Two-objective Optimization Problem Research Articles

Accuracy degradation aware bit rate allocation for layer-wise uniform quantization of weights in neural network

Abstract Motivated by the fact that optimizing quantization error fails to minimize the accuracy degradation caused by the quantization of Neural Network (NN) weights, in this paper, we highlight the need for a comprehensive analysis of post-training quantization, covering average bit rate, accuracy degradation and SQNR. One such analysis, for the layer-wise uniform quantization and its application is NN weight compression is presented in this paper. We introduce an additional aspect of Uniform Quantizer (UQ) choice, and we allow the selection of one of two UQs (2-bit or 3-bit UQs) for each layer of NN. However, choosing a particular bit rate allocation to minimize average bit rate and accuracy degradation requires finding a trade-off solution. To solve the issue underpinning our motivation, for a post-training layer-wise uniform quantization framework with two UQs, we propose an algorithm for generating bit rate allocation patterns and corresponding pairs of average bit rate and accuracy degradation. We analyze the output of this algorithm and determine a solution of the elaborated two-objective optimization problem. To confirm the validity of the results we also apply the Pareto dominance method. This work can be considered a solid foundation for further analyses of more complex and deeper NNs.

Torque ripple reduction and increasing of torque per volume for hybrid electrical vehicle

Hybrid electrical vehicles (HEV) should be designed somehow torque is smooth. Because torque ripple not only reduces control precision but also increases elements vibration that causes acoustic noise, mechanical instability and early aging parts. Furthermore, torque per volume should be maximized and heat removal should be accomplished without torque weakening. It is proposed the volume and internal dimensions are determined due to the thermal considerations and maximize torque per volume. The mentioned application is neglected heat removal so volume is constant. Therefore, HEV is manufactured by two objective functions: either minimum fluctuations or maximum average torque. In this paper series hybrid excitation synchronous machine (SHESM) is utilized as HEV. Two-objective optimization problems are solved by MOEA/D, NSGA II, PESA II and SPEA II algorithms based on a two-dimensional (2-D) model. The performance indices of optimal structure are evaluated by 2-D and confirmed by numerical method.

Optimizing regression testing with AHP-TOPSIS metric system for effective technical debt evaluation

Regression testing is essential to ensure that the actual software product confirms the expected requirements following modification. However, it can be costly and time-consuming. To address this issue, various approaches have been proposed for selecting test cases that provide adequate coverage of the modified software. Nonetheless, problems related to omitting and/or rerunning unnecessary test cases continue to pose challenges, particularly with regard to technical debt (TD) resulting from code coverage shortcomings and/or overtesting. In the case of testing-related shortcomings, incurring TD may result in cost and time savings in the short run, but it can lead to future maintenance and testing expenses. Most prior studies have treated test case selection as a single-objective or two-objective optimization problem. This study introduces a multi-objective decision-making approach to quantify and evaluate TD in regression testing. The proposed approach combines the analytic-hierarchy-process (AHP) method and the technique of order preference by similarity to an ideal solution (TOPSIS) to select the most ideal test cases in terms of objective values defined by the test cost, code coverage, and test risk. This approach effectively manages the software regression testing problems. The AHP method was used to eliminate subjective bias when optimizing objective weights, while the TOPSIS method was employed to evaluate and select test-case alternatives based on TD. The effectiveness of this approach was compared to that of a specific multi-objective optimization method and a standard coverage methodology. Unlike other approaches, our proposed approach always accepts solutions based on balanced decisions by considering modifications and using risk analysis and testing costs against potential technical debt. The results demonstrate that our proposed approach reduces both TD and regression testing efforts.

