Pareto Curve Research Articles

Simulation and experimental demonstration of helium purification from He/N2 mixtures by pressure swing adsorption

Terrestrial helium is an indispensable non-renewable resource used in medicine, space, electronics, and nuclear research. This paper reports a high-pressure five-step pressure swing adsorption (PSA) cycle using Zeolite 5A for purification of He from dilute He/N2 mixtures. A Dual-Site Langmuir (DSL) model fitted both the low-pressure N2 and high-pressure N2 isotherm data. Dynamic column breakthrough (DCB) experiments were used to confirm volumetric equilibrium loadings. The DCB model predicted the experimental breakthrough curves for a wide range of feed compositions (100% N2, 74.5% N2, and 51.5% N2) and feed pressures (1 bar and 11.2 bar). A large experimental campaign studied the impact of various operating conditions on the He purity and recovery achievable from the PSA process. The study showed that a single-stage PSA experiment could enrich He up to 13% purity with greater than 90% recovery from a feed containing 1% He. Helium purity of 95% and a recovery of 90% can be achieved from a feed containing 10% He. All trends were predicted well by numerical simulations. A multi-objective optimization was performed to maximize helium purity and recovery for various He feed compositions. The study also showed that points from the Pareto curve can be realized experimentally.

Early attempts to integrate kinetic theory into economics in Italy between the wars

Between the two world wars, a group of Italian mathematicians, statisticians and economists set out to use the tools of statistical mechanics to interpret the Pareto income distribution curve as a probability distribution. Models based on Boltzmann's thermal equilibrium were independently developed to find an economic variable, comparable to the kinetic energy of gas theory, that could explain the heavy tail of the Pareto curve. The various avenues explored eventually led them back to Pareto's much debated explanation, namely that the hyperbolic distribution of income was due to the unequal distribution of talent.

Spatial patterns of landslides in a modest topography of the Ozark and Ouachita Mountains, USA

Controls on landslides vary as a function of landscape and regional activity. For example, low-relief, woodland regions have slope gradients, soil types, and substrate lithologies that contrast with steeper mountainous regions prone to rock fall and debris flows. Similarly, regional variations in precipitation, earthquakes, and other impacts on landslide surfaces create regional variations in landslide properties. While the controls on landslide characteristics have been extensively studied for high-relief coastal and tectonically active regions, controls on low-relief landslides have received comparatively less attention. We focus here on a part of the Ozark and Ouachita Mountains in the US southern mid-continent to explore such characteristics of landslides and potential controls in low-relief regions. The area exhibits frequent landslides in soil-covered low-relief forested hillslopes. We evaluated the frequency-size scaling of landslides occurred during periods of different earthquake frequency and precipitation amount (pre- and post-2005). We also produced maps of landslide susceptibility based on random forest machine learning applied to remotely sensed data. We found that landslides are clustered mostly in upland hillslopes, and that small landslides dominate the area, quantified by a landslide frequency-size distribution fitting a double Pareto curve. Additionally, the overall landslide frequency, and potentially the porportion of smaller landslides relative to the larger ones, significantly increased after 2005, the period during which the area also experienced increased induced seismicity and extreme storm events. Approximately 94 % of historical landslides were within random-forest-classified high-landslide probability (probability > 0.5) zones, coinciding with moderate to steep (18° ± 9°) and convergent upland slopes underlain by shale and sandstone. Anomalously high frequency landslides appear to result from triggering by extreme weather, human-induced earthquake activity, and human-induced hillslope modification.

Day-ahead optimal scheduling considering thermal and electrical energy management in smart homes with photovoltaic–thermal systems

The environmental impact on the energy sector has become a significant concern, necessitating the implementation of Home Energy Management Systems (HEMS) to enhance the energy efficiency of buildings, reduce costs and greenhouse gas emissions, and ensure user comfort. This paper presents a novel approach to provide optimal day-ahead energy management plans in smart homes with Photovoltaic/Thermal (PVT) systems, aiming to achieve a balance between energy cost and user comfort. This multi-objective problem employs the Non-dominated Sorting Genetic Algorithm III as the optimization algorithm and the Nonlinear Auto-regressive with External Input to forecast the day-ahead meteorological variables, which serve as inputs to predict the PVT electrical and heat production in the thermal resistance model. The HEMS benefits from the time-of-use tariff due to the flexibility provided by the energy storage from a battery bank and a boiler. Furthermore, it performs a load scheduling for 10 controllable loads based on three feature parameters to characterize occupant behavior. A study case analysis revealed a cost reduction of approximately 66% in the solution close to the knee of the Pareto curve (S3 solution). The environmental impact on the energy sector has become a The PVT heat production was sufficient to meet the thermal demand of the showers. The proposed hybrid battery management model effectively eliminated the export of electricity to the grid, reducing consumption during peak periods and the maximum peak demand.

