Pareto Front Research Articles

Unsupervised Learning Bioreactor Regimes

Efficient operation of bioreactors is pivotal for the success of biomanufacturing. Traditional Computational Fluid Dynamics (CFD) simulations, while detailed, often suffer from long computation times and complexity, making them impractical for real-time applications. This study introduces a novel multivariate unsupervised learning algorithm for clustering bioreactors into coherent regions based on CFD-generated and real-world data. The resulting clusters can be used to determine regimes inside a reactor, or can work as an initial step for compartment models. Our method employs a custom k-means clustering algorithm that not only ensures spatial continuity within clusters but also optimizes the number of compartments based on clustering scores. This optimization process focuses on defining compartments clearly while retaining maximum information from the continuous body, as demonstrated by a Pareto front analysis. The efficacy and adaptability of this approach were validated through two case studies: a 202 m³ Rushton impeller bioreactor and an 840 m³ airlift reactor. The results underscore the benefits of 3-D compartmentalization in capturing the complex dynamics of fluid motion and cellular activities. By establishing a robust method for scaling down experiments and enhancing bioreactor design, this study paves the way for more efficient industrial applications.

Multi-objective optimization of power networks integrating electric vehicles and wind energy

In the ever-evolving landscape of power networks, the integration of diverse sources, including electric vehicles (EVs) and renewable energies like wind power, has gained prominence. With the rapid proliferation of plug-in electric vehicles (PEVs), their optimal utilization hinges on reconciling conflicting and adaptable targets, including facilitating vehicle-to-grid (V2 G) connectivity or harmonizing with the broader energy ecosystem. Simultaneously, the inexorable integration of wind resources into power networks underscores the critical need for multi-purpose planning to optimize production and reduce costs. This study tackles this multifaceted challenge, incorporating the presence of EVs and a probabilistic wind resource model. Addressing the complexity of the issue, we devise a multi-purpose method grounded in collective competition, effectively reducing computational complexity and creatively enhancing the model's performance with a Pareto front optimality point. To discern the ideal response, fuzzy theory is employed. The suggested pattern is rigorously tested on two well-established IEEE power networks (30- and 118-bus) in diverse scenarios featuring windmills and PEV producers, with outcomes showcasing the remarkable excellence of our multi-purpose framework in addressing this intricate issue while accommodating uncertainty.

Sustainable Operation Strategy for Wet Flue Gas Desulfurization at a Coal-Fired Power Plant via an Improved Many-Objective Optimization

Coal-fired power plants account for a large share of the power generation market in China. The mainstream method of desulfurization employed in the coal-fired power generation sector now is wet flue gas desulfurization. This process is known to have a high cost and be energy-/materially intensive. Due to the complicated desulfurization mechanism, it is challenging to improve the overall sustainability profile involving energy-, cost-, and resource-relevant objectives via traditional mechanistic models. As such, the present study formulated a data-driven many-objective model for the sustainability of the desulfurization process. We preprocessed the actual operation data collected from the desulfurization tower in a domestic ultra-supercritical coal-fired power plant with a 600 MW unit. The extreme random forest algorithm was adopted to approximate the objective functions as prediction models for four objectives, namely, desulfurization efficiency, unit power consumption, limestone supply, and unit operation cost. Three metrics were utilized to evaluate the performance of prediction. Then, we incorporated differential evolution and non-dominated sorting genetic algorithm-III to optimize the multiple parameters and obtain the Pareto front. The results indicated that the correlation coefficient (R2) values of the prediction models were greater than 0.97. Compared with the original operation condition, the operation under optimized parameters could improve the desulfurization efficiency by 0.25% on average and reduce energy, cost, and slurry consumption significantly. This study would help develop operation strategies to improve the sustainability of coal-fired power plants.

