Multi-objective Optimization Algorithm Research Articles

An efficient and resilient energy management strategy for hybrid microgrids inspired by the honey badger's behavior

This manuscript introduces a highly efficient hybrid renewable energy system (HRES) that combines photovoltaic (PV) panels and wind turbines (WTs) as primary power sources, supplemented by three backup systems: batteries, hydrogen energy storage systems (HESSs), and supercapacitors (SCs). This system employs a multi-objective optimization algorithm to dynamically identify the best energy management system (EMS). The performance of the proposed EMS across different operational scenarios is assessed using seven distinct algorithms to identify the best solution, particularly emphasizing two main objective functions: operating cost and loss of power supply probability (LPSP). Furthermore, the study rigorously evaluates the performance of these algorithms against nine benchmarks to determine the most appropriate algorithm for the HRES under consideration. In the 1st scenario, power demand is met using both primary and backup energy sources. The honey badger algorithm (HBA) proved its cost-effectiveness and efficiency by achieving the lowest overall operating cost and the highest efficiency of 95.893 %. Additionally, its computation time was notably faster, being 70 s–488 s quicker than the other algorithms. The 2nd scenario arises when power demand exceeds the available generation capacity because of the charging limits of all energy storage systems (ESSs), which prevents them from providing power to the load. The HBA achieved the lowest cost and matched the highest efficiency score of 96.691 %. Furthermore, HBA provided the quickest optimization, completing the process 400 s–450 s faster than the other techniques. In the 3rd scenario, the generated power surpasses the current load demand, and the ESS components are fully charged therefore, the proposed EMS efficiently directs excess power to a dummy load, preventing overcharging of storage components and enhancing grid stability. The HBA consistently exceeded the performance of other algorithms, achieving the lowest average cost, maintaining the highest efficiency of 95.305 %, and solving the optimization problem 300 s–500 s faster than the alternatives. Consequently, these results highlight HBA's flexibility and effectiveness, positioning it as a reliable choice for optimizing energy systems across various operational scenarios.

Design and optimization of squeeze-shear mode MR brake with multi-fluid flow channels based on multi-objective sooty tern optimization algorithm

Abstract Aiming at the deficiency of magnetic field utilization rate and the mass–torque ratio of magnetorheological fluid brake (MRB), a novel MRB is proposed in this paper. Initially, a squeeze-shear mode MRB with multi-fluid flow channels (S-MRB) is designed and its structure and working principle are described. Based on the analysis of the magnetic circuit, mathematical models are established to describe the rotary torque of the S-MRB. Furthermore, COMSOL software is carried out to model and simulate the electromagnetic field of the S-MRB, which verified the rationality of structure design. Then, with the braking torque and mass of the S-MRB as objective function, multi-objective optimization algorithm is adopted to optimize the structural parameters of the S-MRB. The optimization results show that the braking torque is increased by 25.34% and the mass of the MRB is decreased by 2.7%. Finally, a MRB braking performance test platform is established, and the effectiveness and superiority of the S-MRB are verified by braking torque dynamic response characteristic experiments.

Productivity analysis by insulation design of well with vacuum insulated tubing in SAGD process

This study aims to design insulation and demonstrate its performance on the vertical section of a well in a steam-assisted gravity drainage (SAGD) process. Utilizing the reservoir characteristics of the Athabasca oil sands in Canada, we analyzed oil productivity and derived optimal operating conditions through a multi-objective optimization algorithm. For the simulation, the well's vertical section was insulated with 0.006 W/m‧°C, the thermal conductivity of vacuum insulated tubing (VIT), exhibiting high insulation efficiency. The results indicated that cumulative production increased by up to 20.24%, and production efficiency improved. Additionally, sensitivity analysis using response surface methodology (RSM) revealed that the injection bottom-hole pressure (inj_BHP) was the most significant factor in the insulated well design when parameters varied. A multi-objective optimization using particle swarm optimization (PSO) was conducted to determine the optimal operating conditions, aiming to maximize cumulative oil production and minimize the cumulative steam-oil ratio (cSOR). The optimization resulted in a 39.8% improvement in cumulative oil production and an 88.19% reduction in cSOR, compared to the non-insulation scenario. The findings of this study are anticipated to serve as a guideline for wellbore insulation design in SAGD processes.

Learnable self-supervised support vector machine based individual selection strategy for multimodal multi-objective optimization

Multimodal multi-objective optimization problem (MMOP) is a frontier research problem, which can provide decision makers with more choices without making trade-offs. Many multimodal multi-objective evolutionary algorithms (MMOEAs) have been proposed to solve MMOP. However, most MMOEAs tend to prioritize the objective dominance of individuals in the process of individual selection, and only individuals with the same objective dominance will be considered the diversity, which leads to the loss of many promising solutions. To solve the above problem, this paper proposes a learnable self-supervised support vector machine (SVM) based multimodal multi-objective optimization algorithm (SVMEA). Support vector machine can learn the knowledge about distinguishing the advantages and disadvantages of individuals from the data in the existing training set and select individuals, in which the objective dominance of individuals is as important as diversity. Moreover, a crowding distance calculation method based on Manhattan distance is designed. Compared with the traditional method using Euclidean distance to calculate crowding distance, it can better evaluate the diversity of individuals in the decision space and assist the selection of elite solutions. Experimental results show that the proposed SVMEA is competitive with seven other advanced MMOEAs on 34 benchmark problems and a practical application problem.

