Multi-objective Optimization Algorithm Research Articles

Optimization of operational parameters of marine methanol dual-fuel engine based on RSM-MOPSO

Methanol and natural gas, as green fuels for environmental protection, have shown great potential in the field of maritime transportation. This study explores how the methanol energy fraction (MEF), exhaust gas recirculation (EGR), excess air ratio (λ), and engine injection timing (EIT) influence combustion and emission traits in marine dual-fuel (DF) engine. Initially, a DF engine model was formulated through experiments using CONVERGE software, while the CHEMKIN program devised a chemical mechanism involving 100 compounds and 512 reactions. The response surface methodology (RSM) was subsequently utilized to design the experiment and develop the regression model. The improved multi-objective particle swarm optimization (MOPSO) algorithm was applied to optimize three critical variables: brake thermal efficiency (BTE), carbon monoxide (CO), and nitrogen oxide (NOx) emissions. Ultimately, feature-optimized scenarios from the Pareto front were chosen for comparative evaluation to derive the optimal configuration. The results show that when the decision variables MEF, EGR, λ and EIT are 22.33 %, 10 %, 1.81 and 11°CA BTDC respectively, there is a better trade-off between the three target variables. Compared with the original case, the change of ITE, NOx and CO emissions in the optimal case are +0.97 %, −39.53 % and −14.51 %, respectively. Overall, based on the intelligent optimization approach, the rational selection of DF engine parameters improved the ITE and most NOx and CO emissions were effectively suppressed.

Multi-objective optimization of chemical reaction characteristics of selective catalytic reduction in denitrification of diesel engine using ELM-MOPSO methodology

This study systematically investigated the effects of structural parameters in a two-stage selective catalytic reduction (SCR) catalyst on ammonia storage, NO conversion efficiency, and ammonia slip using computational fluid dynamics (CFD) simulations. The rank ordering of the correlations between structural parameters and performance metrics was determined by gray relational analysis (GRA). Both the catalyst diameter and the upstream catalyst porosity had correlations exceeding 0.9, making them key parameters affecting SCR performance. An extreme learning machine (ELM) prediction model was trained using data obtained from CFD simulations. The prediction performance of this ELM model was then evaluated using statistical metrics. Finally, the optimized Pareto frontier diagram was obtained through the multi-objective particle swarm optimization (MOPSO) algorithm, and the optimal results were selected for further CFD modeling analysis. The results showed that the upstream NO conversion efficiency of the SCR system was improved by 7.7 %, the downstream NO conversion efficiency was improved by 18.67 %, the ammonia slip was reduced by 71.97 %, and the upstream ammonia storage capacity was improved by 6.83 % compared with the original model.

A multi-objective optimization and evaluation framework for LID facilities considering urban surface runoff and shallow groundwater regulation

Currently, the goals of sponge city construction mostly focus on urban surface water, with few considerations of groundwater indicators, and there is a lack of simulation methods that consider the interaction between surface water and groundwater under low impact development (LID) scenarios. Taking a sponge campus in Xi'an as the research object, this paper proposes a method to realize the interaction between surface water and groundwater at different spatial and temporal scales, so as to construct a SWMM-MODFLOW coupled numerical model to carry out the analysis of hydrological effect of sponge city comprehensively taking into account both surface water and groundwater. Simultaneously, the SWMM is coupled with the NSGA-III algorithm for multi-objective optimization of LID facility configurations, aiming to identify a globally optimal solution set for LID facility configurations under both long and short-duration rainfall scenarios. A novel framework for a comprehensive evaluation system of surface water-groundwater benefits is also developed to comprehensively assess LID facility optimization schemes that meet the goals of stormwater runoff infiltration and reduction, pollution interception and purification, and groundwater recharge conservation. The simulation results show that after optimization, the LID scheme has good surface runoff regulation effects and pollution reduction capabilities, reducing the runoff peak from 2.297 m3/s to 2.128 m3/s, significantly lowering the risk of inundation and effectively reducing the total suspended solids (SS) load by 42.38 kg at the outfall. Meanwhile, the groundwater recharge effect is particularly significant in September. Compared to the baseline scenario, the average groundwater levels from June to September were raised by 3.966 cm, 5.120 cm, 6.743 cm, and 7.639 cm, respectively. The maximum daily groundwater level rise reached 7.82 cm, while the average groundwater level for the whole year of 2023 increased by 2.61 cm. The maximum transport area of pollutants decreased from 2359.44 m2 to 1796.54 m2, and the maximum transport distance reduced from 79.985 m to 69.977 m. Additionally, the central concentration of pollutants also decreased. This optimization evaluation framework will aid decision-makers in selecting LID facility management strategies that balance the dual benefits of surface water runoff and groundwater regulation.