Multi-Objective Design of An Induction Motor Using A New Method For Finding The Optimal Solution By The Pareto Front Based On Harmony Search

Multi-Objective Design of An Induction Motor Using A New Method For Finding The Optimal Solution By The Pareto Front Based On Harmony Search

Conceptual hybrid energy model for different power potential scales: Technical and economic approaches

This research attempts to address the gap between the theoretical fundamentals of hybrid renewable energy systems and their practical implementation at different scales through a new Conceptual Hybrid Energy Model (COHYBEM). The main objective was to develop a multi-variable model to allow a new complete and comprehensive techno-economic analysis of the performance of possible hybrid renewable power systems at different scales. The purpose is to evaluate the influence of critical parameters by changing key parameters in the developed model and identifying their impacts. It covers big data analyses, simulation and optimization of hybrid energy solutions, combining wind, solar and hydropower energy sources with the energy storage technology of pump hydropower storage. The research also denoted the Pareto front with the increasing power installed, for the maximum efficiency and total satisfied demand by Wind + PVSolar and by Hydro converges to a higher percentage, while a minimum waste by Wind + PVSolar is also progressing towards the increasing scales. In terms of investment costs for the 243 analyzed case studies, it varies between 45 k€ to 2.1 M€, resulting in a net present value (NPV) between 18 and 600 k€ and a payback period around 6–17 years depending on the power scale analyzed.

Learning-based Pareto-optimum routing of ships incorporating uncertain meteorological and oceanographic forecasts

In modern shipping logistics, multi-objective ship route planning has attracted considerable attention in both academia and industry, with a primary focus on energy conservation and emission reduction. The core challenges in this field involve determining the optimal route and sailing speed for a given voyage under complex and variable meteorological and oceanographic conditions. Typically, the objectives revolve around optimizing fuel consumption, carbon emissions, duration time, energy efficiency, and other relevant factors. However, in the multi-objective route planning problem involving variable routes and speeds, the extensive solution space contains a substantial number of unevenly distributed feasible samples. Traditional heuristic optimization techniques, such as multi-objective evolutionary algorithms, which serve as the core component of optimization programs, suffer from inefficiencies in exploring the solution space. Consequently, these algorithms may tend to converge toward local optima during population iteration, resulting in a solution set characterized by sub-optimal convergence and limited diversity. This ultimately undermines the potential benefits of routing optimization. To address such challenging problem in route planning tasks, we propose a self-adaptive intelligent learning network aiming at capturing the potential evolutionary characteristics during population iteration, in order to achieve high-efficiency directed optimization of individuals. Additionally, an uncertainty-driven module is developed by incorporating ensemble forecasts of meteorological and oceanographic variables to form the Pareto frontier with more reliable solutions. Finally, the overall framework of the proposed learning-based multi-objective evolutionary algorithm is meticulously designed and validated through comprehensive analyses. Optimization results demonstrate its superiority in generating routing plans that effectively minimize costs, reduce emissions, and mitigate risks.

Multi-User Optimal Load Scheduling of Different Objectives Combined with Multi-Criteria Decision Making for Smart Grid

Load balancing between required power demand and the available generation capacity is the main task of demand response for a smart grid. Matching between the objectives of users and utilities is the main gap that should be addressed in the demand response context. In this paper, a multi-user optimal load scheduling is proposed to benefit both utility companies and users. Different objectives are considered to form a multi-objective artificial hummingbird algorithm (MAHA). The cost of energy consumption, peak of load, and user inconvenience are the main objectives considered in this work. A hybrid multi-criteria decision making method is considered to select the dominance solutions. This approach is based on the removal effects of criteria (MERECs) and is utilized for deriving appropriate weights of various criteria. Next, the Vlse Kriterijumska Optimizacija Kompromisno Resenje (VIKOR) method is used to find the best solution of load scheduling from a set of Pareto front solutions produced by MAHA. Multiple pricing schemes are applied in this work, namely the time of use (ToU) and adaptive consumption level pricing scheme (ACLPS), to test the proposed system with regards to different pricing rates. Furthermore, non-cooperative and cooperative users’ working schemes are considered to overcome the issue of making a new peak load time through shifting the user load from the peak to off-peak period to realize minimum energy cost. The results demonstrate 81% cost savings for the proposed method with the cooperative mode while using ACLPS and 40% savings regarding ToU. Furthermore, the peak saving for the same mode of operation provides about 68% and 64% for ACLPs and ToU, respectively. The finding of this work has been validated against other related contributions to examine the significance of the proposed technique. The analyses in this research have concluded that the presented approach has realized a remarkable saving for the peak power intervals and energy cost while maintaining an acceptable range of the customer inconvenience level.

