Set Of Pareto-optimal Solutions Research Articles

Multi-objective optimization of phase change cooling battery module based on optimal support vector machineoptimal support Vector Machine

An optimization model based on Particle Swarm Optimization-Support Vector Machine(PSO-SVM) and improved NSGA-II algorithm is established in this paper to balance the heat dissipation performance and lightweight of battery. First, the data set is obtained by orthogonal experiments, and then the PSO-SVM model for predicting the battery heat dissipation performance (maximum temperature and maximum temperature difference) is acquired by optimizing the parameters of the support vector machine through particle swarm optimization. With the goal of improving the battery heat dissipation performance and reducing the system mass, the improved NSGA-II algorithm is used for multi-objective optimization to obtain the Pareto solution set. Results show that the R2 (goodness of fit) of the maximum temperature and maximum temperature difference prediction models are 0.99478 and 0.9787, respectively, which verifies the accuracy of the PSO-SVM model. The maximum temperature, the maximum temperature difference, and the mass of the phase change material are in conflict. The temperature rise and temperature difference of the battery can be effectively controlled by sacrificing the mass of the phase change material. Four optimal solutions were selected by using LINMAP and TOPSIS. Compared with the initial model, the mass of phase change materials was reduced by 34.5 %, 29.5 %, 55.3 %, and 2.5 %. On the premise of meeting the requirements of thermal management performance, the entire system becomes lighter. Based on the four optimal solutions, the decision maker can choose from the Pareto optimal solution set according to different requirements for heat dissipation performance and lightweight.

Pareto optimal solution set strategy based on multiobjective optimization for the clinching tools

Pareto optimal solution set strategy based on multiobjective optimization for the clinching tools

Navigating Uncertainty in Weapon System-of-Systems Planning: A Hybrid Multiobjective Network-Based Optimization and Fuzzy Set Approach

The evaluation of the capability of network-based systems of systems has replaced the simple method that considers return on investment, becoming a new paradigm for planning national defence capabilities. However, the dual uncertainty of the key system attributes of scenes and weapons has brought great challenges for decision-making. Based on this, we developed a multiobjective optimization model with multiple stages and scenarios under uncertainty to determine plans. In this study, we consider planning risk and planning cost as the two objectives. To solve this problem, we propose a hybrid solution for a network-based optimization method integrated with fuzzy set theory. The network-based optimization method combines the NSGA-II-DE and complex network theory. We use the characteristics of the network to evaluate the capabilities of the WSoS, and the NSGA-II-DE is used to generate a development plan and finally output a set of Pareto optimal solutions. We use fuzzy sets to determine the fuzzy membership of each plan on the Pareto front and determine a satisfactory solution. Finally, we conduct simulation experiments to verify the rationality of the methods proposed in this article. The results can provide a set of efficient solutions for military planners, helping generate a variety of planning solutions and trade-offs according to their preferences.Graphical

Optimal design of a Low-Cost SAE JA2954 compliant WPT system using NSGA-II

Wireless Power Transfer (WPT) systems for electric vehicle charging are one of the most promising methods that, given the advantages they bring, will help the desired deployment of electric vehicles. This paper presents a mathematical optimisation method applied to the design of an 11 kW S-S system that complies with the SAE J2954 standard. A proposal is made to calculate the electrical parameters of the circuit based on equations that are compared with the results obtained by simulation with finite elements and experimental measurements, achieving very tight results with a reduced computational time. The NSGA-II multi-objective genetic algorithm is then applied together with the secant method, defining three different scenarios: minimisation of the primary copper volume, minimisation of the secondary copper volume and a compromise solution optimising the total primary and secondary copper volume. The result is a set of Pareto optimal solutions, from which the one that meets the standard can be extracted that suits the designer’s needs.

