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Alzheimer’s disease (AD) is a neurological condition that gradually weakens the brain and impairs cognition and memory. Multimodal imaging techniques have become increasingly important in the diagnosis of AD because they can help monitor disease progression over time by providing a more complete picture of the changes in the brain that occur over time in AD. Medical image fusion is crucial in that it combines data from various image modalities into a single, better-understood output. The present study explores the feasibility of employing Pareto optimized deep learning methodologies to integrate Magnetic Resonance Imaging (MRI) and Positron Emission Tomography (PET) images through the utilization of pre-existing models, namely the Visual Geometry Group (VGG) 11, VGG16, and VGG19 architectures. Morphological operations are carried out on MRI and PET images using Analyze 14.0 software and after which PET images are manipulated for the desired angle of alignment with MRI image using GNU Image Manipulation Program (GIMP). To enhance the network’s performance, transposed convolution layer is incorporated into the previously extracted feature maps before image fusion. This process generates feature maps and fusion weights that facilitate the fusion process. This investigation concerns the assessment of the efficacy of three VGG models in capturing significant features from the MRI and PET data. The hyperparameters of the models are tuned using Pareto optimization. The models’ performance is evaluated on the ADNI dataset utilizing the Structure Similarity Index Method (SSIM), Peak Signal-to-Noise Ratio (PSNR), Mean-Square Error (MSE), and Entropy (E). Experimental results show that VGG19 outperforms VGG16 and VGG11 with an average of 0.668, 0.802, and 0.664 SSIM for CN, AD, and MCI stages from ADNI (MRI modality) respectively. Likewise, an average of 0.669, 0.815, and 0.660 SSIM for CN, AD, and MCI stages from ADNI (PET modality) respectively.

In the framework of induction hardening, the coil design task is particularly suitable to be formulated as multi-objective optimization problem. In fact, the Pareto front estimation raises the issue of guaranteeing a satisfactory diversity and number of non-dominated solutions to be provided to the decision maker (DM). In this paper, a generative adversarial network (GAN) and a forward neural network (FNN), which is cascade connected to the GAN generator, produce additional Pareto optimal solutions starting from the results of a genetic algorithm (NSGA-II) used as training set. The FNN ensures an accurate prediction of the objectives of the added solutions, removing the need for further field analyses. This method is first tested against two analytical problems and subsequently validated on a 3-objective coil design task to illustrate its utility for a real-world case.

The paper presents an evaluation of a Pareto-optimized FaceNet model with data preprocessing techniques to improve the accuracy of face recognition in the era of mask-wearing. The COVID-19 pandemic has led to an increase in mask-wearing, which poses a challenge for face recognition systems. The proposed model uses Pareto optimization to balance accuracy and computation time, and data preprocessing techniques to address the issue of masked faces. The evaluation results demonstrate that the model achieves high accuracy on both masked and unmasked faces, outperforming existing models in the literature. The findings of this study have implications for improving the performance of face recognition systems in real-world scenarios where mask-wearing is prevalent. The results of this study show that the Pareto optimization allowed improving the overall accuracy over the 94% achieved by the original FaceNet variant, which also performed similarly to the ArcFace model during testing. Furthermore, a Pareto-optimized model no longer has a limitation of the model size and is much smaller and more efficient version than the original FaceNet and derivatives, helping to reduce its inference time and making it more practical for use in real-life applications.

The paper presents an evaluation of a Pareto-optimized FaceNet model with data preprocessing techniques to improve the accuracy of face recognition in the era of mask-wearing. The COVID-19 pandemic has led to an increase in mask-wearing, which poses a challenge for face recognition systems. The proposed model uses Pareto optimization to balance accuracy and computation time, and data preprocessing techniques to address the issue of masked faces. The evaluation results demonstrate that the model achieves high accuracy on both masked and unmasked faces, outperforming existing models in the literature. The findings of this study have implications for improving the performance of face recognition systems in real-world scenarios where mask-wearing is prevalent. The results of this study show that the Pareto optimization allowed improving the overall accuracy over the 94% achieved by the original FaceNet variant, which also performed similarly to the ArcFace model during testing. Furthermore, a Pareto-optimized model no longer has a limitation of the model size and is much smaller and more efficient version than the original FaceNet and derivatives, helping to reduce its inference time and making it more practical for use in real-life applications.

The research introduces a unique deep-learning-based technique for remote rehabilitative analysis of image-captured human movements and postures. We present a ploninomial Pareto-optimized deep-learning architecture for processing inverse kinematics for sorting out and rearranging human skeleton joints generated by RGB-based two-dimensional (2D) skeleton recognition algorithms, with the goal of producing a full 3D model as a final result. The suggested method extracts the entire humanoid character motion curve, which is then connected to a three-dimensional (3D) mesh for real-time preview. Our method maintains high joint mapping accuracy with smooth motion frames while ensuring anthropometric regularity, producing a mean average precision (mAP) of 0.950 for the task of predicting the joint position of a single subject. Furthermore, the suggested system, trained on the MoVi dataset, enables a seamless evaluation of posture in a 3D environment, allowing participants to be examined from numerous perspectives using a single recorded camera feed. The results of evaluation on our own self-collected dataset of human posture videos and cross-validation on the benchmark MPII and KIMORE datasets are presented.

Collimated gamma-based techniques are widely used to study nuclear fuel, especially for non-destructive post-irradiation examination (PIE). Examples of such techniques include gamma emission tomography (GET) and gamma transmission densitometry (GTD). Further development in designing collimated GET and GTD setups can be foreseen, optimizing the spatial resolution from a millimetre scale to a hundred-micron scale. The enhanced performance would be an asset in PIE, providing a unique combination of high spatial resolution and low interrogation effort. The experimental data would provide a detailed insight into the fuel for modelling its performance at high burnup or in accident scenarios. However, optimizing new instrument designs is not trivial. Multiple performance metrics exist, and their interdependence with the setup configuration and sample characteristics requires evaluation. At the same time, trade-offs should be identified and considered according to the application requirements. Monte Carlo (MC) radiation transport tools are generally unsuitable for modelling such collimated setups due to the intrinsic transmission inefficiency of gammas through the collimator slit. Therefore, alternative methods are desired for evaluating the collimator response. This study proposes a structured optimization methodology, where the trade-offs between the performance metrics are considered to suggest optimal collimator designs for GET applications. The method combines analytical methodologies for fast collimator response calculation and accurate MC simulations to evaluate sample self-attenuation and detector response. The results indicate that for sub-millimetric slits, a few hundred microns resolution can be achieved in suitable conditions (high burnup and short cooling time fuel samples) with reasonable investigation time and noise. Furthermore, the methodologies developed were used to evaluate the feasibility of radial gamma transmission micro-densitometry. Such a technique was also demonstrated through a first experimental campaign using calibration standards and an ADOPTTM irradiated nuclear fuel sample.

