Pareto Front Research Articles

Multi‐criteria hydraulic turbine optimization using a genetic algorithm and trust‐region postprocessing

AbstractA two‐stage, multi‐objective optimization approach is proposed to improve the overall efficiency of the time‐consuming and computationally expensive optimization process for hydraulic turbines. The purpose is to optimize the shape of the turbine blades, designed using 30 parameters, in order to maximize its efficiency and minimize both the cavitation volume and the deviation between the desired and the calculated design head. In the first step of the routine, the genetic algorithm “Non‐Dominated Sorting Genetic Algorithm II (NSGA‐II)” is used to generate an initial approximation of the Pareto front that covers a wide variety of possible solutions, that is, optimal trade‐offs between the conflicting objectives. Subsequently, to ensure convergence, the trust region optimizer “Constrained Multiobjective Problem Optimizer with Model Information to Save Evaluations (CoMPrOMISE)” is used, which is initialized with individuals selected from the Pareto set generated by the genetic algorithm.

SparseAuto: An Auto-scheduler for Sparse Tensor Computations using Recursive Loop Nest Restructuring

Automated code generation and performance enhancements for sparse tensor algebra have become essential in many real-world applications, such as quantum computing, physical simulations, computational chemistry, and machine learning. General sparse tensor algebra compilers are not always versatile enough to generate asymptotically optimal code for sparse tensor contractions. This paper shows how to generate asymptotically better schedules for complex sparse tensor expressions using kernel fission and fusion. We present generalized loop restructuring transformations to reduce asymptotic time complexity and memory footprint. Furthermore, we present an auto-scheduler that uses a partially ordered set (poset)-based cost model that uses both time and auxiliary memory complexities to prune the search space of schedules. In addition, we highlight the use of Satisfiability Module Theory (SMT) solvers in sparse auto-schedulers to approximate the Pareto frontier of better schedules to the smallest number of possible schedules, with user-defined constraints available at compile-time. Finally, we show that our auto-scheduler can select better-performing schedules and generate code for them. Our results show that the auto-scheduler provided schedules achieve orders-of-magnitude speedup compared to the code generated by the Tensor Algebra Compiler (TACO) for several computations on different real-world tensors.

Multi-objective scheduling for an energy-efficient flexible job shop problem with peak power constraint

Controlling electricity costs, which are closely related to the peak power reached, while simultaneously reducing completion time and energy consumption, is crucial for achieving sustainability in the manufacturing industry. However, most existing research on energy-efficient flexible job shop scheduling problems primarily focuses on optimizing completion time and energy consumption, often neglecting the critical aspect of controlling electricity costs. With decreasing resources and increasing energy prices, it is necessary to control electricity costs by limiting the peak power reached during production. To address this gap, this paper investigates an energy-efficient flexible job shop scheduling problem with peak power constraint considering setup and transportation time (EEFJSSP-PPST). We establish a mathematical model for EEFJSSP-PPST and propose an improved non-dominated sorting genetic algorithm II (INSGA-II) incorporating several key improvements. We first introduce three scheduling rules in decoding to optimize objectives and employ heuristic rules to generate a high-quality initial population. Then, we propose an innovative cluster crossover method to accelerate convergence and design an adaptive-based local optimization strategy to further enhance performance. Finally, our experiments explore the impacts of different degrees of the peak power constraint on objectives and evaluate the effectiveness of the three scheduling rules. Additionally, the performance of INSGA-II is tested using 135 benchmark instances. The results indicate that INSGA-II outperformed its variations without improvements, achieving the best hypervolume (HV) indicator in 80% of the instances and the best inverted generational distance (IGD) indicator in 68.89% of the instances. Compared to other state-of-the-art algorithms, INSGA-II achieves the best HV and IGD indicators in 82.2% and 81.5% of the instances, respectively, and demonstrates better convergence and a superior Pareto front. Therefore, we conclude that the improvements in INSGA-II are effective and enhance the algorithm’s performance, making it outstanding in solving EEFJSSP-PPST.

Energy Aware Technology Mapping of Genetic Logic Circuits.