Study of a hull form optimization system based on a Gaussian process regression algorithm and an adaptive sampling strategy, Part II: Multi-objective optimization

Ships have a wide variety of performance specifications and experience complex navigation conditions. Thus, an efficient numerical optimization system for general hull forms must be able to deal with multi-objective optimization problems. Based on a Gaussian process regression (GPR) algorithm and an adaptive sampling strategy, the authors have developed a single-objective optimization system, SBO-MSE + LCB, which is more efficient than the conventional simulation-based design (SBD) optimization system. However, the application of this system to hull form multi-objective optimization problems presents problems such as excessive new samplings, insufficient exploration of new sample points, and unsuitable convergence criteria. To solve the above problems, we first propose an adaptive sampling strategy based on the idea of spatial clustering. The strategy not only effectively controls the number of sampling numbers at each iteration in the SBO-MSE + LCB optimization system but also enables new sample points to achieve the multi-objective efficient exploration of optimal solution sets for optimization. Then, from the perspective of the convergence and diversity of Pareto optimal solution sets, we design adaptive sampling convergence criteria suitable for multi-objective optimization problems. Based on this, we enable the SBO-MSE + LCB optimization system to solve multi-objective optimization problems and verify its applicability with several cases for which the multi-objective mathematical optimization is performed. Finally, we use the SBO-MSE + LCB multi-objective optimization system and the SBD optimization system to optimize the total resistance coefficient of a deep-sea aquaculture vessel at the scantling and ballast drafts. The results show that the optimization efficiency of the SBO-MSE + LCB multi-objective optimization system is improved by 33.33% from the SBD optimization system for similar optimization performance, proving its advantage in efficiency in practical applications.

Selection of Optimal Well Trajectory Using Multi-Objective Genetic Algorithm and TOPSIS Method

This study presents a novel approach for optimizing well paths in extended reach drilling (ERD) wells. Different trajectories can be used for ERD wells, each with its pros and cons. Previous research overlooked certain objective functions in single-objective optimization and lacked an autonomous method for selecting the best solution from Pareto optimal solutions in multi-objective optimizations. Furthermore, they lacked comparing different profiles in well design. Risk assessment and operational factors, which greatly influence optimization and drilling success, were insufficiently considered. This study utilized the multi-objective genetic algorithm (MOGA) and the technique for order preference by similarity to an ideal solution (TOPSIS) method to select the optimal well path based on torque, wellbore length, risk (e.g., keyseat), and required tools. First, all possible trajectories were determined, and MOGA identified the optimal path with minimal torque and length. The fuzzy decision-making method automatically selected the best solution from the Pareto optimal solution set. The associated risks and required tools are evaluated for each trajectory. Finally, the TOPSIS method selected the optimal trajectory based on torque, length, risks, and required tools. The case study demonstrated that the undersection path was the most advantageous trajectory for ERD wells, with a 60% closeness to the ideal state. The multiple build trajectory achieved 57% closeness, while the build and hold and double build paths had lower closeness values (43 and 28%, respectively). Consequently, it can be inferred that in the context of ERD wells, it is preferable to carry out the deviation process at deeper depths.

Optimization of CNC Milling Parameters Based on Tool Life and Process Carbon Emission Prediction Models

Aiming at the problems of short tool life and high carbon emission in the process of CNC milling, a multi-objective optimization method of process parameters based on the BP neural network and NSGA-II algorithm is proposed. Based on the data sets generated by CNC milling under different process parameters, with tool life and process carbon emissions as outputs and different process parameter combinations as inputs, a BP neural network-based tool life and process carbon emissions prediction model is constructed. Taking the maximum tool life and minimum process carbon emission as the optimization goals, the NSGA-II process parameter multi-objective optimization main model is constructed. The model is then used as the objective function of the main model and optimized to obtain the Pareto optimal solution set. The optimal solution decision is made on the Pareto optimal solution set using the Topsis method, and the optimal process parameter combination is obtained. The optimization results show that the method can accurately predict the tool life and process carbon emission of CNC milling. It can also effectively optimize the process parameters, which provides a new method for the low-carbon optimization of CNC milling parameters.

