Non-dominated Sorting Genetic Algorithm Research Articles

Smart allocation and sizing of fast charging stations: a metaheuristic solution

ABSTRACT The widespread adoption of electric vehicles (EVs) hinges significantly on effective network management, particularly the allocation and sizing of fast-charging stations (FCS) for EV users. Applying queuing theory based on M/M/c, the model seeks to identify the most effective number of chargers to minimise waiting time for electric vehicle users and ensure optimal utilisation of the FCS. The problem is formulated as a multi-optimisation problem where finding the optimal solution is done by implementing the non-dominated sorting genetic algorithm focusing on EV user satisfaction, voltage stability, and carbon dioxide emissions. Simulation results indicate that the model successfully enhances EV user satisfaction, environmental impact, and overall FCS utilisation. In a comparative analysis with state-of-the-art models, the proposed approach demonstrates a notable 40% improvement in EV user satisfaction and a significant 45% enhancement in FCS utilisation. This proves the effectiveness of the proposed model in optimising the performance of the network.

Optimization of femtosecond laser processing parameters of SiC using ANN-NSGA-II

Abstract In the field of femtosecond laser machining, it is essential to select the appropriate process parameters to obtain near thermal damage-free and high efficient machining of SiC wafer. In this work, a method of process parameter optimization for femtosecond laser machining of 4H-SiC was proposed by using the predictive ability of the Artificial Neural Network (ANN) and the optimization algorithm of the non-dominated sorting genetic algorithm (NSGA-II). Firstly, the femtosecond laser was used to fabricate microgrooves on SiC wafers, and the effects of process parameters (laser average power, scanning speed and repetition rate) on groove depth, width, heat affected zone (HAZ) and material removal rate (MRR) were investigated. Secondly, The ANN model is established based on experimental data. Other experiments verify the accuracy of the model, and the average error in the model's predictions is around 5%. Thirdly, Pareto optimal solutions are obtained by global optimization of the ANN model using the NSGA-II. The experimental results show that the Pareto optimal solutions are effective and reliable. This proposed method offers dependable guidance for the selecting and optimizing process parameters of high hardness and brittle materials in the field of femtosecond laser processing, and reduces the cost of selecting the appropriate processing parameters in the production process. The method can also be extended to other machining means, such as turning and milling.

Multi-objective capacity configuration optimization of a nuclear-renewable hybrid system

Integrating the energy storage and the base-load energy can be an efficient solution to cover the fluctuation of renewable energy. A nuclear-renewable hybrid energy system consisting of a small modular thorium molten salt reactor, solar photovoltaics, wind turbines, thermal energy storage and battery storage with two operation modes is proposed to meet the community load demand. The methodology combining multi-objective evolutionary algorithms with multi-criteria decision-making method is used to identify the optimal operation mode and gain the optimal configuration of the proposed nuclear-renewable hybrid energy system. In the first stage, the multi-objective evolutionary algorithm with better performance is utilized to gain Pareto solutions to minimize the levelized cost of energy while ensuring an acceptable level of deficiency of power supply probability. In the second stage, the multi-criteria decision-making method is adopted to select the best solution from the obtained Pareto frontiers. The optimization results demonstrate that the nondominated sorting genetic algorithm has the best performance compared with other algorithms and the operation mode with battery discharged first is more cost competitive. It is concluded from the results analysis that the selection of optimal mode is influenced by seasonal variation that contributes to large energy storage capacity requirement.

Solubility prediction of refrigerants in PEC lubricants based on back-propagation neural network combined with genetic algorithm

In the present study, a backpropagation neural network combined with genetic algorithm (GA-BP) model was constructed for prediction the solubility of refrigerants in linear chained precursors of POE lubricants (PECs). A total of 2248 experimental solubility data of refrigerants in PECs reported in literature were collected with temperatures from 243.15 K to 363.15 K and pressures up to 10 MPa. The input variables of the model were optimized using non-dominated sorting genetic algorithm with elite strategy (NSGA-II). The optimized inputs include temperature, pressure, molecular weight, critical temperature, and acentric factor. Results indicate that the GA-BP model using the optimized inputs can correlate the solubility data with good accuracy, the average absolute relative deviation between calculated results from the model and the literature is 0.98 %. Moreover, in order to validate the predictive ability of the established GA-BP model, the solubility of R1243zf in PEC4 and PEC5 was measured at the temperature range from 278.15 K to 343.15 K. The calculated values from the GA-BP model were compared with the experimental data, and the average absolute relative deviation is 8.85 %. Finally, sensitivity analysis was performed by Partial Derivatives (PaD) method to assess the contribution of input variables. Leverage approach was used for outlier detection to ensure the robustness of the model.