Crime dynamics in Edmonton’s train stations: analysing hot spots, harm spots and offender patterns

PurposeThe objectives of this study are to (a) identify spatial and temporal crime concentrations, (b) supplement the traditional place-based analysis that defines hot spots based on counted incidents with an analysis of crime severity and (c) add to the research of hot spots with an analysis of offender data.Design/methodology/approachThis study explores crime concentration in mass transit settings, focusing on Edmonton’s Light Rail Transit (LRT) stations in 2017–2022. Pareto curves are used to observe the degree of concentration of crime in certain locations using multiple estimates; trajectory analysis is then used to observe crime patterns in the data on both places and offenders.FindingsA total of 16.3% of stations accounted for 50% of recorded incidents. Train stations with high or low crime counts and severity remained as such consistently over time. Additionally, 3.6% of offenders accounted for 50% of incident count, while 5% accounted for 50% of harm. We did not observe differences in the patterns and distributions of crime concentrations when comparing crime counts and harm.Research limitations/implicationsHot spots and harm spots are synonymous in low-crime-harm environments: high-harm incidents are outliers, and their weight in the average crime severity score is limited. More sensitive severity measures are needed for high-frequenty, low-harm enviornments. Practical implicationsThe findings underscore the benefits of integrating offender data in place-based applied research.Originality/valueThe findings provide additional evidence on the utility of place-based criminology and potentially cost-effective interventions.

Optimization of NOX emissions of a CRDI DIESEL engine using CMA-ES method

Engine calibration is the tuning of embedded parameters in the engine control unit (ECU) software to improve vehicle characteristics and meet legal requirements. Due to the stricter emission limits and rising customer expectations, current ECU software may include variables up to 30,000, which require very much time for engine calibration development. For this reason, automotive manufacturers continuously develop mathematical-based optimization methods to find optimum operating conditions for the engines. This study aimed to develop an online optimization algorithm to conduct automated dynamometer tests in the calibration development process. A modified covariance matrix adaptation (CMA) algorithm, which is an evolutionary strategy (ES) method belonging to meta-heuristic optimization, was integrated with an automation system for online calibration optimization. Some CMA method parameters such as step size and damping factor were initially revised to achieve the method to function efficiently in online engine calibration. Optimization was conducted at three different operating points of a 2-liter common rail direct injection (CRDI) diesel engine, where NOx emission mainly impacts the New European Driving Cycle (NEDC) results. The main injection timing, rail pressure, pilot injection quantity and timing, manifold pressure, and mass air flow were controlled in the optimization process. Optimization targets were determined according to the NOx-PM Pareto curve for each operating point. Covariance matrix adaptation was used to generate Pareto curves. Sixty-five measurements were taken for each operating point in the optimization process. Once optimization targets were determined, optimization occurred at each operating point. A total NOx emission reduction of 3.8% was obtained in the NEDC test, while fuel consumption and PM remained almost the same at steady-state operating points. The modified CMA-ES algorithm is expected to be an efficient method for online calibration optimization.

Analysis of the amount of latent carbon in the reconstruction of residential buildings with a multi-objective optimization approach

Purpose Due to the increase in energy demand and the effects of global warming, energy-efficient buildings have gained significant importance in the modern construction industry. To create a suitable framework with the aim of reducing energy consumption in the building sector, the external walls of a residential building were considered with two criteria of global warming potential and energy consumption. Design/methodology/approach In the first stage, to achieve a nearly zero-energy building, energy analysis was performed for 37 different states of thermal insulation. Then, the insulation materials’ life cycle assessment was performed. These results were used to find a set of optimal modes in the Pareto front by using non-dominated sorting genetic algorithm II multi-objective genetic algorithm. Thus, based on the data obtained from this method, it was possible to compare and choose different thermal insulation materials based on the distance from the Pareto front, reducing the environmental effects. Findings The results showed that replacing the windows was possible to save 3.24% in energy consumption. Also, selecting the proper insulation reduced energy consumption value by 63.13%. Finally, this building can save 69.31% of energy consumption compared to the base building by following the zero-energy building standard. As a result, the Pareto curve was introduced as a guide for the optimal design of the building’s wall insulation. Originality/value The proposed method provides designers with a framework for latent carbon analysis to access quickly and select optimal scenarios. It can also be used without restrictions for other decisions with different goals and criteria.