Energy and its dissipation are fundamental to all living systems, including cells. Insufficient abundance of energy carriers─as caused by the additional burden of artificial genetic circuits─shifts a cell's priority to survival, also impairing the functionality of the genetic circuit. Moreover, recent works have shown the importance of energy expenditure in information transmission. Despite living organisms being non-equilibrium systems, non-equilibrium models capable of accounting for energy dissipation and non-equilibrium response curves are not yet employed in genetic design automation (GDA) software. To this end, we introduce Energy Aware Technology Mapping, the automated design of genetic logic circuits with respect to energy efficiency and functionality. The basis for this is an energy aware non-equilibrium steady state model of gene expression, capturing characteristics like energy dissipation─which we link to the entropy production rate─and transcriptional bursting, relevant to eukaryotes as well as prokaryotes. Our evaluation shows that a genetic logic circuit's functional performance and energy efficiency are disjoint optimization goals. For our benchmark, energy efficiency improves by 37.2% on average when comparing to functionally optimized variants. We discover a linear increase in energy expenditure and overall protein expression with the circuit size, where Energy Aware Technology Mapping allows for designing genetic logic circuits with the energetic costs of circuits that are one to two gates smaller. Structural variants improve this further, while results show the Pareto dominance among structures of a single Boolean function. By incorporating energy demand into the design, Energy Aware Technology Mapping enables energy efficiency by design. This extends current GDA tools and complements approaches coping with burden in vivo.

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>

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.

Optimal design of vibration resistance of fiber-reinforced composite sandwich plates embedded in a viscoelastic square honeycomb core

This work focuses on investigating the optimal design of composite sandwich plates (FCSPs) with a viscoelastic square honeycomb core (VSHC). Firstly, using the cross-fill theory, the complex modulus technique, the first-order shear deformation theory, the minimum strain energy principle, and the Newmark-β method, a theoretical model of the VSHC-FCSPs under half-sine pulse excitation is formulated to calculate the inherent frequencies, the peak and vibration decay time of the transient response in time domain. The peak and vibration decay time are taken as the indexes of the anti-vibration performance. Considering an index of structural stiffness performance, the average value of the inherent frequencies is adopted to calculate the overall stiffness. After a set of literature validations and optimization validations, the multi-objective genetic algorithm is employed to study the optimization issue of VSHC-FCSPs. The optimization objectives are to minimize the three design variables of the transient response peak, vibration decay time, and reciprocal of overall stiffness. Then, the fiber laying angle of each layer, the core thickness ratio and the modulus ratio are assumed as optimization variables. Finally, the results with good vibration resistance and structural stiffness in the Pareto front are chosen as references, and these corresponding variations of the design variables and optimization objectives are obtained. The optimization results have revealed that the optimization variables corresponding to the intermediate points should be selected as references to improve the anti-vibration capacity and ensure the structural stiffness performance.

Multiobjective optimization by using cutting angle methods and hypervolume criterion

We translate a multiobjective optimization problem into a single objective Lipschitz problem by using the hypervolume criterion of the Pareto set. Deterministic global optimization methods allow one to track the whole Pareto front rather than converging to a single non-dominated solution. We augmented an efficient hypervolume computation technique with hypervolume increment strategy, and established Lipschitzianity of the resulting objective function. We used two deterministic Lipschitz optimization methods together with the hypervolume objective and benchmarked them against some state-of-the-art alternative multiobjective optimization methods, establishing the competitiveness of the proposed approach.

Multi-Criteria Calibration of a Thermo-Mechanical Model of Steel Plate Welding in Vacuum

This paper proposes a procedurefor multi-criteria calibration of a thermo-mechanical model for numerical simulation of welding in the space vacuum. A finite-element model of a steel plate is created. Experimental and computational data are obtained. An inverse problem is formulated for the vector identification of five calibration parameters from the heat-flow model. They are evaluated for adequacy with controlled accuracy according to four criteria. An optimization problem is solved using a two-step interactive procedure. The parameter space studying method (PSI) has been applied to the study of multidimensional regions by means of quasi-uniform sounding. A Pareto-optimal set is defined. It is used to determine reduced ranked Pareto subsets by μ-selection. Salukvadze optimum is also determined.

Decomposition based estimation of distribution algorithm for high-level synthesis design space exploration

High-Level Synthesis (HLS) has evolved significantly due to the increasing complexity of integrated circuit design and the demand for efficient design methodologies. HLS, which raises the abstraction level of design specification, allows designers to focus on hardware functionality, thus enhancing productivity and reducing verification efforts. However, a key challenge in HLS is efficiently exploring the vast design space to find the Pareto-optimal designs. In this paper, we introduce a novel approach for multi-objective design space exploration in HLS. Our methodology decomposes the design space exploration problem into simpler sub-problems using the Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) framework and utilizes the Estimation of Distribution Algorithm (EDA) to build a probabilistic model for generating candidate solutions, thereby reducing the required number of expensive synthesis runs. Experimental results show that the proposed method has a faster convergence speed and reduces the number of syntheses by 24.34% to 32.01%, which significantly outperforms state-of-the-art works. Our approach achieves superior Pareto fronts with the lowest average ADRS value, outperforming Lattice-expl, ϵ -Constraint GA, and NSGA-II by 85.64%, 39.90%, and 33.31% respectively.

