Complex Multi-objective Optimization Problems Research Articles

Enhancing Discovery and Understanding of Atomically Dispersed Single Atom Catalysts for CO2 Reduction Reaction with Density Functional Theory and Machine Learning

Atomically dispersed M-N-C catalysts are a promising class of materials for efficiently reducing CO2 to valuable feedstock chemicals such as carbon monoxide and ethylene. However, for such catalysts to achieve commercial viability it is necessary to optimize several properties in tandem such as activity towards the CO2 reduction reaction, Faradaic efficiency towards selected products, and in situ stability. This complex multi-objective optimization problem cannot be effectively tackled with costly trial-and-error experimentation alone. Therefore, computational modeling is necessary to accelerate fundamental understanding and to aid in identifying viable active sites in silico before preparation of down-selected candidate materials is attempted in the laboratory. Density functional theory (DFT) can be utilized to model catalytic surfaces and obtain useful electrochemical properties (e.g., free energies of reaction), but an advanced framework is necessary to effectively explore the large chemical space of possible permutations of different transition metals, proximity of metal centers, defects, and other structural considerations. Furthermore, machine learning may be leveraged to accelerate materials understanding and discovery for CO2RR beyond what is feasible for DFT alone.In this talk, we will discuss our library-based approach for understanding structure-to-function relationships in these materials and identifying novel active sites. This library is built using our high-throughput DFT framework to calculate different properties (e.g., adsorption energies) for a large number of active sites. The structures of the active sites are combinatorically generated based on permutations of transition metals, defects, and other structural considerations. Our automated framework combines DFT and cheminformatics tools to autonomously run DFT calculations as well as to collect, process, and store the results of our simulations and to evaluate different structural descriptors. We will also discuss considerations made for incorporating solvation and electrification effects in a robust manner into our framework.This library is then used as the basis for the development of machine learning models, which learn to map from descriptor-based structural representations of these surfaces (e.g., metal center, type of defect) to target properties, thereby accelerating understanding of structure to function relationships for M-N-C materials. Game theoretical methods are used to provide model interpretability and insight for how individual structural properties contribute to properties of interest, such as activity or overpotential. We discuss the use of our trained model, capable of screening millions of unique chemistries, in discovering novel M-N-C active sites with optimized properties. By thus combining DFT and machine learning, we aim both to provide fundamental understanding of CO2 reduction activity and durability and to discover new viable active sites. Examples of our modeling strategies applied to direct air capture of CO2 utilizing similar workflows will also be discussed.

Hybrid Optimization Approach Using Multiobjective Genetic Algorithm NSGA‐II, SCAPS‐1D Simulation, and Response Surface Methodology for Organic Solar Cell Analysis

In the field of simulation, it is difficult to find the relevant values for the properties of materials and in this context this approach has been proposed on optimizing the performance of organic solar cells, a promising technology in the field of renewable energy, to increase their efficiency. It adopts a hybrid approach combining the response surface methodology (RSM) with a Box–Behnken design (BBD) and the nondominated sorting genetic algorithm II (NSGA‐II). The RSM BBD method is used to identify objective functions to be optimized, considering interactions between selected parameters such as the thickness of the active layer, electron‐transport layer (ETL), hole‐transport layer (HTL), and the doping of these layers. Concurrently, the NSGA‐II genetic algorithm aims to maximize the performance of the solar cell based on these parameters. The specific importance of NSGA‐II lies in its ability to solve complex multiobjective optimization problems. Indeed, NSGA‐II is designed to simultaneously manage several performance objectives, which is crucial for organic solar cells. Its ability to generate a diverse set of optimal solutions enables efficient configurations to be found that may not be obvious with simpler optimization approaches. The results of this study show that optimum solar cell performance is achieved with active layer, ETL layer, and HTL layer thicknesses of 100.86, 79.9, and 20.24 nm, respectively, and active layer doping of 8.71E + 21 cm−3, HTL layer doping of 9.90E + 21 cm−3, and ETL layer doping of 9.49E + 21 cm−3. Analysis using Solar Cell Capacitance Simulator‐1D (SCAPS‐1D) software shows that optimum performance is achieved with these specific parameter values. After optimization with NSGA‐II, the power conversion efficiency increases by 39% compared to previous work. This study provides evidence of the effectiveness of the proposed hybrid approach for optimizing the performance of organic solar cells. By showing remarkable agreement between the results obtained by NSGA‐II and SCAPS‐1D, this approach opens up promising prospects for the future of renewable energy.