Data-driven modeling and multi-objective optimization of a continuous kraft pulping digester

Understanding wood characteristics is essential for enhancing the economic sustainability of the kraft process. In a recent work, we included wood characteristics in the phenomenological modeling of digesters. The developed model allows the optimization of the process. Here, we propose a constrained multi-objective optimization approach to minimize the residual lignin content while maximizing the carbohydrate content in the cellulose pulp, using the Non-dominated Sorting Genetic Algorithm II. In order to reduce computational costs during the optimization, we developed a surrogate model, based on simulated data, to predict key performance indicators. We evaluated two machine learning techniques: Multilayer Perceptron (MLP) and decision tree-based methods, considering single and multiple outputs. The combination between the multiple-output approach and MLP performed well and resulted in a more simplified surrogate model. The results for the simulation and the surrogate model were similar, and the computational cost was approximately 50 times lower for the surrogate model. An uncertainty was associated with the multiplicative factor of the delignification rate as a way to observe how its estimate interferes with the Pareto curve. The present work presents contributions to data-driven modeling and multi-objective optimization of digesters, allowing us to determine the importance of wood characteristics in operation.

A novel multi-objective optimization strategy based on vibrating particle system algorithm applied to chemical process design

Chemical process design is a highly interesting field within the chemical engineering community due to the numerous potential applications it offers. Traditionally, this problem involves multiple objectives and constraints related to mass, energy, and momentum balances, as well as limitations based on environmental, physical, and operating conditions. Over the past few decades, various multi-objective optimization strategies incorporating evolutionary algorithms have been proposed and tested using test cases of varying complexity. In this study, we propose a new Multi-objective Optimization Vibrating Particle System (MOVPS) algorithm. This numerical strategy extends the Vibrating Particle System Algorithm to a multi-objective context by incorporating three operators into the original algorithm: Pareto dominance, crowding distance, and a mutation strategy. To expedite the convergence process and avoid local optima, an external repository is considered. We evaluate the performance of the proposed methodology by applying it to mathematical functions (ZDT functions) and chemical process design problems. Regarding the ZDT functions, the computational cost (number of objective function evaluations and the processing time) was not increased considering the proposed methodology, as well as the values of convergence and diversity metrics are in agreement with those calculated considering other multi-objective optimization strategies. For most engineering case studies, it was possible to verify that the proposed methodology was able to obtain good estimates for the Pareto curve without increasing the computational cost. However, for the industrial styrene reactor problem it was possible to improve the Pareto curve and reduce the computational cost in relation to other multi-objective optimization algorithms.

A comparative study of membrane reactor and cylindrical reactor using multi-objective optimization for methane reforming process

Multi-objective optimization (MOO) of methane reforming process has been performed for hydrogen and oxygen perm-selective membrane reactor (MR) considering three objectives, namely H2 yield maximization, CO2 minimization and reactor length minimization. The performance of the MR has been compared with that of the cylindrical reactor (CR) using the same objective functions. Four MOO problems have been formulated and solved in this work. Among these, three problems consist of 2-objectives, while one has 3-objectives. Comparative results and discussions of the two reactors are presented based on the multi-objective pareto curve analysis and the trends of decision variables. The results in this work indicate that MR performs better than CR in all the four multi-objective scenarios. We further optimize the reactor with the above mentioned all the three objectives to produce syngas with different (H2/CO) ratios in the product stream. This is especially useful for producing the syngas targeting a specific end application.