Optimizing and investigating the charging time of phase change materials in a compact-latent heat storage using pareto front analysis, artificial neural networks, and numerical simulations

There's a growing emphasis on adopting eco-friendly energy sources to mitigate greenhouse gas emissions and foster sustainability. While renewable energy sources like solar power offer numerous benefits, they have some limitations. Additionally, storing electricity generated from solar panels can be costly and challenging due to limitations in battery technology and storage capacity. Therefore, phase change material-based thermal energy storage systems offer a promising solution to these challenges. These systems also play a crucial role in enhancing buildings' energy efficiency and sustainability. The dimensionality of these systems affects their performance. Traditional systems often rely on fixed dimensions, leading to non-uniform thermal conditions within the storage medium. To address these challenges, adopting a compact-latent heat storage (C-LHS) mechanism was recommended herein. Besides, some fins were inserted into the C-LHS system to alter the heat transfer dynamics within the device. Three of the critical parameters of the fins were changed to examine their impact on the charging time. Artificial neural networks and genetic algorithms were employed to determine the optimal positioning of fins to minimize the duration of material to get both part (melt fraction of 0.8) and full (melt fraction of 1) melting capacities. Here, the primary aim was to present a predictive model capable of accurately forecasting the charging time of the material. In all the presented finned samples, the entire PCM melted in less than 15,110 s (4 h and 12 min) and was able to fully utilize the energy absorption capacity in latent form, whereas in the non-finned system, only 68.6 % of the material managed to melt within the entire duration of the investigation (5 h). After analyzing the data, two optimal configurations of OS1 and OS2 with the minimum time for melt fractions of 0.8 and 1 were introduced. In the OS2 configuration, it took 16,200 s (4 h and 30 min) to absorb 4929 kJ of energy. The non-finned sample absorbed only 3250 kJ of energy during the same period. In General, OS2 achieved total energy absorption 51.6 % faster than the non-finned sample. Therefore, the introduced system has the potential to increase absorbed energy in the rest of the daylight hours to further amounts by increasing the number of units and employing a larger volume of material.

An adaptive co-evolutionary competitive particle swarm optimizer for constrained multi-objective optimization problems

In constrained multi-objective optimization problems, it is challenging to balance the convergence, diversity and feasibility of the population, especially encountering complex infeasible regions. In order to effectively balance the three indicators, from the aspects of the handling of infeasible solution and the quality of individuals, a multi-population co-evolutionary competitive particle swarm optimization algorithm hybridized with infeasible solution transfer and an adaptive technique (ACCPSO) is proposed. Firstly, the information of feasible and infeasible individuals is fully utilized and the individuals are classified by Hamming distance. Then, a novel constraint handling technique based on learning from the promising feasible direction is designed to make individuals cross large infeasible regions and explore more potential feasible regions. Moreover, aiming to provide robust search capability and consequently further generate high-quality solutions, the genetic operators and the particle swarm optimization operator with the competitive mechanism are introduced as operators with an adaptive mechanism. Finally, compared with the state-of-the-art methods, the performance of the proposed algorithm is verified on LIR-CMOP, MW and DTLZ, as well as two real-world problems. The results indicate that ACCPSO exhibits stronger competitiveness in terms of convergence, the solution quality, and distribution diversity on the feasible Pareto front.

Analyzing Passive Design Retrofits using Pareto Front Optimization to Reduce Operational Carbon in Commercial Laboratory Spaces

Buildings are one of the leading sources of carbon emissions in the world. Most of the carbon emissions are released during the operation phase of the building. It is essential for buildings to provide thermal and visual comfort for the users. In the case of existing buildings, it is necessary to offer retrofit solutions so that the operational carbon emissions can be reduced without compromising on the other essential factors. In this study a Multi-Objective Optimization (MOO) of passive design strategies was conducted for a commercial laboratory in India situated in a moderate climate zone. The design variables considered for the study are wall and roof insulation, glazing material, window-wall ratio (WWR), depth of shading device and the number of shading devices used. The objective functions are: 1. reduced energy use intensity and operational carbon emissions, 2. increased thermal comfort hours and 3. increased daylight autonomy. Rhinoceros and grasshopper software along with Ladybug and Honeybee plug-ins were used for the study which resulted in 1296 iterations. MOO technique namely Pareto front optimization was used to optimize the objective functions. Out of 1296 solutions (excluding base case), 72 solutions were non-dominated. Two methods are described in the study to identify the recommendations for retrofit. The first method describes a Heuristic method of selection using Design Explorer recommending 5 good solutions. In the second method a factor is evolved to identify the 5 best solutions in sequential order. The overall study recommends the use of EPS insulation for the RCC roof, WWR of 20% on all sides, 3 horizontal shading devices of depth 0.75 m for all window openings. When compared with the base case scenario, this solution minimizes the EUI by 3.7%, maximizes average TCH by 106.6% and maximizes average DA by 66.9%. The overall operational carbon emissions are reduced by 7095.6 kgCO2.

