Pareto Optimal Solutions Research Articles

Multi-objective optimization for generative morphological design using energy and comfort models with a practical design of new rural community in China

In recent years, the development of new rural communities has emerged as a pivotal new trend in china, aimed at enhancing energy efficiency and residential comfort in rural regions. This study introduces a multi-objective optimization design framework for the morphological design of residential area, with a focus on performance objectives such as building energy use intensity, summer thermal comfort, and winter thermal comfort. A case study of a new rural community design project in Hongnan Village, Yancheng City, was conducted. Utilizing the Rhino-Grasshopper parametric platform, this study undertook parametric modeling, performance simulation, and multi-objective optimization to receive the Pareto-optimal solutions. ParetoResults indicate that in the Pareto-optimal morphology scheme for the Hongnan Village community, open spaces are predominantly located on the upwind side with respect to the prevailing summer winds of the site. The number of duplex houses is often 28, and the building orientations are predominantly aligned at 23°, mirroring the direction of the surrounding structures. There is a significant correlation between residential unit configuration, building spacing, and energy use intensity, with correlation coefficients of 0.53 and −0.43, respectively. This study would like to offer valuable insights into the energy-efficient design of new rural communities, thereby contributing to the creation of a more sustainable and habitable rural living environment.

Reactive Power Optimization in Distribution Networks of New Power Systems Based on Multi-Objective Particle Swarm Optimization

The new power system effectively integrates a large number of distributed renewable energy sources, such as solar photovoltaic, wind energy, small hydropower, and biomass energy. This significantly reduces the reliance on fossil fuels and enhances the sustainability and environmental friendliness of energy supply. Compared to distribution networks in traditional power systems, the new-generation distribution network offers notable advantages in improving energy efficiency, reliability, environmental protection, and system flexibility, but it also faces a series of new challenges. These challenges include potential harmonic issues introduced by the widespread use of power electronic devices (such as inverters for renewable energy generation systems and electric vehicle charging stations) and the voltage fluctuations and flickering caused by the intermittency and uncertainty of renewable energy generation, which may affect the normal operation of electrical equipment. To address these challenges, this study proposes an optimization model aimed at minimizing network losses and voltage deviations, utilizing traditional capacitor adjustments and static var compensators (SVCs) as optimization measures. Furthermore, this study introduces an improved version of the multi-objective particle swarm optimization (MOPSO) algorithm, specifically enhanced to address the unique challenges of reactive power optimization in modern distribution networks. The test results show that this algorithm can effectively generate a large number of Pareto optimal solutions. The application of this algorithm on a 33-node network case study demonstrates its advantages in reactive power optimization. The optimization results highlight the effectiveness and feasibility of the proposed improved algorithm in the application of distribution network reactive power optimization, offering users a uniform and diverse range of reactive compensation solutions.

A Causality-Aware Perspective on Domain Generalization via Domain Intervention

Most mainstream statistical models will achieve poor performance in Out-Of-Distribution (OOD) generalization. This is because these models tend to learn the spurious correlation between data and will collapse when the domain shift exists. If we want artificial intelligence (AI) to make great strides in real life, the current focus needs to be shifted to the OOD problem of deep learning models to explore the generalization ability under unknown environments. Domain generalization (DG) focusing on OOD generalization is proposed, which is able to transfer the knowledge extracted from multiple source domains to the unseen target domain. We are inspired by intuitive thinking about human intelligence relying on causality. Unlike relying on plain probability correlations, we apply a novel causal perspective to DG, which can improve the OOD generalization ability of the trained model by mining the invariant causal mechanism. Firstly, we construct the inclusive causal graph for most DG tasks through stepwise causal analysis based on the data generation process in the natural environment and introduce the reasonable Structural Causal Model (SCM). Secondly, based on counterfactual inference, causal semantic representation learning with domain intervention (CSRDN) is proposed to train a robust model. In this regard, we generate counterfactual representations for different domain interventions, which can help the model learn causal semantics and develop generalization capacity. At the same time, we seek the Pareto optimal solution in the optimization process based on the loss function to obtain a more advanced training model. Extensive experimental results of Rotated MNIST and PACS as well as VLCS datasets verify the effectiveness of the proposed CSRDN. The proposed method can integrate causal inference into domain generalization by enhancing interpretability and applicability and brings a boost to challenging OOD generalization problems.