Analysis of multi-objective optimization applied to the simulation of a natural gas separation plant

This study concentrated on simulating and optimizing a natural gas separation plant using Unisim Design® software. The optimization procedure aimed to maximize gas production and the higher-molecular-weight hydrocarbons (yC5+) in the produced gas. The maximum water dew point of −45 °C of the produced gas was specified. The Nelder Mead/Weight Sum Method (NM/WSM) algorithm was employed in Python to optimize five decision variables involving the temperature and pressure of the main process streams. Results indicated that the relative deviations below 1%, compared to reference values, were obtained for the main process variables. The multi-objective optimization (MOO) results showed an increase in gas production of up to 5.58% (maximum value of 62,736.10 kg/h) and a rise in the molar fraction of yC5+ by up to 32.2% compared to the reference values. However, it was noted that maximizing gas production indirectly maximizes the yC5+, with only a single decision variable differing in the optimal direction, represented by the intermediate temperature of one compression stage. A Pareto curve was built to display the range of optimal solutions, showing variations of 0.035% in optimal gas production and 0.11% in yC5+. Furthermore, various simulation scenarios were optimized with different thermodynamic conditions at the unit's inlet. In all cases, the optimization resulted in an average gain of 1.57% in gas production regarding the reference (non-optimal case).

Optimizing a machine learning design of dielectric properties in lead-free piezoelectric ceramics

Designing lead-free piezoelectric ceramics with tailored electrical properties remains a critical challenge for various applications. In this paper we present a novel methodology integrating Machine Learning (ML) and optimization procedures to fine-tune electrical properties in lead-free (1-x) Na0.5 Bi0.5 TiO3 - x CaTiO3 piezoelectric ceramics. A comprehensive dataset of dielectric measurements serves as the foundation for training ML models that accurately predict the permittivity (ε′) and dielectric loss (tan δ) as functions of Ca2+ concentration (x % Ca), temperature and frequency. Two ML techniques are evaluated: random forest regression, and Multi-Layer Perceptron neural network Regression (MLPR). The MLPR model exhibited a superior regression performance, achieving a correlation coefficient of 0.931 and a root mean squared error of 0.029. The MLPR was then optimized by the Non-dominated Sorting Genetic Algorithm II (NSGA-II) to maximizes ε′ while minimizes tan δ. Within the NSGA-II framework, the optimal values were found at the Pareto curve knee, corresponding to a frequency, temperature, and x % Ca of 609.739 kHz, 398.15 K, and 6.10, respectively, resulting in ε′ equal to 857.87 and tan δ equal to 0.0120. This approach demonstrates the effectiveness of combining ML and optimization for designing the electrical properties of piezoelectric ceramics, paving the way for more efficient and targeted material development.

Congressional Apportionment: A Multiobjective Optimization Approach

Two events, with major implications for U.S. voters, occur after each decennial census. First, congressional “apportionment” takes place, followed by congressional “districting.” Apportionment determines how to allocate the 435 seats in the House of Representatives across the 50 states, whereas districting determines the geographic boundaries assigned to representatives within each state. Although districting and the practice of gerrymandering often receive great attention in the media and courts, the best way to apportion representatives across states has been debated for nearly 250 years. Historical methods (including the current method) each satisfy some desirable optimality criteria that the others are not guaranteed to satisfy. Moreover, none are guaranteed to optimize certain reasonable fairness measures (e.g., minimum range, minimum bias). To our knowledge, we are the first to formulate and analyze a multiobjective optimization approach to apportionment, allowing policymakers to identify Pareto-optimal allocations and quantify their trade-offs between several competing criteria. Some of these models can be formulated and solved as mixed-integer linear programs, whereas others require the solution of mixed-integer, nonconvex, quadratically constrained quadratic programs. We take advantage of recent software advances that allow one to solve these problems with optimality guarantees. Policy implications of our work include Pareto curves from historical censuses and simulations, which suggest opportunities for improvement in some objectives at little sacrifice to others. This paper was accepted by David Simchi-Levi, operations management. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2023.02472 .

