Multi-objective Evolutionary Algorithm Based On Decomposition Research Articles

Full-color electrophoretic display with high halftone image quality, reduced power, and deep-learning-enabled fast implementation

The electrophoretic display (EPD) with low power consumption, good sunlight readability, and flexibility is ideal for the Internet of Things. However, color EPDs have very limited grayscales (typically 1-bit) because it is challenging to precisely control the electrophoretic particles of multiple colors. Thus, halftone is usually employed to achieve continuous-tonal full-color EPDs alternatively. Nevertheless, halftone achieves continuous tones at the expense of a significant increase in driving current. This study first proposes and experimentally verifies a model that can accurately predict a driving current from image content. Next, a multi-objective optimized (MOO) halftone algorithm based on MOEA/D (multi-objective evolutionary algorithm based on decomposition) is proposed to consider image quality and driving current simultaneously. As a result, Pareto optimality is achieved, i.e., no image simultaneously performs better in image quality and driving current. A mean driving current reduction of 33.8% concerning the traditional error-diffusion algorithm is experimentally verified on a seven-color EPD with maintained halftone image quality. Considering the high computational complexity of the iteration-based MOO algorithm, this study also discusses the real-time generation of optimal halftone images using a generative adversarial network (GAN). Compared with the optimal halftone images slowly generated by the MOO, the GAN achieves almost the same driving current and a mean absolute error of 2.04, in terms of CIE76 color difference. The proposed algorithm enables full-color EPDs with high-quality continuous tones, reduced power consumption, and a GAN-based real-time implementation.

An Optimization Method for Green Permutation Flow Shop Scheduling Based on Deep Reinforcement Learning and MOEA/D

This paper addresses the green permutation flow shop scheduling problem (GPFSP) with energy consumption consideration, aiming to minimize the maximum completion time and total energy consumption as optimization objectives, and proposes a new method that integrates end-to-end deep reinforcement learning (DRL) with the multi-objective evolutionary algorithm based on decomposition (MOEA/D), termed GDRL-MOEA/D. To improve the quality of solutions, the study first employs DRL to model the PFSP as a sequence-to-sequence model (DRL-PFSP) to obtain relatively better solutions. Subsequently, the solutions generated by the DRL-PFSP model are used as the initial population for the MOEA/D, and the proposed job postponement energy-saving strategy is incorporated to enhance the solution effectiveness of the MOEA/D. Finally, by comparing the GDRL-MOEA/D with the MOEA/D, NSGA-II, the marine predators algorithm (MPA), the sparrow search algorithm (SSA), the artificial hummingbird algorithm (AHA), and the seagull optimization algorithm (SOA) through experimental tests, the results demonstrate that the GDRL-MOEA/D has a significant advantage in terms of solution quality.

Decomposition based estimation of distribution algorithm for high-level synthesis design space exploration

High-Level Synthesis (HLS) has evolved significantly due to the increasing complexity of integrated circuit design and the demand for efficient design methodologies. HLS, which raises the abstraction level of design specification, allows designers to focus on hardware functionality, thus enhancing productivity and reducing verification efforts. However, a key challenge in HLS is efficiently exploring the vast design space to find the Pareto-optimal designs. In this paper, we introduce a novel approach for multi-objective design space exploration in HLS. Our methodology decomposes the design space exploration problem into simpler sub-problems using the Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) framework and utilizes the Estimation of Distribution Algorithm (EDA) to build a probabilistic model for generating candidate solutions, thereby reducing the required number of expensive synthesis runs. Experimental results show that the proposed method has a faster convergence speed and reduces the number of syntheses by 24.34% to 32.01%, which significantly outperforms state-of-the-art works. Our approach achieves superior Pareto fronts with the lowest average ADRS value, outperforming Lattice-expl, ϵ -Constraint GA, and NSGA-II by 85.64%, 39.90%, and 33.31% respectively.

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.

