Improved Multi-objective Particle Swarm Optimization Research Articles

Prediction and optimization of hobbing parameters for minimizing energy consumption and gear geometric deviations

Improving gear precision and achieving green sustainability in gear machining are two important aspects of the gear manufacturing process. However, to achieve these two goals simultaneously, it may be necessary to make trade-offs when selecting the gear processing parameters. In this work, both energy consumption and gear geometric deviations were considered simultaneously to optimize the hobbing parameters. The relationships between the hobbing parameters, energy consumption, and gear geometric deviations were modeled using the response surface method (RSM). The statistical significance of the model was tested using analysis of variance (ANOVA). An improved multi-objective particle swarm optimization (IMOPSO) was then performed to solve optimization problems that involved multiple and conflicting objectives in the hobbing process. The results obtained indicate that both the energy consumption ( E) and the gear geometric deviations are parameter-dependent. The feed rate ( f) and the spindle speed ( n) have opposing effects on both energy consumption E and the gear geometric deviations. The optimum hobbing parameter sets obtained from the calculated Pareto frontier can provide a feasible solution for manufacturers to solve the trade-off problems that occur in the hobbing process, and the experimental results confirmed the effectiveness of the IMOPSO approach.

Influence Maximization in Social Networks Using an Improved Multi-Objective Particle Swarm Optimization

Abstract The influence maximization (IM) problem has received great attention in the field of social network analysis, and its analysis results can provide reliable basis for decision makers when promoting products or political viewpoints. IM problem aims to select a set of seed users from social networks and maximize the number of users expected to be influenced. Most previous studies on the IM problem focused only on the single-objective problem of maximizing the influence spread of the seed set, ignoring the cost of the seed set, which causes decision makers to be unable to develop effective management strategies. In this work, the IM problem is formulated as a multi-objective IM problem that considers the cost of the seed set. An improved multi-objective particle swarm optimization (IMOPSO) algorithm is proposed to solve this problem. In the IMOPSO algorithm, the initialization strategy of Levy flight based on degree value is used to improve the quality of the initial solution, and the local search strategy based on greedy mechanism is designed to improve the Pareto Frontier distribution and promote algorithm convergence. Experimental results on six real social networks demonstrate that the proposed IMOPSO algorithm is effective, reducing runtime while providing competitive solutions.

Improved multi objective particle swarm optimization based reactive power optimization for ensuring voltage security of power systems

In this study an improved multi objective particle swarm optimization (IMOPSO) algorithm is proposed for power system reactive power optimization with the objective of ensuring voltage security. The multi objective particle swarm optimization (MOPSO) is improved by introducing an adapted binary crossover (ABX) to the new positions obtained by the basic particle swarm optimization (PSO) algorithm. Additionally, diversity maintenance strategy is added to the algorithm by employing crowding distance (CD) calculation. The developed algorithm is tested and compared with standard MOPSO and non dominated sorting genetic algorithm (NASGA II). The comparison is made based on the degree of closeness to the true pareto front, as measured by the inverted generational distance (IGD), and based on diversity, as measured by the CDs . The test is made using ZDT1, ZDT2, and ZDT3 test functions. The IMOPSO showed improved performance over MOPSO and NASGA II algorithms in terms of convergence to the true pareto front (PF) and in terms of the speed of convergence as well as in maintaining diversity. The algorithm is then implemented to reactive power optimization of IEEE 14 bus test system. For the implementation purpose, the voltage stability and voltage deviation components of voltage security are formulated as a multi objective functions. The implementation has resulted diverse options of optimal settings of reactive power controlling parameters. The optimal settings proved to produce an improved voltage security as measured in terms of voltage deviation and voltage stability.

A novel online combustion optimization method for boiler combining dynamic modeling, multi-objective optimization and improved case-based reasoning

A new boiler combustion optimization method for online application is proposed based on data-driven and case-based reasoning principle. First, an improved constrained fuzzy association rule (ICFAR) is proposed to extract the boiler combustion rules from historical combustion data. Second, improved particle swarm optimization-based long short-term memory neutral network (IPSO-LSTM) is utilized to constructed an adaptive dynamic combustion model for boiler to adapt to time-variability of boiler combustion system. Whereafter, an improved multi-objective particle swarm optimization (IMOPSO) is designed to achieve the multi-objective combustion optimization of boiler with the goal of increasing boiler efficiency and decreasing NOx emission simultaneously. Case-based reasoning based on error correction mechanism (CBR_ECM) is applied to realize the boiler online combustion optimization. The effectiveness of proposed online combustion optimization technology for boiler is testified by applying it to an actual combustion process. The results illustrated that it could take less time to gain a series of excellent operating solutions based on proposed online combustion optimization method, the boiler efficiency increased by 0.082 % on average and the NOx emission reduced by 6.491 mg/m3 on average. Therefore, proposed online combustion optimization method for boiler has the ability to achieve the online combustion optimization of boiler.