One of the most difficult components of stroke therapy is regaining hand mobility. This research describes a preliminary approach to robot-assisted hand motion therapy. Our objectives were twofold: First, we used machine learning approaches to determine and describe hand motion patterns in healthy people. Surface electrodes were used to collect electromyographic (EMG) data from the forearm’s flexion and extension muscles. The time and frequency characteristics were used as parameters in machine learning algorithms to recognize seven hand gestures and track rehabilitation progress. Eight EMG sensors were used to capture each contraction of the arm muscles during one of the seven actions. Feature selection was performed using the Pareto front. Our system was able to reconstruct the kinematics of hand/finger movement and simulate the behaviour of every motion pattern. Analysis has revealed that gesture categories substantially overlap in the feature space. The correlation of the computed joint trajectories based on EMG and the monitored hand movement was 0.96 on average. Moreover, statistical research conducted on various machine learning setups revealed a 92% accuracy in measuring the precision of finger motion patterns.

This article concerns the study of mixed Pareto-lexicographic multiobjective optimization problems where the objectives must be partitioned in multiple priority levels (PLs). A PL is a group of objectives having the same importance in terms of optimization and subsequent decision making, while between PLs a lexicographic ordering exists. A naive approach would be to define a multilevel dominance relationship and apply a standard EMO/EMaO algorithm, but the concept does not conform to a stable optimization process as the resulting dominance relationship violates the transitive property needed to achieve consistent comparisons. To overcome this, we present a novel approach that merges a custom nondominance relation with the Grossone methodology, a mathematical framework to handle infinite and infinitesimal quantities. The proposed method is implemented on a popular multiobjective optimization algorithm (NSGA-II), deriving a generalization of it called by us PL-NSGA-II. We also demonstrate the usability of our strategy by quantitatively comparing the results obtained by PL-NSGA-II against other priority and nonpriority-based approaches. Among the test cases, we include two real-world applications: one 10-objective aircraft design problem and one 3-objective crash safety vehicle design task. The obtained results show that PL-NSGA-II is more suited to solve lexicographical many-objective problems than the general purpose EMaO algorithms.

Multiparametric indices offer a more comprehensive approach to voice quality assessment by taking into account multiple acoustic parameters. Artificial intelligence technology can be utilized in healthcare to evaluate data and optimize decision-making processes. Mobile devices provide new opportunities for remote speech monitoring, allowing the use of basic mobile devices as screening tools for the early identification and treatment of voice disorders. However, it is necessary to demonstrate equivalence between mobile device signals and gold standard microphone preamplifiers. Despite the increased use and availability of technology, there is still a lack of understanding of the impact of physiological, speech/language, and cultural factors on voice assessment. Challenges to research include accounting for organic speech-related covariables, such as differences in conversing voice sound pressure level (SPL) and fundamental frequency (f0), recognizing the link between sensory and experimental acoustic outcomes, and obtaining a large dataset to understand regular variation between and within voice-disordered individuals. Our study investigated the use of cellphones to estimate the Acoustic Voice Quality Index (AVQI) in a typical clinical setting using a Pareto-optimized approach in the signal processing path. We found that there was a strong correlation between AVQI results obtained from different smartphones and a studio microphone, with no significant differences in mean AVQI scores between different smartphones. The diagnostic accuracy of different smartphones was comparable to that of a professional microphone, with optimal AVQI cut-off values that can effectively distinguish between normal and pathological voice for each smartphone used in the study. All devices met the proposed 0.8 AUC threshold and demonstrated an acceptable Youden index value.

An integrated approach is proposed in the study of rational schemes for the distribution of cargo flows at a regional transport loop for multimodal transportation, considered within the framework of an oligopolistic market. A technique has been developed for the parallel application of two approaches, differing in their mathematical nature, to the issues of increasing the economic efficiency of these transportations. The results obtained by the previously developed method of economic and geographical delimitationof «influence areas» of loading stations serve as a justification for the correctness of the results obtained by using an algorithm based on the Pareto optimization of the freighttransportation process. Rational variants for organizing the freight transportation, taking into account time and cost indicators, have been obtained. The system of analytical calculations is used as a software tool to obtain a mathematically sound and transport–logistic diversified model of a regional oligopolistic freight market.

Model-based reinforcement learning is expected to be a method that can safely acquire the optimal policy under real-world conditions by using a stochastic dynamics model for planning. Since the stochastic dynamics model of the real world is generally unknown, a method for learning from state transition data is necessary. However, model learning suffers from the problem of bias-variance trade-off. Conventional model learning can be formulated as a minimization problem of expected loss. Failure to consider higher-order statistics for loss would lead to fatal errors in long-term model prediction. Although various methods have been proposed to explicitly handle bias and variance, this paper first formulates a new loss function, especially for sequential training of the deep neural networks. To explicitly consider the bias-variance trade-off, a new multi-objective optimization problem with the augmented weighted Tchebycheff scalarization, is proposed. In this problem, the bias-variance trade-off can be balanced by adjusting a weight hyperparameter, although its optimal value is task-dependent and unknown. We additionally propose a general-purpose and efficient meta-optimization method for hyperparameter(s). According to the validation result on each epoch, the proposed meta-optimization can adjust the hyperparameter(s) towards the preferred solution simultaneously with model learning. In our case, the proposed meta-optimization enables the bias-variance trade-off to be balanced for maximizing the long-term prediction ability. Actually, the proposed method was applied to two simulation environments with uncertainty, and the numerical results showed that the well-balanced bias and variance of the stochastic model suitable for the long-term prediction can be achieved.

Complexity has been argued to limit operational efficiency, hinder decision-making and induce disruption in supply chain networks. The main aim of this paper is to investigate the architectural trade-off between complexity and modularity in modular assembly supply chain networks. Towards this, an information-entropic complexity model is developed and applied to the domain of assembly supply chains and logistics. This approach characterises complexity as a combination of the intrinsic complexity of the system modules/interfaces and the influence of the topological composition of the network. The model is then used within an optimisation framework, where the optimal granularity level for assembly supply chain design solutions for a given assembly product can be automatically verified by considering the trade-off between complexity and network modularity. It is concluded that the proposed methodology could help to minimise the complexity of supply chain assembly configurations while maximising their modularity and thereby help to increase both the reliability and performance of supply chain networks.