Test case prioritization based on fault sensitivity analysis using ranked NSGA-2

AbstractThis paper discusses regression testing in software maintenance, focusing on test case prioritization to verify modifications to software functionality efficiently. The primary goal is to rank test cases, prioritizing those covering more code or faults with minimal execution time. The challenge lies in prioritizing numerous test cases generated during development and maintenance. Various algorithms, including greedy approaches and meta-heuristic techniques, address this challenge. The paper introduces a ranking-based non-dominated sorting genetic algorithm (NSGA-2) for test case prioritization, emphasizing cases sensitive to faults caused by modifications or new functionality. Historical data is prioritized, with key objectives including the sensitive index, execution cost, and average percentage of fault detection (APFD). The proposed model is tested on handcrafted and benchmark Java-based applications, comparing its performance to state-of-the-art algorithms in test case prioritization.

Optimal low-impact development Facility Design in Urban Environments: A multidimensional optimization approach employing slime mould and nondominated sorting genetic algorithms

This study presents the application of the slime mould algorithm (SMA) and the nondominated sorting genetic algorithm II (NSGA-II) to optimize low-impact development (LID) strategies in urban areas. The focus is on minimizing costs and improving water quality, using three LID practices (vegetated swales, bioretention systems, and porous pavements) in combination with a drainage system. The effectiveness of this stormwater management model (SWMM)-SMA-NSGA-II model is demonstrated in Tehran, Iran, where bioretention is found to be the most successful approach for improving water quality. The results also show that the SMA outperforms the NSGA-II in optimizing cost-effective LID solutions and is more computationally efficient, potentially due to its crossover operator. This research highlights the importance of considering qualitative aspects of urban runoff management. The study demonstrates that the combination of multiple LID strategies and the use of SMA and NSGA-II have the potential to achieve optimal solutions for managing stormwater in urban areas.

Carbon and economic prices optimization of a solar-gas coupling energy system with a modified non-dominated sorting genetic algorithm considering operating sequences of water-cooled chillers

To promote the continuous operating of solar energy systems and increase the proportion of renewable energy consumption, solar devices are often integrated with conventional energy systems to reduce greenhouse gas emissions. In this study, a solar-natural gas coupling system is constructed, utilizing solar photovoltaics, thermal collectors, and high-efficiency energy conversion devices. After modelling the energy system, the operating modes are illustrated considering working sequences of water-cooled devices. A modified genetic algorithm, which incorporates reverse learning, controlled elite, and dynamic crowding distance theory, is constructed to optimize the configurations of the proposed energy system, with the aim of minimizing carbon and economic prices of the products. The performance of the energy system is compared with different algorithms and cases, and the results demonstrate that the proposed optimization algorithm addresses the limitations of conventional methods, albeit with increased optimization times. Moreover, the proposed operating mode (Case 1) exhibits a stable performance, leading to a higher environmental and economic performance compared to conventional modes, with carbon and economic prices of 0.242 kg/kWh and 0.067 $/kWh, respectively. This study provides new insights into carbon footprints and economic performance evaluation of high-efficiency energy systems, offering valuable directions for future research in this field.

Multi-Objective Optimization of a Multi-Cavity, Significant Wall Thickness Difference Extrusion Profile Mold Design for New Energy Vehicles.

