Set Of Solutions Research Articles

Development of a multi-leader multi-follower game to design industrial symbioses

The implementation of industrial symbioses all over the world has been proven to be a significant lever to decarbonize production facilities. By enhancing cooperation and exchanging resources, important decrease of emissions can be achieved while reducing operating costs. In the light of our previous work, a game theory model is developed to design resources exchanges in eco-industrial parks (EIP). This new model allows to take into account each authority of an industrial park as an independent player, thus becoming a multi-leader-multi-follower game (MLMFG) model. Water and energy networks are generated simultaneously in the model through a well-known case study. The bi-level model is designed with the water and energy managers as leaders and the plants as followers. In this way, the plants play a Nash game with each other and so do the EIP managers. These managers choose a solution from among the equilibria of the followers before reaching their own equilibrium. The results obtained are then compared with those of the previous article, demonstrating that the MLMFG model provides fairly interesting conclusions for the factories and also for the authorities. The relative gain for the companies is around 30 % for all the factories, which constitutes a strong argument of fairness to convince them to participate in the symbiosis. The result obtained after solving the MLMFG problem is very different from that obtained using the AHP method on the set of feasible solutions. To demonstrate the decision-making aspect of the MLMFG method, the coefficients of the AHP method were identified to find the solution to the MLMFG problem among all the feasible points. It is shown that the coefficients are difficult to determine for an expert, despite the relevance of the solution found.

On a question of Erdős on doubly stochastic matrices

In a celebrated paper of Marcus and Ree [M. Marcus, R. Ree. Diagonals of doubly stochastic matrices. Quart J Math Oxford Ser. 1959; 10(1):296–302], it was shown that if A = [ a i j ] is an n × n doubly stochastic matrix, then there is a permutation σ ∈ S n such that ∑ i , j = 1 n a i , j 2 ≤ ∑ i = 1 n a i , σ ( i ) . Erdős asked for which doubly stochastic matrices the inequality is saturated. Although Marcus and Ree provided some insight for the set of solutions, the question appears to have fallen into oblivion. Our goal is to provide a complete answer in the particular, yet non-trivial, case when n = 3.

Rapid prediction of indoor airflow field using operator neural network with small dataset

Indoor airflow is one of the most critical factors affecting room comfort. The accurate prediction of indoor airflow fields is essential for efficient environmental control. However, representative methods for calculating indoor airflow organization, such as computational fluid dynamics (CFD), are complex and time consuming. Therefore, this study proposes a machine learning approach that can rapidly reconstruct indoor airflow fields. This method employs an improved deep operator network (DeepONet) and a Fourier neural operator (FNO) neural network to learn a set of solutions to a problem resembling a flow field and then realizes an accuracy-preserving prediction of an unseen domain. First, we decompose the computational domain into subdomains and then reconstruct the flow field for the subdomains. Subsequently, the subdomains are stitched into the original computational domain. Using data enhancement techniques along with a small dataset, this method achieves satisfactory training results. The results indicate that for a two-dimensional isothermal flow field problem, both the improved DeepONet and FNO models accurately reconstruct the flow field. The mean squared errors are 0.28% and 1.89% for the improved DeepONet and FNO models, respectively, with both requiring less than 0.01s. This method does not require repeated training under different operating conditions, which significantly reduces the computation time. Compared with conventional CFD technology, the proposed method improves the speed by up to three to six orders of magnitude.

Transformations of mixed solution types of interval linear equations system with boundaries on its left-hand side to linear inequalities with binary variables

To determine the solution set of an interval linear equations system Ax=b, it is necessary to know the semantics of the system. In addition to strong and weak semantics, there are four other important semantics: tolerance, control, left-localized, and right-localized. A solution x with one of these semantics provides that particular behavior in every equation of the system. It could happen that there is a solution x with one semantic in some equations and another semantic in the remaining equations of the system. This solution generates another solution type. We provide fifteen combinations of solution types generated by tolerance, control, left-localized, and right-localized semantics and prove that the solution set containing all four semantics is the weak (united) solution set. We show that each of these fifteen nonnegative solution types with some given boundaries on Ax can be transformed to be the solution set of linear inequalities with binary variables. The transformed system is deterministic and can be used in a linear programming problem with interval linear equation constraints to find an optimistic solution satisfying the semantics of the interval linear equations. Task management and course assignment examples are provided to show the necessity of these solution types.