Multi-criteria optimization problems represent a crucial task for any designer of a public service system due to conflicting criteria, which have to be faced. Possible solution of this almost unsolvable situation can be seen in obtaining a series of solutions, where it is impossible to improve one of the criteria without worsening some of the others. Full set of such non-dominated solutions is called Pareto front. The multi-criteria optimization problem can be solved by submitting the Pareto front or its approximation on contracting authority’s board for possible negotiation with representative of public. This paper deals with methods, which are able to produce a series of non-dominated solutions of bi-criteria public service system design problem. The first criterion considered is average response time and the second one corresponds to the number of users located behind a given limit of response time. We suggest two approaches to the problem. The first of them is an exact approach, which produces Pareto front of the bi-criteria problem. The second approach makes use of an evolutionary hybridized algorithm, which uses so called elite set, to save temporary non-dominated solutions. In the computational study, we try to verify the hypothesis that it is possible to approximate the Pareto front by utilizing the evolutionary algorithm. We also suggest a way of hybridization and tuning the algorithm to obtain a good approximation in acceptable computational time.

In the immediate aftermath of large-scale disasters, emergency logistics services play important roles in saving lives and reducing losses. Efficient relief logistics scheduling depends on the accurate transport time information for available routes. However, this information cannot be obtained precisely until a vehicle uses the road. Considering the correlation between information acquisition and logistics operations, this paper focuses on a multiperiod online decision-making problem to simulate the information acquiring process. This problem can be referenced for emergency resource scheduling scenarios in which previous decisions impact knowledge for future logistics plans. A multi-trip cumulative capacitated vehicle routing problem with uncertain transportation time is investigated as the basic model. The tradeoff between transportation efficiency and the unknown transport time discovery rate is considered in a multiobjective evolutionary algorithm (MOEA). A memetic algorithm (MA) and a robust optimization (RO) -MA for single-period post-disaster emergency logistics are also proposed to solve the problem for comparison. In these algorithms, evolutionary operators that benefit solution fixing and variation are proposed. In the experiments, a real-world instance is employed. A simulative experimental environment is established. Dynamic information gained within the process of logistics scheduling is highlighted via multi-period online optimization. Different scenarios corresponding to estimates in emergency situations are provided to validate the performance of the algorithms. The experimental results show that the hybrid strategy, MOEA+MA, can obtain the best result in more than half of the considered cases which demonstrates the necessary balance between obtaining information and transportation efficiency.

Apart from improving motion accuracy, increasing productivity while reducing computer numerical control machine tools’ carbon footprint is vital in the manufacturing industry. Several studies have proposed corner smoothing methods that improve cycle time for piecewise linear paths by exploiting axial limits to achieve time-optimal trajectories. Energy-saving is not considered an objective in these methods. This paper presents a method of generating Pareto optimal corner smoothing trajectories that trade-off the contradicting objectives of minimizing cycle time and energy consumption. The trajectories along linear paths and smoothed corners are respectively described using jerk limited acceleration profiles and kinematic corner smoothing methods. An energy consumption model of an industrial two-axis feed drive system is identified and used in solving the bi-objective optimization problem. From the resulting Pareto frontier, the best trade-off trajectory is selected as the one that minimizes both objectives. The proposed method’s effectiveness is vindicated experimentally, where the best trade-off trajectory achieves respectively 65.87 % and 60.44 % of the time and energy-saving potentials.

In order to improve the energy efficiency of urban rail transit system, it is necessary to figure out the key factor(s) that restrain(s) train rapidity and energy conservation and understand the inner complex relationships among them. We first define energy-saving and rapid train control/operation, then simulate and analyze the microscopic train behavior between two successive stations. The result reflects that due to the constraint of the short inter-station distance, the train has no space and time to take advantage of its excellent performance in speed and has to stop frequently at every station, which leads to the increase of energy consumption and the prolongation of running time. Based on the above energy consumption analysis of the microscopic train behavior, a hierarchical Pareto 0–1 integer programming with consideration of passenger flow distribution and public transport characteristics is presented to organically integrate microscopic train control with macroscopic train organization. The case study shows that the presented method can greatly promote the energy-efficient and rapid train operation of urban rail transit system. This study is also helpful to the planning and construction of future cities and urban rail transit systems.

Manufacturing industries aim to improve product quantity and quality. These trade-off objectives are typically manifested as cycle time reduction and motion accuracy improvement. Corner smoothing approaches that reduce the cycle time of piecewise linear trajectories are proposed in the literature. This study tackles the two objectives by Pareto-optimal corner smoothing with constraints imposed as kinematic limits, continuity conditions and user-specified cornering tolerance. Linear and cornering motions along a contour are respectively described by jerk-limited acceleration profiles and a modified kinematic corner smoothing with interrupted acceleration (KCSIA) approach. A Pareto frontier is generated by the divide and conquer algorithm, where the solution nearest to the utopia point is selected as the best trade-off solution. The effectiveness of the proposed method is validated through experiments, where the best trade-off solution reduces the maximum and average contouring errors by 47.53% and 25.40% while it increases cycle time by 2.53% compared to KCSIA.

Demand response (DR) has received much attention for its ability to balance the changing power supply and demand with flexibility. DR aggregators play an important role in aggregating flexible loads that are too small to participate in electricity markets. In this work, a DR operation framework is presented to enable local management of customers to participate in electricity market. A novel optimization model is proposed for the DR aggregator with multiple objectives. On one hand, it attempts to obtain the optimal design of different DR contracts as well as the portfolio management so that the DR aggregator can maximize its profit. On the other hand, the customers' welfare should be maximized to incentivize users to enroll in DR programs which ensure the effective and flexible load control. The consumer psychology is introduced to model the consumers' behavior during contract signing. Several simulation studies are performed to demonstrate the feasibility of the proposed model. The results illustrate that the proposed model can ensure the profit of the DR aggregator whereas the customers' welfare is considered.