Optimal design of supercritical He–H2 PCHE in SABER system by multi-objective genetic algorithm

A double-circle straight-channel printed circuit heat exchanger (PCHE) was first employed in a synergistic air-breathing rocket engine (SABER) system for supercritical He and H2 heat transfer. The heat transfer mechanism of the supercritical flow in the PCHE channel was numerically analyzed. For considered the pressure drop, heat transfer efficiency, and ratio of heat flux to weight, simultaneously, the design of the PCHE is multi-objective genetic optimized. The results shown that the supercritical H2 flow is chaotic near the pseudo-critical point, which is a coupled effect of buoyancy and gravity. Chaotic flow leads to an asymmetrical temperature distribution, which deteriorates the heat transfer performance. For 27 numerical experimental cases designed using the center composite surface method, the determine factors of the regression models of the three objectives for both cold and hot sides were all above 92 %. The Pareto optimal solutions for the supercritical He - H2 PCHE design and performance were obtained based on the nondominated sorting genetic algorithm II. From a comprehensive view of the three targets, the optimal designs were the A-4 and B-4 solutions for the cold and hot sides, respectively.

Solving Convex Multi-Objective Optimization Problems via a Capable Neural Network Scheme

A neural network architecture is constructed to solve Convex Multi-objective Programming Problem (CMPP). By using the weighted sum method, a single-objective optimization problem related to the CMPP is formulated, in which the scalar objective is summation of weighted original objective functions. The Pareto Optimal Solution (POS) is given by using different values of weights. A neural network framework is then designed for solving the obtained convex problem. Based on employing Lyapunov theory, the proposed model is established to be stable in the sense of Lyapunov and it is globally convergent to an exact optimal solution of the convex programming problem with different values of weights. The computer simulations shows the feasibility and the efficiency of the suggested model.

Multi-objective generalized normal distribution optimization: a novel algorithm for multi-objective problems

This study introduces the Multi-objective Generalized Normal Distribution Optimization (MOGNDO) algorithm, an advancement of the Generalized Normal Distribution Optimization (GNDO) algorithm, now adapted for multi-objective optimization tasks. The GNDO algorithm, previously known for its effectiveness in single-objective optimization, has been enhanced with two key features for multi-objective optimization. The first is the addition of an archival mechanism to store non-dominated Pareto optimal solutions, ensuring a detailed record of the best outcomes. The second enhancement is a new leader selection mechanism, designed to strategically identify and select the best solutions from the archive to guide the optimization process. This enhancement positions MOGNDO as a cutting-edge solution in multi-objective optimization, setting a new benchmark for evaluating its performance against leading algorithms in the field. The algorithm's effectiveness is rigorously tested across 35 varied case studies, encompassing both mathematical and engineering challenges, and benchmarked against prominent algorithms like MOPSO, MOGWO, MOHHO, MSSA, MOALO, MOMVO, and MOAOS. Utilizing metrics such as Generational Distance (GD), Inverted Generational Distance (IGD), and Maximum Spread (MS), the study underscores MOGNDO's ability to produce Pareto fronts of high quality, marked by exceptional precision and diversity. The results affirm MOGNDO's superior performance and versatility, not only in theoretical tests but also in addressing complex real-world engineering problems, showcasing its high convergence and coverage capabilities. The source codes of the MOGNDO algorithm are publicly available at https://nimakhodadadi.com/algorithms-%2B-codes.