A MOEA/D with adaptive weight subspace for regular and irregular multi-objective optimization problems

The performance of the decomposition-based multi-objective optimization algorithm (MOEA/D) is dependent on the consistency of the Pareto front and the distribution of the weight vectors. Uniformly distributed weight vectors have a great advantage in solving Pareto fronts with simplex-like shapes. However, the fronts of real-world problems to be solved are often irregular, and fixed weight vectors are likely to cause deterioration of the solution. To obtain a set of solution sets that are uniformly distributed in the objective space, a MOEA/D-based weight adaptive updating algorithm (called MOEA/D-AWS) is proposed. First, the subproblem evolutionary matrix similarity is used to determine when to adjust the weight vectors. Second, the objective space is divided by creating a subspace of weight vectors to increase population diversity. Third, partial weights are given a second chance to be selected based on the subspace size. Experimental tests are conducted with seven representative algorithms on benchmark functions DTLZ1-7, IDTLZ1-2, MaF1-7, and WFG1-5 (with objective numbers of 3, 5, 8, 10, and 15). The results show that MOEA/D-AWS is more effective for irregular Pareto fronts, especially discontinuous, degenerate, and sharp-tailed Pareto front problems.

Existence of solution sets for Φ-Laplacian for random impulsive differential equations

In this article, we provide results on the existence and compactness of the set of solutions for a class of initial-value problem representing a first-order random impulsive differential equation. The key tool to achieve our goal is based on an alternative nonlinear Leary-Schauder type theorem in the settings of generalized Banach spaces.

Preference-based multi-objective evolutionary algorithm with linear combination scalarizing function and reference point adjustment

In practice, the decision-maker (DM) may be only interested in a particular part of Pareto optimal front (PF). For this reason, many preference-based multi-objective evolutionary algorithms (MOEA) have been proposed to find a solution set that approximates the region of the interest (ROI). Most existing preference-based methods focus on selecting solutions in the ROI. Nevertheless, the enhancement of convergence in preference-based MOEAs has been neglected. Most decomposition-based approaches often employ the achievement scalarizing function (ASF) as their scalarizing function. However, it holds a weaker search ability than the weighted sum function (WSF) despite its capability to tackle problems with arbitrary PF geometries. In order to strengthen the selective pressure toward the PF, this paper proposes a new scalarizing function, LSF, which is a linear combination of the WSF and the ASF. Then, a simple adaptive penalty scheme is employed in LSF to balance the search ability and robustness. To focus the search on the ROI, we develop a reference point adjustment method that dynamically adjusts the position of the reference point according to the distance from the approximated target point. We apply the above two innovations to the MOEA/D framework and propose a new preference-based MOEA, namely RAMOEAD. Experimental results show that RAMOEAD is highly competitive when compared with five state-of-the-art preference-based MOEAs. Finally, the proposed algorithm is extended to double reference points for solving the problems in which the ROIs are defined by the reservation and aspiration points.

An Improved Multi-Objective Brain Storm Optimization Algorithm for Hybrid Microgrid Dispatch

The increasing integration of renewable energy sources into microgrids has led to challenges in achieving daily optimal scheduling for hybrid alternating current/direct current microgrids (HMGs). To solve the problem, this article presents a novel hybrid AC/DC microgrid scheduling method based on an improved brain storm optimization (BSO) algorithm. Firstly, with economic and energy storage device health as the primary objective functions, this paper proposes a dispatch model for AC-DC hybrid microgrids. To overcome the limitations of traditional algorithms, including premature convergence and can only find non-inferior solution sets, this article proposes a multi-objective BSO algorithm that integrates learning and selection strategies. Additionally, a fuzzy decision-making method is employed to achieve optimal daily dispatching and select the most suitable compromise solution. Finally, experiments are conducted to verify the effectiveness of the proposed multi-objective optimal scheduling method and to demonstrate the practicality and effectiveness of the method in real application scenarios.