Predicting the success of National Football League drafts has always been an exciting issue for the teams, fans and even for scientists. Among the numerous approaches, one of the best techniques is to ask the opinion of sport experts, who have the knowledge and past experiences to rate the drafts of the teams. When asking a set of sport experts to evaluate the performances of teams, a multicriteria decision making problem arises unavoidably. The current paper uses the draft evaluations of the 32 NFL teams given by 18 experts: a novel multicriteria decision making tool has been applied: the sum of ranking differences (SRD). We introduce a quick and easy-to-follow approach on how to evaluate the performance of the teams and the experts at the same time. Our results on the 2021 NFL draft data indicate that Green Bay Packers has the most promising drafts for 2021, while the experts have been grouped into three distinct groups based on the distance to the hypothetical best evaluation. Even the coding options can be tailored according to the experts’ opinions. Statistically correct (pairwise or group) comparisons can be made using analysis of variance (ANOVA). A comparison to TOPSIS ranking revealed that SRD gives a more objective ranking due to the lack of predefined weights.

This paper develops a multi-objective mixed-integer linear programming model for the problem of robust rescheduling for capacitated urban rail transit (URT) trains to serve passengers from delayed high-speed railway (HSR) trains. The capacity of each extra train is not assumed to be unlimited in this paper. Robust passenger assignment constraints are developed to ensure that delayed passengers can board the URT trains under different random delay scenarios of HSR operations. Robust dispatching constraints of URT trains are designed for a stable disrupting number of URT trains across different scenarios. The multi-objective model is used to maximize the number of expected transported passengers and minimize the number of extra trains and operation-ending time of all extra trains. An iterative solution approach based on a revised version of the epsilon-constraint method combined with the weighted-sum method is designed for the computation of the multi-objective model. Computational experiments are performed on the Beijing URT lines and the Beijing-Shanghai HSR line. We evaluate the impact of the robustness constraints of passenger assignment and the number of extra trains to ensure that the number of trains are maintained and the passengers can successfully take the trains during different delayed scenarios.

This article takes on solving the problem of multicriteria conditional optimization. This problem is one of the most key tasks of the current time and has its application in many areas. Reuse of various existing algorithms for solving unconstrained optimization is proposed. Different methods of multicriteria unconditional optimization are reviewed. The advantages and disadvantages of each algorithm are analyzed. The algorithms modified to take into account the constraints. Additional algorithms of transition from solving an unconditional optimization problem to a conditional optimization problem are developed. A genetic algorithm SPEA2 was used to test the developed algorithms. Examples of solving the problem at hand using the aforementioned algorithms are presented. A comparative analysis of the final results was conducted.

Proposed work addresses the existing thermal problem of OR-XNOR based circuit by introducing design time thermal management technique at the logic level. The approach is used to reduce the peak temperature by eliminating local hotspots. In proposed thermal-aware synthesis, non-dominated sorting genetic algorithm-II (NSGA-II) based meta-heuristic search algorithm is used to select a suitable input polarity of Mixed Polarity Dual Reed-Muller Expansion (MPDRM) to reduce the power and power-density by optimizing the area sharing. A parallel tabular technique is used for input polarity conversion from Product-of-Sum (POS) to MPDRM function. Finally, the optimized solutions are implemented in the physical design level to obtain the actual values of area, power, and temperature. MCNC benchmark suit is considered for performance evaluation. A comparative study of the proposed approach with existing state-of-art algorithms such as fixed and mixed polarity Reed-Muller network is reported. A significant reduction in area occupancy, power dissipation, and peak temperature generation are reported.

This paper analyzes the potential of Artificial Neural Networks (ANNs) for the modeling and optimization of magnetic components and, specifically, inductors. After reviewing the basic properties of ANNs, several potential modeling and design workflows are presented. A hybrid method, which combines the accuracy of 3D Finite Element Method (FEM) and the low computational cost of ANNs, is selected and implemented. All relevant effects are considered (3D magnetic and thermal field patterns, detailed core loss data, winding proximity losses, coupled loss-thermal model, etc.) and the implemented model is extremely versatile (30 input and 40 output variables). The proposed ANN-based model can compute 50'000 designs per second with less than 3% deviation with respect to 3D FEM simulations. Finally, the inductor of a 2 kW DC-DC buck converter is optimized with the ANN-based workflow. From the Pareto fronts, a design is selected, measured, and successfully compared with the results obtained with the ANNs. The implementation (source code and data) of the proposed workflow is available under an open-source license., IEEE Open Journal of Power Electronics, 1, ISSN:2644-1314

Herein, noise, gain and port mismatchings of a microwave small-signal transistor are expressed as all the set of acceptable Pareto optimal solutions and trade-off relations within the device operation ( $\text{V}_{\mathrm {DS}}$ , $\text{I}_{\mathrm {DS}}$ , $f$ ) domain without any need of expert knowledge of microwave device. In this multi-objective optimization problem, non-dominated sorting genetic algorithm (NSGA) -III is applied to an ultra-low noise amplifier (LNA) transistor NE3511S02 (HJ-FET) where the noise $\text{F}_{\mathrm {req}}\ge \text {F}_{\mathrm {min}}$ and output mismatching $\text{V}_{\mathrm {outreq}} \ge 1$ are preferred as the reference points, while the input mismatching $\text{V}_{\mathrm {inopt}} \ge 1 $ and gain $\text{G}_{\mathrm {Tmax}}$ are optimized with respect to source $\text{Z}_{\mathrm {S}}$ and load $\text{Z}_{\mathrm {L}}$ within the unconditionally stable working area. Thus, diverse set of the Pareto optimal (the required noise $\text{F}_{\mathrm {req}}$ , the optimum input $\text{V}_{\mathrm {inopt}}$ , the required output $\text{V}_{\mathrm {outreq}}$ , the maximum transducer gain $\text{G}_{\mathrm {Tmax}}$ ) quadruples are resulted from a fast search of the solution space. Furthermore, the optimum bias condition ( $\text{V}_{\mathrm {DS}}$ , $\text{I}_{\mathrm {DS}}$ ) and sensitivities of the terminations to fabrication tolerances are also determined using the cost analysis in the operation domain for the required $\text{P}_{\mathrm {max}}$ , $\text{I}_{\mathrm {DSmax}}$ and performance quadruple. Finally, this work is expected to enable a designer to provide the feasible design target space (FDTS) consisting of all trade-off relations among all the transistor’s performance ingredients to be used in the challenging LNA designs.