Multi-Objective Hybrid Algorithm Integrating Gradient Search and Evolutionary Mechanisms

The current multi-objective evolutionary algorithm (MOEA) has attracted much attention because of its good global exploration ability, but its local search ability near the optimal value is relatively weak, and for optimization prob lems with large-scale decision variables, the number of populations and iterations required by MOEA are very large, so the optimization efficiency is low. Gradient-based optimization algorithms can overcome these problems well, but they are difficult to be applied to multi-objective problems (MOPs). Therefore, this paper introduced random weight function on the basis of weighted average gradient, developed multi-objective gradient operator, and combined it with non-dominated genetic algorithm based on reference points (NSGA- III) proposed by Deb in 2013 to develop multi-objective optimization algorithm (MOGBA) and multi-objective Hybrid Evolutionary algorithm (HMOEA). The latter greatly enhances the local search capability while retaining the good global exploration capability of NSGA-III. Numerical experiments show that HMOEA has excellent capture capability for various Pareto formations, and the efficiency is improved by times compared with typical multi-objective algorithms. And further HMOEA is applied to the multi-objective aerodynamic optimization problem of the RAE2822 airfoil, and the ideal Pareto front is obtained, indicating that HMOEA is an efficient optimization algorithm with potential applications in aerodynamic optimization design.

Variable Geometry Turbine Turbocharger Optimization Using Machine Learning for On-Highway Fuel Cell Applications

<div>Turbocharger design involves adjustment of various geometric parameters to improve the performance and suit mechanical constraints, depending on the application-specific requirements. In designing the turbine stage, these parameters are optimized to maximize durability and efficiencies at the required operating points. For a heavy-duty class eight truck, “road load” and “rated power” are generally considered the two most important operating points. The objective of this article is to improve the efficiencies of these two operating points.</div> <div>The common challenge in the development of a turbine wheel design is the large number and interdependence of parameters to optimize. For example, increasing the blade thickness improves structural strength but reduces the mass flow capacity, thus influencing its performance. It is general practice to optimize the wheel geometry using iterative CFD analysis. However, running simulations for every single change in geometry involves significant computation time and does not guarantee the global optimum.</div> <div>This study proposes a machine learning (ML)-driven optimization process for variable turbine geometry (VTG) wheels with two target operating points. Initial CFD data is collected and used to train/validate a ML model for each operating point. A multi-objective optimization algorithm utilizes these ML models to provide a list of ideal turbine wheel designs, and the best candidates are validated in CFD for accuracy. The results are a balanced maximization in efficiency for both operating points, with an improvement in the pareto front by 1.4% points over CFD optimization alone.</div>

Cold Coastal City Neighborhood Morphology Design Method Based on Multi-Objective Optimization Simulation Analysis

In the context of global warming and the frequent occurrence of extreme weather, coastal cities are more susceptible to the heat island effect and localized microclimate problems due to the significant influence of the oceanic climate. This study proposes a computer-driven simulation optimization method based on a multi-objective optimization algorithm, combined with tools such as Grasshopper, Ladybug, Honeybee and Wallacei, to provide scientific optimization decision intervals for morphology control and evaluation factors at the initial stage of coastal city block design. The effectiveness of this optimization strategy is verified through empirical research on typical coastal neighborhoods in Dalian. The results show that the strategy derived from the multi-objective optimization-based evaluation significantly improves the wind environment and thermal comfort of Dalian neighborhoods in winter and summer: the optimization reduced the average wind speed inside the block by 0.47 m/s and increased the UTCI by 0.48 °C in winter, and it increased the wind speed to 1.5 m/s and decreased the UTCI by 0.59 °C in summer. This study shows that the use of simulation assessment and multi-objective optimization technology to adjust the block form of coastal cities can effectively improve the seasonal wind and heat environment and provide a scientific basis for the design and renewal of coastal cities.