Developing a crash severity model based on multi objective evolutionary feature selection approaches

The main purpose of this article is assessing the capability of multiobjective optimisation evolutionary algorithms (MOEAs) along with machine learning method on predicting the crash injury severity with the approach of reducing input variables. Dataset of crashes which were occurred in Iran was analysed over the period of 2016–2020. The data were classified into two classes in terms of injury severity: fatal and non-fatal datasets. At first, general prediction models were created by inserting 31 available input variables into support vector machine (SVM) method based on two imbalanced and obtained balanced datasets. A cluster based under sampling technique was used to obtained balanced data. Then evolutionary algorithms of two objectives optimisation algorithms namely non-dominated sorting genetic algorithm (NSGA-II), multi-objective evolutionary algorithm based on decomposition (MOEA/D), and pareto envelope-based selection algorithm (PESA-II) along with SVM were used to select features that significantly affect the severity of crashes and developed the simplified models. Then the simplified developed model was compared to the model which was prepared with random forest (RF) method in feature selection. It is shown that the simplified model developed by combined MOEAs and SVM is more appropriate to accurately predict the crash severity, considering the number of input variables in comparison to RF.

A parallel variable-fidelity algorithm for efficient constrained multi-objective aerodynamic design optimization

Modern aerodynamic design optimization aims to discover optimal configurations using computational fluid dynamics under complex flow conditions, which is a typical expensive multi-objective optimization problem. The multi-objective evolutionary algorithm based on decomposition (MOEA/D) combined with efficient global optimization is a promising method but requires enhanced efficiency and faces limitations in its application to multi-objective aerodynamic design optimization (MOADO). To address the issues, an efficient parallel MOEA/D assisted with variable-fidelity optimization (VFO) is proposed for solving MOADO, called the MOEA/D-VFO algorithm. Variable-fidelity surrogates are built for objectives and constraints, achieving higher accuracy using fewer high-fidelity samples and a great number of low-fidelity samples. By retaining more good candidates, the sub-optimization problems defined by decomposing original objectives are capable of discovering more favorable samples using MOEA/D, which prompts optimization convergence. A constraint-handling strategy is developed by incorporating the probability of feasibility functions in the sub-optimizations. The selection of new samples for parallel evaluation is improved by filtering out poor candidates and selecting effective promising samples, which improves the feasibility and diversity of solved Pareto solutions. A Pareto front (PF) can be efficiently found in a single optimization run. The proposed approach is demonstrated by four analytical test functions and verified by two aerodynamic design optimizations of airfoils with and without constraints, respectively. The results indicate that the MOEA/D-VFO approach can greatly improve optimization efficiency and obtain the PF satisfying constraints within an affordable computational budget.

A steady-state weight adaptation method for decomposition-based evolutionary multi-objective optimisation

In decomposition-based multi-objective evolutionary algorithms (MOEAs), the inconsistency between a problem’s Pareto front shape and the distribution of the weights can lead to a poor, unevenly distributed solution set. A straightforward way to overcome this undesirable issue is to adapt the weights during the evolutionary process. However, existing methods, which typically adapt many weights at a time, may hinder the convergence of the population since changing weights essentially means changing sub-problems to be optimised. In this paper, we aim to tackle this issue by designing a steady-state weight adaptation (SSWA) method. SSWA employs a stable approach to maintain/update an archive (which stores high-quality solutions during the search). Based on the archive, at each generation, SSWA selects one solution from it to generate only one new weight while simultaneously removing an existing weight. We compare SSWA with eight state-of-the-art weight adaptative decomposition-based MOEAs and show its general outperformance on problems with various Pareto front shapes.

Study on the performance and efficiency of multi-objective evolutionary algorithms for trimaran outrigger layout seakeeping optimization problem

Trimaran as a high-performance vessel, possesses excellent characteristics such as high speed, low wave-making resistance, and good seakeeping performance. Different from conventional monohull ship, the design of a trimaran requires additional consideration of the outrigger layout, as the position of two outriggers can affect its hydrodynamic performance. In this study, high-speed slender body potential flow theory (also named the 2D+t theory or the 2.5D method) was employed to calculate the heave and pitch motion in order to evaluate the seakeeping performance of trimarans with different outrigger layouts at varying speeds. Model experiments were subsequently conducted to validate the effectiveness of the 2.5D method in simulating the motion of trimarans under different outrigger layouts. Three multi-objective evolutionary algorithms, including Non-dominated sorting genetic algorithm II (NSGA-II), Non-dominated sorting genetic algorithm III (NSGA-III), and Multi-objective evolutionary algorithm based on decomposition (MOEA/D), as well as their applications in the optimization of trimaran outrigger layouts were introduced. Utilizing the 2.5D method based computational program as the solver, the efficiency and performance of these multi-objective evolutionary algorithms were compared. Discuss the advantages and disadvantages of three multi-objective evolutionary algorithms in solving trimaran outrigger layout optimization problem by comparing the optimization results from two aspects: optimization efficiency, and optimal solution performance. The results indicate that for optimization efficiency, the weighted sum approach based MOEA/D exhibits best optimization efficiency. NSGA-II and NSGA-III show a good advantage in terms of optimal solution performance, and compared to NSGA-II, NSGA-III can obtain more Pareto solutions.