Production Sequencing and Layout Optimization of Precast Concrete Components under Mold Resource Constraints

Precast concrete components have attracted a lot of attention due to their efficient production on off-site production lines. However, in the precast component production process, unreasonable production sequence and mold layout will reduce production efficiency and affect the workload balance between each process. Due to the multi-species and small-lot production characteristics of precast concrete components, the number of molds corresponding to each precast concrete component is generally limited. In this paper, a production sequence and layout optimization model for assembling precast concrete components under a limited number of molds is proposed, aiming to improve the comprehensive utilization efficiency of the mold tables and balance the workload between each production process of precast components. In order to obtain a better production sequence and a richer combination of mold layout schemes, a multi-objective teaching-learning-based optimization algorithm based on the Pareto dominance relation is developed, and an enhancement mechanism is embedded in the proposed algorithm. To verify the superior performance of the enhanced teaching-learning-based optimization algorithm in improving the comprehensive utilization efficiency of the mold tables and balancing the workload between various processes, three different sizes of precast concrete component production cases are designed. The research results show that the proposed model and optimization algorithm can help production managers to efficiently formulate more reasonable precast component production sequence and layout schemes, especially for those enterprises that are struggling to improve the efficiency of precast concrete component production.

Comparative and optimal study of energy, exergy, and exergoeconomic performance in supercritical CO2 recompression combined cycles with organic rankine, trans-critical CO2, and kalina cycle

The bottom cycle in supercritical carbon dioxide (sCO2) recompression Brayton combined cycle (RCBC) effectively recovers substantial waste heat for electricity generation, enhancing energy utilization. The recovery efficiency is significantly influenced by the bottom cycle configurations and specific working conditions. Besides, implementing these bottom cycles introduces challenges related to increased system dimensions and design complexity. The present study aims to understand and evaluate the characteristics and optimal trade-offs of various bottom cycles, including trans-critical, subcritical, and non-azeotropic mixed working fluids, by establishing 3E (energy, exergy and Exergoeconomic) models for sCO2/tCO2, sCO2/ORC, and sCO2/KC combined cycle systems. To analysis and enhance interpretability, statistical Global Sensitivity Analysis (GSA) alongside unsupervised learning-based Self-Organizing Map (SOM) techniques and parametric analysis are employed. These methods identify key parameters and discern system patterns. Subsequently, the Non-Dominated Sorting Whale Optimization Algorithm (NSWOA) and entropy weight-based Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) are applied to establish a Pareto-optimal decision space and identify compromised ideal design points for each combined cycle. The results quantitatively rank sensitivity for objective variables within the design space in different combined cycles and visually represent system nonlinearity and coupling relationships in 2D weight planes using SOM. The TOPSIS trade-off points based on the Pareto frontier for the three combined cycles are ηth = 45.08 %, cp,tot = 8.5199 $/GJ, ηth = 45.13 %, cp,tot = 8.3739 $/GJ, and ηth = 48.97 %, cp,tot = 8.4783 $/GJ, respectively. Integrating machine learning techniques provides a comprehensive understanding of system patterns, offering valuable insights for decision-makers in the design and optimization of combined cogeneration cycles.

Policy Learning for Many Outcomes of Interest: Combining Optimal Policy Trees with Multi-objective Bayesian Optimisation

AbstractMethods for learning optimal policies use causal machine learning models to create human-interpretable rules for making choices around the allocation of different policy interventions. However, in realistic policy-making contexts, decision-makers often care about trade-offs between outcomes, not just single-mindedly maximising utility for one outcome. This paper proposes an approach termed Multi-Objective Policy Learning (MOPoL) which combines optimal decision trees for policy learning with a multi-objective Bayesian optimisation approach to explore the trade-off between multiple outcomes. It does this by building a Pareto frontier of non-dominated models for different hyperparameter settings which govern outcome weighting. The method is applied to a real-world case-study of pricing targetting subsididies for anti-malarial medication in Kenya.

