Set Of Pareto-optimal Solutions Research Articles

Multicriteria Optimization of Stochastic Robust Control of the Tracking System

A multicriteria optimization of stochastic robust control with two degrees of freedom of a tracking system with anisotropic regulators has been developed to increase accuracy and reduce sensitivity to uncertain object parameters. Such objects are located on a moving base, on which sensors for angles, angular velocities and angular accelerations are installed. Improvements in the accuracy of control with two degrees of freedom include closed-loop feedback control and open-loop feedback control through the use of reference and perturbation effects. The multicriteria optimization of the stochastic robust control tracking system with two degrees of freedom with anisotropic controllers is reduced to the iterative solution of a system of four coupled Riccati equations, the Lyapunov equation, and the determination of the anisotropy norm of the system by an expression of a special form, which is numerically solved using the homotopy method, which includes vectorization matrices and iterations according to Newton's method. The objective vector of robust control is calculated in the form of a solution of a vector game, the vector gains of which are direct indicators of the quality that the system should achieve in different modes of its operation. The calculation of the vector gains of this game is related to the simulation of a synthesized system with anisotropic regulators for different modes of operation with different input signals and object parameter values. The solutions of this vector game are calculated on the basis of a set of Pareto-optimal solutions taking into account the binary relations of preferences on the basis of the metaheuristic algorithm of multi-swarm Archimedes optimization. Based on the results of the synthesis of stochastic robust control of a tracking system with two degrees of freedom with anisotropic controllers, it is shown that the use of synthesized controllers made it possible to increase the accuracy of system control, reduce the time of transient processes by 3–5 times, reduce the variance of errors by 2.7 times, and reduce the sensitivity of the system to the change of object parameters compared to typical regulators.

Optimizing High-Performance Predictive Modeling of the Medium-Speed WEDM Processing of Inconel 718

The purpose of this research was to create a predictive model for a medium-speed wire electrical discharge machine (WEDM) utilizing an artificial neural network (ANN). Medium-speed WEDM experiments were developed based on the I-optimal mixture design for machining, the Inconel 718 superalloy. During the experiment, the input parameters were the spark ontime, spark offtime, wire feed, and current, with the material removal rate (MRR) and surface roughness (Ra) selected as performance indicators. The ANN model was trained on experimental data and built using a feed-forward backpropagation neural network with a (4-8-2) structure and the Bayesian regularization (BR) learning approach. The model correctly predicted the relationship between the medium-speed WEDM’s primary process parameters and machining performance. An integrated ANN model and the Non-Dominated Sorting Genetic Algorithm-II (NSGA-II) were used to determine the ideal parameters for the MRR and Ra, resulting in a set of Pareto-optimal solutions. The confirmation experiment revealed that the mean prediction error between the experimental and ideal solutions had a maximum error percentage of 1% for the MRR and 2% for the Ra, which are within acceptable ranges. This showed that the best process–parameter combinations were better for the MRR and Ra.

Intelligent mix design of steel fiber reinforced concrete using a particle swarm algorithm based on a multi-objective optimization model

Steel fiber reinforced concrete (SFRC) is widely used in construction and is important for concrete-based applications. Nevertheless, compared with conventional concrete, it is difficult to efficiently and accurately design SFRC with a given mix ratio, because many factors affect the SFRC performance. This study proposes a multi-objective optimization model using numerical simulations and artificial intelligence to effectively derive the optimal SFRC mix proportion. For a quick and accurate relationship between the SFRC mix ratio and compressive strength, Latin hypercube sampling was used for sampling the random variables determining the mix ratio, yielding a set of random numbers. Subsequently, a finite-element simulation dataset was constructed, and a backpropagation neural network (BPNN) was used for predicting the complex nonlinear relationship between the raw material mix proportions and uniaxial compressive strength (UCS). The BPNN model was then utilized as the objective function in the multi-objective particle swarm optimization model, with the mix ratio parameters as the input variables and the compressive strength, unit production cost, and carbon dioxide emission as objective functions, which facilitated the search for the optimal mix proportion, yielding a Pareto-optimal solution set. Finally, based on the engineering preferences, the best solution was determined to be the recommended mix proportion.

