effect of body weight descriptors on LEV clearance and, ultimately, outcomes.

Memory function and early exit from paid employment through different pathways among ageing European workers.

Understanding memory function's role in early workforce exit is key in supporting sustainable employment among ageing workers. This study examined the impact of memory function on early exit from paid employment, analyzed changes in memory function before, during and after such transitions, and assessed memory function trajectories in relation to the presence or absence of effort-reward imbalance at work. This study included 16 339 respondents from the Survey of Health, Ageing, and Retirement in Europe (SHARE) between age 50 and the country-specific retirement age. The effects of objective and subjective memory functioning on early exit were assessed using Cox proportional hazards with Fine-Gray sub distribution models. Changes in memory function before and after a transition to non-employment were assessed using generalized linear mixed-effects models. These changes were described and compared based on exposure to job effort-reward imbalance. Workers with poor subjective memory were 2.3 times more likely to exit employment prematurely due to disability ([sub-distribution hazard ratio (SHR) 2.30, 95% confidence interval (CI) 1.77-3.00] and 1.3 times more likely to exit through unemployment (SHR 1.29, 95% CI 1.06-1.55). Workers with low objective memory were 1.6 times more likely to exit through unemployment (SHR 1.56, 95% CI 1.30-1.87). Subjective memory generally declined prior to, and during early exit from paid employment. While subjective memory generally improved post-exit, objective memory function declined after exiting. An accelerated decline in objective memory functioning was noted among early retirees who had been exposed to effort-reward imbalance at work (β -0.45, standard error 0.16). Workers with poor memory function are at higher risk of early involuntary exit from paid employment. Promoting memory function and balancing job efforts and rewards may help mitigate the risk of a premature exit.

A grey wolf optimization approach for evaluating the engine responses of various biodiesel blends in an internal combustion engine

The knowledge of the exact thresholds of parameters in the diesel engines, during combustion, is essential to simulate the combustion process, establish parametric values, reduce cost and predict exhaust emissions. Accordingly, the present paper applies the grey wolf optimization method to determine the optimal threshold of parameters and engine responses in a direct ignition engine. Twelve formulated linear equations of engine responses are introduced to the objective function of the grey wolf optimizer. A computer program in C++ was applied successfully using literature data to validate the grey wolf optimization procedure based on the encircling, hunting and attacking of prey by the wolf. The results show that load demand and turbocharge boast air pressure have the least and highest values of engine outputs, respectively. The blend ratio had its highest values when optimized alongside the main injection duration. The responses and parameters greatly improved from initial values to stopping criterion of 200 iterations. Instances reported include brake specific fuel consumption, which improved from 2.6468 to 1.0816 g/kWhr, blend ratio changes from 0.5031 to 0.4760%, speed drop from 0.0031 to 0.0010rpm, and load drop from 0.0017 to 0.0010%. The main contribution of this paper is to establish the optimal thresholds of engine responses using the grey wolf optimizer in a diesel engine combustion chamber. The development of a new method to optimize response and parameters of an internal combustion process using grey wolf optimizer is the novel aspect of this work. The results have essential practical significance to establish new emission profile for biodiesel. The practising engineers and researchers have a holistic insight into the problem’s solution and can utilize the results to enhance their engine responses.

A multi-commodity multi-sourcing location-allocation model for managing post-disaster material convergence considering budget constraint and equity

This paper proposes an integrated multi-commodity multi-sourcing location-allocation model to address issues caused by post-disaster material convergence. It also helps improve the efficient utilisation of disaster relief resources, as well as distribution equity. The objective of the model is to allocate relief items of varying priorities, aiming to minimise the suffering of affected individuals while operating within a limited budget. The decisions of the model include the selection of distribution centres, shipment sizes, and delivery frequencies for post-disaster humanitarian logistics. To capture the inter-temporal effects of delivery strategies, deprivation costs are used to evaluate the economic costs of human suffering resulting from a lack of access to relief supplies. The model is formulated as a multi-sourcing model, allowing one demand point to be served by multiple points of distribution. To enhance distribution equity, this model incorporates the Gini index into the objective function. An immune algorithm (IA) is proposed to solve large-scale instances of the model. This algorithm has shown promising results and can handle complex scenarios efficiently. Computational experiments were conducted using data from Chengdu, an earthquake-prone megacity in southwest China. The results demonstrate that the proposed algorithm provides effective solutions within a reasonable timeframe.