Multi-Objective Five-Element Cycle Optimization Algorithm Based on Multi-Strategy Fusion for the Bi-Objective Traveling Thief Problem

In this paper, we propose a Multi-objective Five-element Cycle Optimization algorithm based on Multi-strategy fusion (MOFECO-MS) to address the Bi-objective Traveling Thief Problem (BITTP), an extension of the Traveling Thief Problem that incorporates two conflicting objectives. The novelty of our approach lies in a unique individual selection strategy coupled with an innovative element update mechanism rooted in the Five-element Cycle Model. To balance global exploration and local exploitation, the algorithm categorizes the population into distinct groups and applies crossover operations both within and between these groups, while also employing a mutation operator for local searches on the best individuals. This coordinated approach optimizes parameter settings and enhances the search capabilities of the algorithm. Extensive experiments were conducted on nine BITTP instances, comparing MOFECO-MS against eight state-of-the-art multi-objective optimization algorithms. The results show that MOFECO-MS excels in both Hypervolume (HV) and Spread (SP) indicators, while also maintaining a high level of Pure Diversity (PD). Overall, MOFECO-MS outperformed the other algorithms in most instances, demonstrating its superiority and robustness in solving complex multi-objective optimization problems.

Prediction of emission and performance of internal combustion engine via regression deep learning approach

Strict environmental laws increase the importance of reducing emissions. While; improving three-way catalyst (TWC) technology can help reduce emission levels, attention should also be given to reducing exhaust gases before they enter the TWC. This can be achieved through the development of engine technology and calibration strategies. By doing so, low-cost TWC can be used, and emissions increase less after catalyst aging. In addition to reducing emissions at the engine-out stage before entering the TWC, it is important to reduce emissions after the TWC during the cold start and engine warm-up phase, known as the TWC light-off period. During this stage, the TWC does not reach optimal working efficiency, which can result in higher emissions. Therefore, to comply with environmental regulations, it is necessary to calculate the reduction of emissions while maintaining optimal engine and vehicle performance. Finding the optimal values of control parameters to reduce fuel consumption and emissions simultaneously makes engine calibration a complex multi-objective optimization problem. To meet calibration requirements, it is essential to accurately identify the nonlinear and multivariable behavior of engines. Thus, this study focuses on empirical engine modeling and developing an emissions model for internal combustion engines in both warm and cold engine conditions through an intelligent identification method. To enhance steady state engine modeling in warm conditions, this study proposes a hybrid MLP+CNN method based on the benefits of regression deep neural network. Additionally, the hybrid MLP+CNN+LSTM method adds a long short-term memory (LSTM) neural network, enabling the model to capture the dynamic behavior of emissions during cold start conditions and under the impact of oxygen storage and the temperature in TWC. The results demonstrate that these approaches significantly improve the accuracy of emission modeling when compared to conventional methods. The results demonstrate that using the deep learning approach and dividing the engine emission modeling into two parts, static in warm conditions and dynamic in cold conditions, significantly improve the accuracy of emission modeling compared to conventional methods. Developed models can be used in the model-based calibration due to their high accuracy in emission prediction as well as predicting Torque, BSFC, and other outputs. By coupling the developed model with optimization techniques, calibration of the engine map and cold start can be performed by considering the emissions, torque, etc., simultaneously.

Multiobjective Optimization of Papermaking Wastewater Treatment Processes under Economic, Energy, and Environmental Goals.