Reinforcement learning-based optimization for power scheduling in a renewable energy connected grid

Power scheduling is an NP-hard optimization problem that demands a delicate equilibrium between economic costs and environmental emissions. In response to the growing concern for climate change, global environmental policies prioritize decarbonizing the electricity sector by integrating renewable energies (REs) into power grids. While this integration brings economic and environmental benefits, the intermittency of REs amplifies the uncertainty and complexity of power scheduling. Existing optimization approaches often grapple with a limited number of units, overlook critical parameters, and disregard the intermittency of REs. To address these limitations, this article introduces a robust and scalable optimization algorithm for renewable integrated power scheduling based on reinforcement learning (RL). In this proposed methodology, the power scheduling problem is decomposed into Markov decision processes (MDPs) within a multi-agent simulation environment. The simulated MDPs are used to train a deep reinforcement learning (DRL) model for solving the optimization. The validity and effectiveness of the proposed method are validated across various test systems, encompassing single-to tri-objective problems with 10–100 generating units. The findings consistently demonstrate the superior performance of the proposed DRL algorithm compared to existing methods, such as multi-agent immune system-based evolutionary priority list (MAI-EPL), binary real-coded genetic algorithm (BRCGA), teaching learning-based optimization (TLBO), quasi-oppositional teaching learning-based algorithm (QOTLBO), hybrid genetic-imperialist competitive algorithm (HGICA), three-stage priority list (TSPL), real-coded grey wolf optimization (RCGWO), multi-objective evolutionary algorithm based on decomposition (MOEAD), and non-dominated sorting algorithms (NSGA-II and NSGA-III). Regarding the experimental results, it is important to highlight the importance of integrating RESs into larger power systems. In a 10-unit system with 2.81 % RE penetration, reductions of 3.42 %, 4.03 %, and 3.10 % were observed in costs, CO2 emissions, and SO2 emissions, respectively. Similarly, in a 100-unit system with a RE penetration rate of only 0.28 %, reductions of 3.75 % in cost, 4.42 % in CO2, and 3.34 % in SO2 were observed. These findings emphasize the effectiveness of RES integration, even at lower penetration rates, in larger-scale power systems.

An Agile Approach for Adopting Sustainable Energy Solutions with Advanced Computational Techniques

In the face of the burgeoning electricity demands and the imperative for sustainable development amidst rapid industrialization, this study introduces a dynamic and adaptable framework suitable for policymakers and renewable energy experts working on integrating and optimizing renewable energy solutions. While using a case study representative model for Sub-Saharan Africa (SSA) to demonstrate the challenges and opportunities present in introducing optimization methods to bridge power supply deficits and the scalability of the model to other regions, this study presents an agile multi-criteria decision tool that pivots on four key development phases, advancing established methodologies and pioneering refined computational techniques, to select optimal configurations from a set of Policy Decision-Making Metrics (PDM-DPS). Central to this investigation lies a rigorous comparative analysis of variants of three advanced algorithmic approaches: Swarm-Based Multi-objective Particle Swarm Optimization (MOPSO), Decomposition-Based Multi-objective Evolutionary Algorithm (MOEA/D), and Evolutionary-Based Strength Pareto Evolutionary Algorithm (SPEA2). These are applied to a grid-connected hybrid system, evaluated through a comprehensive 8760-hour simulation over a 20-year planning horizon. The evaluation is further enhanced by a set of refined Algorithm Performance Evaluation Metrics (AL-PEM) tailored to the specific constraints. The findings not only underscore the robustness and consistency of the SPEA2 variant over 15 runs of 200 generations each, which ranks first on the AL-PEM scale, but the findings also validate the strategic merit of combining multiple technologies and empowering policymakers with a versatile toolkit for informed decision-making.

