Set Of Pareto-optimal Solutions Research Articles

Microstructure Design of Multiphase Compositionally Complex Alloys II: Use of a Genetic Algorithm and a Vanishing Cracked Particle Model

AbstractAchieving high strength, ductility, and toughness via microstructure design is challenging due to the interrelated dependencies of strength and ductility on microstructural variables. As a natural extension of the microstructure design work in Bhattacharyya and Agnew (Microstructure design of multiphase compositionally complex alloys I: effects of strength contrast and strain hardening, 2024), an optimization framework to obtain the microstructure that maximizes the toughness is described. The strategy integrates a physics-based crystal plasticity model, which accounts for damage evolution within the reinforcement through a “vanishing cracked particle” model that is governed by Weibull statistics, and a genetic algorithm-based optimization routine. Optimization constraints are imposed in the form of bounds on the microstructure parameters such that they are most likely attainable by conventional thermomechanical processing. Various matrix strain hardening behaviors are considered, as well as the strength contrast between the two phases and fracture behavior of the reinforcement. It is shown that the addition of a fine-grained (hard) reinforcing phase is preferred as is a matrix that exhibits sustained strain hardening such as is observed under TRIP/TWIP scenarios. Finally, the Pareto-optimal set of solutions for several scenarios are presented which offer new insights into the linkages between microstructure and mechanical properties.

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.

Study on flexible job shop scheduling problem considering energy saving

The Flexible Job Shop Scheduling Problem (FJSP) is an extension of the classical Job Shop Scheduling Problem (JSP). The research objective of the traditional FJSP mainly considers the completion time, but ignores the energy consumption of the manufacturing system. In this paper, a mathematical model of the energy-efficient flexible job shop scheduling problem is constructed. The optimization objectives are completion time, delay time, and total equipment energy consumption. To solve the model, an improved non-dominated sorting genetic algorithm (CT-NSGA-II) is proposed to obtain the optimal scheduling solution. First, the heuristic rules of GLR were used to generate the initial population with good quality and diversity. Second, different crossover and variation operators are designed for the process sequencing and equipment selection parts to enhance the diversity of the evolutionary population. The sparsity theory is introduced to find sparse solutions and three neighborhood structures are designed to perform local search on sparse solutions to improve the uniformity of the optimal solution set distribution. Finally, a competitive selection strategy based on the bidding mechanism is proposed for the Pareto optimal solution set to obtain a better scheduling scheme. The experimental results show that the proposed improved algorithm is feasible and effective in the FJSP problem considering energy consumption, and the algorithm has some application value in improving the efficiency of smart shop operation.

Low-carbon-oriented commercial district urban form optimization and impact assessment analysis

Commercial buildings have become one of the main sources of carbon emissions. However, the current research on urban form optimization has lacked analyses of the low-carbon indicators of buildings. With the Beijing commercial district as an example, a low-carbon-oriented urban form optimization path is established in this study, and a new method of urban form optimization is developed from a low-carbon perspective. With the help of the parametric platform and multiobjective optimization algorithm, a dynamic optimization model of urban morphology based on parametric modeling, numerical simulation and algorithm optimization is developed, and the morphological characteristics of low-carbon commercial blocks in Beijing are assessed with a Pareto-optimal solution set. Through principal component regression analysis, the correlations between urban form factors and low-carbon evaluation indicators are discussed. The study shows that the multiobjective optimization algorithm effectively optimizes the low-carbon indicators of buildings at the block scale. The urban forms obtained from the Pareto solution set display several commonalities reflected from three perspectives: building type, vertical dimension and building orientation. It is found that the optimal block layout form reduces the building carbon emission intensity and the building outer skin radiation difference, and the renewable energy-based carbon reduction is large. The urban form factors that have a significant impact on the carbon emission intensity of buildings include the maintenance coefficients, the average area to perimeter ratio, and the sky view factor, with respective impact coefficients of 0.301, −0.309, and −0.319.

Mechanisms of Characteristic Parameters of Plasma Actuator on Film Cooling and Turbulent Transport Based on Multi-Objective Optimization

In this paper, film cooling effectiveness and pressure loss coefficient are taken as the objective functions to optimize the plasma characteristic parameters such as electrode position, spacing, length and actuation intensity for enhancing film cooling performance. Regression equations of two objective functions are accessed by the Response Surface Method, and Non-Dominated Sorting Genetic Algorithm is applied for bi-objective optimization. Two sets of Pareto optimal solutions are available via the Technique for Order Preference by Similarity to an Ideal Solution decision method. Pareto optimal solutions are calculated by Detached Eddy Simulation to clarify the turbulent transport and heat transfer characteristics induced by the plasma. Wall-averaged cooling effectiveness and pressure loss coefficient without plasma power supply are 64.3% and 3.9% superior to that without electrode, respectively. The plasma fragments the hairpin vortex into a striped structure and induces a large scale streamwise vortex behind the bare electrode. The plasma weakens the velocity diffusion and turbulent heat transport in the ionization zone. Overlapping electrodes render the root-mean-square pulsation velocity and Reynolds stress of the optimal model 1 both less than those of the optimal model 2 without overlapping electrodes, and flow field disorder is decreased. Electrode position interferes with the action location of plasma on cooling jet. Actuation intensity affects the ionization intensity and has a maximum value of 8.88 to optimize the actuator performance. Compared with no plasma actuation, wall-averaged cooling effectiveness of optimal model 1 and optimal model 2 are enhanced by 30.7% and 21.8%, and pressure loss coefficient are declined by 7.7% and 7.1%, respectively.