A multi-objective optimization approach to design bistable collapsible tubular mast

The collapsible tubular mast (CTM) is a deployable structure made of two omega shaped shells, with each omega composed of three arc segments. In the bistable CTM (Bi-CTM), in addition to the strain energy well associated with the stable deployed state, another strain energy well can be found corresponding to the stable coiled state. The arcs’ geometries influence the existence of the second strain energy well and the associated stable coiled radius, responsible for the boom’s packaging efficiency. Besides packaging efficiency, factors like bending stiffness are also contingent on the geometries of the arcs, leading to significant trade-offs among these metrics. In this work, we propose a multi-objective optimization (MOO) to find optimal compromises that balance these conflicting requirements of a CTM. Particularly, a coupling analytical models and evolutionary algorithms (EA) technique is presented, utilizing and bench-marking various state-of-the-art EAs. The MOO approach gives as output the Pareto front, a set of the non-dominated design points, which showcases different trade-offs solutions tailorable for specific space-applications. Different design points are presented and discussed based on higher-level considerations.

A dynamic multi-objective optimization model for inner-industry carbon responsibility allocation based on carbon tax and carbon offsets accounting

The setting of Intergovernmental Panel on Climate Change (IPCC) raises concerns on curbing the excessive carbon emissions, and European Union (EU) has been proactively attempting “green” initiatives striving to achieve carbon neutrality. The current Carbon Border Adjustment Mechanism (CBAM) only works on short-term carbon reduction without much “greenness” investment incentives so far, and few studies focus on the long-standing inner-industrial carbon reduction coordination. To address these issues, this paper creatively presents a dynamic multi-objective carbon responsibility allocation model (CRAM) for EU carbon market, allows the carbon trade with a taxation based on carbon offsets accounting, and considers the final targets of sustainable “greenness” investment incentives. To find the optimal results of the designed dynamic CRAM, an improved KT-NSGA-II algorithm is proposed to detect the Pareto frontiers of each successive periods. Data from EU Cement and Aluminium industries are then selected for empirical analysis to compare the proposed CRAM to conventional CBAM model. The findings demonstrate that the superiority of CRAM in carbon emissions reduction, economic benefits improvement and green invests encouragement. With the adjustment of the inner-industrial carbon allowance trade, total carbon emissions decreased by 28.03% and the “greenness” investment initiative increased by 39.24% in contrast to the CBAM. The sensitivity analysis of the model also provides suggestions on the settings of carbon quota and tax with different industrial production process, and proposes policy recommendations for CRAM implementation.

General integration method for system configuration of organic Rankine cycle based on stage-wise concept

