Pareto Optimal Solutions Research Articles

GIS spatial optimization for agricultural crop allocation using NSGA-II

This study focuses on the shift from traditional farming methods, reliant on farmer intuition and manual processes, to modern, automated approaches crucial for Thailand’s agricultural sustainability. Despite its vital role in the country’s economy, outdated practices lead to supply imbalances and perpetuate poverty among smallholder farmers. Using geographic information systems (GIS) and mathematical optimization, the present study aims to determine optimal agricultural crop allocation. A multi-objective optimization crop spatial allocation model leverages geospatial data, including crop, soil and climate suitability, to enhance the accuracy of our model. Additionally, we incorporate agricultural economics data, such as market price, crop yield, production cost, distances to secondary producers, production budget limitations, and minimum crop production requirements. To speedup the convergence of the algorithm, we introduce more suitable crossover and mutation operators in NSGA-II, aiming to direct the search towards the Pareto optimal solutions. We demonstrate the effectiveness of our approach in a case study of the agricultural area in Chiang Mai province, Thailand, focusing on three major industrial crops: corn, cane, and rice. Our model suggests land allocation that adheres to both the budget constraint and the minimum production requirements, while retaining only a small surplus for each crop. The successful implementation of this approach in our case study marks a significant advancement in Thai agricultural research, paving the way for long-term economic and environmental sustainability.

Hybrid Active and Passive Cable Contour Shielding of Magnetic Fields of Double-Circuit Overhead Power Lines

The purpose of the work is to design a hybrid screen designed to reduce the level of the magnetic field generated by double-circuit overhead power lines, to increase the efficiency of shielding the original magnetic field in residential buildings, to the level of sanitary standards and to reduce the sensitivity of the system to changes in system parameters. To achieve this goal, the structure of a hybrid screen was determined, consisting of a double contour active and a cable contour passive part. The developed hybrid screen is characterized by increased efficiency in reducing the magnetic field of industrial frequency. Designing a hybrid screen comes down to solving a minimax vector optimization problem, in which the vector objective function is calculated based on solution to Maxwell's equations in a quasi-stationary approximation using the COMSOL Multiphysics software package. The solution to the minimax vector optimization problem is calculated based on multi-particle swarm optimization algorithms from Pareto-optimal solutions taking into account binary preference relations. During the design of the hybrid screen, the coordinates of the spatial location of the two compensation windings, as well as the magnitude of the currents and its phases in the windings of the active screen, were calculated. The important results are theoretical and experimental studies on the effectiveness of the designed hybrid magnetic field shield generated by double-circuit overhead power lines. The significance of the results obtained lies in the fact that practical recommendations are given for a reasonable choice of the spatial arrangement of two shielding windings of a robust system of hybrid shielding of the magnetic field generated by double-circuit overhead power lines.

Sensitivity Analysis and Optimization of Energy-Saving Measures for Office Building in Hot Summer and Cold Winter Regions

To effectively reduce building energy consumption and enhance indoor thermal comfort, this study developed a sensitivity analysis and multi-objective optimization method for an office building in Hangzhou considering the effects of parameter interactions. We utilized Latin hypercube sampling (LHS) to sample the parameters and subsequently simulated the energy consumption and discomfort hours for the building’s four orientations. Following this, Gaussian process regression models were established, and the feature importance ranking method (FIRM) alongside an interaction effects method were employed to quantify the sensitivity of 10 parameters. Lastly, a multi-objective optimization was performed for total energy consumption and discomfort hours, yielding a set of Pareto-optimal solutions. Through the VIKOR method, the optimal solution within the Pareto set was identified, resulting in three sets of optimal solutions.

Multi-Objective Inspection Optimization of Periodically Inspected Multi-Failure Mode System

This paper examines the multi-objective availability and cost optimization of a periodically inspected system. A system with [Formula: see text] independent failure modes is specifically considered. The principal characteristic of the proposed model is that the inspection and maintenance time is nonnegligible and corrective maintenance results in as good as a new unit. This paper focuses on evaluating the general expressions for limiting availability and long-run average cost of the system undergoing periodic inspections. The multi-objective optimization issue is solved by first generating the Pareto-optimal solutions using particle swarm optimization and then selecting the best compromise solution using a fuzzy method. A numerical illustration is also presented to highlight the applicability of the proposed work.