Electric Vehicle and Soft Open Points Co-Planning for Active Distribution Grid Flexibility Enhancement

With the increasing penetration of distributed generation (DG), the supply–demand imbalance and voltage overruns in the distribution network have intensified, and there is an urgent need to introduce flexibility resources for regulation. This paper proposes co-planning of electric vehicles (EVs) and soft opening points (SOPs) to improve the flexibility of the active distribution network, thereby improving the economics and flexibility of the distribution network. Firstly, this paper establishes a charging pile day-ahead dispatchable prediction model and a real-time dispatchable potential assessment model through Monte Carlo sampling simulation. It replaces the traditional energy storage model with this model and then solves the EV and SOP collaborative planning model using a second-order conical planning algorithm with the objective function of minimizing the annual integrated cost. At the same time, the flexibility of the distribution network is analyzed by two indicators: power supply and demand balance and branch load margin. Finally, the optimization method proposed in this paper is analyzed and validated on an improved IEEE 33-node distribution system. Example results show that the planning method proposed in this paper can effectively reduce the annual comprehensive operating cost of distribution networks, meet the flexibility index, and be conducive to improving the economy and flexibility of distribution network operation.

A study on the improvement of supercomputer energy efficiency based on green500 benchmarking data

With the rapid growth of AI-related industries, the need for reducing and optimizing energy consumption in large-scale computational resources, such as supercomputers, has become increasingly important. This study focuses on supercomputers listed in the Green 500, categorizing existing benchmarking evaluation variables into input and output factors. An energy efficiency objective function was introduced, and DEA was conducted using BCC and SEM models. The study analyzed the relative efficiency levels among supercomputers and identified factors and levels of potential efficiency improvements. The results provide insights into the performance factors of individual supercomputers and their potential for improvement. Furthermore, by comparing the energy efficiency evaluated by the Green 500 with the results of DEA, it demonstrated the potential for utilizing DEA as a new means for efficiency improvement. It also highlighted the necessity of a comprehensive evaluation that incorporates various performance factors, rather than a simple efficiency assessment based solely on energy consumption.

Solving combinatorial optimization problems through stochastic Landau-Lifshitz-Gilbert dynamical systems

We present a method to approximately solve general instances of combinatorial optimization problems using the physical dynamics of three-dimensional (3D) rotors obeying Landau-Lifshitz-Gilbert dynamics. Conventional techniques to solve discrete optimization problems that use simple continuous relaxation of the objective function followed by gradient-descent minimization are inherently unable to avoid local optima, thus producing poor-quality solutions. Our method considers the physical dynamics of macrospins capable of escaping from local minima, thus facilitating the discovery of high-quality, nearly optimal solutions, as supported by extensive numerical simulations on a prototypical quadratic unconstrained binary optimization (QUBO) problem. Our method produces solutions that compare favorably with those obtained using state-of-the-art minimization algorithms (such as simulated annealing) while offering the advantage of being physically realizable by means of arrays of stochastic magnetic tunnel-junction devices. Published by the American Physical Society 2025

Optimization Protection Coordination by Optimizing Time Dial Settings at PT. Pupuk Sriwidjaja Palembang Using Grey Wolf Method

Overcurrent Rele (OCR) is an important component in the electric power protection system. One of the parameters that must be set on the OCR is the Pickup Current (Ip) and Time Dial Setting (TDS). To achieve optimum relay coordination by setting the time dial, several optimisation methods have been used such as Genetic Algorithm (GA), Particle Swarm Optimisation (PSO), Fire Fly Algorithm (FA) and Grasshopper Optimisation Algorithm (GOA).In this study, the TDS setting was determined through Using the Grey Wolf Optimisation (GWO) method. The GWO algorithm was able to determine the optimum value of the TDS setting for each OCR process. This is validated by the results of tests conducted using the ETAP application. The primary and secondary relays are able to coordinate effectively to secure three-phase faults that occur on each bus.Furthermore, GWO demonstrated a superior convergence rate in compared to GOA, therefore enhancing its capacity to identify a more optimal TDS setting value. Furthermore, the objective function of GWO is more effective than that of GOA, thereby enhancing its ability to function in a more optimal manner. The results of this test demonstrate that the GWO algorithm is a reliable method for directly identifying the optimal TDS setting value for determining relay coordination settings.Keywords—Protection Coordination Overcurrent Rele ( OCR ), Short Circuit Maximum ( IscMax ), Time Dial Setting ( TDS ), Grey Wolf Optimization ( GWO ).