Multi-objective-based economic dispatch and loss reduction in the presence of electric vehicles considering different optimization techniques

Currently, electric vehicles (EVs) are the most liked mode for green transportation. However, the vehicle-to-grid (V2G) technology can reduce the peak demand on the power grid, which is an efficient way to encourage the integration of EVs. This paper proposes a multi-objective-based economic dispatch management including EVs to minimize the generator cost and active power loss. The entire system is retained for keeping in mind the economic operation of the whole system. Then, EVs are introduced to the system, taking into account vehicle requirements and load demands and considering EV constraints. The target of the proposed work is to demonstrate how effectively large-scale EVs can participate in valley filling and peak load shaving along with multi-objective-based cost and loss reduction. The proposed optimization problem is employed in an IEEE 30-bus system. The multi-objective grasshopper optimization algorithm and the ant-lion optimization are compared to observe the minimum cost and total loss of the system. The results show that the total generation cost and power loss of the system decrease due to the V2G mode of operation. In addition, EVs provide an alternative method for dealing with peak load, while filling the off-peak hours effectively. The total generation cost and power loss for 24 h using MOGOA without implementation of EVs are 8,757.128 $/hr and 65.28509 MW, respectively, and with EVs, the total generation cost and power loss for 24 h are 8,617.077 $/hr and 55.65349 MW, respectively. Thus, with the implementation of EVs, the total generation cost reduced by 1.59% and the total power loss reduced by 14.75%, and with MOALO, the total generation cost and power loss for 24 h without EVs are 8,977.077 $/hr and 44.20877 MW, respectively, and with EVs, the total generation cost and power loss for 24 h are 8,923.529 $/hr and 41.69524 MW, respectively. Thus, with the implementation of EVs, the total generation cost reduced by 0.59% and the total power loss reduced by 5.68%. The analysis of the results demonstrates how effectively EVs in the V2G mode can reduce the dependency over the grid power during the time of peak load demand.

An adaptive assisted method based on MOPSO for THz MMA effective designing

Abstract To address the high time cost and low efficiency of traditional terahertz metamaterial absorber design, an adaptive method based on multi-objective particle swarm optimization was proposed. First, we presented a symmetric absorber of a four-split-ring resonator with a cross-shaped top layer. The structural parameters were optimized by the particle swarm optimization and multi-objective particle swarm optimization algorithms. The simulation results indicated that the multi-objective particle swarm optimization rapidly obtained geometric parameters that balance the high absorptivity and high quality factors. This method quickly identified a symmetric structure with absorptivity greater than 99% and quality factor of 377.45 at 1.584 THz. Additionally, the asymmetric structure achieved near-perfect absorption at 1.585 THz with a Q value of 281.32. By studying the electric field distribution and the surface current distribution, the physical mechanism of the absorber designed has been explained. This adaptive assisted method based on multi-objective particle swarm optimization can efficiently design metamaterial absorbers and offer an artificial intelligence strategy for terahertz functional device design.

Improved NSGA2 algorithm for recovery of interrupted departure flights

To solve the problem of airline flight disruption caused by emergencies, the disrupted departing flights are restored, a dual-objective optimization model is constructed to minimize the total delay cost of airlines and minimize the total delay time of passengers. An adaptive non-dominated sorting genetic algorithm based on dominance intensity is designed, and three improved operations are proposed: a fast dominance sorting method, a new congestion distance and an adaptive elite retention strategy. The proposed algorithm is verified by the operation data of an airline at Fuzhou Airport. The experimental results show that compared with the traditional plan-first-serve method, the solution obtained by the proposed algorithm is greatly optimized. Compared with the constraint method, the solution time is generally lower than the constraint method and the solution result is close to the optimal result obtained by the constraint method. Compared with multi-objective optimization algorithms such as NSGA2 and MOEAD, the proposed algorithm shows better performance and can solve the problem effectively and efficiently, providing a basis for airlines to achieve optimized solutions.

Enhancing energy-efficient building design: a multi-agent-assisted MOEA/D approach for multi-objective optimization

Energy-efficient building design is often challenged by multiple optimization problems due to contradictory objectives that are often hard to balance, so an effective optimization method should be thoroughly considered. Accordingly, a multi-objective evolutionary algorithm is then proposed. Firstly, the multi-agent auxiliary objective evolutionary algorithm for building energy efficiency model is established. According to model result analysis, the proposed algorithm runs fastest for 1640s with the average running time of 1710s in a single-room building, comparing to the least running time of 1680s for the multi-objective particle swarm optimization algorithm. In multi-room buildings, the proposed algorithm runs from 3350s to 3650s, with the average running time of 3500s. In conclusion, the model proposed in this study can comprehensively consider multiple objectives such as energy consumption, cost, comfort, etc. No matter in single-room or multi-room buildings, the model demonstrates superior performance and stability to realize comprehensive optimization of energy conservation design.

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.