Active brake control systems are able to use more accurate control designs on the real-time knowledge of wheel slip such as tire braking forces and external momentums. A multi-objective Pareto type optimization approach is used to evaluate the inconsistent points of the optimization design namely those of minimizing the directional deviation while achieving maximum braking forces on wheels. Moreover, the optimal target slip values defined by the braking purposes like as shorter stopping distance and stability increment by keeping the vehicle in the straight line. This gets by the control of the longitudinal and lateral slip dynamics of each wheel concerning to the road conditions. A controller is optimally brought up by manipulating optimal control law with weights of two control inputs with mathematical and probabilistic characterization. The first-passage probability of critical response levels is used to directly control the vehicle directional stability. An impressive simulation technique based on Monte Carlo method named asymptotic sampling is applied to define the required first-passage probabilities and the Latin Hypercube sampling is used to design of experiments and to cover the design space. Afterwards, a Pareto-type optimization approach is applied to a trade-off between the inconsistent points of the optimization design. The simulation is conducted by the validated vehicle model and the results are indicated that the probability-based control design is represented as a preferable braking performance in comparison with the other systems for braking in sever conditions.

Obstructive sleep apnea (OSA) is a common sleep disorder characterized by interrupted breathing during sleep. Because of the cost, complexity, and accessibility issue related to polysomnography, the gold standard test for apnea detection, automation of the diagnostic test based on a simpler method is desired. Several signals can be used for apnea detection, such as airflow and electrocardiogram. However, the reduction of airflow normally leads to a decrease in the blood oxygen saturation level (SpO2). This signal is usually measured by a pulse oximeter, a sensor that is cheap, portable, and easy to assemble. Therefore, the SpO2 was chosen as the reference signal. Feature based classifiers with shallow neural networks have been developed to provide apnea detection using SpO2. However, two main issues arise, the need for feature creation and the selection of the more relevant features. Deep neural networks can solve these issues by employing featureless methods. Among multiple deep classifiers that have been developed, convolution neural networks (CNN) are gaining popularity. However, the selection of the CNN structure and hyperparameters are typically done by experts, where prior knowledge is essential. With these problems in mind, an algorithm for automatic structure selection and hyper parameterization of a one dimension CNN was developed to detect OSA events using only the SpO2 signal. Three different input sizes and databases were tested, and the best model achieved an average accuracy, sensitivity, and specificity of 94%, 92%, and 96%, respectively.

Various intelligent algorithms are applied in optimization design, and the differential evolution (DE) algorithm is widely applied with its excellent convergence speed and convergence precision. This study analyzed the advantages and disadvantages of the existing multi-objective differential evolution (MODE) algorithm, and developed a MODE algorithm based on the adaptive weight and the multi-population strategy (MODE/AWMS). The proposed algorithm was verified using test functions. MODE/AWMS exhibited certain advantages compared with several other multi-objective optimization algorithms. Taking a polarized magnetic relay as an example, MODE/AWMS was used to optimize its key parameters by establishing a rapid calculation model of its electromagnetic mechanism. The electromagnetic force (EMF) of the release position was improved, which verified the validity of MODE/AWMS.

According to the published papers and books since the turn of the century, Pareto optimization is the dominating assessment method for multi-objective nonlinear optimization problems treated by population-based optimizers like Evolutionary Algorithms. However, is it always the method of choice for real-world applications, where either more than four objectives have to be considered, or the same type of task is repeated again and again with only minor modifications, in an automated optimization or planning process? This paper presents a classification of application scenarios and compares the Pareto approach with an extended version of the weighted sum, called cascaded weighted sum, for the different scenarios. Its range of application within the field of multi-objective optimization is discussed as well as its strengths and weaknesses., 20 pages, 10 figures

Aircraft system identification can either occur in the time-or frequency-domain with each approach having inherent advantages and disadvantages. For example, time-domain modelling generates superior time history matches and has a superior ability to achieve a trim solution. However, time-domain models do not provide a high degree of insight to the frequency responses of the system, which is important for control law development and for matching handling qualities for pilot-in-the-loop simulation — this is a strength of the frequency-domain approach. This paper utilises a Pareto optimization procedure to combine both the time- and frequency-domain approaches and exploit the strengths of both methods. Pareto fronts are generated for the system identification of a 6 degree-of-freedom forward flight model at 90 kts of the National Research Council of Canada’s Bell 412 helicopter. The generated Pareto fronts showed the necessity of balancing the time- and frequency-domain matches whereby moving from the compromise solution to either the isolated time- or frequency-domain solutions resulted in a small improvement in one while the other suffered relatively more. Accordingly, the multi-objective solution using Pareto optimization capitalized on the strengths of both approaches and avoided an overspecialized solution in either of the domains., ASME 2021 International Mechanical Engineering Congress and Exposition, November 1-5, 2021, Virtual, Online

This research proposes an Archive-based Multi-Objective Arithmetic Optimization Algorithm (MAOA) as an alternative to the recently established Arithmetic Optimization Algorithm (AOA) for multi-objective problems (MAOA). The original AOA approach was based on the distribution behavior of vital mathematical arithmetic operators, such as multiplication, division, subtraction, and addition. The idea of the archive is introduced in MAOA, and it may be used to find non-dominated Pareto optimum solutions. The proposed method is tested on seven benchmark functions, ten CEC-2020 mathematic functions, and eight restricted engineering design challenges to determine its suitability for solving real-world engineering difficulties. The experimental findings are compared to five multi-objective optimization methods (Multi-Objective Particle Swarm Optimization (MOPSO), Multi-Objective Slap Swarm Algorithm (MSSA), Multi-Objective Ant Lion Optimizer (MOALO), Multi-Objective Genetic Algorithm (NSGA2) and Multi-Objective Grey Wolf Optimizer (MOGWO) reported in the literature using multiple performance measures. The empirical results show that the proposed MAOA outperforms existing state-of-the-art multi-objective approaches and has a high convergence rate. Web of Science 10 106698 106673

We present a new two-step approach for automatized a posteriori decision making in multi-objective optimization problems, i.e., selecting a solution from the Pareto front. In the first step, a knee region is determined based on the normalized Euclidean distance from a hyperplane defined by the furthest Pareto solution and the negative unit vector. The size of the knee region depends on the Pareto front’s shape and a design parameter. In the second step, preferences for all objectives formulated by the decision maker, e.g., 50–20–30 for a 3D problem, are translated into a hyperplane which is then used to choose a final solution from the knee region. This way, the decision maker’s preference can be incorporated, while its influence depends on the Pareto front’s shape and a design parameter, at the same time favorizing knee points if they exist. The proposed approach is applied in simulation for the multi-objective model predictive control (MPC) of the two-dimensional rocket car example and the energy management system of a building.