Multicriteria analysis of the components of ecological paving stones made from plastic and glass waste, and granular reinforcements

The use of plastic waste as a resource in construction applications is an opportunity for environmental protection, conservation of natural resources and reduction of pollution. Unfortunately, they don't always withstand the stresses to which they are subjected, leading to subsidence and collapsing. An analysis of the causes using the Pareto curve shows that 74.47 % of the causes of this collapse are due to poorly formulated mixes and poor choice of raw materials for the composite. The compressive test carried out on the first sample of pavers studied showed a maximum compressive strength value of 4.6 MPa, which is below the standard requirements. As a result, the pavers were considered unsuitable for use on a T5 road. Through the use of the SUPERDECISION software, we were able to identify two favourable constituent materials - glass/glass waste and gravel - for the production of composite paving stones. By adding low-density plastic waste, collected, cleaned and crushed in the form of aggregates, we obtain a compressive strength of 7 MPa with gravel and 8 MPa with glass waste. These values are below the recommendations of the NF EN 1339 standard (Rc ≥ 20 MPa) for T5 traffic. The best composition for ecological paving is therefore (PET/PP/PEBD) + sand + glass (50/12.5/37.5). Analyzing these results shows that the raw materials used for ecological paving should be adapted to the loads.

The distribution of retail gross margin: analysis and implications

ABSTRACT Prior research on retail sales distributions finds both product concentration and long tails. However, gross margin dollars (rather than sales dollars) are critical drivers of retail financial performance, especially in sectors characterized by short product cycles and declining average selling prices. The paper is the first to use sku level data to estimate both sales and margin distributions for an office supply/technology retailer. We calculate Lorenz curves, Gini coefficients, and Pareto curves for in-store, on-line, and omni-channels. The estimated distribution of gross margin dollars is less skewed than the sales distribution; that is, more of the margin dollars are in the middle of the distribution. Significant differences in sales and margin distributions are found in store, online, and omnichannel products. These differences are only partially explained by price architecture and by private label merchandise. We analyze the decile distributions of sales and margin across channels and develop a classification matrix with implications for merchandise planning. Because merchandise strategies often focus on best sellers and managing long tails, the paper highlights opportunities for increasing profitability by emphasizing the middle of the margin distribution.

Scalable High-Quality Hypergraph Partitioning

Balanced hypergraph partitioning is an NP-hard problem with many applications, e.g., optimizing communication in distributed data placement problems. The goal is to place all nodes across k different blocks of bounded size, such that hyperedges span as few parts as possible. This problem is well-studied in sequential and distributed settings, but not in shared-memory. We close this gap by devising efficient and scalable shared-memory algorithms for all components employed in the best sequential solvers without compromises with regards to solution quality. This work presents the scalable and high-quality hypergraph partitioning framework Mt-KaHyPar . Its most important components are parallel improvement algorithms based on the FM algorithm and maximum flows, as well as a parallel clustering algorithm for coarsening – which are used in a multilevel scheme with log (n) levels. As additional components, we parallelize the n -level partitioning scheme, devise a deterministic version of our algorithm, and present optimizations for plain graphs. We evaluate our solver on more than 800 graphs and hypergraphs, and compare it with 25 different algorithms from the literature. Our fastest configuration outperforms almost all existing hypergraph partitioners with regards to both solution quality and running time. Our highest-quality configuration achieves the same solution quality as the best sequential partitioner KaHyPar , while being an order of magnitude faster with ten threads. Thus, two of our configurations occupy all fronts of the Pareto curve for hypergraph partitioning. Furthermore, our solvers exhibit good speedups, e.g., 29.6x in the geometric mean on 64 cores (deterministic), 22.3x (log (n) -level), and 25.9x ( n -level).

Reliability-based design of high-performance hydrocyclones: Multi-objective optimization, fabrication using 3D-printing and experimental analysis

In the literature, several works aim to improve the performance of hydrocyclones using geometry optimization. However, these approaches do not consider the uncertainties in the models, design variables, and parameters, which can lead to solutions that do not correspond to the expected results when applied to real systems. Considering that, the present work proposed a reliability-based optimization of the hydrocyclone dimensions using the Advanced Mean Value (AMV) technique associated with the Multi-Objective Differential Evolution (MODE) algorithm. For that purpose, the maximization of total efficiency and minimization of underflow-to-throughput ratio and Euler number were taken as objectives and constraints were set to ensure an acceptable performance of the hydrocyclone in the main aspects of the process. Some of the obtained devices were selected to be fabricated through an additive manufacturing technique (3D printing) and, after that, be experimentally tested. The optimization results showed that the reliability-based optimization affected the Pareto curves in two different ways: a shortening or a displacement of the curve in relation to the nominal one, depending on which constraints are being activated. The experimental results demonstrated that the hydrocyclones obtained by the reliable approach had a greater tendency to meet the set constraints in practice. Finally, hydrocyclones with great experimental performance were obtained considering separation efficiency, concentration capacity, and energy consumption.