Multiobjective Evolutionary Generative Adversarial Network Compression for Image Translation

Generative Adversarial Networks (GANs) have achieved remarkable success in image translation tasks. However, its prohibitive computational overhead has been a major hurdle for deployment on resource constrained platforms. Due to the training instability and the complicated network architecture, existing model acceleration techniques cannot appropriately handle the GAN compression problem. To cope with these difficulties, we propose a multi-objective evolutionary algorithm to compress GAN models in the context of image translation tasks, which is termed as MEGC. Particularly, the conflict between the computational cost of the GAN model and the quality of generated image is explicitly modeled as a two-objective optimization problem, and the evolved Pareto set is utilized to guide the sampling process during supernet training, which can in turn divert the focus of the supernet training to well-performing compact subnets. Besides, an evaluation-free strategy is introduced to facilitate exploration in the search space while incurring no extra computational cost. Based on the above design, the proposed MEGC eliminates the requirement of subnet searching in the post-processing procedure. Experiments on image translation tasks under paired and unparied settings demonstrate the effectiveness of the proposed MEGC on reducing the computational cost of GANs while improving the quality of generated images compared to those of the full models.

MEPSI: An MDL-Based Ensemble Pruning Approach with Structural Information

Ensemble pruning that combines a subset of individual learners generated in parallel to make predictions is an important topic in ensemble learning. Past decades have developed a lot of pruning algorithms that focus on the external behavior of learners on samples, which may lead to over-fitting. In this paper, we conjecture that the generalization performance of an ensemble is not only related to its external behavior on samples but also dependent on the internal structure of individual learners. We propose the general MEPSI approach based on Kolmogorov complexity and the Minimum Description Length (MDL) principle, which formulates the ensemble pruning task as the two-objective optimization problem that comprises the empirical error and structural information among individual learners. We also provide a concrete implementation of MEPSI on decision trees. The theoretical results provide generalization bounds for both the general MEPSI approach and tree-based implementation. The comparative experiments conducted on multiple real-world data sets demonstrate the effectiveness of our proposed method.

A nondominated sorting genetic model for co-clustering

Co-clustering aims to cluster the rows and columns of data simultaneously and can be often formulated as a two-objective optimization problem (one objective for rows and the other for columns) and the solution is a Pareto-optimal solution set in principle. Existing methods usually convert the co-clustering problem into a single-objective optimization problem by setting a hyper-parameter λ between the two objectives. However, finding a good value of λ is not easy because of its large parameter space; also, there may exist many equally good λs. In this paper, a nondominated sorting genetic model (NSGC) is proposed to tackle the co-clustering problem, totally bypassing the trade-off parameter λ and returning to the original two-objective problem. The core of our model is to group a row objective function and a column objective function and integrate them into a genetic algorithm as the fitness functions. After this reformulation, we follow a standard genetic algorithm procedure to iteratively find the Pareto-optimal solutions. Finally, to fish out a single best solution we further design a sorting criterion according to which the Pareto-optimal solution set can be totally ordered. Extensive experiments with 16 public datasets are conducted, and the results demonstrate the superiority of our approach.

Data Collection for Target Localization in Ocean Monitoring Radar-Communication Networks

With the ongoing changes in global climate, ocean data play a crucial role in understanding the complex variations in the earth system. These variations pose significant challenges to human efforts in addressing the changes. As a data hub for the satellite geodetic technique, unmanned aerial vehicles (UAVs) instill new vitality into ocean data collection due to their flexibility and mobility. At the same time, the dual-functional radar-communication (DFRC) system is considered a promising technology to empower ubiquitous communication and high-accuracy localization. In this paper, we explore a new fusion of UAV and DFRC to assist data acquisition in the ocean surveillance scenario. The floating buoys transmit uplink data transmission to the UAV with non-orthogonal multiple access (NOMA) and attempt to localize the target cooperatively. With the mobility of the UAV and power control at the buoys, the system throughput and the target localization performance can be improved simultaneously. To balance the communication and sensing performance, a two-objective optimization problem is formulated by jointly optimizing the UAV’s location and buoy’s transmit power to maximize the system throughput and minimize the attainable localization mean-square error. We propose a joint communication and radar-sensing many-objective optimization (CRMOP) algorithm to meliorate the communication and radar-sensing performance simultaneously. Simulation results demonstrate that compared with the baseline, the proposed algorithm achieves superior performance in balancing the system throughput and target localization.