The Optimal Transportation Option in an Underground Hard Coal Mine: A Multi-Criteria Cost Analysis

The issue of transport in underground hard coal mines is very rarely described in the literature. The financial aspects of this issue are even less often analyzed. Publications in this area focus on technical issues and the safety of mining crews. More attention is paid to transport in open-pit mines. The above premises and practical needs imply the need to conduct economic analyses of transport systems in underground hard coal mines. This paper is a scientific communication, which presents the concept of a multi-criteria cost analysis as a tool to support the selection of the optimal transportation option in an underground hard coal mine. Considerations in this area have not been carried out in the relevant literature, and the problem of selecting a transportation option is a complex and necessary issue in the practice of underground mines with extensive mine workings. The methodology presented includes five cost criteria (costs of carrying out the transportation task; route expansion costs; rolling stock maintenance costs; depreciation costs; and additional personnel costs). The simultaneous application of criteria relating to utility properties in addition to cost criteria makes it possible to adopt a specific technical and organizational model of the transportation system based on the indication of the optimal solution, resulting from the mathematical construction of functions of objectives relating to utility and cost. The optimal variant of the designed system and configuration of the material transportation system in underground workings takes into consideration the following: (1) seven utility criteria (KU1—transportation task completion time; KU2—compatibility of transportation systems; KU3—continuous connectivity; KU4—co-use with other transportation tasks; KU5—safety; KU6—inconvenience; KU7—operation under overplanning conditions) and (2) five cost criteria (KK1—costs of implementing the transportation task; KK2—costs of route expansion; KK3—rolling stock maintenance costs; KK4—depreciation costs; KK5—additional personnel costs). Based on the aforementioned criteria, two objective functions are built for each option: utility and cost. They present divergent goals; therefore, they are non-cooperative functions. Both utility and costs strive for the maximum. In the developed methodology, an ideal point is usually a fictitious solution representing a set of maximum values among all the achievable values in a set of solutions, but it is impossible to achieve this simultaneously based on all the criteria. This point illustrates the maximum utility and lowest cost among the alternatives considered, which is obviously impossible for any of the variants to meet at the same time, although it indicates the possibilities of the technique and the range of costs. For the developed method, a so-called “PND” nadir point is also determined, representing the least-preferred level of achievement of all goals simultaneously, determined from the set of optimal points in the Pareto sense. The originality of the conceptual considerations undertaken stems from: filling the gap in the economic methodology of complex transportation systems evaluation; embedding considerations in the trend concerning complex transportation systems of underground mines; and focusing considerations on the pre-investment phase, making it possible to optimize costs before expenditures are incurred.

Multi-objective particle swarm optimization for optimal scheduling of household microgrids

Addressing the challenge of household loads and the concentrated power consumption of electric vehicles during periods of low electricity prices is critical to mitigate impacts on the utility grid. In this study, we propose a multi-objective particle swarm algorithm-based optimal scheduling method for household microgrids. A household microgrid optimization model is formulated, taking into account time-sharing tariffs and users’ travel patterns with electric vehicles. The model focuses on optimizing daily household electricity costs and minimizing grid-side energy supply variances. Specifically, the mathematical model incorporates the actual input and output power of each distributed energy source within the microgrid as optimization variables. Furthermore, it integrates an analysis of capacity variations for energy storage batteries and electric vehicle batteries. Through arithmetic simulation within the Pareto optimal solution set, the model identifies the optimal solution that effectively mitigates fluctuations in energy input and output on the utility side. Simulation results confirm the effectiveness of this strategy in reducing daily household electricity costs. The proposed optimization approach not only improves the overall quality of electricity consumption but also demonstrates its economic and practical feasibility, highlighting its potential for broader application and impact.

Logistic elliptic equation with a nonlinear boundary condition arising from coastal fishery harvesting II

We study positive solutions of a logistic elliptic equation with a nonlinear boundary condition that models coastal fishery harvesting ([18]). An essential role is played by the smallest eigenvalue of the Dirichlet eigenvalue problem, in terms of which, a noncritical case is studied in [32]. In this paper, we extend our analysis to the critical case. We also further study the noncritical case for a more precise description of the positive solution set, including uniqueness and stability analysis for large parameters. Our approach relies on an energy method, sub- and supersolutions, and implicit function analysis.