Optimizing Multi-Stage Project Portfolio Selection Considering Integrating Lifecycle and Interactions

Project portfolio selection is essential for a company to achieve its strategic goals. Due to constraints such as budget and manpower, companies cannot undertake all projects simultaneously and must prioritize those offering the highest value. Projects often interact and progress through various phases, adding complexity to the selection process. To address these challenges, this study introduces a model that accounts for the multi-stage execution of projects, their interactions, and multiple objectives. A novel multi-objective optimization algorithm is developed to solve this problem, along with a refined project selection method designed to offer decision-makers enhanced insights. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approach.

Optimization of laser cladding powder ratio and process parameters based on MOGWO algorithm

Optimizing the process parameters is crucial to obtaining a high-quality fusion coating. The fitted regression model for each response was then analyzed by creating a central composite test with process parameters and power ratios (laser power, scanning speed, and Ni-clad graphite content) as inputs and the quality of the fused coating (dilution rate, microhardness, and width of the fused coating) as responses. The laser cladding process parameters and power ratios were optimized using the multi-objective Gray Wolf Optimization (MOGWO) algorithm. The best combinations of process parameters and power ratios were laser power of 1596 W, scanning speed of 21.7 mm/s, and Ni-clad graphite percentage of 18.4 %. Experimental validation demonstrates the superiority and accuracy of the MOGWO algorithm. The dilution rate of the optimized fusion-clad coating is increased by 47.4 % and the microhardness is increased by 17.8 %.

Stage-Specific Multi-Objective Five-Element Cycle Optimization Algorithm in Green Vehicle-Routing Problem with Symmetric Distance Matrix: Balancing Carbon Emissions and Customer Satisfaction

This study presents a bi-objective optimization model for the Green Vehicle-Routing Problem in cold chain logistics, with a focus on symmetric distance matrices, aiming to minimize total costs, including carbon emissions, while maximizing customer satisfaction. To address this complex challenge, we developed a Stage-Specific Multi-Objective Five-Element Cycle Optimization algorithm (MOFECO-SS), which dynamically adjusts optimization strategies across different stages of the process, thereby enhancing overall efficiency. Extensive comparative analyses with existing algorithms demonstrate that MOFECO-SS consistently outperforms in solving the multi-objective optimization model, particularly in reducing total costs and carbon emissions while maintaining high levels of customer satisfaction. The symmetric nature of the distance matrix further aids in achieving balanced and optimized route planning. The results highlight that MOFECO-SS offers decision-makers flexible route planning options that balance cost efficiency with environmental sustainability, ultimately improving the effectiveness of cold chain logistics operations.

Multi-objective optimal allocation of construction project risks, ant colony optimization algorithm