Multi-objective optimization and algorithm improvement on thermal coupling of SOFC-GT-ORC integrated system

Optimizing thermal coupling of an integrated system and improving its energy cascade utilization (ECU) level are important ways to improve system performance. An integrated power generation system consisting of an anode recirculation internal reforming solid oxide fuel cell (ARIR-SOFC), a gas turbine (GT), an organic Rankine cycle (ORC) waste heat recovery system and a liquefied natural gas (LNG) supply system is established. Additionally, heat exchange network (HEN) subsystem formed by heat exchange streams is specially considered to further improve ECU level. Optimization model is proposed where HEN scheme is optimized simultaneously with operating parameters and working fluids of ORC. Because of the complexity of model, it is key to focus on the solution strategy. An adaptive improved multi-objective particle swarm optimization (IMOPSO) algorithm is established to improve diversity and accuracy of solutions. Finally, a case is solved and results show that HEN scheme plays an important role in system performance.

Solving the Dynamic Weapon Target Assignment Problem by an Improved Multiobjective Particle Swarm Optimization Algorithm

Dynamic weapon target assignment (DWTA) is an effective method to solve the multi-stage battlefield fire optimization problem, which can reflect the actual combat scenario better than static weapon target assignment (SWTA). In this paper, a meaningful and effective DWTA model is established, which contains two practical and conflicting objectives, namely, maximizing combat benefits and minimizing weapon costs. Moreover, the model contains limited resource constraints, feasibility constraints and fire transfer constraints. The existence of multi-objective and multi-constraint makes DWTA more complicated. To solve this problem, an improved multiobjective particle swarm optimization algorithm (IMOPSO) is proposed in this paper. Various learning strategies are adopted for the dominated and non-dominated solutions of the algorithm, so that the algorithm can learn and evolve in a targeted manner. In order to solve the problem that the algorithm is easy to fall into local optimum, this paper proposes a search strategy based on simulated binary crossover (SBX) and polynomial mutation (PM), which enables elitist information to be shared among external archive and enhances the exploratory capabilities of IMOPSO. In addition, a dynamic archive maintenance strategy is applied to improve the diversity of non-dominated solutions. Finally, this algorithm is compared with three state-of-the-art multiobjective optimization algorithms, including solving benchmark functions and DWTA model in this article. Experimental results show that IMOPSO has better convergence and distribution than the other three multiobjective optimization algorithms. IMOPSO has obvious advantages in solving multiobjective DWTA problems.

Data-Driven Real-Time Pricing Strategy and Coordinated Optimization of Economic Load Dispatch in Electricity Market

Compared to the step tariff, the real-time pricing (RTP) could be more stimulated for household consumers to change their electricity consumption behaviors. It can reduce the reserve capacity, peak load, and of course the electricity bill, which could achieve the purpose of saving energy. This paper proposes a coordinated optimization algorithm and data-driven RTP strategy in electricity market. First, the electricity price is divided into two parts, basic electricity price and fluctuating price. When the electricity consumption is equal to the average daily electricity consumption, the price is defined as the basic electricity price, which is the clearing electricity price. The consumer electricity data are analyzed. A random forest algorithm is adopted to predict the load data. Optimal adjustment parameters are obtained and the load fluctuation and the fluctuation of the electricity price are further quantified. Secondly, the appliances are modeled. The operation priority is established based on the preferences of customers and the Monte Carlo method is used to form the power load curve. Then, the smart energy planning unit is proposed to optimize the appliances on/off time and running time of residential electrical appliances. An incentive mechanism is used to further standardize the temporary electricity consumption. An improved multiobjective particle swarm optimization (IMOPSO) algorithm is adopted, which adopts the linear weighted evaluation function method to maximize the consumer’s social welfare while minimizing the electricity bill. The simulation proves that the stability of the power grid is improved while obtaining the best power strategy.