Organic Rankine Cycle (ORC) integrated systems with heat sources consist of heat exchange processes and thermodynamic power conversion processes. Fully exploring feasible system configuration while considering fluid selection is crucial for enhancing ORC power generation and balancing economic costs. This study innovatively proposes a theoretical framework that decomposes the Rankine cycle into basic thermodynamic processes. The design of system configuration is regarded as the adjustment of the series-parallel relationships of these basic processes, aiming to achieve simultaneous optimization of the cycle structure and the HEN structure, thereby greatly expanded the search space for feasible ORC system configurations. The optimization problem is solved using a bi-level strategy, The outer layer determines the number of thermal power conversion components, operating parameters, and working fluid selection, then provides the associated stream information to the inner layer for optimizing the heat exchange scheme. Applying this method to two different case studies from the literature validated its effectiveness in optimizing scenarios with single and complex heat sources. The Pareto frontier obtained under the conditions of Case I indicates that the investment cost can be reduced by $33.04 k/yr while maintaining the same net power output. In exchange for an increase of $1.51 k/yr in investment cost, the maximum net power output can be improved by 124.74 kW. Under the conditions of Case II, the maximum net output power can increase by 9.71 %–52.5 %, and the Pareto frontier featuring outputs exceeding 50 kW is provided. By analyzing the relative positions of literature schemes and Pareto front within the solution space, the impact of system configuration improvements on the objective functions is explained. These results confirm the effectiveness of the proposed approach for designing optimal ORC energy recovery systems for heat sources. This contribution advances optimization methods for similar closed cycle configurations, which is significant for advancing the utilization of waste heat and addressing sustainability challenges.

Modeling solvation dynamics of transition metal redox ion through on-the-fly multi-objective Bayesian-optimized force field.

Modeling solvation dynamics and properties is crucial for developing electrolytes for electrochemical energy storage and conversion devices. This work reports an on-the-fly multi-objective Bayesian optimization (OTF-MOBO) method to parameterize force fields for modeling ionic solvation structures, thermodynamics, and transport properties using molecular dynamics simulations. By leveraging solvation-free energy and solvation radii as training data, we employ the data-driven OTF-MOBO algorithm to actively optimize the force field parameters. The modeling accuracy was evaluated in molecular dynamics simulations until the Pareto front in the parameter space was reached through minimized prediction errors in both solvation-free energy and solvation radii. Using transition metal redox ions (Fe3+/Fe2+, Cr3+/Cr2+, and Cu2+/Cu+) in aqueous solution as examples, we demonstrate that simple force fields combining the Lenard-Jones potential and Coulombic potential can achieve relative error below 2% in both solvation free energy and solvation radii. The optimized force fields can be further extrapolated to predict solvation entropy and diffusivities with relative error below 10% compared with experiments.

Pareto front of sodium void worth and breeding ratio in metal-fueled sodium fast reactor with axially heterogeneous core design by coupling neutronics and genetic algorithm

For sodium-cooled fast reactors (SFRs), achieving low sodium void worth (SVW) and flexible breeding ratios (BR) is crucial. This study establishes a method coupling neutronics simulations with genetic algorithms (GA) and applies it to a 3000 MWth metal-fueled SFR to optimize the SVW, BR, and the power distribution of axially heterogeneous cores. The Pareto front, i.e. optimal front, between SVW and BR is determined, quantitatively clarifying the trade-off relationship between these two parameters. Axially heterogeneous cores with equal inner and outer fissile heights can achieve SVW adjustments from −71 to 3148 pcm and BR adjustments from 1.26 to 1.62. Designs with unequal fissile heights slightly expand the feasible region, but the impact on the optimal front for equal-height designs is limited. Through the analysis of the spatial distribution of the sodium void effect, it is shown that the bond sodium model significantly influences the SVW in low sodium void cores, while its impact on high breeding cores is minimal. The results indicate that the power distribution can be optimized by adjusting the enrichment of subregions within the constraints of SVW and BR. For low sodium void cores, retaining a certain amount of lower fertile material is necessary to flatten the power distribution. While the criticality search during depletion calculations affects the parameters, its impact on identifying the optimal front is limited.