With the rapid development of the new energy vehicle market, the demand for extruded profiles for battery trays, mainly characterized by significant wall thickness differences in multiple chambers, is increasing, posing new challenges to production and quality control. This study examines the multi-objective optimization problem in the design process of aluminum profile dies with multi-cavity profiles and significant wall thickness differences. Using QFORM-extrusion professional aluminum extrusion finite element analysis software and the response surface analysis method, the standard deviation of the velocity (SDV), standard deviation of the pressure (SDP), and thick wall hydrostatic pressure (TWHP) on the profile section at the die exit are optimized. By analyzing the functional relationship between the key die structure parameters (the height of the baffle plates, the length of the bearing, and the height of the false mandrel) and the optimization objective, the optimal combination scheme of die structure parameters was obtained using the NSGA2 (non-dominated sorting genetic algorithm-2) multi-objective genetic optimization algorithm. The results show that, compared with the initial design scheme, the standard deviation of profile section velocity was reduced by 5.33%, the standard deviation of pressure was reduced by 11.16%, and the thick wall hydrostatic pressure was increased by 26.47%. The die designed and manufactured using this scheme successfully completed the hot extrusion production task, and the profile quality met the predetermined requirements, thus verifying the effectiveness of this study in optimizing the design of a multi-cavity aluminum profile die with significant differences in wall thickness for complex structures.

Long Short-Term Memory Parameter Optimization Based on Improved Sparrow Search Algorithm for Molten Iron Quality Prediction

Blast furnace (BF) ironmaking is a key process in iron and steel production. Because BF ironmaking is a dynamic time series process, it is more appropriate to use a recurrent neural network for modeling. The long short-term memory (LSTM) network is commonly used to model time series data. However, its model performance and generalization ability heavily depend on the parameter configuration. Therefore, it is necessary to study parameter optimization for the LSTM model. The sparrow search algorithm (SSA) holds advantages over traditional optimization algorithms in several aspects, such as no need for prior knowledge, fewer parameters, fast convergence, and high scalability. However, the algorithm still faces some challenges, such as the tendency to become trapped in the local optimum and the imbalance between global search ability and local search ability. Therefore, on the basis of SSA, this study examined the Levy flight strategy, sine search strategy, and step size factor adjustment strategy to improve it. This algorithm, improved by three strategies, is called the improved sparrow search algorithm (ISSA). Then, the ISSA-LSTM model was established. Furthermore, considering the limitations of SSA in dealing with multi-objective problems, the fast non-dominated sorting genetic algorithm (NSGAII) was introduced, and the ISSA-NSGAII model was established. Finally, experimental validation was performed using real blast furnace operation data, which demonstrated the proposed algorithm’s superiority in parameter optimization for the LSTM model and prediction for real industrial data.

Low-carbon planning of urban charging stations considering carbon emission evolution characteristics and dynamic demand

As a new generation of transportation, electric vehicles play an important role in carbon-peak targets. The development of electric vehicles needs the support of a charging network, and improper planning of charging stations will result in a waste of resources. In order to expand the charging network of electric vehicles and give full play to the low-carbon and efficient characteristics of electric vehicles, this paper proposed a charging station planning method that considers the characteristics of carbon emission trends. This paper combined the long short-term memory (LSTM) network with the stochastic impacts by regression on population, affluence, and technology (STIRPAT) model to predict the carbon emission trend and quantified the correlation between the construction speed of a charging station and the evolution characteristics of carbon emission by Pearson’s correlation coefficient. A multi-stage charging station planning model was established, which captures the dynamic characteristics of the charging demand of the transportation network and determines the station deployment scheme with economic and low-carbon benefits on the spatiotemporal scale. The Pareto frontier was solved by using the elitist non-dominated sorting genetic algorithm. The model and solution algorithm were verified by the actual road network in a certain area of Shanghai. The results showed that the proposed scheme can meet the charging demand of regional electric vehicles in the future, improve the utilization rate of charging facilities, and reduce the carbon emission of transportation networks.

Optimized data driven fault detection and diagnosis in chemical processes

Fault detection and diagnosis (FDD) is crucial for ensuring process safety and product quality in the chemical industry. Despite the large amounts of process data recorded and stored in chemical plants, most of them are not well-labeled, and their conditions are not adequately specified. In this study, an optimized data-driven FDD model was developed for a chemical process based on automatic clustering algorithms. Due to data preprocessing importance, feature selection was performed by a non-dominated sorting genetic algorithm (NSGAII) based on k-means clustering. The optimal subset of features is selected by comparing clustering results for each subset. The performance of the proposed feature selection method was compared with the Fisher discriminant ratio (FDR), and XGBoost methods. The t-distributed stochastic neighbor embedding (t-SNE), Isomap, and KPCA dimension reduction methods were also employed for feature extraction. Finally, automatic clustering was performed based on metaheuristic algorithms for fault detection and diagnosis. Results were compared with non-automatic clustering methods. The performance of the proposed method was evaluated by examining the Tennessee Eastman and four water tank processes as case studies. The results showed that the proposed method is reliable and capable of online and offline chemical process fault detection and diagnosis. As a result, the findings of this study can be used to stabilize the operation of chemical processes.