Due to the heterogeneity of recycled paper materials and the production conditions, pollutants in papermaking wastewater fluctuate sharply over time. Quality control of the papermaking wastewater treatment process (PWTP) is challenging and costly. As regulations are also growing about the environmental effects of the PWTP on greenhouse gas (GHG) emission, energy consumption, etc., the PWTP formulates a complex multiobjective optimization problem. This research established a multiagent deep reinforcement learning framework to simultaneously optimize process cost, energy consumption, and GHG emission in the PWTP, subjected to the effluent quality, to realize economic, energy, and environmental (3E) goals. The biological treatment process of wastewater in paper mills was simulated using benchmark simulation model no. 1 (BSM1). The data generated based on the BSM manual was utilized for model training, and real data acquired from a local papermaking factory was used to estimate the model performance. The results show that the proposed method outperforms conventional techniques in identifying the best control strategies for multiple targets.

Adaptive Sampling Offspring Generation Strategy for Multi-objective Optimization

A covariance adaptive sampling offspring generation strategy (CASS) based on fuzzy clustering is proposed, and a multi-objective distribution estimation algorithm (MEDCA) based on this strategy is introduced. The GK-FCM clustering partitioning strategy is designed to build a Gaussian model for each individual, collectively approximating the manifold of the Pareto solution set and generating offspring through sampling. The introduction of an individual’s survival generation adapts the individual’s preference for exploration and exploitation. This is achieved by incorporating it as a scaling factor of the covariance matrix in the sampling model, in order to satisfy the individual’s preferences for development and exploration in different evolutionary stages. This method significantly improves the performance of MEDCA in solving complex multi-objective optimization problems through covariance matrix adaptation sampling strategy and scaling factor adaptation strategy. The experimental results demonstrate the advantages of MEDCA in the application of offspring generation strategies during model sampling.

Optimization method of building energy efficiency design based on decomposition multi objective and agent assisted model

In today's global climate crisis, energy-efficient building design is crucial for achieving energy efficiency, environmental sustainability, and resident well-being. However, traditional architectural design is difficult to solve complex multi-objective and multivariate optimization problems. To overcome these challenges, this study proposes a solution: a strategy that combines decomposed multi-objective and agent assisted modeling. The proposed method decomposes complex architectural design problems into multiple manageable sub problems, with each sub problem optimized for a specific design objective. This method effectively simplifies the problem structure, allowing each subproblem to explore its solution space more focused and in-depth. Meanwhile, by combining proxy assisted modeling and utilizing proxy models to approximate actual physical processes or performance evaluations, the computational cost is reduced and the optimization process is accelerated. This study indicates that the improved multi-objective backbone particle swarm optimization algorithm relies on adaptive perturbation factors, with an average measured super volume of 29311 for one bedroom buildings and 49504 for three bedroom buildings. For the same building type, the average volume measurements of the multi-objective particle swarm optimization algorithm assisted by the decomposed surrogate model are 21153 and 40230, respectively. The proposed method effectively addresses complex multi-objective optimization problems in the field of building energy efficiency design, simplifies the problem structure, reduces computational costs through surrogate models, accelerates the optimization process, improves energy efficiency, and can support building construction to better cope with the challenges of climate change.

A resilient and intelligent multi-objective energy management for a hydrogen-battery hybrid energy storage system based on MFO technique

In this paper, a new design and flexible energy management strategy are presented for microgrids. The proposed intelligent energy management system (IEMS) achieves effective integration between the resilient microcontroller, chosen for its rapid response speed and its capability to perform multiple operations simultaneously, and the optimization techniques to enhance the power quality. The IEMS is designed using the FPGA board, chosen for its flexibility and capability to handle multiple and complex operations simultaneously. The experimental testing of the IEMS demonstrates a significant level of effectiveness in managing energy. To enhance system performance and ensure cost-effective reliability, advanced optimization techniques are employed. This study deals with a complex multi-objective optimization problem involving the limitations of energy generation, load demand, and a hydrogen-battery hybrid energy storage system. The moth-flame optimization (MFO) algorithm is chosen to solve this optimization problem due to its rapid convergence rate and accuracy. The effectiveness of the MFO algorithm is assessed by comparing it with several new algorithms. The obtained results show the robust performance of the IEMS and its high responsiveness to dynamic operational scenarios. It can observe, gather, and analyze data in real-time. It achieves a remarkable 1.287 % reduction in operating costs within a short timeframe.