A multi-objective optimization method for enclosed-space lighting design based on MOPSO

With the rapid development of underground spaces and manned cabins, the design of enclose-space has received attention. Humans working in enclosed-space for a long period of time are prone to fatigue, which in serious cases can lead to human errors and major accidents. Therefore, the optimized design of enclosed-space is of great research significance to enhance the efficiency and comfort of workers. The lighting environment is one of the important objectives of the optimized design of enclosed-space, and the current research on lighting design often focuses on single-objective reduction of energy consumption or improvement of visual effects, and lacks attention to non-visual effects. We propose multi-objective optimal control strategy for enclosed-space lighting systems, taking the visual effects, non-visual effects, and energy efficiency of lighting as the optimization objectives and constraints, combined with multi-objective particle swarm optimization algorithm. Firstly, we obtain a set of optimal Pareto front solution for the dimming level by improving the algorithm. Secondly, to select appropriate lighting strategies according to different working scenarios, we introduce the fuzzy integrated evaluation method of experts to find the best compromise. Finally, we used a manned simulated enclosed cabin based on DIALux evo for a case study to compare the optimization results with baseline solutions. The results show that when we employed the improved dimming strategy, the energy efficiency and visual comfort were significantly improved compared with the baseline lighting design. The proposed method can satisfy human non-visual effects requirements, providing a research reference for future enclosed-space lighting optimization.

Many-objective coevolutionary learning algorithm with extreme learning machine auto-encoder for ensemble classifier of feedforward neural networks

In artificial neural network (ANN) learning, empirical risk can be expressed by training error, while structural risk can be expressed by network complexity. Learning from data is often seen as a tradeoff between these two risks. Additionally, balancing training error and validation error can overcome the overfitting problem to some extent. It is known that the network performance is also related to regularization term. In order to consider four factors, i.e. training error, validation error, network complexity and regularization term simultaneously in the training process of a single-hidden layer feedforword neural network (SLFN), a many-objective coevolutionary learning algorithm (MOCELA) integrated with extreme learning machine auto-encoder (ELMAE), called MOCELA-ELMAE is presented. In MOCELA, the non-dominated sorting genetic algorithm III (NSGA-III) is improved for handling the many-objective optimization model with hybrid variables, where binary coding is used for structure learning and real coding is utilized for representing input parameters, referring to all input weights and hidden biases of the AE network. Output parameters of AE, i.e. output weights are analytically calculated by the non-iterative learning rule. The network structure and connection parameters of SLFN are determined based on those of AE. A set of Pareto optimal solutions are eventually collected by the MOCELA-ELMAE, which represents multiple optimal SLFNs. To make the final decision, three best SLFNs with minimum validation errors are selected as the base classifiers for selective ensemble learning. Extensive experiments are implemented on the benchmark classification data sets of UCI machine learning repository, and obvious improvements have been observed when the proposed MOCELA-ELMAE is compared with the NSGA-III based on hybrid coding and completely non-iterative learning of SLFN respectively. The experimental results also illustrate that the MOCELA-ELMAE performs much better than other state-of-the-art learning algorithms on many data sets.

A learning and evolution-based intelligence algorithm for multi-objective heterogeneous cloud scheduling optimization

The multi-objective directed acyclic graph scheduling problem (MDAGSP) is prevalent in cloud scheduling systems, involving the selection, assignment, and execution of multiple tasks/jobs with complex coupling interdependencies. High-quality solutions can yield substantial economic benefits. However, prevailing methods face challenges in obtaining a set of superior solutions for MDAGSP, due to the multifaceted nature of its variables, objectives, constraints, and heterogeneity. Firstly, this paper formulates a three-objective MDAGSP that includes makespan, energy costs and revenue, to model cloud scheduling systems. Subsequently, we propose a composite algorithm consisting of a selection phase and an assignment phase to automatically generate an efficient scheduling policy for this model. During the selection phase, a graph convolutional neural network learns high-level features to extract complex dependencies between tasks. During the assignment phase, an adaptive evolutionary algorithm assigns tasks to the appropriate executors. Finally, a series of experiments are conducted to validate the model’s accuracy and assess the algorithm’s efficiency. Compared to heuristic approaches, the algorithm achieves at least a 20.1% makespan reduction and 3.17% revenue increase. Remarkably, the algorithm obtains at least an 8.86% reduction in energy costs over the eleven baselines. In conclusion, the proposed algorithm provides decision-makers with a global view of scheduling plan.