Dynamic switched crowding-based multi-objective particle swarm optimization algorithm for solving multi-objective AC-DC optimal power flow problem

In this paper, the multi-objective AC-DC optimal power flow (MO/AC-DC OPF) problem in the presence of renewable energy sources (RESs), flexible AC transmission system (FACTS) devices and multi-terminal direct current (MTDC) systems is introduced for the first time. Conflicting objective functions and the high complexity of the objective and constraint spaces are the main challenges in finding optimal solutions for MO/AC-DC OPF. To overcome these challenges, twelve different versions of the dynamic switched crowding-based multi-objective particle swarm optimization (DSC-MOPSO) algorithm are introduced in this paper. Studies on multimodal optimization problems have shown that all DSC-MOPSO versions have better performance metrics than the MOPSO algorithm. Using the developed DSC-MOPSO and its strong competitors, the Pareto-optimal solution sets of the MO/AC-DC OPF problem are investigated. In these investigations, the performances of the algorithms are tested for the minimization of dual and triple objectives such as fuel cost, voltage level deviation, emission and power loss in a modified IEEE 30-bus power grid. According to the simulation results, the proposed DSC-MOPSO achieved an improvement in fuel cost between 0.02 % and 5.05 % and a reduction in active power loss between 0.44 % and 30.74 % compared to its competitors. The Hypervolume (HV) performance metric was used to evaluate the Pareto-front coverage performance of DSC-MOPSO and other optimizers. The results from nine case studies of the MO/AC-DC OPF were statistically analyzed by the Friedman test according to the 1/HV metric. According to the Friedman test results, the rankings of DSC-MOPSO and MOMA are 1.984 and 3.079, respectively, ranking first and second among all competitors. Finally, in this study, feasible solutions for MO/AC-DC OPF problem are identified for the first time and the stability of competitive algorithms in finding these solutions is analyzed for the first time. The success rates and search times of DSC-MOPSO and MOMA algorithms in finding feasible solutions for MO/AC-DC OPF are 91.01 % (30.641 s) and 82.01 % (46.038 s), respectively.

A new prediction-based evolutionary dynamic multiobjective optimization algorithm aided by Pareto optimal solution estimation strategy

Dynamic multiobjective optimization problems (DMOPs) typically involve multiple conflicting time-varying objectives that require optimization algorithms to quickly track the changing Pareto-optimal front (POF). To this end, several methods have been developed to predict new locations of moving Pareto-optimal solution set (POS) so that populations can be re-initialized around the predicted locations. In this paper, a dynamic multi-objective optimization algorithm based on a multi-directional difference model (MOEA/D-MDDM) is proposed. The multi-directional difference model predicts the initial population through the estimated populations developed by a designed POS estimation strategy. An adaptive crossover-rate approach is incorporated into the optimization process to cope with different POS structures. To investigate the performance of the proposed approach, MOEA/D-MDDM has been compared with six state-of-the-art dynamic multiobjective optimization evolutionary algorithms (DMOEAs) on 19 benchmark problems. The experimental results demonstrate that the proposed algorithm can effectively deal with DMOPs whose POS has a single-modality characteristic and continuous manifolds.