Hypersonic inlet flow field reconstruction dominated by shock wave and boundary layer based on small sample physics-informed neural networks

High Mach number inlets face complex challenges such as shock wave/boundary layer interference, adversely impacting the aerodynamic characteristics and stable operating boundaries. Traditional computational fluid dynamics (CFD) simulations for performance and flow field analysis are slow, and data-driven deep learning technologies struggle with predicting flow fields in complex aerodynamic phenomena like shock wave/boundary layer interactions, boundary layer separation, and Mach disks. This study introduces a rapid, robust method for reconstructing hypersonic viscous inlet flow fields using inlet geometry design parameters. This method is called shock wave and boundary layer dominated two-dimensional multiphysical field reconstruction model based on multi-scale sensory field fusion residual physical information neural network (PIMSRF_ResNet), ensuring high-precision training data. Using the optimal Pareto solution set from multi-objective optimization with a small sample intelligence method, 150 sets of multi-physics fields under Ma10 conditions with varying geometric design parameters are calculated. Compared to traditional pure data-driven models, PIMSRF_ResNet's structural similarity in the test set reaches 0.9773, with a peak signal-to-noise ratio close to 30 dB and a correlation coefficient exceeding 98%. These experimental results demonstrated that the proposed method is a promising tool for real-time prediction of complex internal flow fields dominated by high Mach number shock waves and boundary layers.

Multi-objective optimization strategy for regional multi-energy systems integrated with medium-high temperature solar thermal technology

The high proportion and volatility of renewable energy pose a significant challenge to efficient collaboration between photovoltaic/thermal and wind power in multi-energy systems. Therefore, this paper proposes a Regional Multi-Energy System (RMES) based on Medium-High Temperature Solar Thermal (MHTST) technology. The novelty of the solution integrates dispatchable photovoltaic and photothermal conversion pathways, facilitating flexible and controllable utilization of solar energy via installed Thermal Energy Storage (TES). A multi-objective optimization model is developed to ensure the optimal operation of the proposed system under typical seasonal scenarios. The method that combines Branch-and-Reduce with Multi-Learning-Task is used to handle the formulated Mixed Integer Nonlinear Programming (MINLP) and swiftly identify optimal Pareto solutions. Case studies are performed over the improved united communities of the Test Region for Energy Transition and Comprehensive Reform in Taiyuan, China. Compared with the conventional photovoltaic technology, the simulation results show that the proposed solution has superior performance in both winter-heating and summer-cooling operations across 24-hour scheduling periods: operating costs reduced by 12.5% and 18.7%, carbon emissions decreased by 7.4% and 21.4%, with local solar power accommodation increased by 263.89kW and 487.47kW, respectively.

A multi-objective planning and scheduling model for elective and emergency cases in the operating room under uncertainty

Hospitals are paramount hubs for delivering healthcare services, with their Operating Rooms (ORs) as a pivotal and financially substantial component. Efficient surgery ward planning is crucial in healthcare institutions, aiming to improve medical service quality while reducing costs. This research delves into the intricacies of integrated OR planning and scheduling, focusing on elective and emergency patients in an uncertain environment. To address these challenges, a mixed integer programming (MIP) framework is developed to minimize inactivity and patient wait times while optimizing high-priority resource allocation. Both upstream and downstream units of the ward, the Pre-operative Holding Unit (PHU), Post Anesthesia Care Unit (PACU), and Intensive Care Unit (ICU) are included. The inherently uncertain aspects of surgery, including surgical duration, Length of Stay (LOS), and the influx of emergency patients, demand an intelligent optimization approach. Consequently, a robust optimization strategy is harnessed to effectively grapple with this pervasive uncertainty. A deterministic model is introduced and improved using an enhanced epsilon constraint method. The culmination of this analytical journey yields a collection of Pareto-optimal solutions. Empirical results, supported by managerial insights, highlight the superiority of the proposed method over the traditional weighting approach.