Bandit algorithms: A comprehensive review and their dynamic selection from a portfolio for multicriteria top-k recommendation

This paper discusses the use of portfolio approaches based on bandit algorithms to optimize multicriteria decision-making in recommender systems (accuracy and diversity). While previous research has primarily focused on single-item recommendations, this study extends the research to consider the recommendation of several items per iteration. Two methods, Multiple-play Gorthaur and Budgeted-Gorthaur, are proposed to solve the algorithm selection problem and their performances on real-world datasets are compared. Both methods provide a generalization of the Gorthaur method, which enables it to operate with any Multi-Armed Bandit (MAB) and Contextual Multi-Armed Bandit (CMAB) algorithm as meta-algorithm in a multi-item recommendation scenario. For Multiple-play Gorthaur, an empirical evaluation shows that the use of Thompson Sampling for algorithm selection (Gorthaur-TS) yields better results than the original EXP3 method (Gorthaur-EXP3) and the exclusive use of the optimal algorithm in the portfolio in contextual recommendation problems. Additionally, the paper includes a theoretical regret analysis based on the TS sketch proof applied for this variant of the method. Concerning Budgeted-Gorthaur, experiments show that it allows more flexibility to achieve a suitable trade-off between criteria and a broader coverage of the Pareto set of solutions, overcoming a natural limit of “a-priori” methods. Finally, this paper provides a detailed review, including pseudocodes and theoretical bounds, for all the fundamental MAB and CMAB algorithms used in this study.

Trajectory planning of tire laser engraving orthogonal robot based on an improved multi-objective grasshopper optimization algorithm

The traditional tire laser engraving robots have the low and stable running capability and discontinuous motion trajectory during operation, leading to long running time, high energy consumption, and uneven operation. In order to solve these problems, this paper proposes an orthogonal robot trajectory planning method based on an improved multi-objective grasshopper optimization algorithm (IMOGOA) with the orthogonal robot as the research object. Firstly, this paper used the quintic non-uniform rational b-splines (NURBS) curves to construct the trajectory. Secondly, the optimization objectives of the orthogonal robot’s running time, energy consumption, and smoothness were used to obtain the Pareto optimal solution by using the IMOGOA to establish the objective function. Then, the optimization method was simulated and analyzed, and the optimal solution was selected to compare with the rest of the non-dominated solution sets. The simulation results showed that the proposed method reduced the running time by 33.68%, improved the energy consumption and smoothness performance by 34.48% and 56.58%, and achieved multi-objective comprehensive optimization of the orthogonal robot. Thus, the effectiveness and feasibility of the proposed method were verified. Finally, a tire laser engraving orthogonal robot experimental platform was built for physical verification experiments. The experimental results showed that the experimental trajectory deviated from the simulated trajectory by only 5.63%, further proving the proposed method’s practicality.

Piezoelectric impedance-based high-accuracy damage identification using sparsity conscious multi-objective optimization inverse analysis

Two elements are essential in structural health monitoring utilizing dynamic responses: response measurement with high-frequency contents, i.e., small characteristic wavelengths, that can adequately reflect damage features, and effective inverse identification analysis that is however oftentimes under-determined. The advancement of smart structure integration has led to active interrogation through frequency-sweeping piezoelectric impedance measurement at high frequency range. In this research we develop a multi-objective optimization formulation for the identification of damage location and severity utilizing piezoelectric impedance. While one optimization objective is to match the response measurement with finite element model prediction in the damage parametric space, the other is the number of locations of damage, i.e., the sparsity of damage index as the solution vector, since damage usually occurs within a small number of locations. This multi-objective formulation fits well the under-determined nature of damage identification, as it naturally provides multiple solutions as basis for further elucidation. The challenge remaining is how to find a small solution set that can include the actual damage scenario. Here we develop a novel inverse identification framework utilizing the intelligent swarm optimizer which possesses flexibility for enhancement. We first embed a sparsity enforcement process into the population generation of the optimizer, which yields a solution repository intrinsically possessing sparsity. We then apply reinforcement learning so the agents can adaptively opt for local strategies with the aim of enriching the searching patterns to diversify the solutions. Through the incorporation of a Q-table, searching toward more promising directions will be rewarded. Our case analyses employing experimental data indicate that this sparsity-conscious multi-objective particle swarm optimization technique can lead to a small solution set which generally encompasses the true damage scenario. This effectively solves the structural damage identification problem with piezoelectric impedance measurement.

A nonlinear total variation based computed tomography (CT) image reconstruction method using gradient reinforcement.