Comfort, carbon emissions, and cost of building envelope and photovoltaic arrangement optimization through a two-stage model

The design of a high-performance building necessitates tradeoffs among multiple performance objectives, and many simulation-based optimization tools have been developed for this purpose. In practice, these tools are often constrained by excessive computational load and tight project deadlines. This study aimed to develop a holistic approach to rapidly identify optimal building design schemes. A novel two-stage model was developed as a surrogate to conventional physics-based models, which were then linked to multi-objective optimization algorithms, namely, NSGA-II, NSGA-III, and C-TAEA, in search of the Pareto optimal and best design schemes. The performance of the two-stage model was further enhanced by applying the least absolute shrinkage and selection operator (LASSO) and Neural Architecture Search methods and learning from the statistical layer. The above approach was tested in the design of an apartment building for seniors in Northern China such as thermal comfort, carbon, and cost. The optimal design achieved through the compromise optimum can significantly reduce thermal discomfort, life-cycle carbon emissions, and high levels of daylighting conditions. The design scheme was visualized using a geometrical remodel module. This study contributes methodologically to complex multi-objective building optimization problems with practical implications for design.

Enhancing the performance of radial distribution systems via optimal integration of electric vehicles

<span lang="EN-US">Electric vehicles (EVs) and their associated charging stations (CSs) are a promising avenue for greenhouse gas reduction and energy security. However, improper location and size of the EV charging station (CSs/EVs) negatively affect the power system. It results in some technical challenges such as increased real power-loss, decreased voltage stability and increased voltage deviation. This paper suggests optimum planning of CSs/EVs locations to conserve voltage, improve power-loss and reduce the effect of CSs/</span><span lang="EN-US">EVs in electrical distribution systems. The multi objective genetic algorithm method (MOGA) is utilized to solve the optimization problem and reduce the impact of the random location of CSs/EVs. <span>The simulations are</span> performed on IEEE 33-bus and IEEE 69-bus radial distribution systems (RDS). In addition, the optimal EV allocation is carried out with two fixed levels of loading from 100% to 150% of the candidate EV load. A comparison between the proposed MOGA technique and other optimization techniques is carried out. The results demonstrated the capability of the proposed technique for optimal placement of CSs/EVs in RDS. </span><span lang="EN-US">Moreover, it is providing an objective value to solve a complex multi-objective nonlinear optimization problem to reduce the total power-loss, improve the voltage profile and extend the voltage stability.</span>

Multi‐objective optimization method for control parameters of flexible direct current transmission converters based on intelligent algorithms

AbstractIn order to meet the current needs of power transmission, people have turned their attention to direct current (DC) transmission. When the alternating current(AC) power grid (PG) fails, it is easy to cause commutation failure in the DC system, thereby increasing the fault scope of the system. Therefore, this article adopts a flexible DC transmission system. Flexible DC converters have many control parameters, and there are mutual influences and conflicts between these parameters. By applying intelligent algorithms to multi‐objective optimization (MOP), these complex MOP problems can be effectively solved and an optimal set of control parameter combinations can be found. This method has an important contribution and novelty for optimizing the converter control parameters of flexible DC transmission systems. This article achieves fast and accurate MOP of the control parameters of flexible DC transmission converters by continuously detecting the similarities between antibodies and maintaining the diversity of the population. The research results show that the average DC side current is about 405A in the first 20 seconds, and the DC side current fluctuates regularly after 20 seconds. This article lays the foundation for establishing a real‐time simulation model of flexible DC transmission systems suitable for real‐time simulation systems.