RBSS: A fast subset selection strategy for multi-objective optimization

Multi-objective optimization problems (MOPs) aim to obtain a set of Pareto-optimal solutions, and as the number of objectives increases, the quantity of these optimal solutions grows exponentially. However, a plethora of optimal solutions can impose significant decision stress on decision-makers. Subset selection, as the extension of a model, can extract a representative set of solutions, thereby alleviating the decision-makers’ choice pressure. In addition, extending a model undoubtedly incurs additional time costs. To cope with the foregoing issues, a fast subset selection method named ranking-based subset selection (RBSS) is proposed in this paper. It can efficiently select a small number of optimal solutions within an unbounded external archive and can be directly applied to any multi-objective evolutionary algorithm. This allows it to maintain good distribution and diversity with very little time investment. We employed a ranking-based approach to map the objective space to a ranking space (an integer space) defined by us and then selected the corresponding subset in the ranking space. The well-behaved mathematical properties of the ranking space and the advantages of using integer calculations accelerated the subset selection process. Experimental results indicate that compared to several state-of-the-art subset selection methods, RBSS is capable of selecting a set of representative and diverse solutions across different types of MOPs, while consuming significantly less time. Specifically, for problems where the Pareto front is a two-dimensional manifold and a one-dimensional manifold, the time consumption of RBSS is approximately only 0.028% to 27.5% and 4.6e−4% to 0.15% of that required by other algorithms, respectively.

Balloonless spinning spindle head shape optimisation

Abstract The article presents a procedure for assessing and selecting the shape of the ring spinner spindle head that is optimum for yarn manufacturing using the balloonless system, considering multiple criteria. This procedure consists of two stages: the Pareto-optimal method and the distance function method. Twelve spindle head variants were designed and manufactured of 100Cr6 bearing steel composed of C (0.93–1.05%), Si (0.15–0.35%), Mn (0.25–0.45%) along with aluminium alloys EN AW-6060 (AlSi1MgMn) containing Si (0.70–1.3%), Mg (0.6–1.2%), Mn (0.4–1.0%) and EN AW-6060 (AlMgSi) containing Si (0.30–0.60%) and Mg (0.35–0.60%). The shapes of the heads were developed on the basis of the design solutions used previously by the leading ring-spinning machine and spinning spindle manufacturers. Four design variants of spindle heads, made of AlMgSi wrought aluminium alloy, have a unique shape that enables shaping their teeth (notches) by extrusion on a hydraulic press. The assessment criteria were production cost per unit, head weight, maximum surface hardness HV0.1, and four yarn technological quality criteria: maximum yarn tension values during the formation of the base, body and head of the package, and the tension amplitude. The assessment values for the criteria obtained through calculations and measurements were normalized. Then, a set of Pareto-optimal solutions was determined using seven criteria. Due to the fact that this set consisted of six variants, the distance function was used to select the best one. The best design variant of the head is the one corresponding to the lowest distance function value. In our case, the variant is a unique shape, made of AlMgSi alloy, with teeth thickened on the outer diameter of the head, ensuring the lowest yarn tension value at the height during the formation of the package.

Non-dominated sorting simplified swarm optimization for multi-objective omni-channel of pollution-routing problem

Abstract The activities of the traffic department mainly contribute to the generation of greenhouse gas (GHG) emissions. The swift expansion of the traffic department results in a significant increase in global pollution levels, adversely affecting human health. To address GHG emissions and propose impactful solutions for reducing fuel consumption in vehicles, environmental considerations are integrated with the core principles of the vehicle routing problem. This integration gives rise to the pollution-routing problem (PRP), which aims to optimize routing decisions with a focus on minimizing environmental impact. At the same time, the retail distribution system explores the use of an omni-channel approach as a transportation mode adopted in this study. The objectives of this research include minimizing total travel costs and fuel consumption while aiming to reduce GHG emissions, promoting environmental sustainability, and enhancing the convenience of shopping and pickup for customers through the integration of online and offline modes. This problem is NP-hard; therefore, the Non-dominated Sorting Simplified Swarm Optimization (NSSO) algorithm is employed. NSSO combines the non-dominated technique of Non-dominated Sorting Genetic Algorithm II (NSGA-II) with the update mechanism of Simplified Swarm Optimization to obtain a set of Pareto-optimal solutions. Moreover, the NSSO, a multi-objective evolutionary algorithm, is adopted to address multi-objective problems. The PRP benchmark dataset is utilized, and the results are compared with two other multi-objective evolutionary algorithms: NSGA-II and Non-dominated Sorting Particle Swarm Optimization (NSPSO). The findings of the study confirm that NSSO exhibits feasibility, provides good solutions, and achieves faster convergence compared with the other two algorithms, NSGA-II and NSPSO.