Deep reinforcement learning assisted novelty search in Voronoi regions for constrained multi-objective optimization

Solving constrained multi-objective optimization problems (CMOPs) requires optimizing multiple conflicting objectives while satisfying various constraints. Existing constrained multi-objective evolutionary algorithms (CMOEAs) cross infeasible regions by ignoring constraints. However, these methods might neglect promising search directions, leading to insufficient exploration of the search space. To address this issue, this paper proposes a deep reinforcement learning assisted constrained multi-objective quality-diversity algorithm. The proposed algorithm designs a diversity maintenance mechanism to promote evenly coverage of the final solution set on the constrained Pareto front. Specifically, first, a novelty-oriented archive is created using a centroid Voronoi tessellation, which divides the search space into a desired number of Voronoi regions. Each region acts as a repository of non-dominated solutions with different phenotypic characteristics to provide diversity information and supplementary evolutionary trails. Secondly, to improve resource utilization, a deep Q-network is adopted to learn a policy to select suitable Voronoi regions for offspring generation based on their novelty scores. The exploration of these regions aims to find a set of diverse, high-performing solutions to accelerate convergence and escape local optima. Compared with eight state-of-the-art CMOEAs, experimental studies on four benchmark suites and nine real-world applications demonstrate that the proposed algorithm exhibits superior or at least competitive performance, especially on problems with discrete and narrow feasible regions.

Energy Aware Technology Mapping of Genetic Logic Circuits.

Energy and its dissipation are fundamental to all living systems, including cells. Insufficient abundance of energy carriers -as caused by the additional burden of artificial genetic circuits- shifts a cell's priority to survival, also impairing the functionality of the genetic circuit. Moreover, recent works have shown the importance of energy expenditure in information transmission. Despite living organisms being non-equilibrium systems, non-equilibrium models capable of accounting for energy dissipation and non-equilibrium response curves are not yet employed in genetic design automation (GDA) software. To this end, we introduce Energy Aware Technology Mapping, the automated design of genetic logic circuits with respect to energy efficiency and functionality. The basis for this is an energy aware non-equilibrium steady state (NESS) model of gene expression, capturing characteristics like energy dissipation -which we link to the entropy production rate- and transcriptional bursting, relevant to eukaryotes as well as prokaryotes. Our evaluation shows that a genetic logic circuit's functional performance and energy efficiency are disjoint optimization goals. For our benchmark, energy efficiency improves by 37.2% on average when comparing to functionally optimized variants. We discover a linear increase in energy expenditure and overall protein expression with the circuit size, where Energy Aware Technology Mapping allows for designing genetic logic circuits with the energy efficiency of circuits that are one to two gates smaller. Structural variants improve this further, while results show the Pareto dominance among structures of a single Boolean function. By incorporating energy demand into the design, Energy Aware Technology Mapping enables energy efficiency by design. This extends current GDA tools and complements approaches coping with burden in vivo.

GRNMOPT: Inference of gene regulatory networks based on a multi-objective optimization approach

Background and objectiveThe reconstruction of gene regulatory networks (GRNs) stands as a vital approach in deciphering complex biological processes. The application of nonlinear ordinary differential equations (ODEs) models has demonstrated considerable efficacy in predicting GRNs. Notably, the decay rate and time delay are pivotal in authentic gene regulation, yet their systematic determination in ODEs models remains underexplored. The development of a comprehensive optimization framework for the effective estimation of these key parameters is essential for accurate GRN inference. MethodThis study introduces GRNMOPT, an innovative methodology for inferring GRNs from time-series and steady-state data. GRNMOPT employs a combined use of decay rate and time delay in constructing ODEs models to authentically represent gene regulatory processes. It incorporates a multi-objective optimization approach, optimizing decay rate and time delay concurrently to derive Pareto optimal sets for these factors, thereby maximizing accuracy metrics such as AUROC (Area Under the Receiver Operating Characteristic curve) and AUPR (Area Under the Precision-Recall curve). Additionally, the use of XGBoost for calculating feature importance aids in identifying potential regulatory gene links. ResultsComprehensive experimental evaluations on two simulated datasets from DREAM4 and three real gene expression datasets (Yeast, In vivo Reverse-engineering and Modeling Assessment [IRMA], and Escherichia coli [E. coli]) reveal that GRNMOPT performs commendably across varying network scales. Furthermore, cross-validation experiments substantiate the robustness of GRNMOPT. ConclusionWe propose a novel approach called GRNMOPT to infer GRNs based on a multi-objective optimization framework, which effectively improves inference accuracy and provides a powerful tool for GRNs inference.