Multiobjective Combinatorial Optimization Using a Single Deep Reinforcement Learning Model.

This article proposes utilizing a single deep reinforcement learning model to solve combinatorial multiobjective optimization problems. We use the well-known multiobjective traveling salesman problem (MOTSP) as an example. Our proposed method employs an encoder-decoder framework to learn the mapping from the MOTSP instance to its Pareto-optimal set. Specifically, it leverages a novel routing encoder to extract information for both the entire multiobjective aspect and every individual objective from the MOTSP instance. The global embeddings and each objective's embeddings are adaptively aggregated via a routing network to form the subproblems' embedding that can well represent the MOTSP features. Using a modified context embedding, the subproblems' embeddings are fed into a decoder to produce a set of approximate Pareto-optimal solutions in parallel. Additionally, we develop a Top-k baseline to enable more efficient data utilization and lightweight training for our proposed method. We compare our method with heuristic-based and learning-based ones on various types of MOTSP instances, and the experimental results show that our method can solve MOTSP instances in real-time and outperform the other algorithms, especially on large-scale problem instances.

Optimization of responses in single and multi-point machining processes using Dragon-fly algorithm coupled with TOPSIS and VIKOR decision-making approaches

Due to complex production practices, it is becoming crucial to provide greater thermal management and friction reduction in manufacturing processes. Lubricants play a crucial role by effectively reducing friction, minimizing wear and tear thereby extending the lifespan of the tool. It is observed that there is a shortage of studies associated with the machining of hard materials like Ti-6Al-4V. The present work has therefore focused on the machining of high-grade Titanium alloy under dry and Neem oil aerosol-mist spray wet conditions. The machining is performed on two kinds of machining processes, such as plain facing with single point tool and co-axial turn-mill facing with multi-point cutting tools on computer numerical controlled Turn-mill machine tool. Furthermore, there are very few articles reported on usage of Neem oil (AzadirachtaIndicaL.) as a lubricant. This has motivated the authors to use Neem oil in a mist condition to minimize the quantity of coolant, without compromising on the tool temperature, surface quality, and tool-wear. The responses obtained are subjected to regression analysis to evolve the fitness functions. Multi-objective optimization of these functions is than adopted using Dragon-fly algorithm (MODA) under the constraints of the machining parameters. A set of pareto optimal solutions for each of the machining cases are obtained and are further evaluated using TOPSIS and VIKOR decision-making approaches to achieve the optimal values of the cutting parameters. The optimum parameters for single point cutting under wet conditions were observed as speed (592 rpm), feed (0.058 mm rev−1) and depth of cut (1.00 mm).The corresponding values of responses were tool temperature (37.05 °C), surface roughness (0.128 μm) and tool wear (155.19 μm). The equivalent values for multi-point cutting were determined as 510 rpm, 0.086 mm rev−1 and 0.25 mm. The responses for these optimal conditions are 32.17 °C, 0.725 μm and 45.72 μm in that order.

DERNA Enables Pareto Optimal RNA Design.

The design of an RNA sequence that encodes an input target protein sequence is a crucial aspect of messenger RNA (mRNA) vaccine development. There are an exponential number of possible RNA sequences for a single target protein due to codon degeneracy. These potential RNA sequences can assume various secondary structure conformations, each with distinct minimum free energy (MFE), impacting thermodynamic stability and mRNA half-life. Furthermore, the presence of species-specific codon usage bias, quantified by the codon adaptation index (CAI), plays a vital role in translation efficiency. While earlier studies focused on optimizing either MFE or CAI, recent research has underscored the advantages of simultaneously optimizing both objectives. However, optimizing one objective comes at the expense of the other. In this work, we present the Pareto Optimal RNA Design problem, aiming to identify the set of Pareto optimal solutions for which no alternative solutions exist that exhibit better MFE and CAI values. Our algorithm DEsign RNA (DERNA) uses the weighted sum method to enumerate the Pareto front by optimizing convex combinations of both objectives. We use dynamic programming to solve each convex combination in time and space. Compared with a CDSfold, previous approach that only optimizes MFE, we show on a benchmark data set that DERNA obtains solutions with identical MFE but superior CAI. Moreover, we show that DERNA matches the performance in terms of solution quality of LinearDesign, a recent approach that similarly seeks to balance MFE and CAI. We conclude by demonstrating our method's potential for mRNA vaccine design for the SARS-CoV-2 spike protein.