PurposeThe purpose of this paper is to introduce a new approach for finding the most appropriate risk allocation among construction contract parties. Although risk allocation is a strategic decision that can greatly affect the cost and time of the project, it is often made based on the personal judgments of employers. That is why owners usually find it a very time-consuming and expensive decision process, while most contractors feel that risk sharing is not done fairly. In this paper, a quantitative model for risk allocation is introduced to fulfill clients’ conflicting expectations in the risk allocation process.Design/methodology/approachBy defining conflicting expectation of owners in the form of three quantitative objectives (lowest cost, maximum reliability and minimum risk exposure), a multi-objective optimization algorithm was developed to select the most appropriate risk allocation. Using experts’ knowledge through fuzzy set theory, a multi-objective decision-making model is developed based on an ant colony optimization algorithm. The proposed model is able to find the optimum risk allocation at the lowest cost and highest reliability while protecting the client against risk exposure within multiple parties projects.FindingsThe proposed model has the ability to select the most appropriate risk allocation in multi-parties projects (such as public–private partnerships) and quantitatively measure the impact of each employer’s choice on project results in the form of cost and time. The results of implementing the proposed model in a case study project revealed that optimum risk allocation requires a balanced attitude, and the transfer of all risks to the other parties will not necessarily lead to the lowest cost. The client should bear more responsibilities in risk management to avoid extreme time delay and cost overrun.Research limitations/implicationsThe proposed model can be implemented in multi-parties projects (such as public–private partnership), while other methods introduced in previous studies can only be used for projects with two party (client and contractor).Practical implicationsBy implementing the proposed model in a real project in this article and comparing its results with previous works, it has been shown that the proposed model has a good performance. Using this model can help clients drastically reduce cost and time and ultimately successfully conclude risk allocation negotiations (which is the most difficult part of any contract negotiation).Originality/valueIn this paper, the risk allocation process is modeled in the form of a multi-objective decision problem. This method helps employers to measure their conflicting goals and choose the most appropriate risk allocation according to their objectives. Also, in this article, the conflicting expectations of the employer in the process of contract negotiations are introduced as three measurable goals, which gives the decision-maker the ability to balance his expectations and not miss an objective. In the final step, an optimization model is developed to select the best option, which can choose the most appropriate party to bear the risk in a short time and among an unlimited number of participants.

Multi-energy synergistic planning of distributed energy supply system: Wind-solar-hydrogen coupling energy supply

This study is to improve the efficiency of energy utilization with the continuous growth of global energy demand and the increasingly severe environmental problem. A hydrogen-containing distributed energy supply system is proposed, which includes a hydrogen energy subsystem. The main driver of the system is renewable energy, while hydrogen energy is used as a carrier to assist the flow of energy. This study proposes an improved following electric load (FEL) strategy based on a comprehensive consideration of energy interactions within the system, and designs an optimal configuration model aimed at improving its economic, environmental and energy benefits. In addition, an improved rime algorithm (IRIME) is proposed, whose convergence performance and solution stability are greatly improved. A multi-objective optimization algorithm with better convergence performance, multi-objective improved rime algorithm (MO-IRIME), is proposed for solving the optimal configuration model to obtain the optimal capacity of the equipment inside hydrogen-containing distributed energy supply system. The total annual cost is reduced by 44.80%, the primary energy consumption by 68.47% and the pollutant gas emissions by 75.79% compared to the reference system. In addition, the way of interaction and coordination of multiple energy sources in the daily cycle is analyzed.

A novel method of high-density urban block form generation based on multi-objective solar performance optimization: A case study of Nanjing

Efficiently harnessing solar radiation in high-density urban environments to optimize block forms holds significant potential for advancing urban low-carbon development. This paper introduces a novel method for generating high-density block forms based on comprehensive solar utilization. Grasshopper was used to compile an automated workflow for block form generation, solar simulation, and multi-objective optimization algorithms. Leveraging maximum solar radiation within and surrounding the block and effective photovoltaic utilization ratio are the three objectives in the multi-objective optimization process. From 60,000 generated samples, 1200 block forms were selected as the Pareto fronts. As the plot ratio of the generated blocks increases from 3 to 7, the annual mean solar radiation around the block decreases from 891.3 kWh/m2 to 863.5 kWh/m2, a reduction of only 3.1 %. When the number of blocks within the block increases from 1 to 4, the average solar radiation inside the block increases from 484.8 kWh/m2 to 516.1 kWh/m2, an increase of about 6.5 %. Additionally, as site coverage increased from 30 % to 60 %, the average solar radiation inside the block decreased from 549.2 kWh/m2 to 459.8 kWh/m2, a decrease of approximately 17 %. Notably, the photovoltaic power generation fell from 90.3 kWh/m2 to 61.2 kWh/m2, a decrease of about 32 %. The results indicate that the grid modeling method and multi-objective optimization algorithm adopted in this study can significantly improve the diversity of block morphology and achieve multiple solar performance requirements. The findings support designers in swiftly assessing building volume rationality and solar utilization potential at the early stages of urban design.