Cooperation and profit allocation for two-echelon logistics pickup and delivery problems with state–space–time networks

Cooperation is a powerful strategy to reduce the costs of pickup and delivery services in the conventional two-echelon pickup and delivery problems (2E-PDPs). This study develops a cooperative 2E-PDP with state–space–time network (C2E-PDPSST) and incorporates vehicle routing problem and profit allocation optimization. Transportation resource sharing (trucks/vehicles) is presented as a major cooperative strategy in C2E-PDPSST to reduce the number of vehicles and improve resource utilization. A bi-objective mixed integer model is proposed to minimize total operating costs and number of vehicles and is formulated based on state–space–time networks. A novel methodology, which combines the time-dependent forward dynamic programming algorithm and a hybrid heuristic algorithm comprising modified k-means clustering algorithm and improved multi-objective particle swarm optimization (IMOPSO) algorithm, is designed for solving C2E-PDPSST. The clustering process speeds up the solution by reducing the computational complexity. The IMOPSO algorithm combines inter- and intra-route operations to find the Pareto optimal solutions with predefined iteration and termination rules. The inter-route operations will improve the population diversity, while the intra-route operations will generate an optimal solution for each vehicle route. Thus, an effective combination of local and global solution search can be achieved. Profit allocation schemes are investigated using the criteria of minimum cost remaining savings. Our results on benchmark instances show that the proposed IMOPSO has better computational performance than the conventional MOPSO and multi-objective genetic algorithm. A case study based on the realistic logistics network in Chengdu City, China is conducted for validation. The proposed methodology considering state–space–time network performs better in terms of reducing traveling costs, and improving the flexibility and efficiency of the entire network.

Semantic and Trade-Off Aware Location Privacy Protection in Road Networks Via Improved Multi-Objective Particle Swarm Optimization

Location privacy protection is an essential but challenging topic in the field of network security. Although the existing research methods, such as k-anonymity, mix zone, and differential privacy, show significant success, they usually neglect the location semantic and the proper trade-off between privacy and utility, which may allow attackers to obtain user privacy information by revealing the semantic correlation between the anonymous region and user's real location, thus causing privacy leakage. To solve this problem, we propose a location privacy protection scheme based on the k-anonymity technique, which provides practical location privacy-preserving through generating an anonymous set. This paper proposes a new location privacy attack strategy termed semantic relativity attack (SRA), which considers the location semantic problem. Correspondingly, a semantic and trade-off aware location privacy protection mechanism (STA-LPPM) is presented to achieve privacy protection with both high-level privacy and utility. To be specific, we model the location privacy protection as a multi-objective optimization problem and propose the Improved Multi-Objective Particle Swarm Optimization (IMOPSO) to generate the optimal anonymous set calculating the well-design fitness functions of the multi-objective optimization problem. In this way, the privacy scheme can provide mobile users with the right balance of privacy protection and service quality. Experiments reveal that our privacy scheme can effectively resist the semantic relativity attack while preventing significant utility degrading.

An optimal singularity-free motion planning method for a 6-DOF parallel manipulator

PurposeThis paper aims to present a method of optimal singularity-free motion planning under multiple objectives and multiple constrains for the 6-DOF parallel manipulator, which is used as an execution mechanism for the automated docking of components.Design/methodology/approachFirst, the distribution characteristics of the Jacobian matrix determinant in local workspace are studied based on the kinematics and a sufficient and necessary condition of singularity-free path planning in local workspace is proposed. Then, a singularity-free motion path of the end-effector is generated by a fifth-order B-spline curve and the corresponding trajectories of each actuator are obtained via the inverse kinematics. Finally, several objective functions are defined to evaluate the motion path and an improved multi-objective particle swarm optimization algorithm-based on the Pareto archive evolution is developed to obtain the optimal singularity-free motion trajectories.FindingsIf the initial pose and the target pose of the end-effector are both singularity-free, a singularity-free motion path can be planned in the local workspace as long as all the values of each pose elements in their own directions are monotonous. The improved multi-objective particle swarm optimization (IMPSO) algorithm is effective and efficient in the optimization of multi-objective motion planning model. The optimal singularity-free motion path of the end-effector is verified in the component docking test. The docking result is that the movable component is in alignment with the fixed one, which proves the feasibility and practicability of the proposed motion path method to some extent.Originality/valueThe proposed method has a certain novelty value in kinematic multi-objective motion planning of parallel manipulators; it also increases the application prospect of parallel manipulators and provides attractive solutions to component assembly for those organizations with limited cost and that want to find an option that is effective to be implemented.