Multi-criteria optimization calculations to improve the efficiency of an agricultural moving power units in fleet

BACKGROUND: Due to the fact that the development of one target function for separately assessing each agricultural machine used in the fleet seems insufficient to fully assess the efficiency of agricultural moving power units in fleet, a multi-criteria formulation of the problem was applied using the previously developed hardware and software complex MOVI 1.4 and the development of computer programs to carry out their optimization calculations of the efficiency of the agricultural moving power units in fleet the example of a specific farm. AIMS: The goal of the work is to develop software tools for carrying out multi-criteria optimization calculations in order to increase the efficiency of agricultural moving power units in fleet in the context of digitalization of agriculture. METHODS: The analysis is based on the collection of scientific publications, scientific articles and other sources of information on the development of research and experimental design work on the creation of intelligent transport and technical means and the improvement of methodological and software for multi-criteria optimization calculations of the efficiency of the agricultural moving power units in fleet. Methods of scientific generalization and statistical processing of available information and analytical materials from domestic and foreign sources were also used. RESULTS: To calculate the values of quality criteria for the MES fleet, an interface subprogram for MOVI 1.4 was developed in the Pascal programming language, adequate for implementing calculations based on mathematical models of criteria at trial points. After introducing functional and criterion restrictions, an admissible set and a set of Pareto-optimal solutions were constructed, and correlation graphs between quality criteria were constructed. The scientific novelty lies in the development of computer programs for multi-criteria justification of the efficiency of the agricultural moving power units in fleet. CONCLUSION: The practical value lies in the fact that the developed mathematical and software tools can be successfully used for multi-criteria optimization of the efficiency of an agricultural moving power units in fleet using the example of specific agricultural organizations, regions or the country as a whole.

Multi-objective optimization design of high-pressure plate-fin ammonia boiler based on MO-SHERPA algorithm

With the rapid development of electrification, the high-pressure plate-fin ammonia boiler has been widely used as an effective thermal management solution, which has stimulated the demand for its structure design and optimization. The aim of this study was to establish a multi-objective optimization design method for high-pressure plate-fin ammonia boiler based on the hybrid and adaptive search strategy of MO-SHERPA and CFD simulation. Based on this method, a set of pareto-optimal solutions were obtained, and then the optimal configuration with lightest weight and high heat transfer performance was determined by calculating the deviation for weighted sum of comprehensive performance factor, entropy generation rate and structure weight. The effects of fin structural parameters of ammonia boiler were further examined on its performance. The results showed that increasing the spacing and height of offset strip fin and reducing its thickness could effectively improve the heat transfer performance. This study provides a theoretical method and some guidelines for the structural design of ammonia boiler with high operating pressure.

Multi-objective optimization of heat treatment criteria on the corrosion and wear behaviour of ZA27/SiC/TiB2 hybrid metal matrix composite