A prerequisite for value stream design is the segmentation of products into families. This means that all products of a family are assigned to the same group of workstations so that the resulting material flows are separated as good as possible, and a higher degree of transparency is reached on the shop floor. However, since the number of workstations as well as their capacity is limited, shared resources cannot always be avoided in practice. Furthermore, the objective of product family orientation may compete with the objective of fulfilling product-workstation preferences. These preferences result, for example, from required equipment like specific tooling or from capability requirements. An optimization heuristic for this product-workstation allocation problem is presented within this article. First, the mathematical problem is formally described, then the heuristic is introduced and the required data for its application is outlined. For the evaluation, an extensive test set is generated, comparison heuristics are implemented, and solutions are made comparable through problem-specific bounds for both objectives. The results show that the solution quality of the pareto heuristic for both objective functions achieves almost the level of the comparison heuristics, which optimize only one of the objectives in isolation.

This study investigates the benefits of adding a cut-off barrier to the design space of synchronous reluctance machines. The design space is explored using quasi-Monte Carlo sampling and a number of objectives are evaluated using Finite Element Method. Results show that rotors with a cut-off barrier tend to have higher mean torque and lower iron losses, while rotors without cut-off barrier tend to have slightly lower Von Mises stresses, lower torque ripple, and higher sensorless capability. When several objectives are involved, such as maximizing mean torque and the sensorless capability at the same time, then the best performing topology depends on the trade-off put between the objectives. It is shown that the location of the switching point, where one topology becomes better than the other, can be obtained accurately using inexpensive metamodels. Hence, the proposed method can be used to quickly select the best performing topology for many sets of objectives without performing costly optimizations.

The abstract is available here: https://uscholar.univie.ac.at/o:1676014

Publisher Copyright: Author In this paper, we develop a novel method to design the elements of an antenna array and their feed weights simultaneously. The method is based on formulating the design problem as a non-linear multi-objective optimization model that estimates the realized gain at certain angles as a function of the element-level port signals and impedances, and the array-level weights for the elements. This enables utilization of genetic algorithms to find optimal signals, impedances, and weights for given steering range requirements. As an example, an array consisting of multi-port antenna elements is simulated and modeled with its impedance and radiation matrices. These matrices are used in the calculation of realized gain with the model. The model is then applied as part of the method to find as wide scanning range for the array as possible. The antenna elements are designed such that the multi-port system can be reduced to a single feed with physically realizable matching components and a matching network. The array designed with the proposed method is also compared to a reference antenna array of the same size. Both the simulations and measurements verify that the method can provide substantial improvements in the scanning range as compared to the reference.

With the development of ecological economics, energy-saving green energy chain management has been a wide concern of academia and industries. However, the relatively high cost of green investment makes manufacturers face the problem of financial constraints. On this basis, because the green level information of products is proprietary to manufacturers, manufacturers will lie about the green level of products in order to improve their profits out of the principle of profit maximization. As a result, banks cannot obtain the true green level of products, reducing the benefits of the green energy-efficient supply chain system and making the market of green products volatile. In view of this, blockchain technology is introduced in this paper to improve customer’s product green level sensitivity and obtain lower green credit interest rates from banks. In this paper, a green supply chain financing model based on blockchain technology was constructed under the condition of green information misreporting, and it is compared with the benchmark without blockchain technology. Research shows that the adoption of blockchain can achieve Pareto improvement of green supply chain members. In addition, manufacturers have an incentive to adopt blockchain if the cost of blockchain investment falls below a certain threshold, and consumer green sensitivity increases below that threshold. We compared the profits of green manufacturers with those of retailers and the total emissions of manufacturers. The results show that: (1) When the financing intensity exceeds a certain value, there is an optimal coverage of green financing to ensure that the profit target of manufacturers, the profit target of retailers and the emission reduction target are achieved simultaneously. (2) The adoption of blockchain can achieve Pareto improvement of green energy supply chain members. The actual data of green transformation of Jinyuan New Technology Company were cited. Through calculation, it was found that green transformation can reduce the emissions of enterprises. When the financing intensity is in a certain range, the profits of manufacturers and retailers can be maximized, and the emission reduction degree is the highest. Thus, the practicability and reliability of this model were proved. (3) Manufacturers have an incentive to adopt blockchain if the cost of blockchain investment falls below a certain threshold, and consumer green sensitivity increases below that threshold. The research results of this paper provide solutions for enterprises with limited funds for green transformation and provide a theoretical basis for the government to formulate emission reduction incentive mechanism.

The aim of this paper is to select a depth controller for innovative biomimetic underwater vehicle drives. In the process of optimizing depth controller settings, two classical controllers were used, i.e., the proportional–integral–derivative (PID) and the sliding mode controllers (SM). The parameters of the regulators’ settings were obtained as a result of optimization by three methods of the selected quality indicators in terms of the properties of the control signal. The starting point for the analysis was simulations conducted in the MATLAB environment for the three optimization methods on three types of indicators for three different desired depth values. The article describes the methods and quality indicators in detail. The paper presents the results of the fitness function obtained during the optimization. Moreover, the time courses of the vehicle position relative to the desired depth, the side fin deflection angles, the calculated parameters of the control signals, and the observations and conclusions formulated in the research were presented.

For a practical structural health monitoring (SHM) system, the traditional single objective methods for optimal sensor placement (OSP) cannot always obtain the optimal result of sensor deployment without sacrificing other targets, which creates obstacles to the efficient use of the sensors. This study mainly focuses on establishing a bi-objective optimization method to select the sensor placement positions. The practical significance of several single-objective criteria for OSP is firstly discussed, based on which a novel bi-objective optimization method is proposed based on the Pareto optimization process, and the corresponding objective functions are established. Furthermore, the non-dominated sorting genetic algorithm is introduced to obtain a series of the Pareto optimal solutions, from which the final solution can be determined based on a new defined membership degree index. Finally, a numerical example of a plane truss is applied to illustrate the proposed method. The Pareto optimization-based bi-objective OSP framework presented in this study could be well suited for solving the problem of multi-objective OSP, which can effectively improve the efficiency of the limited sensors in SHM system.

In contrast to internal combustion engine vehicles, electric vehicles (EVs) obtain the power required for the compressor of air conditioning system from an electric source. Therefore, an optimal design for electric motor, the main component of an electric compressor, is essential for improving EV mileage. A multi-objective optimal design is required because the characteristics of the motor are in a trade-off relationship with each other. When the finite element method (FEM) is used, multi-objective optimal designs for the motor take a significant amount of time because of the diversity analyses required for the optimal-model search. To solve this problem, in this study, a multi-objective optimal design method of an SPMSM for an EVs air conditioner system compressor was proposed and applied using the NSGA-II and an analytical method. The validity of the proposed method was confirmed by comparing the characteristics of the optimal design model with those of the initially designed model.