Prediction after a Horizon of Predictability: Nonpredictable Points and Partial Multistep Prediction for Chaotic Time Series

This paper introduces several novel strategies for multi-step-ahead prediction of chaotic time series. Introducing a concept of “generalized z-vectors” (vectors of nonsuccessive time series observations) makes it possible to generate sets of possible prediction values for each point we are trying to predict. Through examining these sets, unified predictions are calculated, which are in turn used as a basis for predicting subsequent points. The key difference between the strategy presented in this paper and its conventional counterparts is the concept of “nonpredictable” points (points which the algorithm categorized as “incalculable” and excluded from the calculations altogether). The results obtained for the benchmark and real-world time series indicate that while typically the number of nonpredictable points tends to grow exponentially with the number of steps ahead to be predicted, the average error for predicted points remains small and nearly constant. Thus, we redefine the problem of multi-step-ahead prediction as a two-objective optimization problem: on one hand, we aim to minimize the number of nonpredictable points and the average error among the predictable ones. The resulting strategy demonstrates accurate results for both benchmark and real-world time series, with the number of predicted steps exceeding that of any other published algorithm.

DESCO: Decomposition-Based Co-Design to Improve Fault Tolerance of Security-Critical Tasks in Cyber Physical Systems

Confidentiality-Specific Faults (CSFs) will put cyber physical systems in threat, since they can result in corrupted information or even retrieve the cryptographic key of security-critical applications. In this paper, we will look into fault-tolerant co-design optimization for security-critical cyber physical systems with resource constraints, such that the encryption/decryption of confidential messages are protected against transient CSF faults. We consider imperfect fault detection mechanisms to identify transient CSF faults happened on confidentiality protection, and utilize duplication code to recovery from such faults. We utilize FPGA to accelerate the executions of security tasks, reducing the overheads of fault-tolerant implementations. The system-level design problem is formulated as a two-objective optimization problem, i.e., to minimize the average reliability degradation of the fault tolerant assignments and to minimize the balanced degree of the reliability degradation, subject to available FPGA budget, deadline, and application execution constraints. Since finding Pareto-optimal solutions is NP-hard, we propose an improved multi-objective optimization algorithm, called DEcomposition-based Security Co-design Optimization (DESCO), to search for Pareto-optimal solutions of fault-tolerant assignments. Experimental results demonstrate that DESCO is effective and can outperform other candidates, proving that our approach is promising in dealing with system-level optimization problem for security-critical applications on cyber physical systems.

A Collaborative Transit Signal Priority Method Considering Gaming among Traffic Participants

How to realize the game equilibrium between bus and nontransit vehicle is a hot topic in the field of transit signal priority (TSP). To this end, a collaborative transit signal priority (Co-TSP) method is proposed. The core of Co-TSP is a two-objective optimization problem which takes the expected delays of buses and the average delays of nontransit vehicles as the objectives. Different from previous studies, Co-TSP uses game theory to realize collaborative optimization, instead of transforming the problem into a single objective optimization problem by weighting. A finite state machine-based algorithm is developed to estimate the average delays of nontransit vehicles. The stochasticity of bus arrival time is also considered in the estimation of bus delays to improve the robustness. Candidate timing plans obtained by the nondominated sorting genetic algorithm (NSGA) are divided into three priority levels based on the delays of buses. The final timing plans can be picked intuitively from the candidates by rules representing expert knowledge and demands to control the priority level. Co-TSP guarantees theoretically by preliminary screening that the expected delays of bus after optimization must be no higher than that before optimization. Simulation experiments are conducted in Shanghai, China, to verify the performance. Results show that Co-TSP reduces the delays of buses by 27.7%∼41.0% and still performs well under low and high congestion levels, while the conventional TSP (CTSP) fails in some cases. Priority control proves to be effective at last. The research provides a new idea for the benefit allocation among participants at intersections.