Investigation on carbon fiber-reinforced polymer combined with graphene nanoparticles subjected to drilling operation using response surface methodology and non-dominated sorting genetic algorithm-II

In this article, drilling of carbon fiber-reinforced plastics combined with graphene nanoparticles is investigated. These nanocomposites have the potential to be used widely in different industrial applications such as electrical, biomedical and aerospace engineering due to their superior mechanical and thermal specifications. Nonetheless, to be assembled on different sets, drilling nanocomposites is required especially for rivets and joints. In drilling carbon fiber-reinforced polymers (CFRPs), delamination is one of the main challenges that should be minimized in order to enhance the produced hole quality. Besides, machining force is a chief factor to control the drilling-induced damages, especially delamination. This article evaluates the effects of machining parameters on machining force and delamination using response surface methodology experimental design and non-dominated sorting genetic algorithm-II (NSGA-II) multiobjective optimization methodology. Examining delamination is conducted in two parts including peel-up and push-down delamination which are the principal drawbacks in drilling of fiber-reinforced composites. Analysis of variance is also carried out in order to examine the effects of the machining parameters. In addition, predictive quadratic correlations are established by regression analysis. Eventually, multiobjective optimization was implemented by NSGA-II and the optimal values were obtained from pareto-optimal solution set aimed at enhancing the drilling process.

Evolutionary multimodal multiobjective optimization guided by growing neural gas

Evolutionary multimodal multiobjective optimization aims to search for a set of Pareto optimal solutions that are well distributed in both the objective and decision spaces. In recent years, there has been a growing interest in enhancing the search ability of evolutionary algorithms using machine learning techniques. However, there are few studies on machine learning-assisted evolutionary multimodal multiobjective optimization. In this paper, we propose an evolutionary multimodal multiobjective algorithm guided by growing neural gas, which learns the topological structure of the obtained good solutions during the evolution process. These good solutions are well-converged and well-distributed in the decision space, which indicate the shape of the Pareto optimal solution set. The proposed algorithm employs three novel mating selection operators based on the topological structure to efficiently and effectively search for Pareto optimal solutions. The first operator exploits Pareto optimal solutions within the topological structure, while the others explore Pareto optimal solutions around and far away from the topological structure, respectively. The proposed algorithm is compared with eight state-of-the-art evolutionary multimodal multiobjective algorithms on 20 test problems. Experimental results demonstrate that the proposed algorithm is competitive in solving these problems.

Multi-Criteria Optimization Conditions for the Recovery of Bioactive Compounds from Levisticum officinale WDJ Koch Roots Using Green and Sustainable Ultrasound-Assisted Extraction

Given that ultrasound-assisted aqueous extraction is gaining importance within “green technology” and to increase the efficiency of extracting bioactive compounds from Levisticum officinale root waste, optimization of its parameters was undertaken. Multi-objective (multi-criteria) optimization can be an extremely promising tool not only for designing and analyzing the extraction process, but also for making process-control decisions. Therefore, the main objective of this study was to develop and optimize an environmentally friendly ultrasound-assisted extraction methodology for the aqueous extraction of bioactive compounds from the roots of Levisticum officinale, which are considered a by-product. The focus was on determining the optimal extraction conditions of the independent variables, such as solid–liquid ratio, extraction time and ultrasound power, so that the optimized extracts present the highest bioactive potential expressed in terms of levels of phenolic compounds, flavonoids, sugars and antioxidant potential. Based on the Pareto-optimal solution sets, it was found that to maximize the criteria, aqueous extraction should be carried out at a Levisticum officinale biomass/solvent ratio of 0.0643 g/mL for a time of 8.1429 to 9.0000 min, with ultrasound assistance of 162.8571 to 201.4286 W. Among the compromise solutions, the so-called “best efficient solution” was indicated as the solution for which the Euclidean distance from the ideal point of Utopia was the smallest (among all analyzed points of the collection), which had coordinates x1comp = 0.0750 g/mL, x2comp = 9.0000 min and x3comp = 214.2857 W. The results obtained will provide a valuable tool to assist in the decision-making process of controlling such an extraction process.

Two-stage evolutionary algorithm with fuzzy preference indicator for multimodal multi-objective optimization

Multimodal multi-objective optimization problems (MMOPs) are multi-objective optimization problems (MOPs) involving multiple equivalent global or local Pareto optimal solution sets (PSs). For decision-makers, not only the global optimal solution sets need to be found, but also the value of local optimal solution sets cannot be ignored. However, most multimodal multi-objective evolutionary algorithms (MMOEAs) tend to select solutions with better convergence, and it is difficult to obtain the global PSs and local PSs at the same time. Therefore, we propose a fuzzy preference indicator-based two-stage evolutionary algorithm (FPITSEA) in this paper. To evaluate more comprehensively the potential of each solution in the population for locating the global and local PS during the evolutionary process, a fuzzy preference indicator is designed in FPITSEA. The fuzzy preference indicator is used to guide the evolution of the population in the first stage to find the global and local Pareto optimal regions. Subsequently, an independent evolution strategy is implemented in the second stage to distinguish different PSs as accurately as possible while also ensuring the convergence quality of the solution set. In addition, an improved distance-based subset selection method is proposed, aiming to simultaneously improve the distribution of the solution set in the decision space and objective space. Experimental results on several test sets of MMOPs show the advantages of FPITSEA over several state-of-the-art MMOEAs.