Multi-Objective BiLevel Optimization by Bayesian Optimization

In a multi-objective optimization problem, a decision maker has more than one objective to optimize. In a bilevel optimization problem, there are the following two decision-makers in a hierarchy: a leader who makes the first decision and a follower who reacts, each aiming to optimize their own objective. Many real-world decision-making processes have various objectives to optimize at the same time while considering how the decision-makers affect each other. When both features are combined, we have a multi-objective bilevel optimization problem, which arises in manufacturing, logistics, environmental economics, defence applications and many other areas. Many exact and approximation-based techniques have been proposed, but because of the intrinsic nonconvexity and conflicting multiple objectives, their computational cost is high. We propose a hybrid algorithm based on batch Bayesian optimization to approximate the upper-level Pareto-optimal solution set. We also extend our approach to handle uncertainty in the leader’s objectives via a hypervolume improvement-based acquisition function. Experiments show that our algorithm is more efficient than other current methods while successfully approximating Pareto-fronts.

Multi-Objective Collaborative Optimization of Stiffness and Damping Performance of Acoustic Black Hole Plate

This paper uses embedded Acoustic Black Hole (ABH) on the wallboard for structure lightening and improving the performance in broadband vibration reduction. The distribution and size of multiple ABHs affect the generalized static stiffness (GSS) and the upper limit of the structure's maximum kinetic energy (ULMKE) in practical applications, which express the ability to resist static load and vibration reduction performance, respectively. In this research, the structure's GSS and ULMKE are considered optimization objectives due to the trade-off between them. The method based on the Pareto optimal solution is adopted to optimize the layout and the radii of the ABHs. The Non-dominated Sorting Genetic Algorithm (NSGA-II) is used as the multi-objective optimization algorithm. Two 2D-ABHs embedded in a plate are optimized as numerical examples. The optimization generated several groups of Pareto optimal solutions, providing more feasible solutions for different applications faster. The verification further proved the necessity and the effectiveness of multi-objective optimization.

На пути к автоматизированному и оптимальному проектированию систем IIoT

In today’s world, the Internet of Things has become an integral part of our lives. The increasing number of intelligent devices and their pervasiveness has made it challenging for developers and system architects to plan and implement systems of Internet of Things and Industrial Internet of Things effectively. The primary objective of this work is to automate the design process of Industrial Internet of Things systems while optimizing the quality of service parameters, battery life, and cost. To achieve this goal, a general four-layer fog-computing model based on mathematical sets, constraints, and objective functions is introduced. This model takes into consideration the various parameters that affect the performance of the system, such as network latency, bandwidth, and power consumption. The Non-dominated Sorting Genetic Algorithm II is employed to find Pareto optimal solutions, while the Technique for Order of Preference by Similarity to Ideal Solution is used to identify compromise solutions on the Pareto front. The optimal solutions generated by this approach represent servers, communication links, and gateways whose information is stored in a database. These resources are chosen based on their ability to enhance the overall performance of the system. The proposed strategy follows a three-stage approach to minimize the dimensionality and reduce dependencies while exploring the search space. Additionally, the convergence of optimization algorithms is improved by using a biased initial population that exploits existing knowledge about how the solution should look. The algorithms used to generate this initial biased population are described in detail. To illustrate the effectiveness of this automated design strategy, an example of its application is presented.

Identification of energy management configuration concepts from a set of pareto-optimal solutions

Implementing resource efficient energy management systems in facilities and buildings becomes increasingly important in the transformation to a sustainable society. However, selecting a suitable configuration based on multiple, typically conflicting objectives, such as cost, robustness with respect to uncertainty of grid operation, or renewable energy utilization, is a difficult multi-criteria decision making problem. The recently developed concept identification technique can facilitate a decision maker by sorting configuration options into semantically meaningful groups (concepts).In this process, the partitioning of the objectives and design parameters into different sets (called description spaces) is a very important step. In this study we focus on utilizing the concept identification technique for finding relevant and viable energy management configurations from a very large data set of Pareto-optimal solutions. The data set consists of 20,000 realistic Pareto-optimal building energy management configurations generated by a many-objective evolutionary optimization of a high quality Digital Twin energy management simulator. We analyze how the choice of description spaces, i.e., the partitioning of the objectives and parameters, impacts the type of information that can be extracted. We show that the decision maker can introduce constraints and biases into that process to meet expectations and preferences. The iterative approach presented in this work allows for the generation of valuable insights into trade-offs between specific objectives, and constitutes a powerful and flexible tool to support the decision making process when designing large and complex energy management systems.