Efficient Deep Learning Models for Privacy-Preserving People Counting on Low-Resolution Infrared Arrays

Ultra-low-resolution Infrared (IR) array sensors offer a low-cost, energy-efficient, and privacy-preserving solution for people counting, with applications such as occupancy monitoring. Previous work has shown that Deep Learning (DL) can yield superior performance on this task. However, the literature was missing an extensive comparative analysis of various efficient DL architectures for IR array-based people counting, that considers not only their accuracy, but also the cost of deploying them on memory- and energy-constrained Internet of Things (IoT) edge nodes. In this work, we address this need by comparing 6 different DL architectures on a novel dataset composed of IR images collected from a commercial 8x8 array, which we made openly available. With a wide architectural exploration of each model type, we obtain a rich set of Pareto-optimal solutions, spanning cross-validated balanced accuracy scores in the 55.70-82.70% range. When deployed on a commercial Microcontroller (MCU) by STMicroelectronics, the STM32L4A6ZG, these models occupy 0.41-9.28kB of memory, and require 1.10-7.74ms per inference, while consuming 17.18-120.43 $\mu$J of energy. Our models are significantly more accurate than a previous deterministic method (up to +39.9%), while being up to 3.53x faster and more energy efficient. Further, our models' accuracy is comparable to state-of-the-art DL solutions on similar resolution sensors, despite a much lower complexity. All our models enable continuous, real-time inference on a MCU-based IoT node, with years of autonomous operation without battery recharging.

Multi-Objective Parameter Optimization of Submersible Well Pumps Based on RBF Neural Network and Particle Swarm Optimization

In order to improve the hydraulic performance of a submersible well pump, steady and transient simulations were carried out based on ANSYS CFX software. The head and efficiency of the submersible well pump under standard operating conditions were taken as the optimization objectives, and the impeller outlet placement angle, outlet width, and vane wrap angle were selected as the optimization variables using the Plackett-Burman experimental design method. The RBF neural network training samples were constructed using the uniform experimental design method to build a hydraulic performance prediction model for the submersible well pump, and a multi-objective particle swarm optimization was used to solve the model and obtain the Pareto optimal solution set. Using the head and efficiency of the initial model as the boundary, the Pareto optimal solution and the corresponding structural parameters are sought. After the optimization, the head of the individual with the better head is increased by about 2.65 m, and the efficiency of the individual with the better efficiency is increased by about 2.3 percentage points compared with that of the initial model. The pressure gradient in the impeller flow channel is more obvious, the work capacity is significantly improved, the vortex area of the spatial guide vane is smaller, the flow line is more regular, and the pressure pulsation amplitude at the inlet and outlet of the impeller and the spatial guide vane is significantly reduced.

Plowing operation: labor productivity and specific operating costs. Part 1. Multifactor simulation of plowing operation

One of the most important problems in grain production in the Republic of Belarus is increasing labor productivity, which is 4–5 times less than labor productivity in the EU countries. A great influence on labor productivity and specific operating costs is exerted by energyand material-intensive operations, such as plowing and harvesting. The main patterns of the plowing operation, which is a complex technical system, is connected with the use of a large volume of agrotechnological, technical, operational, resource and economic information (operation duration, working length of the harrow, physical and mechanical properties of soil, depth of treatment, permissible interval of the unit speed, fuel and energy, engine power and traction characteristics, width of the unit, economic indicators, etc.) are considered. Currently, as a result of introduction of computer mathematics systems, there are effective methods available for studying complex technical systems, allowing for multi-factor modeling and multi-criteria optimization of the production processes and formation of a set of machines by system analysis. A prerequisite for a complete and comprehensive description of the functioning of a complex technical system is the presence of conflicting optimization parameters, as well as a complete set of independent control factors significantly affecting these parameters. A distinctive feature of the proposed method is to determine not one optimal solution, but a set of Paretooptimal solutions, giving the producer new opportunities of choice when organizing the production processes, increasing the efficiency of plowing operation and, consequently, the profitability of grain production in general. Therefore, increasing productivity at permissible specific operating costs through the formation of a rational set of machines and modes of its operation under specific conditions of production is an important scientific and engineering task. A mathematical illustration of the method is provided for natural-production conditions of the Republic of Belarus.