Bi-indicator driven surrogate-assisted multi-objective evolutionary algorithms for computationally expensive problems

This paper presents a bi-indicator-based surrogate-assisted evolutionary algorithm (BISAEA) for multi-objective optimization problems (MOPs) with computationally expensive objectives. In BISAEA, a Pareto-based bi-indictor strategy is proposed based on convergence and diversity indicators, where a nondominated sorting approach is adopted to carry out two-objective optimization (convergence and diversity indicators) problems. The radius-based function (RBF) models are used to approximate the objective values. In addition, the proposed algorithm adopts a one-by-one selection strategy to obtain promising samples from new samples for evaluating the true objectives by their angles and Pareto dominance relationship with real non-dominated solutions to improve the diversity. After the comparison with four state-of-the-art surrogate-assisted evolutionary algorithms and three evolutionary algorithms on 76 widely used benchmark problems, BISAEA shows high efficiency and a good balance between convergence and diversity. Finally, BISAEA is applied to the multidisciplinary optimization of blend-wing-body underwater gliders with 30 decision variables and three objectives, and the results demonstrate that BISAEA has superior performance on computationally expensive engineering problems.

Optimization of Selective Laser Sintering/Melting Operations by Using a Virus-Evolutionary Genetic Algorithm

This work presents the multi-objective optimization results of three experimental cases involving the laser sintering/melting operation and obtained by a virus evolutionary genetic algorithm. From these three experimental cases, the first one is formulated as a single-objective optimization problem aimed at maximizing the density of Ti6Al4V specimens, with layer thickness, linear energy density, hatching space and scanning strategy as the independent process parameters. The second one refers to the formulation of a two-objective optimization problem aimed at maximizing both the hardness and tensile strength of Ti6Al4V samples, with laser power, scanning speed, hatch spacing, scan pattern angle and heat treatment temperature as the independent process parameters. Finally, the third case deals with the formulation of a three-objective optimization problem aimed at minimizing mean surface roughness, while maximizing the density and hardness of laser-melted L316 stainless steel powder. The results obtained by the proposed algorithm are statistically compared to those obtained by the Greywolf (GWO), Multi-verse (MVO), Antlion (ALO), and dragonfly (DA) algorithms. Algorithm-specific parameters for all the algorithms including those of the virus-evolutionary genetic algorithm were examined by performing systematic response surface experiments to find the beneficial settings and perform comparisons under equal terms. The results have shown that the virus-evolutionary genetic algorithm is superior to the heuristics that were tested, at least on the basis of evaluating regression models as fitness functions.

Balanced k-means revisited

<abstract><p>The $ k $-means algorithm aims at minimizing the variance within clusters without considering the balance of cluster sizes. Balanced $ k $-means defines the partition as a pairing problem that enforces the cluster sizes to be strictly balanced, but the resulting algorithm is impractically slow $ \mathcal{O}(n^3) $. Regularized $ k $-means addresses the problem using a regularization term including a balance parameter. It works reasonably well when the balance of the cluster sizes is a mandatory requirement but does not generalize well for soft balance requirements. In this paper, we revisit the $ k $-means algorithm as a two-objective optimization problem with two goals contradicting each other: to minimize the variance within clusters and to minimize the difference in cluster sizes. The proposed algorithm implements a balance-driven variant of $ k $-means which initially only focuses on minimizing the variance but adds more weight to the balance constraint in each iteration. The resulting balance degree is not determined by a control parameter that has to be tuned, but by the point of termination which can be precisely specified by a balance criterion.</p></abstract>

A fast identification method of train axle crack parameters based on semi-inverse Kriging method