Integrated passive design method optimized for carbon emissions, economics, and thermal comfort of zero-carbon buildings

Improving passive design methods are important for achieving zero-carbon building (ZCB) targets. Data-driven design approaches are more accurate than conventional methods for multiple-objective optimization (MOO) targets such as carbon emissions (CE), economics, and thermal comfort. In this study, a comprehensive data-driven-based PSO-SVM-NSGA-III method that assists in optimizing passive design parameters are proposed. First, the simulation results for the objectives of CE, incremental cost (IC), and time not comfort (TNC) are performed for an office building in a cold region in China using EnergyPlus and jEPlus software. Then, key influencing factors are chosen via a sensitivity analysis. Second, nonlinear mapping relationships between the passive design parameters and objectives are established with the PSO-SVM model. Compared to the BPNN, SVM, and PSO-BPNN algorithms, the PSO-SVM model exhibits superior prediction performance, with R2 values of 0.977, 0.925, and 0.903 for CE, IC, and TNC, respectively. Third, the nonlinear mapping relationships are used in the established objective functions of NSGA-II and NSGA-III. NSGA-III performed 100 iterations within 21 min and exhibited robust diversity within its population, with a hypervolume value of 0.738. Finally, the Pareto-optimal solution set is formed with the PSO-SVM-NSGA-III framework. This data-driven method offers an efficient approach for improving building performance.

Optimization Design of Medium-Voltage High-Frequency Transformers Based on Parallel Sampling Kriging Surrogate Model

In the design process of medium-voltage high-frequency transformers, numerical simulation methods often result in long design cycles and significant computational resource consumption. To achieve rapid and high-precision design for medium-voltage high-frequency transformers, a parallel kriging surrogate model is proposed based on the maximum expected improvement criterion. Initially, Latin hypercube sampling is employed to establish the initial sampling points, and corresponding three-dimensional models of medium-voltage high-frequency transformers are constructed for each sampling point configuration. Finite element simulation software is then used to compute the transformer loss and volume for each model. Subsequently, a kriging surrogate model is developed based on the initial sampling point configuration, and an enhanced parallel sampling strategy is implemented to enhance the fitting accuracy of the kriging surrogate model. Finally, the high-precision kriging surrogate model is utilized as the fitness function for a particle swarm optimization algorithm, with the objectives of minimizing transformer loss and volume. The Pareto optimal solution is sought under multi-objective optimization. The effectiveness of the proposed optimization method is verified through experimental measurements of the loss in a prototype of a medium-voltage high-frequency transformer.

Strong core and Pareto-optimality in the multiple partners matching problem under lexicographic preference domains

We study strong core and Pareto-optimal solutions for multiple partners matching problem under lexicographic preference domains from a computational point of view. The restriction to the two-sided case is called stable many-to-many matching problem and the general one-sided case is called stable fixtures problem. We provide an example to show that the strong core can be empty even for many-to-many problems, and that deciding the non-emptiness of the strong core is NP-hard. On the positive side, we give efficient algorithms for finding a near feasible strong core solution and for finding a fractional matching in the strong core of fractional matchings. In contrast with the NP-hardness result for the stable fixtures problem, we show that finding a maximum size matching that is Pareto-optimal can be done efficiently for many-to-many problems. Finally, we show that for reverse-lexicographic preferences the strong core is always non-empty in the many-to-many case.

Multi-objective optimization of reactive power dispatch problem using fuzzy tuned mayfly algorithm

The recent multi-objective optimization problems are very complex which require an effective and robust evolutionary method for obtaining a global Pareto-optimal solutions. Most of these multi-objective evolutionary techniques are population-based methods which usually work on random search approaches and often trapped into local minima during their execution. A new fuzzy tuned mayfly algorithm (FTMA) is presented in this paper, to obtain the Pareto-optimal solutions for any complex multi-objective power system problem. It has a self-adapting global exploration capability to get the best Pareto-optimal solutions by varying two crucial parameters i.e., crossover (Pc) and mutation Pm probabilities. Moreover, a model of Pareto-dominance is employed to rank non-dominating solutions to maintain the diversity within the populations. The proposed evolutionary approach is examined on a standard ZDT benchmark test suite and its algorithmic performance is statistically compared with a few of the recent optimization techniques such as NSGA-II, NSGA-III, MMODE, MOAVOA and MMA algorithm. It is further applied to minimize two distinct objective functions (i.e., total transmission loss and voltage stability index) for IEEE-118 bus system and IEEE-24 bus RTS. A comprehensive statistical analysis is presented for the obtained numerical results, which proves that proposed FTMA has better convergence with better solution diversity in comparison to the other competing algorithms. A comprehensive analysis based on statistical results reveal that the proposed FTMA is superior for obtaining better non-dominating pareto-fronts as compared to other competing methods.