Thermo-economic investigation and comparative multi-objective optimization of dual-pressure evaporation ORC using binary zeotropic mixtures as working fluids for geothermal energy application

This contribution performs an energy, exergy, and exergoeconomic (3E) analysis of a dual-pressure evaporation organic Rankine cycle system employing twenty different binary zeotropic mixtures as working fluids for power production from a geothermal field. To this end, the designed system is modeled, invoking the mass and energy conservation laws and the exergy and cost balance analyses. Specific Exergy Costing (SPECO) procedure is utilized to provide practical insights into the exergoeconomic aspect of the system. Comparative optimization based on the multi-objective genetic algorithm is accomplished for each mixture in order to simultaneously maximize the exergy efficiency and minimize the total cost rate using the design variables of pressure factor in low-pressure and high-pressure stages, mixture fraction, pinch point temperature differences in low-pressure and high-pressure heat exchangers, and degree of superheat in the high-pressure heat exchanger. In this regard, the Pareto frontiers are drawn for the system with all twenty different binary zeotropic mixtures. The optimal point for each mixture is obtained via the decision-making technique of LINMAP. Subsequently, the LINMAP is re-utilized to find the preferred mixture. The optimization results suggest the R123/C2Butene (96.89/3.11) mixture for this system as the optimum working fluid, considering a trade-off between a low-cost rate of $88.0651 per hr and a high exergy efficiency of 64.07 %. Finally, the exergy flow diagram is plotted to provide the exergy flow rate and the amount of exergy destruction in each segment of the system considering the optimal working fluid. In the proposed system, exergy destruction chiefly occurs within the low-pressure preheater with a value of 1061 kW, followed by the low-pressure turbine and condenser with magnitudes of about 669 kW and 266 kW, respectively.

Designing a new ultra-high strength steel with multicomponent precipitates under material genetic design

Ultra-high strength steels with excellent strength, ductility and toughness have become one of indispensable high-performance structural materials. The development of ultra-high strength steels with higher performance has been widely concerned to break the strength-ductility trade-off. This study proposes a material inverse design strategy that combines material genetic design with thermodynamic calculation to search for new alloys with desirable microstructure and optimal strengthening contributions. Based on the advancement of the 'Pareto Front', a new steel with superior properties was successfully screened from 390,625 candidate individuals, which was verified by experiments. The experimental results show that a new steel Fe-0.25C-14.8Ni-17.0Co-2.54Mo-1.56Cr-0.53Al-1.06Cu-0.38V (wt. %) has been successfully developed. After quenching-cryogenic-aging process, the new steel achieved a superior combination of strength, ductility and toughness, with a yield strength of 2.2 GPa, an elongation-to-failure of 10% and a V-notch impact energy of 15 J. Multi-scale microstructure characterization indicates that such superior property synergy arises from the unique microstructure: lath martensite matrix with high-density dislocations and interstitial solid soluble carbon atoms, embedded fine M2C, NiAl and Cu-rich nanoprecipitates. We present an in-depth discussion on the origins of superior strength/ductility/toughness combinations of the new steel to validate the design strategy and provide an accessible pathway exploiting high-performance ultra-high strength steels.

Fuzzy optimization of the photo-Fenton process on o-toluidine degradation in the aspect wastewater treatment

Significant volumes of wastewater, particularly from the textile industry, pose environmental concerns due to the presence of hazardous substances such as ortho-toluidine (OT). The photo-Fenton process can be used to break down and remove this hazardous organic compound. Previous studies on the photo-Fenton process have focused on local optimization of operating variables without considering cost factors. The photo-Fenton process is studied in this paper with UVA irradiation, Fe2+ dosage, and H2O2 concentration considered as variables. The study uses fuzzy optimization in a multi-objective framework for making decisions to determine the optimal values of OT degradation with its corresponding cumulative uncertainty error (YA), and the total operating cost (CT), both of which are essential for assessing the techno-economic feasibility of the process. The Pareto front was generated from the objective functions to establish the boundary limits for YA and CT. The results show an overall satisfaction level of 71.81% for the objective functions, indicating a partially satisficing solution for maximizing OT degradation while minimizing operating cost. The optimum conditions of the variables require 85.70 W m−3 UVA irradiation, 0.5177 mM for Fe2+ dosage, and 7.85 mM for the H2O2 concentration. These conditions yielded an OT degradation value of 83.22% and a total operating cost of 768.61 USD·m−3. Comparison with previous literature showed an OT degradation efficiency that was 16.78% lower. However, this tradeoff in the process efficiency is offset by a total operating cost that is 2.28 times cheaper, emphasizing the cost-effectiveness of the fuzzy optimized solution.

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.