Dual objective bounded abstaining model to control performance for safety-critical applications

Abstaining models have been widely used in safety-critical fields to avoid uncertain classification and reduce misclassification costs. Previous abstaining models have two main disadvantages. First, the costs of classification and rejection need to be set. Unfortunately, it is difficult to obtain or estimate costs in practical applications. When costs change, the trained model will be no longer applicable. Second, a single indicator, such as the error rate or AUC, is optimized, which has poor robustness for different application requirements. To solve such problems, a dual objective bounded abstaining (DOBA) model is proposed. DOBA optimizes the binary confusion matrix with rejection by minimizing the false positive and negative rates under class-specific reject constraints. The DOBA model is solved using an evolutionary multi-objective optimization algorithm. The requirement-oriented abstaining classifier can be selected from a set of Pareto-optimal solutions. Extensive experiments prove the effectiveness and superiority of DOBA compared to other abstaining models.

Multi-objective optimal dispatch strategy for power systems with Spatio-temporal distribution of air pollutants

Accurate and effective pollutant emission control models are key in mitigating the environmental impact of energy supply systems. This paper proposes a novel high-dimensional multi-objective optimal dispatching strategy for power systems considering the spatial and temporal distribution of multiple pollutants. Firstly, a spatial and temporal distribution model of pollutants in thermal power plants is constructed, which is truly applicable to power dispatch. For modeling the pollution situation, the daily changes in the atmospheric boundary layer are taken into account, fully reflecting the pollutant dispersion characteristics of thermal power plants and improving the result accuracy. Next, a high-dimensional multi-objective optimization model is developed to simultaneously reduce the cost of power generation, carbon emission and the impact air quality from VOCs (volatile organic compounds), SO2 and NO2. This model combines the spatial and temporal distribution characteristics of various pollutants and environmental capacity. Finally, a representative high-dimensional multi-objective optimization algorithm is employed to obtain an approximate Pareto-optimal solution set. And a multi-objective decision method is proposed to filter the compromise solution. The results show that the APCs of VOCs, SO2 and NO2 are reduced by 27.5%, 10.13% and 23.16%, respectively, in the pollution day model. On non-pollution days, the proposed scheduling method not only effectively improves air quality, but also achieves cost savings of $1276.59 and reduces CO2 emission by 0.168 × 104t compared to the emission limitation method. The proposed scheduling method can not only effectively improve air quality, but also make corresponding adjustments according to the spatial and temporal changes of environmental capacity, which can truly realize economic and environmental-friendly power scheduling.

Multi-objective medical supplies distribution open vehicle routing problem with fairness and timeliness under major public health emergencies

Fair and timely delivery of supplies plays a critical role under major public health emergencies. In this paper, aiming at fairness and timeliness, an optimization model of open vehicle routing problem for medical supplies distribution is established considering the urgency of the demand. We adopt a differential evolutionary algorithm with fast non-dominated solution sorting to solve the proposed model, obtaining an approximate Pareto optimal solution set. Through the comparison of algorithms, the results showed that the differential evolutionary algorithm with non-dominated sorting is superior with a shorter runtime and more diverse solutions, while the epsilon constraint method has more accurate solutions. In the case verification, the quality of the solutions of both algorithms was within the acceptable range, but the runtime of the epsilon constraint method was too long to be applicable. The results can provide theoretical suggestions and practical guidance for decision-makers in emergency supplies distribution.