Multisource information fusion for real-time prediction and multiobjective optimization of large-diameter slurry shield attitude

Abnormal large-diameter slurry shield attitudes (SA) lead to safety and quality problems in shield construction. To achieve intelligent prediction and optimization of the large-diameter slurry SA, a combination of Bayesian optimization categorical boosting (BO-CatBoost) and a multiobjective evolutionary algorithm based on decomposition (MOEAD) is proposed for the prediction and optimization of the tunnel large-diameter slurry SA, as well as the corresponding digital twin framework. Using the Yangtze River large-diameter slurry shield project in Wuhan as an example, data were collected for three soil conditions, namely, silty fine sand, angular gravelly soils and chalky clays, and gravelly soil. The results show that: (1) The R2 values of the three predicted types of soils are all above 0.9, the RMSE values are less than 1.2, and the MAE values are less than 0.9. (2) Based on the results of the SHapley Additive exPlanations (SHAP), the propulsive thrust had the greatest influence on the large-diameter slurry SA. (3) The large-diameter slurry SA optimization improves when the number of adjusted construction parameters increases, with a maximum optimization rate of 23.436%. In addition, a digital twin framework based on BO-CatBoost-MOEAD is proposed, which can effectively control large-diameter slurry SAs and improve overall project safety and quality.

Research on decomposition-based multi-objective evolutionary algorithm with dynamic weight vector

In recent years, multi-objective evolutionary algorithm based on decomposition has gradually attracted people's interest. However, this algorithm has some problems. For example, the diversity of the algorithm is poor, and the convergence and diversity of the algorithm are unbalanced. In addition, users don't always care about the entire Pareto front. Sometimes they may only be interested in specific areas of entire Pareto front. Based on the above problems, this paper proposes a decomposition-based multi-objective evolutionary algorithm with dynamic weight vector (MOEA/D-DWV). Firstly, a weight vector generation model with uniform distribution or preference distribution is proposed. Users can decide which type of weight vector to generate according to their own wishes. Then, two combination evolution operators are proposed to better balance the convergence and diversity of the algorithm. Finally, a dynamic adjustment strategy of weight vector is proposed. This strategy can adjust the distribution of weight vector adaptively according to the distribution of solutions in the objective space, so that the population can be uniformly distributed in the objective space as much as possible. MOEA/D-DWV algorithm is compared with 9 advanced multi-objective evolutionary algorithms. The comparison results show that MOEA/D-DWV algorithm is more competitive. Data availabilityData will be made available on request.

Multiobjective Evolutionary Component Effect on Algorithm Behaviour

The performance of multiobjective evolutionary algorithms (MOEAs) varies across problems, making it hard to develop new algorithms or apply existing ones to new problems. To simplify the development and application of new multiobjective algorithms, there has been an increasing interest in their automatic design from their components. These automatically designed metaheuristics can outperform their human-developed counterparts. However, it is still unknown what are the most influential components that lead to performance improvements. This study specifies a new methodology to investigate the effects of the final configuration of an automatically designed algorithm. We apply this methodology to a tuned Multiobjective Evolutionary Algorithm based on Decomposition (MOEA/D) designed by the iterated racing (irace) configuration package on constrained problems of 3 groups: (1) analytical real-world problems, (2) analytical artificial problems and (3) simulated real-world. We then compare the impact of the algorithm components in terms of their Search Trajectory Networks (STNs), the diversity of the population, and the anytime hypervolume values. Looking at the objective space behavior, the MOEAs studied converged before half of the search to generally good HV values in the analytical artificial problems and the analytical real-world problems. For the simulated problems, the HV values are still improving at the end of the run. In terms of decision space behavior, we see a diverse set of the trajectories of the STNs in the analytical artificial problems. These trajectories are more similar and frequently reach optimal solutions in the other problems.

Correction: Bu et al. A Decomposition-Based Multi-Objective Evolutionary Algorithm for Solving Low-Carbon Scheduling of Ship Segment Painting. Coatings 2024, 14, 368

In the original publication [...]