Improved Multi-Objective Particle Swarm Optimization Algorithm for DNA Sequence Design

The DNA sequence design is a vital step in reducing undesirable biochemical reactions and incorrect computations in successful DNA computing. To this end, many studies had concentrated on how to design higher quality DNA sequences. However, DNA sequences involve some thermodynamic and conflicting conditions, which in turn reflect the evolutionary algorithm process implemented through chemical reactions. In the present study, we applied an improved multi-objective particle swarm optimization (IMOPSO) algorithm to DNA sequence design, in which a chaotic map is combined with this algorithm to avoid falling into local optima. The experimental simulation and statistical results showed that the DNA sequence design method based on IMOPSO has higher reliability than the existing sequence design methods such as traditional evolutionary algorithm, invasive weed algorithm, and specialized methods.

A Multiobjective Particle Swarm Optimization Algorithm Based on Competition Mechanism and Gaussian Variation

In order to solve the shortcomings of particle swarm optimization (PSO) in solving multiobjective optimization problems, an improved multiobjective particle swarm optimization (IMOPSO) algorithm is proposed. In this study, the competitive strategy was introduced into the construction process of Pareto external archives to speed up the search process of nondominated solutions, thereby increasing the speed of the establishment of Pareto external archives. In addition, the descending order of crowding distance method is used to limit the size of external archives and dynamically adjust particle parameters; in order to solve the problem of insufficient population diversity in the later stage of algorithm iteration, time-varying Gaussian mutation strategy is used to mutate the particles in external archives to improve diversity. The simulation experiment results show that the improved algorithm has better convergence and stability than the other compared algorithms.

Optimization of the powertrain and energy management control parameters of a hybrid hydraulic vehicle based on improved multi-objective particle swarm optimization

ABSTRACT The concurrent optimization of powertrain component parameters and energy management strategy for a hybrid hydraulic vehicle (HHV) is the key to implementing improved fuel economy while satisfying driving performance criteria. In this article, which considers coupled parameters and conflicting objectives in the optimization, an improved multi-objective particle swarm optimization (IMOPSO) is proposed from the perspective of inertia weight, and global and local optimal information to overcome the problem of multi-objective particle swarm optimization (MOPSO) falling into local optimization prematurely. The IMOPSO is applied to the component parameter optimization to find the Pareto optimal solution set that provides a wide range of options for HHV powertrain design successfully. In order to improve the management control effect of the equivalent consumption minimization strategy (ECMS), the equivalence factors (EFs) are optimized offline by the IMOPSO to obtain the EF map between different torque demands and the state of charge of the accumulator, and further, to establish the online ECMS with the EFs optimized by the IMOPSO (I-ECMS). The simulation results verify the advantage of the IMOPSO-based component parameter optimization and the proposed I-ECMS.

Integrated Polarity Optimization of MPRM Circuits Based on Improved Multi‐objective Particle Swarm Optimization

Aiming at the multi-objective polarity design of Mixed-polarity Reed-Muller (MPRM) circuit, such as small area and low power consumption, an integrated polarity optimization scheme based on improved Multi-objective particle swarm optimization (MOPSO) is proposed. In the Improved MOPSO (IMOPSO) algorithm, particles in the external archive can be actively evolved through self-learning operations to find better circuit polarity. The particles in the population achieve selflearning fractals by comparing the differences between their own states and individuals in external archive to enhance the evolutionary level of the population. A multiobjective decision model of area and power consumption is established according to the characteristics of MPRM circuit. The tabular technique and the IMPOPO algorithm are combined to obtain the Pareto optimal polarity set of the MPRM circuit for area and power consumption. The MCNC Benchmark circuit is used to test the performance of the algorithm. The results verify the effectiveness of the proposed algorithm.