The current study presents a methodology for examining the effect of solutionizing and aging parameters on the wear and corrosion behaviour of ZA27/SiC/TiB2, a Hybrid Metal Matrix Composite(HMMC). ZA27 alloy is widely used in applications where high bearing resistance and wear resistance properties are desired. However, its usability is limited to temperatures less than 1000 C as its properties exhibit a declining trend. The addition of SiC and TiB2 were found to contribute in circumventing this lacuna. Furthermore, no studies were reported on the process of augmenting the corrosion and wear resistance of this hybrid composite. This research gap is specifically addressed in this work. The chosen Hybrid Composite consisting of 15% of reinforcing elements(SiC + TiB2) proportioned equally among them along with 85% of ZA27 alloy matrix is produced by Mechanical Stir casting method. The experimental work has been broadly divided into two major spectrums. The first part consisting of analysing the change in properties being studied before and after heat treatment. Besides, this part of the work also involved the study of the variation in artificial aging temperature on the properties under consideration. The Potentiodynamic Polarisation tests showed that the solution heat treatment produces a significant decline in corrosion rate. Further, aging at a temperature of 1800 C has also evidently improved the properties of corrosion and wear resistance. However, results also depicted that over aging would deteriorate these properties. The final and subsequent part was completely devoted to identifying the best and optimised heat treatment parameters viz., solutionising time, aging temperature and time. Further, Taguchi L9 orthogonal array is taken to design the experiments in the second phase. Regression Equations were developed from the observations of this set of experiments. These equations were later subjected to Multi-Objective Genetic Algorithm (MOGA) which produces a pareto set of optimal solutions. The Pareto frontier was then analysed using Multi criteria decision making approaches viz., VIKOR, LINMAP and TOPSIS to arrive at the most optimal solution. This approach has culminated in an optimal solution of corrosion and Wear rates of 2.27mpy, 2.75 ˟ 10-3 mm3/m and coefficient of friction as 0.271 at the input variables of solutionizing time −5 h, aging temperature-1890 C and aging time-2 h.

Constructing a MOEA approach for product form Kansei design based on text mining and BPNN

Kansei Engineering (KE) is a product design method that aims to develop products to meet users’ emotional preferences. However, traditional KE faces the problem that the acquisition of Kansei factors does not represent the real consumers demands based on manual and reports, and using traditional methods to calculate relationship between Kansei factors and specific design elements, which can lead to the omission of key information. To address these problems, this study adopts text mining and backward propagation neural networks (BPNN) to propose a product form design method from a multi-objective optimization perspective. Firstly, Term Frequency-Inverse Document Frequency (TF-IDF) and WordNet are used to extract key user Kansei requirements from online review texts to obtain more accurate Kansei knowledge. Secondly, the BPNN is used to establish the non-linear relationship between product Kansei factors and specific design elements, and a preference mapping prediction model is constructed. Finally, BPNN is transformed into an iterative prediction value of non-dominated sorting genetic algorithm-II (NSGA-II), and the model is solved through multi-objective evolutionary algorithm (MOEA) to obtain the Pareto optimal solution set that satisfies the user’s multiple emotional needs, and the fuzzy Delphi method is used to obtain the best product form design scheme that meets the user’s multiple emotional images. Using the example of electric bicycle form design could show that this proposed method can effectively complete multi-objective product solutions innovation design.

Sensitivity Analysis and Optimization of Energy-Saving Measures for Office Building in Hot Summer and Cold Winter Regions

To effectively reduce building energy consumption and enhance indoor thermal comfort, this study developed a sensitivity analysis and multi-objective optimization method for an office building in Hangzhou considering the effects of parameter interactions. We utilized Latin hypercube sampling (LHS) to sample the parameters and subsequently simulated the energy consumption and discomfort hours for the building’s four orientations. Following this, Gaussian process regression models were established, and the feature importance ranking method (FIRM) alongside an interaction effects method were employed to quantify the sensitivity of 10 parameters. Lastly, a multi-objective optimization was performed for total energy consumption and discomfort hours, yielding a set of Pareto-optimal solutions. Through the VIKOR method, the optimal solution within the Pareto set was identified, resulting in three sets of optimal solutions.

Multi-Objective BiLevel Optimization by Bayesian Optimization

In a multi-objective optimization problem, a decision maker has more than one objective to optimize. In a bilevel optimization problem, there are the following two decision-makers in a hierarchy: a leader who makes the first decision and a follower who reacts, each aiming to optimize their own objective. Many real-world decision-making processes have various objectives to optimize at the same time while considering how the decision-makers affect each other. When both features are combined, we have a multi-objective bilevel optimization problem, which arises in manufacturing, logistics, environmental economics, defence applications and many other areas. Many exact and approximation-based techniques have been proposed, but because of the intrinsic nonconvexity and conflicting multiple objectives, their computational cost is high. We propose a hybrid algorithm based on batch Bayesian optimization to approximate the upper-level Pareto-optimal solution set. We also extend our approach to handle uncertainty in the leader’s objectives via a hypervolume improvement-based acquisition function. Experiments show that our algorithm is more efficient than other current methods while successfully approximating Pareto-fronts.