Research on the Short-Term Economic Dispatch Method of Power System Involving a Hydropower-Photovoltaic-Pumped Storage Plant

The auxiliary regulation capacity of pumped-storage power stations can be utilized as an effective method to regulate the output of a hydro-photovoltaic complementary system, further mitigating the power fluctuations of the system and enhancing the photovoltaic absorption. This study aims to minimize power fluctuations and maximize the economic benefits of electricity generation in a hydropower-photovoltaic-pumped-storage complementary system (HPPCS), which are treated as the objective functions. It explores the participation of the HPPCS in grid active power balance auxiliary services. By modulating the participation ratio of the HPPCS in the grid’s active balance service, the system output is aligned to fluctuate proportionally with the daily load curve trend. Consequently, a short-term economic dispatch model for the integrated HPPCS is developed. The case study focuses on the considerable impact of weather conditions on photovoltaic (PV) power generation. In this model, the outputs of cascading hydro-power stations and pumped-storage power stations are considered as the decision variables. A decomposition-based multi-objective evolutionary algorithm is applied to derive an optimized intra-day dispatch Pareto solution set for the cascading HPPCS in each of these scenarios. Additionally, this study compares the Pareto solution sets for the HPPCS in various extents of its participation in grid auxiliary services. The results of the case study suggest that the system is capable of timely adjustments during the peak and trough periods of load demand. Considering the economic benefits, it enables the pumped-storage station to generate electricity for the grid during periods of high electricity prices and to store energy by pumping water when prices are low.

A Decomposition-Based Multi-Objective Evolutionary Algorithm for Solving Low-Carbon Scheduling of Ship Segment Painting

Ship painting, as one of the three pillars of the shipping industry, runs through the whole process of ship construction. However, there are low scheduling efficiency and excessive carbon emissions in the segmental painting process, and optimizing the scheduling method is an important means to achieve the sustainable development of the ship manufacturing industry. To this end, firstly, a low-carbon scheduling mathematical model for the segmented painting workshop is proposed, aiming to reduce carbon emissions and improve the painting efficiency of the segmented painting workshop. Second, an artificial bee colony algorithm designed based on a decomposition strategy (MD/ABC) is proposed to solve the model. In the first stage, five neighborhood switching methods are designed to achieve the global search employed for each solution. In the second stage, the Technique of Ordering the Ideal Solutions (TOPSIS) improves the competition mechanism through the co-evolution between neighboring subproblems and designs the angle to define the relationship between neighboring subproblems to enhance the localized search and improve population quality. The solution exchange strategy is used in the third stage to improve the efficiency of the algorithm. In addition, a two-stage coding method is designed according to the characteristics of the scheduling problem. Finally, the algorithm before and after the improvement and with other algorithms is analyzed using comparative numerical experiments. The experimental results show the effectiveness of the algorithm in solving the low-carbon scheduling problem of ship segmental painting and can provide reliable guidance for the scheduling program of segmented painting workshops in shipyards.

Multi-objective liver cancer algorithm: A novel algorithm for solving engineering design problems

This research introduces the Multi-Objective Liver Cancer Algorithm (MOLCA), a novel approach inspired by the growth and proliferation patterns of liver tumors. MOLCA emulates the evolutionary tendencies of liver tumors, leveraging their expansion dynamics as a model for solving multi-objective optimization problems in engineering design. The algorithm uniquely combines genetic operators with the Random Opposition-Based Learning (ROBL) strategy, optimizing both local and global search capabilities. Further enhancement is achieved through the integration of elitist non-dominated sorting (NDS), information feedback mechanism (IFM) and Crowding Distance (CD) selection method, which collectively aim to efficiently identify the Pareto optimal front. The performance of MOLCA is rigorously assessed using a comprehensive set of standard multi-objective test benchmarks, including ZDT, DTLZ and various Constraint (CONSTR, TNK, SRN, BNH, OSY and KITA) and real-world engineering design problems like Brushless DC wheel motor, Safety isolating transformer, Helical spring, Two-bar truss and Welded beam. Its efficacy is benchmarked against prominent algorithms such as the non-dominated sorting grey wolf optimizer (NSGWO), multiobjective multi-verse optimization (MOMVO), non-dominated sorting genetic algorithm (NSGA-II), decomposition-based multiobjective evolutionary algorithm (MOEA/D) and multiobjective marine predator algorithm (MOMPA). Quantitative analysis is conducted using GD, IGD, SP, SD, HV and RT metrics to represent convergence and distribution, while qualitative aspects are presented through graphical representations of the Pareto fronts. The MOLCA source code is available at: https://github.com/kanak02/MOLCA.