Multi-objective optimization of a sequentially inspected system prone to revealing and non-revealing failures via particle swarm optimization and a fuzzy method

ABSTRACT Maintenance models rely heavily on the failure characteristics and inspection or maintenance actions. This paper introduced a sequentially inspected system whose failure alternated between revealing and non-revealing failures. The distinctive characteristic of the proposed model is that inspections are imperfect, inspection and maintenance time are non-negligible, and corrective maintenance is perfect. The proposed study contributed on the multi-objective availability and cost optimization issue of the aforementioned system, which was lacking in the prior studies. This paper focused on evaluating the general expressions for limiting availability and long-run average cost of the sequentially inspected system and addressed the multi-objective optimization issue using particle swarm optimization to generate the Pareto optimal solutions followed by a fuzzy method to select the best compromise solution. Moreover, reasonable results were achieved using a numerical case study and the findings of the existing studies were found to be the special case of this model.

Designing a sustainable-resilient humanitarian supply chain for post-disaster relief process, an earthquake case study in Haiti

Purpose Throughout human history, the occurrence of disasters has been inevitable, leading to significant human, financial and emotional consequences. Therefore, it is crucial to establish a well-designed plan to efficiently manage such situations when disaster strikes. The purpose of this study is to develop a comprehensive program that encompasses multiple aspects of postdisaster relief. Design/methodology/approach A multiobjective model has been developed for postdisaster relief, with the aim of minimizing social dissatisfaction, economic costs and environmental damage. The model has been solved using exact methods for different scenarios. The objective is to achieve the most optimal outcomes in the context of postdisaster relief operations. Findings A real case study of an earthquake in Haiti has been conducted. The acquired results and subsequent management analysis have effectively assessed the logic of the model. As a result, the model’s performance has been validated and deemed reliable based on the findings and insights obtained. Originality/value Ultimately, the model provides the optimal quantities of each product to be shipped and determines the appropriate mode of transportation. Additionally, the application of the epsilon constraint method results in a set of Pareto optimal solutions. Through a comprehensive examination of the presented solutions, valuable insights and analyses can be obtained, contributing to a better understanding of the model’s effectiveness.

Test Center Location Problem: A Bi-Objective Model and Algorithms

The optimal placement of healthcare facilities, including the placement of diagnostic test centers, plays a pivotal role in ensuring efficient and equitable access to healthcare services. However, the emergence of unique complexities in the context of a pandemic, exemplified by the COVID-19 crisis, has necessitated the development of customized solutions. This paper introduces a bi-objective integer linear programming model designed to achieve two key objectives: minimizing average travel time for individuals visiting testing centers and maximizing an equitable workload distribution among testing centers. This problem is NP-hard and we propose a customized local search algorithm based on the Voronoi diagram. Additionally, we employ an ϵ-constraint approach, which leverages the Gurobi solver. We rigorously examine the effectiveness of the model and the algorithms through numerical experiments and demonstrate their capability to identify Pareto-optimal solutions. We show that while the Gurobi performs efficiently in small-size instances, our proposed algorithm outperforms it in large-size instances of the problem.

Multi-Objective Bayesian Optimization with Active Preference Learning

There are a lot of real-world black-box optimization problems that need to optimize multiple criteria simultaneously. However, in a multi-objective optimization (MOO) problem, identifying the whole Pareto front requires the prohibitive search cost, while in many practical scenarios, the decision maker (DM) only needs a specific solution among the set of the Pareto optimal solutions. We propose a Bayesian optimization (BO) approach to identifying the most preferred solution in the MOO with expensive objective functions, in which a Bayesian preference model of the DM is adaptively estimated by an interactive manner based on the two types of supervisions called the pairwise preference and improvement request. To explore the most preferred solution, we define an acquisition function in which the uncertainty both in the objective function and the DM preference is incorporated. Further, to minimize the interaction cost with the DM, we also propose an active learning strategy for the preference estimation. We empirically demonstrate the effectiveness of our proposed method through the benchmark function optimization and the hyper-parameter optimization problems for machine learning models.

Are You Concerned about Limited Function Evaluations: Data-Augmented Pareto Set Learning for Expensive Multi-Objective Optimization

Optimizing multiple conflicting black-box objectives simultaneously is a prevalent occurrence in many real-world applications, such as neural architecture search, and machine learning. These problems are known as expensive multi-objective optimization problems (EMOPs) when the function evaluations are computationally or financially costly. Multi-objective Bayesian optimization (MOBO) offers an efficient approach to discovering a set of Pareto optimal solutions. However, the data deficiency issue caused by limited function evaluations has posed a great challenge to current optimization methods. Moreover, most current methods tend to prioritize the quality of candidate solutions, while ignoring the quantity of promising samples. In order to tackle these issues, our paper proposes a novel multi-objective Bayesian optimization algorithm with a data augmentation strategy that provides ample high-quality samples for Pareto set learning (PSL). Specifically, it utilizes Generative Adversarial Networks (GANs) to enrich data and a dominance prediction model to screen out high-quality samples, mitigating the predicament of limited function evaluations in EMOPs. Additionally, we adopt the regularity model to expensive multi-objective Bayesian optimization for PSL. Experimental results on both synthetic and real-world problems demonstrate that our algorithm outperforms several state-of-the-art and classical algorithms.