A Novel Surrogate-Assisted Multi-Objective Well Control Parameter Optimization Method Based on Selective Ensembles

Multi-objective optimization algorithms are crucial for addressing real-world problems, particularly with regard to optimizing well control parameters, which are often computationally expensive due to their reliance on numerical simulations. Surrogate-assisted models help to reduce this computational burden, but their effectiveness depends on the quality of the surrogates, which can be affected by candidate dimension and noise. This study proposes a novel surrogate-assisted multi-objective optimization framework (MOO-SESA) that combines selective ensemble support-vector regression with NSGA-II. The framework’s uniqueness lies in its adaptive selection of a diverse subset of surrogates, established prior to iteration, to enhance accuracy, robustness, and computational efficiency. To our knowledge, this is the first instance in which selective ensemble techniques with multi-objective optimization have been applied to reservoir well control problems. Through employing an ensemble strategy for improving the quality of the surrogate model, MOO-SESA demonstrated superior well control scenarios and faster convergence compared to traditional surrogate-assisted models when applied to the SPE10 and Egg reservoir models.

An advanced high dimensional model representation approach for internal combustion engine modeling and optimization

This work introduces an efficient data-driven approach for engine performance modeling and optimization. A highly accurate and robust high-dimensional model representation (HDMR) surrogate model is developed based on the dataset generated from a coupled KIVA4-CHEMKIN Ⅱ software. The HDMR model is integrated with a multi-objective optimization algorithm, enabling the automatic identification of optimal combustion strategies. Results suggest that the constructed HDMR model is able to accurately predict the engine performance and exhaust gas emissions with negligible CPU costs. Moreover, the model effectively identifies optimal engine operating conditions, leading to enhanced fuel efficiency.

Layout Optimization of Wave Energy Park Based on Multi-Objective Optimization Algorithm

Abstract In this paper, both semi-analytical method and numerical simulation is applied to investigate the hydrodynamic behavior of large arrays of point-absorber wave energy converters (WECs). To analyze wave interactions among multiple WECs within an array, a semi-analytical model is developed based on the potential flow theory and the matched eigen-function expansions method. The fluid domain is divided into two kinds of regions: interior regions underneath the cylinders and an exterior region surrounding all the cylinders. The matched eigenfunction expansions method is employed to solve the radiation potential problem in each domain, and the hydrodynamic coefficients and motion response of the cylinders in the array are evaluated. To validate the accuracy of the semi-analytical method, WAMIT is adopted to simulate the wave energy park numerically and compared with the results by the semi-analytical model. The hydrodynamic characteristics and power absorption performance of the WECs within the wave energy park are analyzed. The power performance of a wave energy park is studied as functions of layout geometry, incident wave direction and separation distance between WECs respectively. Finally, MOPSO based on a surrogate model is used to optimize the layout of wave energy array.

A research on improving the precision of laser tracker in alignment based on Pareto improvement principle.

The accuracy of laser trackers in large-scale dimensional metrology is subject to various influencing factors, with instrument positioning being a primary source of error. To address this, a multi-objective optimization algorithm, grounded in the Pareto improvement principle, is proposed. This algorithm is designed to optimize instrument placement, thereby minimizing measurement errors and enhancing the algorithm's efficacy in error reduction. Thereby, this article proved that positioning the laser tracker consistently on one side of the measurement area and aligning its height with the measuring points can effectively reduce the uncertainty of control point errors by up to 50%.

A dual-sampling based evolutionary algorithm for large-scale multi-objective optimization

The vast search space in large-scale multi-objective optimization represents a significant challenge for evolutionary algorithms to converge towards the Pareto Front. As an effective search strategy, direction-guided sampling technique could improve the search efficiency by exploring along the approximated directions to approach the Pareto set. However, the approximated directions may fail to interact with the true Pareto set and result in inefficient search. To address this issue, a dual-sampling method is proposed in this paper. In addition to the samples along the directions approximated by direction-guided sampling, fuzzy Gaussian sampling is applied to adjust the search direction and generate more accurate and evenly distributed solutions. Moreover, a convergence-and-diversity-based mating selection is introduced to balance the exploration and exploitation. The experiments on 72 test benchmarks with bi- and tri-objectives and 500 to 5000 decision variables show the superiority of the proposed algorithm compare with the state-of-the-art algorithms.