Efficient economic energy scheduling in smart cities using distributed energy resources

Machine learning provides a powerful mechanism to enhance the capabilities of the next generation of smart cities. Whether healthcare monitoring, building automation, energy management, or traffic management, use cases of capability enhancement using machine learning have been significant in recent years. This paper proposes a modeling approach for scheduling energy consumption within smart homes based on a non-dominated sorting genetic algorithm (NSGA). Distributed energy management plays a significant role in reducing energy consumption and carbon emissions as compared to centralized energy generation. Multiple energy consumers can schedule energy-consuming household tasks using home energy management systems in coordination to reduce economic costs and greenhouse gas emissions. In this work, such a home energy management system is used to collect energy price data from the electricity company via an embedded device-enabled smart meter and schedule energy consumption tasks based on this data. We schedule daily power consumption tasks using a multiobjective optimization method that considers environmental and economic sustainability. Two conflicting objectives are minimizing daily energy costs and reducing carbon dioxide emissions. Based on electricity tariffs, CO2 intensity, and the window of time during which electricity is consumed, energy consumption tasks involving distributed energy resources (DERs) and electricity consumption are scheduled. The proposed model is implemented in a model smart building consisting of 30 homes under 3 pricing schemes. The energy demand is spread out across a 24-hour period for points A2–A4 under CPP-PDC, which produces a more flattened curve than point A1. There are competing goals between electricity costs and carbon footprints at points B2–B4 under the CPP-PDC, where electricity demand is set between 20:00 and 0:00. Power grids’ peak energy demand is comparatively low when scheduling under CPP-PDC for points A5 and B5. Reducing carbon emissions, CPP-PDC reduces the maximum demand for electricity from the grid and the overall demand above the predetermined level. The maximum power demand from the grid is minimized for points A5 and B5, reducing up to 22% compared to A2. The proposed method minimizes both energy costs as well as CO2 emissions. A Pareto curve illustrates the trade-off between cost and CO2 emissions.

The Role of Energy Policies for Air Pollution Control in the Po Valley

This paper examines the use of integrated assessment modelling to select policies aimed at reducing air pollution in response to growing concerns about the deterioration of air quality, especially in highly populated and industrialized areas. The study focuses on the Po Valley region in northern Italy, renowned for its intricate environmental difficulties arising from industrial operations, extensive farming, and topographic characteristics. The goal of the multi-objective decision problem is to find the best plans for reducing emissions that will minimize the average annual concentrations of PM2.5 while also considering the costs of putting these plans into action and incorporating end-of-pipe, energy, and fuel switch measures. Results highlight the trade-offs between air quality improvement and associated costs, presenting a Pareto curve of optimal solutions.

Optimization of coal chemical process parameters and energy saving and emission reduction based on genetic algorithm

Abstract Coal is an important energy resource. How to utilize it efficiently and cleanly is a hot topic nowadays. In the coal gasification process, the process parameter indexes have a significant impact, and the uncertainty of these factors will lead to a decrease in the quality of gas production. Therefore, in this paper, the uncertainty of process parameters is considered, and Aspen plus software with the Monte Carlo method is used to simulate the coal chemical process and measure the effect of uncertainty of process parameters on the yield of the coal gasification process. On this basis, in addition, coal flow rate, pressure, and steam/oxygen are taken as the process parameters and optimized, and three sets of multi-objective optimization models are established with gas calorific value, gasification efficiency, and gas yield, respectively, which are solved by improved multi-objective genetic algorithm based on crossover operator and variational operator to obtain Pareto curves, so as to adjust the parameter values according to the actual needs. The results show that the fluctuation of pressure has a big influence on the carbon conversion rate and gasification efficiency, and the carbon conversion rate and gasification efficiency can be made more stable by controlling the change of pressure. The improved genetic algorithm NSGA-II can reach the actual optimal objective function value in both high and low iteration times, providing the required parameters for the decision maker, and the optimal program results in TEC of 402,758 kW and CO2 content of 0.12%, which is effective in energy saving and emission reduction.