On the adaptation of reference sets using niching and pair-potential energy functions for multi-objective optimization

Multi-objective evolutionary algorithms (MOEAs) have shown a good capability to approximate the Pareto front (PF) of complex multi-objective optimization problems (MOPs). Recently, several decomposition-based, indicator-based, and reference set-based MOEAs have been proposed to tackle MOPs with four or more objective functions, known as many-objective optimization problems (MaOPs). Some well-known MOEAs from these design strategies use a predefined reference set generated with uniformly distributed weight vectors on a unit simplex. These MOEAs have demonstrated good convergence, coverage, and uniformity of solutions on MOPs with regular PF shapes, i.e., simplex-like shapes. However, it has been shown that their performance degrades on MOPs with irregular PF shapes. In this paper, we proposed a pluggable reference set adaptation method based on niching and pair-potential energy functions (PPFs), called AdaK, to enhance the performance of these MOEAs on MOPs with irregular PF shapes while maintaining their good behavior on MOPs with regular PF shapes. Our adaptation method was validated by plugging it into three well-known MOEAs that use a predefined weight vector-based reference set. We perform an empirical study using different PPFs for our adaptation method on the DTLZ, WFG, Minus-DTLZ, Minus-WFG, IMOP, and VNT test suites. Our experimental results show the capability of our adaptation method to promote an invariant performance regardless of the PF shape. Additionally, we show that MOEAs with our adaptation method have a competitive performance against state-of-the-art MOEAs.

An effective surrogate model assisted algorithm for multi-objective optimization: application to wind farm layout design

Due to the intricate and diverse nature of industrial systems, traditional optimization algorithms require a significant amount of time to search for the optimal solution throughout the entire design space, making them unsuitable for meeting practical industrial demands. To address this issue, we propose a novel approach that combines surrogate models with optimization algorithms. Firstly, we introduce the Sparse Gaussian Process regression (SGP) into the surrogate model, proposing the SGP surrogate-assisted optimization method. This approach effectively overcomes the computational expense caused by the large amount of data required in Gaussian Process model. Secondly, we use grid partitioning to divide the optimization problem into multiple regions, and utilize the multi-objective particle swarm optimization algorithm to optimize particles in each region. By combining the advantages of grid partitioning and particle swarm optimization, which overcome the limitations of traditional optimization algorithms in handling multi-objective problems. Lastly, the effectiveness and robustness of the proposed method are verified through three types of 12 test functions and a wind farm layout optimization case study. The results show that the combination of meshing and SGP surrogate enables more accurate identification of optimal solutions, thereby improving the accuracy and speed of the optimization results. Additionally, the method demonstrates its applicability to a variety of complex multi-objective optimization problems.

Improved multi-objective grasshopper optimization algorithm and application in capacity configuration of urban rail hybrid energy storage systems

Aiming at addressing problems of poor diversity and ergodicity of initial population, slow convergence speed, and susceptibility to local optima in conventional multi-objective grasshopper optimization algorithm (MOGOA), an improved MOGOA is proposed in this paper. The proposed algorithm is based on Sobol sequence, adaptive social force, cosine parameter c, as well as Levy flight mechanism (SACLMOGOA), where Sobol sequence is adopted to initialize the population, thereby improving the diversity and ergodicity of the initial population. The adaptive social force is proposed to enhance the global exploration ability in the early stage of iteration and the local development ability in the late stage of iteration. A cosine type parameter c is used to ensure sufficient exploration time and rapid convergence of the algorithm during position update process and Levy flight is used to guide some grasshoppers to mutate, enhancing the ability to escape from the local optima and improving the performance and efficiency of the algorithm. The proposed algorithm is tested with ZDT and DTLZ series benchmark test functions to validate its effectiveness, and it is also compared with conventional MOGOA, multi-objective particle swarm optimization, multi-objective gray Wolf, and multi-objective jellyfish algorithms. The simulation results demonstrate that the proposed algorithm outperforms other algorithms in terms of inverse generational distance (IGD), spread (SP), maximum spread (MS), run time and Wilcoxon rank sum test. Furthermore, the proposed algorithm is successfully applied to the capacity configuration of the urban rail hybrid energy storage systems (HESS) of Changsha Metro Line 1 in China, reducing the traction network voltage fluctuations by 3.3 % and 2.2 % compared to no HESS capacity configuration optimization, and by 14 % and 5.7 % compared to no HESS during train starting and breaking, respectively. While achieving the goal of energy-saving and voltage stabilization, the cost of the hybrid energy storage systems is minimized as well. All of these have demonstrated SACLMOGOA is an effective tool for solving complex multi-objective optimization problems in engineering.