Hydrogen vs. conventional sector-coupling residential energy systems: An economic and environmental comparison based on multi-objective design optimization

Planning residential energy systems faces economic, environmental, and technical challenges, necessitating cost-effective and environmentally friendly solutions. Hydrogen technologies in districts have recently gained interest. However, their economic and environmental potential relative to conventional technologies remains largely unexplored. Therefore, we quantitatively compared the impacts of designing hydrogen-based and conventional sector-coupling systems on total costs and CO2 emissions.We developed a multi-objective optimization model for the design and operation of generation and storage units, aiming to minimize total costs and CO2 emissions. We created three energy system configurations for an exemplary German district, each involving photovoltaics, heat storage, and batteries, while varying the main heat supplier. The first configuration includes a gas combined heat and power unit, the second features a heat pump, and the third incorporates a fuel cell, an electrolyzer, and hydrogen storage.Our comparison of the Pareto fronts revealed that the hydrogen system’s cost is 83% higher than the gas-based system and 33% higher than the heat-pump-based system. Environmentally, the hydrogen system emits 11% less than the gas-based system but 47% more than the heat-pump-based system. In conclusion, hydrogen units offer environmental benefits through improved photovoltaic utilization but perform poorly economically due to high investment and operating costs.

Multi-objective optimization of distributed green infrastructure for effective stormwater management in space-constrained highly urbanized areas

Green infrastructure (GI) is essential for stormwater management, but its implementation in highly urbanized areas is challenging due to the limited space available for GI retrofitting. There is a lack of comprehensive evaluations that assess the spatial adaptability, functionality, and cost-benefit of various GI measures, and optimize their placement to achieve the maximum reduction rate of total runoff (RTR) and reduction rate of pollution load (RPL) while minimizing life cycle cost (LCC) in space-constrained highly urbanized areas (SCHUA). To address this issue, a novel concept of infiltration, retention, and storage integrated GI (IRS-GI) for SCHUA was proposed, and a framework coupling the Storm Water Management Model (SWMM) with multi-objective optimization algorithms was developed to determine the optimal IRS-GI layout, focusing on the objectives of RTR, RPL, and LCC. The impacts of different GI type, size, and location, rainfall return periods, and algorithms (NSGA-II and NSGA-III) were then examined. The results showed that IRS-GI could achieve satisfactory RTR and RPL results while single-type GI may struggle to meet requirements. Optimization outcomes were significantly influenced by rainfall return periods, with cost-benefit decreasing as return periods increasing. Besides, the optimization results of NSGA-II and NSGA-III showed differences, and the comprehensive Pareto frontier obtained by reapplying non-dominated sorting could achieve more comprehensive results for determining the optimal IRS-GI configuration. Under the urban drainage design standard, the optimal IRS-GI layout, covering 32.97 % of the green spaces, 38.57 % of the rooftop, and 60.98 % of the ordinary roads and squares, respectively, could achieve a RTR of 50.09 %, RPL of 57.00 %, and LCC of 0.79 × 108 CNY/yr. Additionally, the optimal configuration suggested that a higher proportion of GI downstream of drainage system may contribute to better cost-benefit, emphasizing the need for location-specific GI solutions. This research offers valuable insights for optimizing GI in SCHUA, advancing sustainable urban stormwater management.