Electric retail rate design is relevant to utilities, customers, and regulators as retail rates impact the utility's revenue as well as the customers' electricity bills. In California, regulators approve rate proposals by privately owned vertical integrated utilities. Approval, however, is subject to compliance with multiple, potentially conflicting objectives such as economic or environmental objectives. Additionally, retail rates are price signals that affect how customers use electricity services. When utility customers change their usage, they also impact the ratemaking objectives to which rates have been designed. This suggests a feedback loop, which is particularly pronounced with prosumers, as they can systematically optimize their interactions with the electricity system. Prevalent ratemaking methods may not deliver retail rates that are optimal for multiple objectives when customers are prosumers. We propose a novel ratemaking method that formalizes the problem of designing retail rates as a multi-criteria optimization problem and accounts for prosumer reactions through a simulation-based optimization approach. Through a fictive case study, we found that the resulting Pareto frontiers are useful in recognizing and balancing tradeoffs among conflicting ratemaking objectives. Additionally, our results indicate that prevailing retail rates in California are not Pareto optimal.

Decision makers with the responsibility of managing policy for the COVID-19 epidemic have faced difficult choices in balancing the competing claims of saving lives and the high economic cost of shutdowns. In this paper, we formulate a model with both epidemiological and economic content to assist this decision-making process. We consider two ways to handle the balance between economic costs and deaths. First, we use the statistical value of life, which in Canada is about C$7 million, to optimize over a single variable, which is the sum of the economic cost and the value of lives lost. Our second method is to calculate the Pareto optimal front when we look at the two variables—deaths and economic costs. In both cases we find that, for most parameter values, the optimal policy is to adopt an initial shutdown level which reduces the reproduction number of the epidemic to close to 1. This level is then reduced once a vaccination programme is underway. Our model also indicates that an oscillating policy of strict and mild shutdowns is less effective than a policy which maintains a moderate shutdown level.

Robustness is a feature of regulatory pathways to ensure signal consistency in light of environmental changes or genetic polymorphisms. The retinoic acid (RA) pathway, is a central developmental and tissue homeostasis regulatory signal, strongly dependent on nutritional sources of retinoids and affected by environmental chemicals. This pathway is characterized by multiple proteins or enzymes capable of performing each step and their integration into a self-regulating network. We studied RA network robustness by transient physiological RA signaling disturbances followed by kinetic transcriptomic analysis of the recovery during embryogenesis. The RA metabolic network was identified as the main regulated module to achieve signaling robustness using an unbiased pattern analysis. We describe the network-wide responses to RA signal manipulation and found the feedback autoregulation to be sensitive to the direction of the RA perturbation: RA knockdown exhibited an upper response limit, whereas RA addition had a minimal feedback-activation threshold. Surprisingly, our robustness response analysis suggests that the RA metabolic network regulation exhibits a multi-objective optimization, known as Pareto optimization, characterized by trade-offs between competing functionalities. We observe that efficient robustness to increasing RA is accompanied by worsening robustness to reduced RA levels and vice versa. This direction-dependent trade-off in the network-wide feedback response, results in an uneven robustness capacity of the RA network during early embryogenesis, likely a significant contributor to the manifestation of developmental defects.

Purpose This paper aims to present an approach to the design of the compensation networks (CNs) based on a genetic optimization algorithm. The algorithm is applied to CNs with T-topology and considers the effects of the parasitic series resistances of their inductive components. The effectiveness of the algorithm is verified using Bode diagrams and simulation results. Design/methodology/approach The paper at first describes the problem and the approach followed to reach a set of optimal solutions, then explains the optimization algorithm, reports the obtained solutions and selects the optimal CNs. Finally, the actual performance of the wireless power transfer system (WPTS) when the selected CNs are used are checked. Findings This approach gave interesting results and made available a number of different sizing solutions of complex networks in a very short time. Most of the obtained solutions outperform the widely used series-series compensation. An accurate post processing of the obtained result is mandatory to discriminate the solutions that could be implemented from those that in a real system would originate uncontrolled high frequency current oscillation. Originality/value This paper offers a rather new approach to solve the problem of sizing the CNs of a dynamic WPTS. This approach makes available a large number of optimal solutions to the problem in a short time, without solving complex system of equations.

In this paper, the feasibility of the application of a dual mass flywheel (DMF) for heavy-duty truck drivetrain systems was studied. The third engine order vibration harmonic was in the focus of analysis as one of the most significant contributions to the oscillatory response in the drivetrain systems of heavy-duty trucks. Global sensitivity analysis (GSA) and Pareto optimization were used for designing torsional vibration absorbers in an operating engine speed range of 600&ndash, 2000 rpm. The optimization method attempted both to minimize the oscillations of the torque at the transmission input shaft and to maximize the energy efficiency of the vibration absorber. The GSA enabled the appropriate scanning of the domain of design parameters by varying all the parameters at the same time. It provided deep insight into the design process and increased the computational efficiency of the optimization. The results obtained show the following: the solution of the bi-objective optimization problem for torsional vibration absorbers does exist, Pareto fronts were obtained and analyzed for the DMF, presenting a trade-off between the measure of the attenuation of the oscillations of the torque at the transmission input shaft and the measure of the energy efficiency of the absorber, the optimized mass inertia, stiffness and damping parameters of a DMF do exist, providing the best attenuation of the torque oscillations, the performance of a DMF was further enhanced by incorporating a torsional tuned mass damper with appropriate optimized parameters. Finally, the results show evidence of the feasibility of the application of dual mass flywheels in heavy-duty truck drivetrain systems.

Fuel cell-gas turbine hybrid system is a potential field of investigation. This study establishes a modeling and optimization framework for a novel hybrid system consisting of a solid oxide fuel cell, a gas turbine and a supercritical carbon dioxide Brayton cycle. Based on the proposed thermodynamical model, a parametric analysis is investigated to determine the impacts of several key parameters on the system exergoeconomic performance. Meanwhile, bi-objective optimization is conducted for maximizing the exergy efficiency and minimizing the levelized cost of electricity via the Epsilon-constraint approach. The Linear Programming Techniques for Multidimensional Analysis of Preference decision-making approach is further employed to select the Pareto optimum solution from Pareto frontiers. The results show that several extreme values for the exergy efficiency and the levelized cost of electricity exist in a series of sensitivity curves, respectively. The Pareto frontiers indicates that with the increase of the exergy efficiency, the levelized cost of electricity shows a moderately increasing trend at first and increases rapidly afterward. Overall, at the Pareto optimum solution, the combined system can achieve an optimal exergy efficiency and levelized cost of electricity by 68% and 0.0575 $ kWh−1, respectively.