Transferable multi-objective factory layout planning using simulation-based deep reinforcement learning

Factory layout planning aims at finding an optimized layout configuration under consideration of varying influences such as the material flow characteristics. Manual layout planning can be characterized as a complex decision-making process due to a large number of possible placement options. Automated planning approaches aim at reducing the manual planning effort by generating optimized layout variants in the early stages of layout planning. Recent developments have introduced deep Reinforcement Learning (RL) based planning approaches that allow to optimize a layout under consideration of a single optimization criterion. However, within layout planning, multiple partially conflicting planning objectives have to be considered. Such multiple objectives are not considered by existing RL-based approaches. This paper addresses this research gap by presenting a novel deep RL-based layout planning approach that allows consideration of multiple objectives for optimization. Furthermore, existing RL-based planning approaches only consider analytically formulated objectives such as the transportation distance. Consequently, dynamic influences in the material flow are neglected which can result in higher operational costs of the future factory. To address this issue, a discrete event simulation module is developed that allows simulating manufacturing and material flow processes simultaneously for any layout configuration generated by the RL approach. Consequently, the presented approach considers material flow simulation results for multi-objective optimization. To investigate the capabilities of RL-based factory layout planning, different RL architectures are compared based on a simplified application scenario. Throughput time, media supply, and material flow clarity are considered as optimization objectives. The best performing architecture is then applied to an exemplary application scenario and compared with the results obtained by a combined version of the genetic algorithm and tabu search, the non-dominated sorting genetic algorithm, and the optimal solution. Finally, two industrial planning scenarios, one focusing on brownfield and one on greenfield planning, are considered. The results show that the performance of RL compared to meta-heuristics depends on the considered computation time. With time the results generated by the RL approach exceed the quality of the best conventional solution by up to 11%. Finally, the potential of applying transfer learning is investigated for three different application scenarios. It is observed that RL can learn generalized patterns for factory layout planning, which allows to significantly reduce the required training time and can lead to improved solution quality. Thus, the use of pre-trained RL models shows a substantial performance potential for automated factory layout planning which cannot be achieved with conventional automated planning approaches.

Solving the multi-objective path planning problem for mobile robot using an improved NSGA-II algorithm

Path planning is one of the most concerned problems in mobile robotics. Given the NP-hard nature of path planning problems, the non-dominated sorting genetic algorithm (NSGA-II), as one of the outstanding evolutionary algorithms with robust optimization capabilities, is a good candidate to deal with them. In this study, an improved NSGA-II (INSGA-II) is proposed to solve the multi-objective path planning problems, in which path length, path safety and path smoothness are optimized simultaneously. First, a grid-based environment model is created, and each feasible solution is encoded as a discrete ordered point set. Second, a hybrid initialization strategy is employed to enrich the diversity of initial population. Third, besides the usual selection, crossover and mutation operators, problem-specific evolutionary operators are developed. In addition, an adaptive variable neighborhood local search strategy is designed to increase the exploitation ability of the algorithm. Moreover, a hybrid global search strategy is applied to further improve the algorithm’s the exploration ability. Finally, the proposed INSGA-II is compared with six state-of-the-art algorithms on 16 instances of four representative maps. Simulation results indicate that INSGA-II can solve the multi-objective path planning problems with high efficiency.