Multi-Objective Optimization with Active–Passive Technology Synergy for Rural Residences in Northern China

Due to the serious problems with energy efficiency, carbon emissions, and thermal comfort of rural residences in northern China, an optimization of active and passive heating technologies for rural residences is necessary. In this paper, an optimization for rural residences in northern China is conducted with four objectives: the whole life cycle carbon emission; the annual energy consumption through heating, ventilation, and air conditioning systems; the annual cost; and thermal comfort. In addition, the optimization model with active–passive heating technology synergy is resolved by NSGA-II genetic algorithm. The active and passive design variables, including the type of air source heat pump, orientation, the type and thickness of envelope insulation, the layer of window glass, the window-to-wall area ratio, as well as sunspace parameters are preferred to obtain the optimal solution. The results indicate that the optimal solution obtained by the ideal point method gives the most outstanding performance. Compared with the prototype, the optimized carbon emissions in severe cold and cold regions decreased by 56.1% and 54.6%, respectively. The annual energy consumption decreased by 59.7% and 62.2%. Finally, the roof insulation thickness is the most sensitive design variable in Pareto-optimal solution sets. This paper offers significant guidance in the application of the optimization method of active–passive technology synergy to the energy-saving design of buildings.

Proposing a procedure for multi-objective optimization of cascade thermoelectric coolers to achieve maximum cooling capacity and COP

Abstract A novel approach is proposed for optimal designing two-stage thermoelectric coolers using the biogeography-based optimization algorithm. For the comprehensiveness of the research, both types of two-stage coolers, including electrically serial and separated stages, have been investigated. Using the proposed procedure, first by selecting the most important performance parameters of the cooler, i.e. COP and the cooling capacity as objective functions, the efficiency and the validity of the approach are proved by comparing the results with results of the previous researchers. In all the examined cases, the proposed approach has led to the enhancing of the cooler performance. The results of single-objective optimization showed that using the proposed method, the cooling capacity and COP can be improved up to 17 % and 8.5 % compared to the previous designs, respectively. In the following, multi-objective optimization of thermoelectric coolers is conducted, taking into account both the objectives of the COP and the cooling capacity. Finally, Pareto optimal solutions and the exergetic efficiency of the optimized cooler were calculated for different values of the weight factor of the multi-objective function. The results of multi-objective optimization showed that by increasing the COP weight factor in the objective function, the exergetic efficiency of the refrigeration system enhances.

Optimizing the Three-Dimensional Multi-Objective of Feeder Bus Routes Considering the Timetable

To optimize the evacuation process of rail transit passenger flows, the influence of the feeder bus network on bus demand is pivotal. This study first examines the transportation mode preferences of rail transit station passengers and addresses the feeder bus network’s optimization challenge within a three-dimensional framework, incorporating an elastic mechanism. Consequently, a strategic planning model is developed. Subsequently, a multi-objective optimization model is constructed to simultaneously increase passenger numbers and decrease both travel time costs and bus operational expenses. Due to the NP-hard nature of this optimization problem, we introduce an enhanced non-dominated sorting genetic algorithm, INSGA-II. This algorithm integrates innovative encoding and decoding rules, adaptive parameter adjustment strategies, and a combination of crowding distance and distribution entropy mechanisms alongside an external elite archive strategy to enhance population convergence and local search capabilities. The efficacy of the proposed model and algorithm is corroborated through simulations employing standard test functions and instances. The results demonstrate that the INSGA-II algorithm closely approximates the true Pareto front, attaining Pareto optimal solutions that are uniformly distributed. Additionally, an increase in the fleet size correlates with greater passenger volumes and higher operational costs, yet it substantially lowers the average travel cost per customer. An optimal fleet size of 11 vehicles is identified. Moreover, expanding feeder bus routes enhances passenger counts by 18.03%, raises operational costs by 32.33%, and cuts passenger travel time expenses by 21.23%. These findings necessitate revisions to the bus timetable. Therefore, for a bus network with elastic demand, it is essential to holistically optimize the actual passenger flow demand, fleet size, bus schedules, and departure frequencies.