In this paper, we propose a new model for the multi-objective multiple allocation hub network design and routing problem which contains determining the location of hubs, the design of hub network, and the routing of commodities between source-destination pairs in the given network. The selected hubs are not assumed to be fully connected, and each node and arc in the network has capacity constraints. The multiple objectives of the problem are the minimization of total fixed and transportation costs and the minimization of the maximum travel time required for routing. We propose a mathematical formulation for the multi-objective problem and present a meta-heuristic solution based on a well-known multi-objective evolutionary algorithm. Using the proposed formulation, we are able to find the optimal solution for small networks of five nodes and seven nodes. To evaluate the performance of our heuristic approach on real data, the computational experiments are conducted on Turkish postal system data set. The results demonstrate that our heuristic approach can find feasible solutions to the problem in reasonable execution time, which is less than 10 min.

Fil: Miguel, Fabio M. Universidad Nacional de Río Negro, Sede Alto Valle y Valle Medio. Villa Regina; Argentina Fil: Frutos, Mariano. Universidad Nacional del Sur, Department of Engineering and IIESS-CONICET, Bahía Blanca; Argentina Fil: Tohmé, Fernando. Universidad Nacional del Sur, Department of Economics and INMABB-CONICET, Bahía Blanca; Argentina Fil: Méndez Babey, Máximo. Universidad de Las Palmas de Gran Canaria and SIANI, Las Palmas G. C.; Spain We present an optimization procedure based on a hybrid version of an evolutionary multi-objective decision-making algorithm for its application in urban freight transportation planning problems. This tool is intended to solve the planning problems of a merchandise distribution firm that dispatches small volume fractional loads of fresh foods on daily schedules. The firm owns a network of distribution centers supplying a large number of small businesses in Buenos Aires and its surroundings. The recombination operator of the evolutionary algorithm used here has been designed specifically for this problem. It is intended to embody a strategy that takes into account constraints like temporary closeness, closeness time window and connectivity in order to improve its performance in the clustering phase. The representation allows incorporating specific information about the actual instances of the problem and uses adaptive control of the parameters in the calibration stage. The performance of the proposed optimizer was tested against the results obtained by two evolutionary algorithms, NSGA II and SPEA 2, widely used in similar problems. We use hypervolume as a measure of convergence and dispersion of Pareto fronts. The statistical analysis of the results obtained with the three algorithms uses the Wilcoxon rank sum test, which yields evidence that our procedure provides good results. Presentamos un procedimiento de optimización basado en una versión híbrida de un algoritmo evolutivo multi-objetivo de toma de decisiones, para su aplicación en problemas de planificación del transporte urbano de mercaderías. Esta herramienta está destinada a resolver los problemas de planificación de una empresa de distribución de mercaderías que despacha pequeños volúmenes de alimentos frescos a cargas fraccionadas con periodicidad diaria. La firma posee una red de centros de distribución que abastecen a una gran cantidad de pequeñas empresas en Buenos Aires y sus alrededores. El operador de recombinación del algoritmo evolutivo utilizado ha sido diseñado específicamente para este problema. Su objetivo es incorporar una estrategia que tenga en cuenta restricciones como la cercanía temporal, la proximidad a la apertura y cierre de la ventana temporal y la conectividad, para mejorar su rendimiento en la fase de clasificación. La representación utilizada permite incorporar información específica sobre las instancias reales del problema y utiliza control adaptativo de parámetros en la etapa de calibración. El rendimiento del optimizador propuesto se probó con los resultados obtenidos por dos algoritmos evolutivos, NSGA II y SPEA 2, ampliamente utilizados en problemas de este tipo. Usamos hipervolumen como medida de convergencia y dispersión de frentes de Pareto. El análisis estadístico de los resultados obtenidos con los tres algoritmos se realizó mediante la prueba de suma de rangos de Wilcoxon, dicho análisis proporciona evidencia suficiente de que nuestro procedimiento proporciona buenos resultados.

The purpose of this article is to develop and study a decentralized strategy for Pareto optimization of an aggregate cost consisting of regularized risks. Each risk is modeled as the expectation of some loss function with unknown probability distribution, while the regularizers are assumed deterministic, but are not required to be differentiable or even continuous. The individual, regularized, cost functions are distributed across a strongly connected network of agents, and the Pareto optimal solution is sought by appealing to a multiagent diffusion strategy. To this end, the regularizers are smoothed by means of infimal convolution, and it is shown that the Pareto solution of the approximate smooth problem can be made arbitrarily close to the solution of the original nonsmooth problem. Performance bounds are established under conditions that are weaker than assumed before in the literature and, hence, applicable to a broader class of adaptation and learning problems.

The paper is devoted to the guaranteeing estimation of parameters in the uncertain stochastic nonlinear regression. The loss function is the conditional mean square of the estimation error given the available observations. The distribution of regression parameters is partially unknown, and the uncertainty is described by a subset of probability distributions with a known compact domain. The essential feature is the usage of some additional constraints describing the conformity of the uncertain distribution to the realized observation sample. The paper contains various examples of the conformity indices. The estimation task is formulated as the minimax optimization problem, which, in turn, is solved in terms of saddle points. The paper presents the characterization of both the optimal estimator and the set of least favorable distributions. The saddle points are found via the solution to a dual finite-dimensional optimization problem, which is simpler than the initial minimax problem. The paper proposes a numerical mesh procedure of the solution to the dual optimization problem. The interconnection between the least favorable distributions under the conformity constraint, and their Pareto efficiency in the sense of a vector criterion is also indicated. The influence of various conformity constraints on the estimation performance is demonstrated by the illustrative numerical examples.

In this paper, we focus on the bandlimited graph signal sampling problem. To sample graph signals, we need to find small-sized subset of nodes with the minimal optimal reconstruction error. We formulate this problem as a subset selection problem, and propose an efficient Pareto Optimization for Graph Signal Sampling (POGSS) algorithm. Since the evaluation of the objective function is very time-consuming, a novel acceleration algorithm is proposed in this paper as well, which accelerates the evaluation of any solution. Theoretical analysis shows that POGSS finds the desired solution in quadratic time while guaranteeing nearly the best known approximation bound. Empirical studies on both Erdos-Renyi graphs and Gaussian graphs demonstrate that our method outperforms the state-of-the-art greedy algorithms.