Dual-space distribution metric-based evolutionary algorithm for multimodal multi-objective optimization

Multimodal multi-objective optimization problems (MMOPs) are characterized by having multiple global or local Pareto solution sets. In most of multimodal multi-objective evolutionary algorithms, the distribution of population in objective space and decision space cannot be taken into account, simultaneously. In this paper, an innovative evolutionary algorithm based on dual-space distribution metric for multimodal multi-objective optimization (DsDMEA) is designed to solve this problem. Specifically, the two enhanced performance metrics are coupled together as a single dual-space distribution metric (DsDM) serving as the criterion for environmental selection. DsDMEA explores solutions on Pareto front and Pareto solutions sets that are not associated with the reference point, which show limited contributions to the distribution in dual spaces. Then DsDMEA removes any bi-noncontributing solutions using DsDM during environmental selection until the population size is met. This achieves a balance between the distribution of solutions and convergence in decision space. At the same time, this paper introduces a novel fitness computation method, enabling the precise localization of local Pareto fronts within the population. Finally, eight state-of-the-art multimodal multi-objective evolutionary algorithms are adopted to make a comparison on two types of benchmark to verify the performance of the DsDMEA. The experimental results demonstrated the DsDMEA effectiveness in solving MMOPs with local problems and traditional MMOPs.

Multi-objective optimal scheduling of electricity consumption in smart building based on resident classification

By the end of 2021, the urbanization rate of China had reached 64.72%. Increasing urbanization rates have led to an 80 percent share of carbon emissions in urban areas. Therefore, a load optimal scheduling model of smart buildings is proposed in this paper, which takes into account the cost of carbon emissions. The model aims to minimize the electric cost for building residents and maximize the utilization of distributed energy. The research focuses on the load optimal scheduling for two types of residents, i.e., the working residents and the retired ones, based on their electricity usage patterns and habits. To address the challenges of uneven load distribution, nonlinear behavior, and uncertainties introduced by electric vehicles and photovoltaic energy, the multi-objective beluga whale optimization algorithm with hybrid reverse learning competitive strategies (RCMBWO) is introduced. It utilizes the energy storage and discharge capabilities of electric vehicles to mitigate the uncertainties of photovoltaic energy generation. The simulation results show that load optimal scheduling for both types of residents can lead to significant cost savings for a smart building with 100 households, approximately 29,554 RMB per year. Furthermore, the optimized results can guide the determination of the appropriate size for the photovoltaic energy storage system, reducing energy waste resulting from insufficient energy consumption capability of smart buildings. The research on targeted load optimal scheduling for classified residents presents a viable solution for enhancing the cost-effectiveness and environmental benefits of smart buildings.

An optimal nonlinear fractional order controller for passive/active base isolation building equipped with friction-tuned mass dampers

This paper presents an optimal nonlinear fractional-order controller (ONFOC) designed to reduce the seismic responses of tall buildings equipped with a base-isolation (BI) system and friction-tuned mass dampers (FTMDs). The parameters for the BI and FTMD systems, as well as their combinations (BI-FTMD and active BI-FTMD or ABI-FTMD), were optimized separately using a multi-objective quantum-inspired seagull optimization algorithm (MOQSOA). The seismic performances of the BI, FTMD, BI-FTMD, and ABI-FTMD systems for a 15-storey building subjected to two far-field (Loma Prieta and Landers) and two near-fields (Tabas and Northridge) earthquakes were evaluated. The results indicated that structures with BI, FTMD, BI-FTMD, and ABI-FTMD systems outperformed the uncontrolled structure in reducing structural responses during the design earthquakes (Loma Prieta and Tabas). However, under validation earthquakes (Landers and Northridge), the peak acceleration of the building with the FTMD system was worse than that of the uncontrolled structure during the near-field Tabas earthquake. To address this issue, we proposed a combination of the active BI system and the FTMD system. Time history analysis results demonstrated that for the building equipped with the ABI-FTMD system, the peak displacement, peak acceleration, and peak inter-storey drift were reduced by approximately 60%, 64%, and 78%, respectively, as compared to the uncontrolled structure.