Long-term multi-objective power generation operation for cascade reservoirs and risk decision making under stochastic uncertainties

The long-term multi-objective power generation operation (LTMOPGO) inherently exists multiple uncertainties coming from streamflow forecasting and decision-making process. With help of multi-criteria decision making (MCDM), reservoir scheduling solutions are evaluated and ranked. However, conventional MCDM provide decision makers (DMs) with deterministic rank sequence ignoring uncertainty effects which may lead to unignorable risk of decision error. Furthermore, algorithm improvements are greatly emphasized on multi-objective reservoir operation, while uncertainty analysis and decision risk are ignored to some degree. To this end, we establish framework for solving LTMOPGO and MCDM under multiple uncertainties, including criteria values (CVs) and criteria weights (CWs). First, reservoir operation solutions with uncertain information are acquired by improved multi-objective particle swarm optimization (IMOPSO) and LHS-Monte Carlo simulation. Then, stochastic multi-criteria acceptability analysis (SMAA) model coupling with grey correlation analysis (GCA) and TOPSIS is developed to assist stochastic decision making. Finally, we conduct simulation experiments for cascade reservoirs in Qingjiang river and disclose effect of uncertain factors on LTMOPGO and MCDM with probabilistic rank sequence and risk information. Comparison analysis indicates feasibility and efficiency of novel SMAA-GCA&TOPSIS model compared with SMAA-2. Overall, novel framework proposed are effective ways for DMs to make highly reliable and risk-informed decisions under stochastic environment.

Collaboration and Resource Sharing in the Multidepot Multiperiod Vehicle Routing Problem with Pickups and Deliveries

In this work, a multidepot multiperiod vehicle routing problem with pickups and deliveries (MDPVRPPD) is solved by optimizing logistics networks with collaboration and resource sharing among logistics service providers. The optimal solution can satisfy customer demands with periodic time characteristics and incorporate pickup and delivery services with maximum resource utilization. A collaborative mechanism is developed to rearrange both the open and closed vehicle routes among multiple pickup and delivery centers with improved transportation efficiency and reduced operational costs. The effects of resource sharing strategies combining customer information sharing, facility service sharing, and vehicle sharing are investigated across multiple service periods to maximize resource utilization and refine the resource configuration. A multiobjective optimization model is developed to formulate the MDPVRPPD so that the minimum total operational costs, waiting time, and the number of vehicles are obtained. A hybrid heuristic algorithm incorporating a 3D clustering and an improved multiobjective particle swarm optimization (IMOPSO) algorithm is introduced to solve the MDPVRPPD and find Pareto optimal solutions. The proposed hybrid heuristic algorithm is based on a selective exchange mechanism that enhances local and global searching capabilities. Results demonstrate that the proposed IMOPSO outperforms other existing algorithms. We also study profit allocation issues to quantify the stability and sustainability of long-term collaboration among logistics participants, using the minimum costs remaining savings method. The proposed model and solution methods are validated by conducting an empirical study of a real system in Chongqing City, China. This study contributes to the development of efficient urban logistics distribution systems, and facilitates the expansion of intelligent and sustainable supply chains.

Multi-objective short-term hydropower generation operation for cascade reservoirs and stochastic decision making under multiple uncertainties

In real-world, the multi-objective short-term hydropower generation operation (STHGO) faces changing environment and challenges derived from inherent uncertainties in streamflow forecast, multi-objective optimization and decision-making processes. For decision makers (DMs), these multiple uncertainties always bring harmful effect and risk on optimal STHGO decision making. Traditionally, studies concerning to STHGO are usually based on deterministic streamflow forecast, optimization and decision making without considering nonnegligible uncertain information. Therefore, in this work, a unified framework is developed for solving multi-objective STHGO under multiple uncertainties and quantifying risk information propagated between each process. First, the modified martingale model of forecast evolution (MMMFE) is used to disclose forecast uncertainty and improvements evolution and generate simulated reservoir inflow scenarios based on historical streamflow. Then, improved multi-objective particle swarm optimization (IMOPSO) is developed to obtain optimal Pareto solutions. Pareto front uncertainty is analyzed by importing synthetic inflow scenarios and risk information is quantified through risk criteria. Meanwhile, novel stochastic multicriteria acceptability analysis (SMAA) model coupling with TOPSIS and grey correlation analysis (GCA) is proposed to solve stochastic decision making for STHGO under uncertain environment. The uncertainty propagated from statistically distributed Pareto non-dominated solutions to stochastic decision making is quantified by risk of errors in decision making process (REDMP). Finally, we demonstrate proposed methodology with case study in Qingjiang cascade hydropower stations. Simulation results effectively reveal risk transmission process and quantify risk information. The effects caused by various levels of inflow forecast uncertainty are disclosed on stochastic decision making for STHGO. Comparison analysis results demonstrate the superiority of novel SMAA model and verify it an efficient tool for showing more convincible solution and measurable risk information to DMs.