Optimizing industrial tunnel kiln operations for ceramic roof tile production: A bi-objective approach

The ceramic firing process constitutes a highly energy-intensive production step that significantly affects the quality and final properties of the ceramic product. This work presents a model-based, bi-objective optimization approach for an industrial-scale tunnel kiln used in ceramic roof tile production, focusing on the exploration of trade-offs between productivity and thermal energy consumption. Initially, sintering kinetics are established based on lab experiments and integrated within a novel physics-based tunnel kiln model, thus allowing sintering evolution to be considered for the derivation of the optimal kiln operation. Two bi-objective optimization studies are then conducted to explore trade-offs under steady-state and transient-state kiln operations, thus generating a set of non-dominated operating policies. The attained Pareto optimal solutions are then evaluated with respect to the values of Specific Energy Consumption (SEC), which is distinctly minimized. This results in optimal SEC values of 0.283 for the steady state and 0.277 kWh/kg for the transient state kiln operation.

An efficient bi-objective optimization approach for the optimal design of omnichannel supply chain distribution networks with sustainability

ABSTRACT This article studies a bi-objective omnichannel supply chain network design (SCND) problem, while simultaneously minimizing the overall supply chain (SC) cost and associated environmental emissions. A novel bi-objective mixed integer linear programming model is formulated, then an efficient optimization approach is proposed for the problem. Experimental studies on a case study and 210 random testing instances were conducted to evaluate the performance of the proposed model and approach. For the case study, 10 Pareto-optimal solutions were obtained within 1.9 s. For the random testing instances, the average number of Pareto-optimal solutions and computational time were 10.19 and 18.85 s, respectively. The overall results show that the proposed method is efficient and outperforms the adapted non-dominated sorting genetic algorithm II on test instances. Computational results indicate that this approach could assist decision makers in making good decisions, with considerable SC cost saving and carbon emission reductions in different situations.

Coalitional Pareto optimal solution of one differential game

This paper is devoted to the differential positional coalitional games with non-transferable payoffs (games without side payments). We believe that the researches of the objection and counter-objection equilibrium for non-cooperative differential games that have been carried out over the last years allow to cover some aspects of non-transferable payoff coalitional games. In this paper we consider the issues of the internal and external stability of coalitions in the class of positional differential games. For a differential positional linear-quadratic six-player game with a two-coalitional structure, the coefficient constraints are obtained which provide an internal and external stability of the coalitional structure.

Modelling and optimization for integrated scheduling problem considering spare parts production, batch transportation and equipment operation

Existing production scheduling research has made great effort to integrate multiple production-related actives to achieve efficient product supply, such as the integration of production and transportation, and the integration of production and equipment operation and maintenance (O&M). However, rare studies are executed to investigate the integration of production, transportation and O&M, which may lead to inefficient supply plans. Encouraged by this, we consider a novel integrated scheduling problem, in which two-stage hybrid flow shop scheduling for spare parts manufacturing, transportation scheduling of the third-party logistics (3PL) and operational strategies of complex equipment are considered simultaneously. To tackle it, a mixed-integer linear programming model is constructed to minimize total production costs, minimize transportation costs and maximize operational utility of the equipment. Furthermore, a two-stage memetic algorithm (TSMA) is designed for addressing the problem. It employs a five-layer encoding method for chromosome representation and three well-tailored initialization methods to generate a high-quality initial population. In the first optimization stage, some problem-specific operators, including three crossovers, two mutations, and an entity-oriented local search operator, are proposed to improve its search capability. Two cost-saving strategies devised in the second optimization stage are designed to further optimize the optimal Pareto solutions generated in the previous stage. Extensive experiments demonstrate the superiority of the proposed designs and TSMA in addressing the considered problem. In addition, the necessity of integrating production, transportation and equipment operation is verified through a set of comparison experiments. The study enriches integrated production scheduling theory, and provides methodological support for improving operational utility of complex equipment.