Combined Interval Prediction Algorithm Based on Optimal Relevancy, Redundancy and Synergy

Traditional point prediction approaches can not reflect the uncertainty, which brings greater risks to decision-makers. To fill this gap, this paper extends a feature selection strategy that relies solely on correlation and redundant feature judgment, proposes a novel combined interval prediction algorithm, 3-Mcip (Combined Interval Prediction Based on Maximize Relevancy, Minimize Redundancy and Maximize Synergy) system, and solves the tradeoff between prediction accuracy and interval width. This system first designs a hybrid feature selection strategy to optimally select candidate variables and reduce model input redundancy. Secondly, the structure of the four ANN models is improved to accommodate the results of feature selection, and an optimization mechanism is introduced to search for the Pareto optimal solution set. In order to measure the comprehensive performance of the 3-Mcip system, hourly power load data and related candidate variables from Pittsburgh and Washington, D.C are considered. The numerical results show that the 3-Mcip system has coverage rates of 53.3333, 90.1667, and 99.4479 for Site 1 at different levels of interval width coefficients, which not only achieves perfect prediction of power load but also analyzes uncertainty. It is also helpful for power system managers to better capture the fluctuation range of future load and improve the flexibility of smart grid dispatching.

Design of an Adiabatic Calorimeter for Cementitious Mixtures by Multi-Objective Optimization

This study aims to design an adiabatic calorimeter for cementitious mixtures using NSGA-II and the Pareto optimal solution set. In this multi-objective optimization, the controller effort and heating time are selected as objective functions. Likewise, the volume and the material to be heated were chosen as decision variables. The optimal solution was selected using Nash bargaining methods. After implementing the optimal solution, the Wilcoxon test was applied to statistically validate the developed work. The measurements performed were compared with other research and it was observed an improvement in the measurement of heat of hydration in cementitious mixtures. Also, it was noted a decrease in the error in the temperature measurement.

Mathematical Multiobjective Optimization Model for Trade-Offs in Small-Scale Construction Projects

As construction projects become more complex and challenging to execute, project managers need to develop work schedules that consider as many objectives as are critical to project success. A work schedule designed to optimize all these objectives is likely to enhance project performance. However, achieving a balance among these objectives is difficult because they frequently conflict with each other. Many optimization models have been developed over the years that can factor in different objectives. Although previous optimization studies have contributed to the body of knowledge by individually adding one or two objectives to the classical time–cost trade-off (TCT) problem, none of these studies simultaneously optimized more than three or four objectives at a time. Clearly, there is a need for a multiobjective optimization model to generate work schedules that increase the likelihood of achieving as many project objectives as necessary. This study was motivated by the need to fill this research gap. The objective of this study was to develop a mathematical multiobjective optimization model for the time–cost–quality–schedule flexibility-resource fluctuation trade-off problem in small-scale construction projects. The proposed model is novel because it (1) considers five important objectives of construction project scheduling at the same time, (2) quantifies all objectives to provide an accurate reflection of construction site conditions, and (3) objectively determines the optimal compromise solution using a distance-based method rather than subjectively from a set of Pareto-optimal solutions. The applicability of the proposed model is demonstrated with an illustrative example. The key results of this study are as follows: (1) the optimal solution obtained depends on the project manager’s priorities relative to the objectives; and (2) in optimization problems with more than two objectives, considering the objectives one at a time may result in misleading solutions, because the effects of the other objectives are ignored in this optimization. Consequently, multiple objectives must be considered simultaneously rather than one at a time. The proposed model is expected to provide project managers with a work schedule that balances five or more objectives, increasing the chances of successful project performance.

The Hot Strip Mill Scheduling Problem With Uncertainty: Robust Optimization Models and Solution Approaches.