On-line monitoring of crack parameters can prevent axle breaking accidents and potentially disastrous consequences, while satisfying the requirement of the damage tolerance, and improving the economy in operation. A fast and reliable crack parameters identification method is required for on-line monitoring of a large number of axles. Based on the response surface characteristics of crack position and depth at two sensors, a new method is proposed adopting two Kriging surrogate models constructed by the 2xRev values of vibration signals from two measurement points. Firstly, by exchanging part of inputs and outputs, a semi-inverse Kriging model is constructed to obtain a crack equivalent line. Then, the crack equivalent line is projected on another Kriging model as the convergence path, which is the key step transforming a two-objective optimization problem into a one-dimensional searching problem. Finally, an improved dichotomy method is used to obtain the result, by which the total number of steps and the calculation time is controlled on the premise of ensuring accuracy. Different from current multi-objective optimization algorithms searching with parallel computing, the proposed method reduces the number of parameters and searching model space to be one, belonging to serial computing. The comparison to other methods shows excellent features in computing speed and stability, and the experiment was implemented on a double-disk rotor system with similar structure to a wheelset, validating the proposed methodology.

A sustainable framework for multi-microgrids energy management in automated distribution network by considering smart homes and high penetration of renewable energy resources

This paper presents a new framework for the scheduling of microgrids and distribution feeder reconfiguration (DFR), taking into consideration the uncertainties due to the load demand, market price, and renewable power generation. The model is implemented on the modified IEEE 118-bus test system, including microgrids and smart homes. The problem has been formulated as a two-stage model, which at the first stage, the day-ahead self-scheduling of each microgrid is carried out as a two-objective optimization problem. The two objectives include the minimization of the total operating cost and maximization of the consumer's comfort index. Then, the solution, obtained from the first stage is delivered to the distribution system operator (DSO). Then, at the second stage, the DSO determines the optimal configuration of the system with the aim of minimizing operating costs of the main grid and the penalty of deviating from microgrid scheduling. Note that the penalty is due to the difference in power exchange requested by the microgrids from the power exchange finalized by the DSO. The presented two-stage optimization problem is modeled in a mixed-integer linear programing (MILP) framework with four case studies, and solved in GAMS by using the GURUBI solver. The simulation results show that in the cases the DSO is able to reconfigure the system, the deviation from the optimal scheduling of microgrids would be considerably lower than the cases with fixed system configuration. • Proposing a two-stage optimization framework for scheduling of microgrids and DFR. • Considering smart homes and traditional loads in the model. • Two-objective modeling of microgrids' scheduling problem by the fuzzy method. • Solving the DFR problem with regard to the optimal scheduling of microgrids. • Investigating the impact of different objective functions on smart homes' scheduling.

A framework for calibration of self-piercing riveting process simulation model

This paper presents a framework that integrates machine learning and global sensitivity analysis to calibrate process simulation model of self-piercing rivet (SPR). In the present framework, surrogate models are trained to represent the intrinsic numerical relationship between selected model parameters (e.g., material properties, interface frictions, and clamping force) and cross-section dimensions of SPR joint obtained from simulation. Under the assistance of surrogate models, a global sensitivity analysis is performed to identify critical parameters that have significant effects on SPR joining process. Then, new surrogate models are trained to present the sensitive parameters and the cross- section dimensions obtained from process simulation. The parameter calibration of the simulation model is described as a two-objective optimization problem to minimize errors of key cross-section dimensions between simulation and experiment. Combined the newly trained surrogate models with genetic algorithm, the model parameters are calibrated efficiently. A case study of simultaneous calibration of four SPR process simulation models is used to illustrate the proposed framework and examine the effectiveness of the proposed framework. A good consistency is achieved between calibrated models and experiments.

Parameter optimisation of sliding window algorithm based on ensemble multi-objective evolutionary computation

The parameters of sliding window algorithm are difficult to determine. Therefore, a sliding window-based method for parameter optimisation of data stream trend anomaly detection algorithm is proposed in this study. This method regards the data stream anomaly detection as a two-objective optimisation problem. Three optimisation algorithms and ensemble strategies were used to obtain the optimal parameter settings of the algorithm. With this strategy, it is no longer difficult to determine the parameters of the data stream trend anomaly detection algorithm based on the sliding window. Through verification of multiple real parameter data in Tarim Oilfield, it could be known that this method could realise the optimal parameter settings, which provides a reference for the parameter setting of the data stream trend anomaly detection algorithm based on sliding window.