Bi-objective model for tactical planning in corn supply chain considering CO2 balance

This paper addresses the Brazilian corn production logistic supply chain with an optimisation model considering carbon emission from transportation and carbon sequestration from corn production. The focus is on the higher-level decision planning, which includes the best regions for corn cultivation, location and sizing of silos to store grains, transportation modes with intermodality, considering several resource constraints to meet the demands of domestic market and export. Two conflicting objectives are considered: the logistics costs of the supply chain and the balance of CO 2 . Accurate data are used to evaluate the model and the Pareto optimal solutions are produced in scenarios potentially feasible in practice. The solutions showed relevant information to guide decisions about investment in logistic infrastructure. We demonstrated that cleaner transportation routes lead to solutions that have larger carbon stocks with 3–5% increase in costs by only choosing more suitable regions for corn cultivation and transportation modes.

A multi-objective two-stage stochastic unit commitment model for wind and battery-integrated power systems

This paper presents a mathematical programming framework for modeling the operations of power systems with high wind power penetration and BESS, accounting for wind and power demand uncertainties. For this, we introduce a multi-objective two-stage stochastic unit commitment model aimed at constructing on/off schedules that balance operating costs and CO2 emissions. Under the realistic limitations imposed by BESS high variable operating cost, we focus on assessing and analyzing the operational impact of BESS for two different integration schemes: wind farm-coupled and stand-alone. The proposed method of solution consists in an augmented ϵ-constrained algorithm with an integrated normalized euclidean distance-based bisection routine to produce more equispaced Pareto optimal solutions. We applied the proposed framework to a modified version of the New England IEEE-39 bus test system for three disjoint cases of analysis: without BESS integration, with BESS integrated into a wind farm, and with a stand-alone BESS integrated into the grid. The results demonstrate the efficacy of the proposed framework and show substantial benefits in terms of CO2 emissions reductions, particularly in the stand-alone configuration, which, although limited in extent of use, promotes the direct injection of wind power into the grid, the decommitment of polluting thermal units, enhance the use of free or low emissions technologies, and contributes as a provider of spinning reserves.

Optimization of landscape garden greening design based on multi objective genetic algorithm

This paper presents a novel approach to optimize landscape garden greening design using a multi-objective genetic algorithm (MOGA)[1]. Incorporating genetic algorithms into landscape architecture offers a promising avenue for efficiently navigating the complex and multidimensional design space inherent in green infrastructure projects. Through a comprehensive bibliometric analysis of existing literature, this study synthesizes key insights into the application of genetic algorithms in landscape design and identifies gaps for further exploration[2]. Leveraging the evolutionary process of genetic algorithms, our methodology focuses on simultaneously optimizing multiple objectives such as biodiversity conservation, aesthetic appeal, water efficiency, and ecosystem services provisioning[3]. By iteratively evolving and selecting landscape configurations based on fitness criteria derived from these objectives, the MOGA enables designers to explore a diverse range of design alternatives and identify Pareto-optimal solutions that balance competing priorities. The integration of genetic algorithms into landscape design facilitates an iterative and adaptive design process, allowing for the exploration of complex trade-offs and the generation of innovative design solutions. Through a case study application, we demonstrate the effectiveness of the MOGA approach in optimizing landscape garden greening designs, showcasing its potential to enhance sustainability, resilience, and functionality in urban green spaces. This research contributes to the growing body of knowledge on computational design methods in landscape architecture and provides valuable insights for practitioners and researchers seeking to leverage genetic algorithms for optimizing green infrastructure projects.

Hybrid Genetic-ADAM Optimizer to Improve Disassembly Line Balancing Problem

Modern products are designed to meet the needs of customized and short-lived products, after a short period of time, these products become waste products, these waste products are accumulating at an exponential rate, resulting in environmental degradation as a result of pollution, in order to keep this environment clean, it is necessary to have disassembly lines for those waste products, so in this research a Hybrid Genetic ADAM optimizer Algorithm was proposed to facilitate the disassembly operations at work stations placed in the disassembly lines, the proposed algorithm used to solve multi-objective disassembly line balancing problem, and Pareto optimal solution was used to determine non inferior solutions from a population. The trend of results reveal 6.1 percent a reduction in disassembly workstations, reduction of at least 0.05 percent of the idle time, reducing to minimum run time 1.5 percent comparing proposed and other meta heuristics algorithms. Furthermore, the plans of disassembly data are created to be valuable regarding trace ability and disassembly improvement processes in the future.