Compressed sensing-based reconstruction algorithms have been proven to be more successful than analytical or iterative methods for sparse computed tomography (CT) imaging by narrowing down the solution set thanks to its ability to seek a sparser solution. Total variation (TV), one of the most popular sparsifiers, exploits spatial continuity of features by restricting variation between two neighboring pixels in each direction as using partial derivatives. When the number of projections is much fewer than the one in conventional CT, which results in much less sampling rate than the minimum required one, TV may not provide satisfactory results. In this study, a new regularizer is proposed which seeks for a sparser solution by reinforcing the gradient of TV and empowering the spatial continuity of features. The experiments are done by using both analitical phantom and real human CT images and the results are compared with conventional, four-directional, and directional TV algorithms by using contrast-to-noise ratio (CNR), signal-to-noise ratio (SNR) and Structural Similarity Index (SSIM) metrics. Both quantitative and visual evaluations show that the proposed method is promising for sparse CT image reconstruction by reducing the background noise while preserving the features and edges.

Individual age determination based on computed tomography knee analysis using artificial neural networks and computer vision: Preliminary results

BACKGROUND: Currently, studies have focused on the modernization of existing methods of forensic age assessment (bone and skeletal) through the active use of modern methods of medical imaging (e.g., computed tomography) and artificial intelligence for their analysis. This approach enables the creation of new methods for assessing biological age, which is characterized by increased accuracy and reproducibility.
 AIM: To develop and test an algorithm for predicting the biological age of an individual based on computed tomography analysis of the knee joint using artificial neural networks and computer vision.
 MATERIALS AND METHODS: This observational retrospective transverse (one time) study analyzed computed tomography scans (334) of the knee joint performed in the Departments of Radiation Diagnostics of the Priorov Central Institute for Trauma and Orthopedics, Vreden National Medical Center for Traumatology and Orthopedics, between 2018 and 2021. The study enrolled persons of both sexes aged 13–45 years. Cases of developmental abnormalities, knee injuries, signs of general connective tissue pathology were excluded. Research methods include the use of intelligent information technologies (a formalized set of mathematical and software solutions).
 RESULTS: Based on the experiments conducted, an algorithm for assessing age according to the computed tomography scans of the knee joint has been developed. The main components of the developed system are as follows: a preprocessing module, an intelligent computing core, a data analysis module, a three-dimensional reconstruction module, a property extraction module, and a final age assessment module. The essence of the proposed method is the simultaneous use of artificial neural networks and clearly formalized mathematical procedures for calculating the properties of the epiphyseal line. To obtain the results and conduct primary experimental studies that confirmed the feasibility, correctness, and operability of the method, software using the YOLOv5 neural network was developed. The result of the error matrix analysis after training shows a probability of correct recognition of the order of 80%. Verification of experimental studies was performed on 46 cases. At present, the age estimation error is approximately 1 year for children and adolescents.
 CONCLUSIONS: The experimental results have confirmed the adequacy of the age estimates obtained to the actual age of the individual and, consequently, the applicability of the proposed method in forensic medical institutions. The proposed method is currently implemented as a set of software components with subsequent manual integration of automatically calculated data. The plan was to supplement the database of computed tomography images to increase the training sample and the accuracy of age prediction.

Multi-objective optimization of regional integrated energy system matrix modeling considering exergy analysis and user satisfaction

Integrated energy system achieves the collaborative optimization of different energy forms such as electricity/gas/heat/cold, and it is an important strategic development direction in the international energy field in the future. However, with the development of smart grid technology and the increase of renewable energy penetration, it needs more flexible load to adapt to the changing energy supply–demand relationship. Considering the impact of user-side load fluctuations on the system, this paper establishes a two-tier closed-loop system model formed by users and the market. The upper-layer is based on the user’s perspective. A comprehensive user satisfaction model is established by the radar chart area method and consumer preference theory. The lower-layer is based on the market perspective. It proposes an improved layering matrix Energy Hub model and conducts the regional integrated energy system exergy efficiency evaluation study. Then, taking economy, carbon emission and exergy efficiency as objective functions, a multi-objective optimization model is constructed. Non-dominated Sorting Genetic Algorithms-II is applied to solve the model, and the output parameters is a Pareto front surface. A combination weighting TOPSIS method is used to select a compromise solution of multi-objective optimization from the optimal solution set. Compared with the primary energy utilization efficiency as the objective function, the exergy efficiency reduces the system cost by 8.64%. Finally, the multi-objective optimization solution based on different user satisfaction is obtained. Through the analysis of the examples, compared with the original load, the introduction of the upper-layer user satisfaction model reduces the system cost by 2.8%. The reasonable setting of user satisfaction and load adjustment amount can improve the economy of system, which verifies the effectiveness of the two-tier closed-loop system based on user satisfaction model.