Identification of energy management configuration concepts from a set of pareto-optimal solutions

Implementing resource efficient energy management systems in facilities and buildings becomes increasingly important in the transformation to a sustainable society. However, selecting a suitable configuration based on multiple, typically conflicting objectives, such as cost, robustness with respect to uncertainty of grid operation, or renewable energy utilization, is a difficult multi-criteria decision making problem. The recently developed concept identification technique can facilitate a decision maker by sorting configuration options into semantically meaningful groups (concepts).In this process, the partitioning of the objectives and design parameters into different sets (called description spaces) is a very important step. In this study we focus on utilizing the concept identification technique for finding relevant and viable energy management configurations from a very large data set of Pareto-optimal solutions. The data set consists of 20,000 realistic Pareto-optimal building energy management configurations generated by a many-objective evolutionary optimization of a high quality Digital Twin energy management simulator. We analyze how the choice of description spaces, i.e., the partitioning of the objectives and parameters, impacts the type of information that can be extracted. We show that the decision maker can introduce constraints and biases into that process to meet expectations and preferences. The iterative approach presented in this work allows for the generation of valuable insights into trade-offs between specific objectives, and constitutes a powerful and flexible tool to support the decision making process when designing large and complex energy management systems.

Integrated passive design method optimized for carbon emissions, economics, and thermal comfort of zero-carbon buildings

Improving passive design methods are important for achieving zero-carbon building (ZCB) targets. Data-driven design approaches are more accurate than conventional methods for multiple-objective optimization (MOO) targets such as carbon emissions (CE), economics, and thermal comfort. In this study, a comprehensive data-driven-based PSO-SVM-NSGA-III method that assists in optimizing passive design parameters are proposed. First, the simulation results for the objectives of CE, incremental cost (IC), and time not comfort (TNC) are performed for an office building in a cold region in China using EnergyPlus and jEPlus software. Then, key influencing factors are chosen via a sensitivity analysis. Second, nonlinear mapping relationships between the passive design parameters and objectives are established with the PSO-SVM model. Compared to the BPNN, SVM, and PSO-BPNN algorithms, the PSO-SVM model exhibits superior prediction performance, with R2 values of 0.977, 0.925, and 0.903 for CE, IC, and TNC, respectively. Third, the nonlinear mapping relationships are used in the established objective functions of NSGA-II and NSGA-III. NSGA-III performed 100 iterations within 21 min and exhibited robust diversity within its population, with a hypervolume value of 0.738. Finally, the Pareto-optimal solution set is formed with the PSO-SVM-NSGA-III framework. This data-driven method offers an efficient approach for improving building performance.

Are You Concerned about Limited Function Evaluations: Data-Augmented Pareto Set Learning for Expensive Multi-Objective Optimization

Optimizing multiple conflicting black-box objectives simultaneously is a prevalent occurrence in many real-world applications, such as neural architecture search, and machine learning. These problems are known as expensive multi-objective optimization problems (EMOPs) when the function evaluations are computationally or financially costly. Multi-objective Bayesian optimization (MOBO) offers an efficient approach to discovering a set of Pareto optimal solutions. However, the data deficiency issue caused by limited function evaluations has posed a great challenge to current optimization methods. Moreover, most current methods tend to prioritize the quality of candidate solutions, while ignoring the quantity of promising samples. In order to tackle these issues, our paper proposes a novel multi-objective Bayesian optimization algorithm with a data augmentation strategy that provides ample high-quality samples for Pareto set learning (PSL). Specifically, it utilizes Generative Adversarial Networks (GANs) to enrich data and a dominance prediction model to screen out high-quality samples, mitigating the predicament of limited function evaluations in EMOPs. Additionally, we adopt the regularity model to expensive multi-objective Bayesian optimization for PSL. Experimental results on both synthetic and real-world problems demonstrate that our algorithm outperforms several state-of-the-art and classical algorithms.