In this article, we focus on a biobjective hot strip mill (HSM) scheduling problem arising in the steel industry. Besides the conventional objective regarding penalty costs, we have also considered minimizing the total starting times of rolling operations in order to reduce the energy consumption for slab reheating. The problem is complicated by the inevitable uncertainty in rolling processing times, which means deterministic scheduling models will be ineffective. To obtain robust production schedules with satisfactory performance under all possible conditions, we apply the robust optimization (RO) approach to model and solve the scheduling problem. First, an RO model and an equivalent mixed-integer linear programming model are constructed to describe the HSM scheduling problem with uncertainty. Then, we devise an improved Benders' decomposition algorithm to solve the RO model and obtain exactly optimal solutions. Next, for coping with large-sized instances, a multiobjective particle swarm optimization algorithm with an embedded local search strategy is proposed to handle the biobjective scheduling problem and find the set of Pareto-optimal solutions. Finally, we conduct extensive computational tests to verify the proposed algorithms. Results show that the exact algorithm is effective for relatively small instances and the metaheuristic algorithm can achieve satisfactory solution quality for both small- and large-sized instances of the problem.

MultiOptForest: An interactive multi-objective optimization tool for forest planning and scenario analysis

MultiOptForest is an open-source software designed to simplify building and solving multi-objective optimization problems for forest planning. It aims to find the optimal portfolio of management regimes that balance the objectives regarding multiple forest ecosystem services and biodiversity. The software flexibly imports data, allowing for the use of a variety of forest simulator outputs. The user provides preference information through a user-friendly graphical interface, where the range of possible values for each objective is provided. MultiOptForest solves the optimization problem producing a set of Pareto optimal solutions, i.e., solutions where none of the objectives can be improved without compromising others. MultiOptForest is versatile enough to design a Pareto optimal forest plan for a small holding to assess management and the trade-off between multiple policy objectives impacting the development of forests across regions and countries.

Mass transfer mechanism and relationship of gas–liquid annular flow in a microfluidic cross-junction device

Mass transfer performance of gas–liquid two-phase flow at microscale is the basis of application of microreactor in gas–liquid reaction systems. At present, few researches on the mass transfer property of annular flow have been reported. Therefore, the mass transfer mechanism and relationship of gas–liquid annular flow in a microfluidic cross-junction device are studied in the present study. We find that the main factors, i.e., flow pattern, liquid film thickness, liquid hydraulic retention time, phase interface fluctuation, and gas flow vorticity, which influence the flow mass transfer property, are directly affected both by gas and liquid flow velocities. But the influences of gas and liquid velocities on different mass transfer influencing factors are different. Thereout, the fitting relationships between gas and liquid flow velocities and mass transfer influencing factors are established. By comparing the results from calculations using fitting equations and simulations, it shows that the fitting equations have relatively high degrees of accuracy. Finally, the Pareto front, namely the Pareto optimal solution set, of gas and liquid velocity conditions for the best flow mass transfer property is obtained using the method of multi-objective particle swarm optimization. It is proved that the mass transfer property of the gas–liquid two-phase flow can be obviously enhanced under the guidance of the obtained Pareto optimal solution set through experimental verification.

An exact approach for finding bicriteria maximally SRLG-disjoint/shortest path pairs in telecommunication networks

The paper addresses a bicriteria optimisation problem in telecommunication networks that aims at finding Pareto efficient pairs of paths between two given nodes, seeking to minimise the number of SRLGs (Shared Risk Link Groups) common to both paths and the path pair cost. This problem is of particular importance in telecommunication routing design, namely concerning resilient routing models where both a primary and a backup paths have to be calculated to minimise the risk of failure of a connection between origin and terminal nodes, in case of failure in the primary path. An exact resolution method is applied for solving this problem, enabling the calculation of the whole set of Pareto optimal solutions, which combines a transformation of the network representation with a path ranking algorithm. A comprehensive experimental study on the application of this approach, using reference network topologies, considering random SRLG assignments to the links and random link bandwidth occupations, together with the discussion on typical examples of solution selection and potential advantages of the method, are presented.