Multiobjective optimal design of reinforced concrete frames using two metaheuristic algorithms

Genetic algorithm (GA) and differential evolution (DE) are metaheuristic algorithms that have shown a favorable performance in the optimization of complex problems. In recent years, only GA has been widely used for single-objective optimal design of reinforced concrete (RC) structures; however, it has been applied for multiobjective optimization of steel structures. In this article, the total structural cost and the roof displacement are considered as objective functions for the optimal design of the RC frames. Using the weighted sum method (WSM) approach, the two-objective optimization problem is converted to a single-objective optimization problem. The size of the beams and columns are considered as design variables, and the design requirements of the ACI-318 are employed as constraints. Five numerical models are studied to test the efficiency of the GA and DE algorithms. Pareto front curves are obtained for the building models using both algorithms. The detailed results show the accuracy and convergence speed of the algorithms.

A novel noise reduction method for natural gas pipeline defect detection signals

Since pipeline defect detection signals are often contaminated by noise, the accuracy of defect identification is reduced if inappropriate noise reduction methods are used. Therefore, the noise reduction of pipeline detection signals is critical for pipeline defect detection preprocessing technology. A denoising method based on differential-based empirical mode decomposition (DEMD) and extremum field mean mode decomposition (EMMD) is proposed in this paper and named derivative extremum field mean mode decomposition (DEMMD). The idea of DEMMD is to replace the EMD part of DEMD with EMMD. To simultaneously reduce the interference of noise and retain useful signal features, intrinsic mode function (IMF) reconstruction is viewed as a two-objective optimization problem. The objective function is constructed by a similarity measure based on a probability density function and a complexity measure based on fuzzy entropy. Monte Carlo simulations are performed to simulate the possible IMF component combinations. Then, based on the idea of a Pareto optimal solution, the IMF components that satisfy the optimization objective are selected to construct the denoised signal. Synthetic signal and field test data are used to verify the proposed method. The denoising results of the synthetic signal show that the method can decompose the main characteristic modes of defect signals and effectively recover the original signal. The results of a case study show that the denoised signal obtained by this method can not only suppress noise but also retain the defect details during reconstruction. The signal-to-noise ratio (SNR) and root mean square error (RMSE) are used to measure and compare the performance of the proposed method. The results show that the SNR of the proposed method is the highest, which is 29.1207, and the RSME is the lowest, which is 0.0045. Compared with other traditional denoised methods, it outperforms and suits pipeline detection signal denoising.

Simultaneous Wireless Information and Power Transfer in a Network of On-body and Implantable Sensors With Temperature Constraint and Intelligent Channel Prediction

The wireless body area network (WBAN) is one of the applications of the Internet of things (IoT) for healthcare, which monitors human physiological parameters. In this paper, a two-objective optimization problem is designed to maximize the sum-throughput and wireless transferred energy simultaneously. The designed one-tier network includes body surface sensors, an implantable sensor, and one coordinator. All of these sensors can harvest energy from the body and radio frequency (RF) signals. A temperature constraint is considered for the implanted sensor due to the sensitivity of internal tissues. Each sensor transmits physiological data to the coordinator in the uplink according to the scheduled time slots obtained by solving the optimization problem. At the beginning of each frame in the downlink, the coordinator transmits a pilot signal to transfer wireless energy and for channel estimation at the sensors. We have used a Recurrent Neural Network (RNN) architecture to predict one time step ahead of the channel. Then by interpolation, the channel gains of all time slots of a frame are estimated and the time scheduling of the sensor access to the channel is improved. The simulation results show that the objective function and time scheduling are improved by the proposed algorithms.