Conditions for length reduction of the parallel sequence of special digraphs’ vertices in the presence of interruptions

In the scheduling theory, both theoretical and applied problems related to the planning of production processes, the design of computer systems, etc. are considered. In particular, there is a subclass of problems called parallel sequencing problems. Their mathematical for-mulation can often be reduced to optimization problems on directed graphs, where a given set of vertices corresponds to a set of jobs required for execution, and arcs specify a partial or-der corresponding to various technological constraints. The classical variant implies that in-put data are the finite set of jobs with equal execution times (defined as 1) represented as di-graph G and one of the sequence parameters (length or width). The undefined parameter needs to be minimized. On the contrary to the classical ones, in applied problems, the duration of the jobs often differs. That is why the question of whether to allow or forbid interruptions during job execu-tion is widely considered. The efficiency of using interruptions was proven for the cases when the corresponding digraph has a series-parallel, bipartite structure or belongs to the subclass of trees which allows graceful labeling. As graph structure plays a key role in the evaluation of profit from interruptions the graph labeling topics are of a big interest as well, such as those that use combinatorial configurations. This paper is devoted to the research of possible profit from interruptions in cases when G is a directed caterpillar. The effectiveness of the impact of interruption allowance on the objective function value was analyzed depending on the arcs' orientation, the weight coeffi-cient values of the vertices, and the structure of specific graphs. Theoretical results for evalu-ating the profit were obtained and formulated in the form of a theorem.

Improved Multi-Objective Strategy Diversity Chaotic Particle Swarm Optimization of Ordered Charging Strategy for Electric Vehicles Considering User Behavior

With the development of the EV industry, the number of EVs is increasing, and the random charging and discharging causes a great burden on the power grid. Meanwhile, the increasing electricity bills reduce user satisfaction. This article proposes an algorithm that considers user satisfaction to solve the charging and discharging scheduling problem of EVs. This article adds an objective function to quantify user satisfaction and addresses the issues of premature local optima and insufficient diversity in the MOPSO algorithm. Based on the performance of different particles, the algorithm assigns elite particle, general particle, and learning particle roles to the particles and assigns strategies for maintaining search, developing search, and learning search, respectively. In order to avoid falling into local optima, chaotic sequence perturbations are added during each iteration process avoiding premature falling into local optima. Finally, case studies are implemented and the comparison analysis is performed in terms of the use and benefit of each design feature of the algorithm. The results show that the proposed algorithm is capable of achieving up to 23% microgrid load reduction and up to 20% improvement in convergence speed compared to other algorithms. It is superior to other algorithms in solving the problem of orderly charging and discharging of electric vehicles and has strong usability and feasibility.

ANALYSIS OF THE IMPACT OF TASK PRIORITIZATION LISTS ON THE POTENTIAL FOR AVOIDING ANOMALIES IN TASK SCHEDULING

This paper addresses relevant issues related to the anomalous deterioration in objective function values when attempting to improve the initial parameters in one of the discrete optimization problems. The primary focus is on investigating the conditions under which it is possible to prevent the occurrence of such anomalies. Contemporary scientific works devoted to schedule optimization and task prioritization management, particularly for location-allocation problems arising in the fields of computer science, engineering, and operations research, are reviewed. A priority dynamic redistribution algorithm is proposed, which al-lows minimizing delays and ensuring efficient resource utilization during parallel task execu-tion. An example of applying the algorithm is provided, and its effectiveness in preventing anomalies.

Multi-objective geometric optimization of protrusion, droplet ribs, and inclined upper plate of a slit jet impingement heat sink to enhance its thermal performance

To meet the needs of heat transfer and temperature uniformity in the heat dissipation of high-heat-flux electronic devices, a novel slit jet impingement heat sink with a protrusion in the stagnation region, droplet ribs in the wall jet region, and an inclined upper-plate (PDI-SJIHS) is proposed, the coolant is Al2O3-H2O nanofluid. The influences of the structural parameters of the above three components and the Reynolds number on the heat transfer and flow of the PDI-SJIHS are studied numerically. Using the comprehensive heat transfer and temperature standard deviation as objective functions, a multi-objective optimization of PDI-SJIHS is conducted using non-dominated sorting genetic algorithm-Ⅱ (NSGA-Ⅱ). The results indicate that the combination of the three components enhances the thermal performance of the PDI-SJIHS, compared with the slit jet impingement heat sink with only one of the above components. Rising the Reynolds number can enhance the thermal characteristics of the PDI-SJIHS. For a Reynolds number of 8000 and nanofluids with a 3% volume fraction, the average convective heat transfer coefficient, friction coefficient, and comprehensive heat transfer coefficient of the optimized PDI-SJIHS are increased by 182%, 153%, and 108%, respectively, and the standard deviation of temperature is 91% less than that of F-SJIHS.