Improving Multi-Objective Optimization Methods of Water Distribution Networks

Water distribution network design is a complex multi-objective optimization problem and multi-objective evolutionary algorithms (MOEAs) such as NSGA II have been widely used to solve this optimization problem. However, as networks get larger, NSGA II struggles to find the diverse and uniform solutions that are critical in multi-objective optimization. This research proposes an improved version of NSGA II that uses three new-generation methods to target different regions of the Pareto front and thus increase the number of solutions in critical regions. These methods include saving an archive, local search around extreme and uncrowded Pareto front, and local search around the knee area of the Pareto front. The improved NSGA II is tested on benchmark networks of different sizes and compared to the best-known Pareto front of the networks determined by MOEAs. The results show that the proposed algorithm outperforms the original NSGA II in terms of broadening the Pareto front solution range, increasing solution density, and discovering more non-dominated solutions. The improved NSGA II can find solutions that cover all parts of the Pareto front using a single algorithm without increasing computational effort.

A State-of-the-Art Review of Task Scheduling for Edge Computing: A Delay-Sensitive Application Perspective

The edge computing paradigm enables mobile devices with limited memory and processing power to execute delay-sensitive, compute-intensive, and bandwidth-intensive applications on the network by bringing the computational power and storage capacity closer to end users. Edge computing comprises heterogeneous computing platforms with resource constraints that are geographically distributed all over the network. As users are mobile and applications change over time, identifying an optimal task scheduling method is a complex multi-objective optimization problem that is NP-hard, meaning the exhaustive search with a time complexity that grows exponentially can solve the problem. Therefore, various approaches are utilized to discover a good solution for scheduling the tasks within a reasonable time complexity, while achieving the most optimal solution takes exponential time. This study reviews task scheduling algorithms based on centralized and distributed methods in a three-layer computing architecture to identify their strengths and limitations in scheduling tasks to edge service nodes.

Improved multi-objective artificial bee colony algorithm-based path planning for mobile robots.

Mobile robots are widely used in various fields, including cosmic exploration, logistics delivery, and emergency rescue and so on. Path planning of mobile robots is essential for completing their tasks. Therefore, Path planning algorithms capable of finding their best path are needed. To address this challenge, we thus develop improved multi-objective artificial bee colony algorithm (IMOABC), a Bio-inspired algorithm-based approach for path planning. The IMOABC algorithm is based on multi-objective artificial bee colony algorithm (MOABC) with four strategies, including external archive pruning strategy, non-dominated ranking strategy, crowding distance strategy, and search strategy. IMOABC is tested on six standard test functions. Results show that IMOABC algorithm outperforms the other algorithms in solving complex multi-objective optimization problems. We then apply the IMOABC algorithm to path planning in the simulation experiment of mobile robots. IMOABC algorithm consistently outperforms existing algorithms (the MOABC algorithm and the ABC algorithm). IMOABC algorithm should be broadly useful for path planning of mobile robots.