Decomposition with adaptive composite norm for evolutionary multi-objective combinatorial optimization

The multi-objective evolutionary algorithm based on decomposition (MOEA/D) decomposes a multi-objective problem into a series of single-objective subproblems for collaborative optimization. The weighted sum (WS) method and the Tchebycheff (TCH) method are the two most popular scalarization methods. They have pros and cons in solving multi-objective combinatorial optimization problems (MOCOPs) the WS method allows MOEA/D to converge faster than the TCH method; the WS-based MOEA/D cannot obtain unsupported non-dominated vectors, while the TCH-based one can overcome this shortcoming. This inspired us to use the WS method to drive the population towards the Pareto front and then switch to the TCH method to maintain a more diverse population. To better balance convergence and diversity, we propose a new scalarization strategy called adaptive composite norm (ACN). The ACN strategy can combine the WS and the TCH with dynamic weighting. The experiments consider 16 instances including 4 MOCOPs and run on the PlatEMO. Results reveal that MOEA/D-ACN can rank first and significantly outperform the other evolutionary multi-objective combinatorial optimization algorithms on almost all instances.

Multi-objective cooperative optimization of reservoir scheduling and water resources allocation for inter-basin water transfer project based on multi-stage coupling model

The efficient coupling of a water allocation model with a reservoir operation model is key to maximizing the benefits of inter-basin water transfer (IBWT) projects. Most existing studies of IBWT operations and management do not account for matching water transfer and demand, and instead seek to optimize either the water allocation model or the reservoir scheduling model. In this paper, we propose a multi-stage joint optimization framework for reservoir scheduling and water allocation models that considers the key operation indicators of the project in the water source area and the multi-dimensional objectives in the receiving area. We derived a functional relationship that balances considerations regarding water, the economy, and ecology (WEE) in the receiving area and applied it to the water allocation model. The reservoir operation model was developed by considering the multiple benefits of water transfer and power generation in the water resource area. To reduce the complexity of the model and the tightness of its coupling, the model was divided into multiple stages of optimization and solved using the Multi-objective Evolutionary Algorithm Based on Decomposition (MOEA/D) algorithm. The results showed the allocation schemes of water resources influenced the competition between the economic and ecological benefits. Using the WEE model, a more reasonable water transfer and allocation method can be selected according to different development needs. As such, the water shortage rate of each user in the receiving area is kept below 8%, and there is significant improvement in all indicators compared with the conventional scheme. In addition, this model enables the reservoir group to achieve a power generation capacity of more than 5.64 kWh with the goal of meeting the water transfer demand, maintaining the reservoir empty rate at about 10%, and reducing the risk of water shortages. Our study can serve as a reference for effectively addressing the challenges associated with IBWT projects, and it can inform socioeconomic development in receiving areas while optimizing water transmission and allocation.

Optimal power flow research of AC–DC hybrid grid with multiple energy routers

AC/DC hybrid grids are the future development trends of grids, and energy routers (ERs) can play key roles in controlling power flow, realizing the regulation of electric energy and improving power quality in the grids. At present, there have been many studies on the structure and control strategy of ERs, but only a few studies are on the power flow distribution and optimization of AC/DC hybrid grids with ERs. To enhance the efficacy of ERs in system-wide regulation and operational optimization, a multi-objective optimal power flow model is formulated for AC–DC hybrid systems with multiple ERs. In order to make ERs play a better role in overall regulation and operation optimization, the multi-objective optimal power flow model of AC–DC hybrid system with multi-ERS is established based on Newton–Raphson method (NR) and alternating iteration method with power consumption and voltage deviation as optimization objectives. The multi-objective evolutionary algorithm based on decomposition (MOEA/D) is used to optimize the model, and a smoother Pareto solution set is obtained compared with multi-objective particle swarm optimization (MOPSO). Then, fuzzy membership method is used to make compromise decision on the Pareto solution set to obtain the optimal compromise solution. Simulation and analysis on an enhanced IEEE 69 bus system verifies the validity of the model. In addition, the results obtained from the compromise solution are compared with the optimization results of MOPF obtained by MOPSO and that of single-objective power flow (SOPF) obtained by Particle Swarm Algorithm (PSO) in the same system. It is proved that the optimization model established can achieve the optimization objectives of reducing voltage deviation and power loss simultaneously to improve the overall performance of the system and optimize the operation state of the system.