Integrated optimization of the building envelope and the HVAC system in office building retrofitting

Increasing the energy efficiency of existing buildings is the major strategy to reach carbon neutral targets, given that the building sector is a major emitter. In particular, one major part of building energy usage is the building heating, ventilation and air-cooling system, which are highly depending on the thermal performance of building envelope and increase the challenge of selecting optimal packages of energy efficiency measures. This paper thereby presents a method for optimizing the building envelope and heating, ventilation and air-cooling system. The simulation-based NSGA-III approach developed in this paper is based on coupling the dynamic simulation models created in EnergyPlus software with the non-dominated sorting genetic algorithm, as the engine that performs an optimization process. A large domain of energy efficiency packages combined with heating, ventilation and air-cooling systems and building envelope are investigated to minimize energy consumption, retrofit cost and thermal discomfort in indoor environments, which including ideal loads air system, four pipe fan coil system and variable refrigerant flow system, insulation materials and insulation thickness for external walls and roof, different types of external windows, and window-wall ratio. An office building in Chongqing was chosen as a case study to demonstrate the practical implementation of the proposed method. The results show that the four pipe fan coil system was superior in the diversity and performance of the Pareto front. Then, the optimal packages were generated by a synthetic method, which have 58.57 kWh/m2 of energy consumption, 30.76 CNY/m2 of retrofit cost and 40.67 % of the percentage of thermal discomfort hours. The results also indicate that the yearly energy savings rates are 17.30 %, 23.05 % and 21.10 % separately for ideal loads air system, four pipe fan coil system and variable refrigerant flow system after performing optimization. These results highlight the importance and necessity of performing an optimization procedure for existing buildings to select the optimal retrofit measures.

An Improved MOEA/D with an Auction-Based Matching Mechanism

Multi-objective optimization problems (MOPs) constitute a vital component in the field of mathematical optimization and operations research. The multi-objective evolutionary algorithm based on decomposition (MOEA/D) decomposes a MOP into a set of single-objective subproblems and approximates the true Pareto front (PF) by optimizing these subproblems in a collaborative manner. However, most existing MOEA/Ds maintain population diversity by limiting the replacement region or scale, which come at the cost of decreasing convergence. To better balance convergence and diversity, we introduce auction theory into algorithm design and propose an auction-based matching (ABM) mechanism to coordinate the replacement procedure in MOEA/D. In the ABM mechanism, each subproblem can be associated with its preferred individual in a competitive manner by simulating the auction process in economic activities. The integration of ABM into MOEA/D forms the proposed MOEA/D-ABM. Furthermore, to make the appropriate distribution of weight vectors, a modified adjustment strategy is utilized to adaptively adjust the weight vectors during the evolution process, where the trigger timing is determined by the convergence activity of the population. Finally, MOEA/D-ABM is compared with six state-of-the-art multi-objective evolutionary algorithms (MOEAs) on some benchmark problems with two to ten objectives. The experimental results show the competitiveness of MOEA/D-ABM in the performance of diversity and convergence. They also demonstrate that the use of the ABM mechanism can greatly improve the convergence rate of the algorithm.

Constrained large-scale multiobjective optimization based on a competitive and cooperative swarm optimizer

Many engineering application problems can be modeled as constrained multiobjective optimization problems (CMOPs), which have attracted much attention. In solving CMOPs, existing algorithms encounter difficulties in balancing conflicting objectives and constraints. Worse still, the performance of the algorithms deteriorates drastically when the size of the decision variables scales up. To address these issues, this study proposes a competitive and cooperative swarm optimizer for large-scale CMOPs. To balance conflict objectives and constraints, a bidirectional search mechanism based on competitive and cooperative swarms is designed. It involves two swarms, approximating the true Pareto front from two directions. To enhance the search efficiency in large-scale space, we propose a fast-converging competitive swarm optimizer. Unlike existing competitive swarm optimizers, the proposed optimizer updates the velocity and position of all particles at each iteration. Additionally, to reduce the search range of the decision space, a fuzzy decision variables operator is used. Comparison experiments have been performed on test instances with 100–1000 decision variables. Experiments demonstrate the superior performance of the proposed algorithm over five peer algorithms.