Performance improvement analysis of the regenerative dual-pressure organic flash cycle assisted by ejectors

We proposed a dual-ejector-based regenerative dual–pressure organic flash cycle (DEj–RDPOFC) with higher performance than the RDPOFC. The effects of high and low pressures and the entrainment ratio of the ejector on the DEj–RDPOFC performance were analyzed from the viewpoints of thermodynamics and thermoeconomics. An exergy-flow distribution diagram revealed why the DEj–RDPOFC outperformed the RDPOFC. Next, the performances of the DEj–RDPOFC and dual–pressure organic Rankine cycle (DORC) were compared under the same boundary conditions. Finally, the performance of the DEj–RDPOFC was optimized using the nondominated sorting genetic algorithm (NSGA-II). According to the results, the power output of the high-pressure (HP) turbine of the DEj–RDPOFC can be increased by replacing the HP throttling valve (TV) with an ejector (which increases the working fluid dryness of the HP vapor separator and the mass flow rate of the HP turbine) and the low-pressure (LP) TV with an ejector (which increases the HP turbine expansion ratio). The DEj–RDPOFC achieves a higher maximum net power output (Wnet) and a lower corresponding levelized cost of electricity (LCOE) than the DORC. Under the optimum condition, the Wnet and LCOE of the DEj–RDPOFC are 9.71 % higher and 6.59 % lower, respectively, than those of the RDPOFC.

Theoretical analysis and crashworthiness optimization of multi-cell Al-CFRP hybrid tube

In this paper, a hybrid thin-walled tube with multiple cells and multiple materials is proposed to achieve lightweight, high energy absorption efficiency, and low cost of structures. Energy absorption characteristics and crushing deformation of the hybrid structures are investigated by experimental testing and numerical analysis. Meanwhile, theoretical prediction models of the mean crushing force for hybrid structures are developed and its accuracy was verified. It is found from the sensitivity analysis that the parameters of the multi-cell structure have significant effects on energy absorption. Furthermore, the multi-objective optimization including surrogate models is performed to obtain optimal crashworthiness of the multi-cell hybrid tube. The same optimal results were obtained using the full factor response mapping optimization algorithm and the non-dominated sorting genetic algorithm with elite strategy algorithm for multi-objective optimization solution. Compared with the original multi-cell hybrid tube and multi-cell pure aluminum (Al) tube, the optimized structure showed an increase of 0.25% and 25.31% in specific energy absorption, an increase of 16% and 77.34% in average crushing force, and an increase of 3.89% and 23.08% in energy absorption efficiency, respectively.

Reliability analysis and optimization design of magnetic fluid dynamic seal shell structure under thermal/mechanical load

In order to study the reliability of Magnetic fluid dynamic seal shell structure under thermal/mechanical load, the improving cooling structure, calculating fuzzy fatigue reliability, and collaborative optimization design of fatigue reliability and lightweight are studied in this paper. The temperature model of the shell structure under four temperature conditions is established to analyze the influence of the thermal deformation caused by excessive local temperature. The cooling structure is improved, and the maximum temperature under the maximum temperature condition is reduced by 40.154 °C. For the sake of calculating the reliability of the new shell structure, a strength analysis model under thermal/mechanical load is built, and the fuzzy fatigue reliability function is obtained based on Latin hypercube sampling and the second-order response surface method. Four kinds of reliability are acquired by coding the functional functions and four kinds of membership functions with MATLAB, but all of them are lower than 90 % of the industrial requirements. To improve the reliability of the new shell structure and carry out the anti-fatigue lightweight design at the same time, an approximate model was constructed based on the interval analysis method and second-order response surface method for analysis. The accuracy of the approximate model was verified by re-sampling and finite element analysis. Based on the non-dominated sorting genetic algorithm, the optimal solution is determined. The optimization results show that the stress target value is reduced by 19.3 %, the weight target value is reduced by 3 %, and the fuzzy fatigue reliability reaches 94.65 %, 94.58 %, 93.89 %, and 96.31 % respectively. A new cooling structure of the Magnetic fluid dynamic seal is obtained and the maximum temperature is reduced. Moreover, the reliability of the new shell structure under thermal/mechanical load coupling is improved.