Multi-Objective Optimization with Active–Passive Technology Synergy for Rural Residences in Northern China

Due to the serious problems with energy efficiency, carbon emissions, and thermal comfort of rural residences in northern China, an optimization of active and passive heating technologies for rural residences is necessary. In this paper, an optimization for rural residences in northern China is conducted with four objectives: the whole life cycle carbon emission; the annual energy consumption through heating, ventilation, and air conditioning systems; the annual cost; and thermal comfort. In addition, the optimization model with active–passive heating technology synergy is resolved by NSGA-II genetic algorithm. The active and passive design variables, including the type of air source heat pump, orientation, the type and thickness of envelope insulation, the layer of window glass, the window-to-wall area ratio, as well as sunspace parameters are preferred to obtain the optimal solution. The results indicate that the optimal solution obtained by the ideal point method gives the most outstanding performance. Compared with the prototype, the optimized carbon emissions in severe cold and cold regions decreased by 56.1% and 54.6%, respectively. The annual energy consumption decreased by 59.7% and 62.2%. Finally, the roof insulation thickness is the most sensitive design variable in Pareto-optimal solution sets. This paper offers significant guidance in the application of the optimization method of active–passive technology synergy to the energy-saving design of buildings.

A nondominated sorting genetic model for co-clustering

Co-clustering aims to cluster the rows and columns of data simultaneously and can be often formulated as a two-objective optimization problem (one objective for rows and the other for columns) and the solution is a Pareto-optimal solution set in principle. Existing methods usually convert the co-clustering problem into a single-objective optimization problem by setting a hyper-parameter λ between the two objectives. However, finding a good value of λ is not easy because of its large parameter space; also, there may exist many equally good λs. In this paper, a nondominated sorting genetic model (NSGC) is proposed to tackle the co-clustering problem, totally bypassing the trade-off parameter λ and returning to the original two-objective problem. The core of our model is to group a row objective function and a column objective function and integrate them into a genetic algorithm as the fitness functions. After this reformulation, we follow a standard genetic algorithm procedure to iteratively find the Pareto-optimal solutions. Finally, to fish out a single best solution we further design a sorting criterion according to which the Pareto-optimal solution set can be totally ordered. Extensive experiments with 16 public datasets are conducted, and the results demonstrate the superiority of our approach.

Improved Multi-objective Particle Swarm Optimization in Software Engineering Supervision

In the 21st century, the software industry has achieved great development. The development complexity and volume of software projects are also continuously increasing. The design of software engineering supervision network plans is becoming increasingly important. In response to the poor optimization performance and poor convergence and distribution of optimal solutions in existing network planning algorithms, the Pareto optimal solution set construction method, global extremum selection method, and fitness value determination method of multi-objective particle swarm optimization algorithm are improved to enhance the convergence and distribution of the algorithm. Traditional methods only optimize one or two objectives of network planning, resulting in inconsistency with actual engineering. A multi-objective model based on resources, duration, cost, and quality is established for comprehensive optimization. Based on the results, the Pareto optimal solution curves obtained by the proposed algorithm on three classic test functions are consistent with the actual theoretical Pareto frontier curves. The proposed method is applied to engineering project examples. 10 solutions that meet the schedule requirements are obtained. Most engineering projects have a quality of over 80%, which verifies the practicality of the algorithm. The algorithm has achieved good results in optimizing engineering quality. Therefore, this model has the ability to consider various indicators such as resources and costs to obtain software engineering quality improvement plans. It has certain application potential.