A note on “A new method for intuitionistic fuzzy multi-objective linear fractional optimization problem and its application in agricultural land allocation problem”

Moges et al. (Inf. Sci. 625 (2023) 457–475) proposed a method to find a Pareto-optimal solution (POS) of intuitionistic fuzzy multi-objective linear fractional optimization problem (MOLFOP). In this method, firstly, an intuitionistic fuzzy MOLFOP is transformed into a crisp MOLFOP with the help of a ranking function. Then, using the existing method (Fuzzy Sets Syst. 125 (2002) 335–342), the transformed crisp MOLFOP is transformed into a crisp multi-objective linear optimization problem (MOLOP). Finally, it is assumed that to find a POS of the considered intuitionistic fuzzy MOLFOP is equivalent to find a POS of the transformed crisp MOLOP. It is pertinent to mention that this assumption is valid only if the transformed crisp MOLFOP is equivalent to the considered intuitionistic fuzzy MOLFOP as well as the transformed crisp MOLOP is equivalent to the transformed crisp MOLFOP. In this note, a numerical example is considered to show that the transformed crisp MOLFOP is not equivalent to the considered intuitionistic fuzzy MOLFOP. Also, on the basis of the existing results (Fuzzy Sets Syst. 246 (2014) 156–159), it is pointed out that the transformed crisp MOLOP is not equivalent to the transformed crisp MOLFOP. Therefore, Moges et al.’s method is not valid and hence, the results of agricultural planning problem of Ethopia for cultivation of different crops, obtained by Moges et al. with their proposed method, are not correct.

A route network resource allocation method based on multi-objective optimization and improved genetic algorithm

In order to solve the problem of imbalance between traffic demand and airspace capacity of high-altitude air route network, reduce unnecessary delay costs, and improve air route operation efficiency, the resource allocation problem of multi-objective air route network for CTOP program is studied. Taking the affected flights in the congested area of air routes as the research object, taking into account the constraints of actual flight operation, FCA time slot resource availability limit, FCA capacity limit, etc., aiming at minimizing the total delay time of each flight and maximizing the fairness of airlines, a multi-objective optimization model for air route network resource allocation is established, and an improved NSGA-II algorithm is designed to solve the model. Based on the actual operation data of air routes in East China, the Pareto optimal solution set is obtained and compared with the traditional RBS algorithm, the average delay time is reduced by 5.49% and the average fair loss degree is reduced by 66.76%. The results show that the proposed multi-objective optimization model and the improved NSGA-II algorithm have better performance, which can take into account the fairness of each airline on the basis of reducing the total delay cost, realize the allocation of optimal flight trajectories and time slot resources, and provide a reference scheme for air traffic control resource scheduling.

Parameter Optimization of Frazil Ice Evolution Model Based on NSGA-II Genetic Algorithm

This study is based on the research results of frazil ice evolution in recent years and proposes an improved frazil ice evolution mathematical model. Based on the NSGA-II genetic algorithm, seven key parameters were used as optimization design variables, the minimum average difference between the number of frazil ice, the mean and the standard deviation of particle diameter of the simulation results, and the observed data were used as the optimization objective, the Pareto optimal solution set was optimized, and the importance of each objective function was analyzed and discussed. The results show that compared to previous models, the improved model has better agreement between simulation results and experimental results. The optimal parameters obtained by the optimization model reduces the difference rate of water temperature process by 5.75%, the difference rate of quantity process by 39.13%, the difference rate of mean particle size process by 47.64%, and the difference rate of standard deviation process by 56.84% during the period of intense evolution corresponding to the initial parameter group. The results prove the validity of the optimization model of frazil ice evolution parameters.