An improved multi-objective brainstorming algorithm with the application of rapeseed germination characteristics optimization

As one of the most important raw materials for daily edible oil, the annual production and quality of oilseed rape have a great impact on the daily lives of people and the development of the country. The germination quality of rapeseed directly affects the future yield and quality of oilseed rape, and seed germination vigor (SGV) and chlorophyll content (CC) are important factors affecting the quality of rapeseed germination. It is very necessary to make the rapeseeds have optimal germination characteristics and seed germination vigor at the early stage of germination by controlling the combination of each decision variable at the segmented harvest. The two objectives are coupled with each other to form a complex multi-objective optimization problem, which is important in the current research field of the rapeseed problem. To solve this problem, a modified brainstorming optimization algorithm based on OPTICS clustering, named MOPCBSO, is proposed in this study. The algorithm uses optics clustering as a new clustering method, chaotic mutation as a new updating method for individuals, and introduces an elite strategy and a tracking strategy. 19 benchmark test functions and nonparametric tests are adopted to examine the performance of the MOPCBSO compared with other optimization algorithms. The results show that the proposed algorithm has significant advantages over other algorithms in terms of convergence and comprehensiveness, demonstrating the effectiveness of the algorithm improvement. To optimize rapeseed germination characteristics, mathematical models are built, in which, cut-down time, after-ripening time and stubble height are selected as decision variables, while chlorophyll concentration and seed germination vigor in seeds as the target characteristics. The data of oliseed rape field trials were collected from 2020 to 2021 in Huanggang City, Hubei Province. Finally, the optimal solution for the germination characteristics of rapeseeds was obtained by the MOPCBSO, which provided an effective basis for the subsequent rapeseed production experiments.

Optimal Allocation and Assessment of Distributed Generation Units with Multi-Objective Planning in Unbalanced Distribution Networks

—Real-world distribution networks are generally unbalanced due to unbalanced loads and asymmetric line parameters. Proper allocation of distributed generation (DG) units in unbalanced radial distribution networks to extract their maximum potential benefits is still quite difficult. Converter-coupled DG units have individual phase real and reactive power regulating ability and provide voltage unbalance compensation. This article proposes a new technique for the suitable allocation and capacity of converter-based multiple DG units considering the unbalanced operation of distribution networks. The objective function contains power loss minimization, multiphase voltage stability augmentation, and reduction of voltage unbalances among different phases in the system. A complex multi-objective optimization problem has been synthesized with the help of a Fast and Flexible Radial Power Flow (FFRPF) and solved by employing a Weighted aggregation (WA) based particle swarm optimization (PSO) approach. The performance of the proposed technique is validated on 19-bus, 25-bus, and 34-bus unbalanced radial distribution networks that consider various power factor modes of the converter-coupled DG units. The analysis of the simulation results indicates a significant enhancement in the power delivery efficiency in all the unbalanced test systems

A two-archive multi-objective multi-verse optimizer for truss design

Multi-objective structure optimization is a complex design issue that involves dealing with multiple conflicting objectives and various constraints. Although metaheuristics have been successful in resolving such issues, their stochastic nature and limitations can make implementation challenging. To address this challenge, an efficient and powerful optimizer called the multi-objective multi-verse optimizer (MOMVO) has been proposed in this study. The MOMVO algorithm is based on a two-archive concept focused on convergence and diversity, respectively, and is termed MOMVO2arc. The effectiveness of MOMVO2arc was evaluated by applying it to five conventional planar and spatial real-world structural optimization problems. These problems had conflicting objectives, such as minimizing structural mass and minimizing maximum nodal deflection, while imposing safety and size constraints related to stress on components and discrete cross-sectional areas. The results were then compared with those of seven advanced optimization techniques, including MOEA/D and NSGA-II, using four globally accepted performance indicators, including Hypervolume, Inverted Generational Difference, Spacing to Extent matrices, and the qualitative behavior of the best Pareto-front plots that each algorithm can produce. The comparative analysis and average Friedman rank test revealed that MOMVO2arc was more effective in solving large structure optimization problems with less computation time. The suggested approach not only found and maintained more Pareto-optimal sets but also achieved good diversity and convergence in both the decision and objective spaces. Therefore, MOMVO2arc can be a promising tool for resolving complex multi-objective structure optimization problems.