A convenient-accurate optimization method of the multi-effect evaporation system

In this work, a convenient-accurate multi-effect evaporation system optimization method that integrates regression analysis and a multi-objective genetic algorithm has been proposed to optimize the design of the multi-effect evaporation system. Firstly, a multitude of numerical simulation calculations are conducted employing precise thermodynamic models. Secondly, regression analysis is performed on the experimental data to establish the approximate model between the design variables and performance parameters. Finally, NSGA-II, a non-dominated sorting genetic algorithm with an elite strategy, is employed to optimize and solve the approximate model derived from regression analysis. Consequently, a series of Pareto solutions satisfying the given conditions are obtained. The two initial schemes of the FF-MEE (forward-feed) system and the PF-MEE (parallel-feed) system are optimized using the proposed optimization method. The results show that following optimization, the Gained Output Ratio (GOR) of the FF-MEE system is increased by 3.6%, while the specific heat transfer area (As) is reduced by 16%. Similarly, for the PF-MEE system, the GOR is enhanced by 7.8%, and As is decreased by 19%. The proposed method provides a comprehensive set of optimization solutions, ensuring rapid solution speed, straightforward application, and high solution accuracy.

Design and optimization of a combined supercritical CO2 recompression Brayton/Kalina cycle by using solar energy and LNG cold energy

Solar energy and LNG cold energy have broad application scenarios as two renewable sources, but their complementary potential has not been fully explored. To fill this gap, this paper constructs a novel combined cycle that utilizes solar energy and recovers LNG cold energy to generate power. This combined cycle consists of a supercritical carbon dioxide recompression Brayton cycle, an ammonia-water mixture Kalina cycle, and an LNG cryogenic power system. A systematic evaluation was conducted on the thermodynamics and exergoeconomic of the model, and the simulation results under basic operating conditions show that the first law efficiency, second law efficiency, net power output and total unit cost reach 55.73 %, 47.72 %, 13.709 MW and 27.44 $·GJ−1 respectively. The genetic algorithm and elitist non-dominated sorting genetic algorithm are used to optimize the system performance. By using the parallel direct search method, the maximum first law efficiency, as well as second law efficiency and a minimum total unit cost of 59.45 %, 52.23 % and 24.81 $·GJ−1 are obtained respectively. The optimal first law efficiency, second law efficiency, and total unit cost of the system, which are 53.52 %, 50.33 % and 26.44 $·GJ−1 respectively, are searched simultaneously from the multi-objective optimization results by LINMAP decision-making method. Furthermore, this paper analyzes the exergy flow rate of the system and heat transfer processes of the heat exchangers under optimal operating condition. A total of 23,059.35 kW of LNG cold energy is fully utilized by the system in the LNG gasification process. The exergy loss ratio and cost ratio of each equipment analysis demonstrates that the heat exchangers (HX) have the largest percentage both exergy loss ratio and cost ratio, especially the HX4.

Multi-objective optimization of CO2 ejector by combined significant variables recognition, ANN surrogate model and multi-objective genetic algorithm

The ejectors are crucial in enhancing the efficiency of the CO2-based refrigeration cycle. Although the ejector can be optimized by experimental and computational fluid dynamic simulation to improve its performance, these methods are time-consuming and complicated. This research aims to present a fast and systematic approach for optimizing CO2 ejector by combining variance analysis, surrogate model, and non-dominated sorting genetic algorithm. Firstly, the key geometric structures affecting the performance of ejector were determined by variance analysis. Secondly, the influence of key geometric structures and boundary conditions on ejector efficiency and entrainment ratio was analyzed by using computational fluid dynamic simulation, and the database was generated. Next, the artificial neural network surrogate model was established to forecast the ejector performance. Finally, the non-dominated sorting genetic algorithm was involved to optimize the ejector for maximizing ejector efficiency and entrainment ratio. The results show that the efficiencies of the optimized ejectors are above 42%, and the entrainment ratios exceed 0.7. Compared with the basic model, the average efficiencies have increased about 13.20%. When the pressure lift is 0.7 MPa, the entrainment ratios of the optimized ejectors are 0.696 (−20 °C ≤ Te < −15 °C), 0.82(-15 °C ≤ Te < −5 °C), 0.60 (−5 °C ≤ Te < 5 °C) and 0.90 (5 °C ≤ Te < 15 °C), respectively. The above research demonstrates that the success of this approach in addressing time-consuming multi-optimization problems. It offers a fast and systematic approach for the multi-objective optimization of CO2 ejector as a valuable reference for engineering applications.

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

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