Hybridization of firefly and Improved Multi-Objective Particle Swarm Optimization algorithm for energy efficient load balancing in Cloud Computing environments

Load balancing, in Cloud Computing (CC) environment, is defined as the method of splitting workloads and computing properties. It enables the enterprises to manage workload demands or application demands by distributing the resources among computers, networks or servers. In this research article, a new load balancing algorithm is proposed as a hybrid of firefly and Improved Multi-Objective Particle Swarm Optimization (IMPSO) technique, abbreviated as FIMPSO. This technique deploys Firefly (FF) algorithm to minimize the search space where as the IMPSO technique is implemented to identify the enhanced response. The IMPSO algorithm works by selecting the global best (gbest) particle with a small distance of point to a line. With the application of minimum distance from a point to a line, the gbest particle candidates could be elected. The proposed FIMPSO algorithm achieved effective average load for making and enhanced the essential measures like proper resource usage and response time of the tasks. The simulation outcome showed that the proposed FIMPSO model exhibited an effective performance when compared with other methods. From the simulation outcome, it is understood that the FIMPSO algorithm yielded an effective result with the least average response time of 13.58ms, maximum CPU utilization of 98%, memory utilization of 93%, reliability of 67% and throughput of 72% along with a make span of 148, which was superior to all the other compared methods.

Multi-population coevolutionary dynamic multi-objective particle swarm optimization algorithm for power control based on improved crowding distance archive management in CRNs

This paper aims to resolve the problem of power control in underlay CRNs better. Firstly, a multi-objective optimization problem of maximizing the throughput of PUs and SUs is proposed, which satisfied the constraints of PU’ interference temperature, the normal communication quality of all users and the transmission power limitation of users. Moreover, according to the theory of penalty function and particle swarm optimization (PSO), an improved multi-objective particle swarm optimization (IMOPSO) algorithm is proposed based on the archives management, which can achieve the maximum throughput of PUs and SUs as well as the minimum penalty constraints term. On this basis, in order to improve the boundary searching ability and diversity of the power control scheme, an improved coevolutionary multi-objective particle swarm optimization (ICMOPSO) in multiple population is proposed based on crowding distance archival management. Further, in order to adapt to the dynamic communication environment well, three different dynamic response schemes are presented correspondingly to cope with the instability of three types of environment. In the end, simulation results show that ICMOPSO and IMOPSO algorithm based on the archives management can obtain the maximum throughput compared with the conventional PSO. Through comparing with the performances in IMOPSO and ICMOPSO, it can be concluded that ICMOPSO algorithm has good abilities of stability, diversity and local search ability, which can provide more throughput optimal allocation schemes for decision makers and ensure the quality of customer service. On the basis of ICMOPSO algorithm, dynamic response strategy is better than the static response strategy at computational cost compared with the average number of iterations. And it can cope with the dimensional change of decision space in dynamic communication environment.

The improved multi-criteria decision-making model for multi-objective operation in a complex reservoir system

Abstract In multi-objective reservoir operation, it is vital for decision-makers to select optimal scheduling schemes through efficient multi-criteria decision-making (MCDM) techniques. However, in the family of MCDM methods, it is difficult for the technique for order preference by similarity to an ideal solution (TOPSIS) to describe grey correlation, thus making decisions with less reliability. To this end, a framework supporting high-quality solutions' acquirement and optimal reservoir operation decision-making is established. The improved multi-objective particle swarm optimization (IMOPSO), a new efficient MCDM model based on TOPSIS and grey correlation analysis (GCA), and combination weighting method based on the minimum deviation (CWMMD) are included in the framework. The non-inferior solution set is efficiently obtained by IMOPSO and optimal decision information is provided for decision-makers using the MCDM model. Moreover, the CWMMD is used to determine weighting information of multiple evaluation indicators. Numerical simulations are conducted to verify the efficiency of the proposed methodology and support decision-making for multi-objective reservoir operation in Hongjiadu and Qingjiang basins. The results indicate that the proposed methodology can provide non-inferior scheduling solutions and decision-making instruction with higher reliability for multi-objective reservoir operation.