Objective Function Research Articles

Optimization of Al2O3 nanoparticle concentration and cutting parameters in hard milling under nanofluid MQL environment

The high cutting heat and cutting forces are still the big obstacles in hard machining technology, which puts more pressure to find out the alternative solution for these problems. The work content presents an experimental study on the effect of nanoparticle concentration and cutting parameters on surface roughness and cutting force during hard milling under MQL environment using Al2O3 nano-cutting oil. The Box-Behnken experimental designs for response surface methodology was used to evaluate the influence of the input parameters and determine the optimal values. The obtained results show that the nanoparticle concentration, cutting speed, and feed rate all have the great influences on surface roughness R z and resultant cutting force F, so the study of the influence of these parameters on the efficiency of the hard milling process is very significant. The proposed reasonable value ranges will help technicians quickly choose to meet their demands for specific objective functions. Furthermore, the optimal parameter set of nanoparticle concentration of 1.27 wt%, cutting speed V c = 103 m/min, and feed rate [Formula: see text] = 0.09 mm/tooth was determined. It revealed that the use of MQL with nano-cutting oils contributed to improve the lubrication and cooling performance in the cutting zone.

Strategies for improving the quality of community detection based on modularity optimization

Community detection is a field of interest in social networks. Many new methods have emerged for community detection solution, however the modularity optimization method is the most prominent. Community detection based on modularity optimization (CDMO) has fundamental problems in the form of solution degeneration and resolution limits. From the two problems, the resolution limit is more concerned because it affects the resulting community's quality. During the last decade, many studies have attempted to address the problems, but so far they have been carried out partially, no one has thoroughly discussed efforts to improve the quality of CDMO. In this paper, we aim to investigate works in handling resolution limit and improving the quality of CDMO, along with their strengths and limitations. We derive six categories of strategies to improve the quality of CDMO, namely developing multi-resolution modularity, creating local modularity, creating modularity density, creating new metrics as an alternative to modularity, creating new quality metrics as a substitute for modularity, involving node attributes in determining community detection, and extending the single objective function into a multi-objective function. These strategies can be used as a guide in developing community detection methods. By considering network size, network type, and community distribution, we can choose the appropriate strategy in improving the quality of community detection.

A pilot study of post-consolidation chemoimmunotherapy for high-risk neuroblastoma (ANBL19P1): A report from the Children’s Oncology Group.

10004 Background: Post-consolidation anti-GD2 antibody-based immunotherapy has improved survival for newly diagnosed patients (pts) with high-risk neuroblastoma (HRNBL). However, nearly half of newly diagnosed pts relapse. Based upon the efficacy of anti-GD2 antibody dinutuximab given with chemotherapy (chemoimmunotherapy) in the relapse setting, we hypothesized that post-consolidation chemoimmunotherapy may further improve frontline outcomes. ANBL19P1 first assessed the feasibility of delivering chemoimmunotherapy after tandem high-dose chemotherapy with autologous stem cell transplant (ASCT). Methods: Pts <31 years old with HRNBL who received 4-6 cycles of Induction chemotherapy +/- up to 4 cycles of post-Induction chemotherapy or chemoimmunotherapy, underwent tandem ASCT, had no evidence of progressive disease (PD), and met organ function criteria were eligible. Therapy, administered every 28 days, consisted of temozolomide and irinotecan on Days 1-5, dinutuximab on Days 2-5, and sargramostim on Days 6-12 during Cycles 1-5; isotretinoin on Days 8-21 during Cycles 1-6. Therapy was deemed feasible if the 95% confidence interval (CI) placed on the percentage of pts that completed 5 cycles of dinutuximab + chemotherapy without PD within 30 weeks contained 75%, and if the interim monitoring rules for feasibility and excessive toxicity were not triggered. Event-free (EFS) and overall survival (OS) were determined from time of enrollment. Results: From 11/30/20-6/30/23, 40 eligible pts enrolled and started protocol therapy. 87.5% (n=35) were ≥18 months old and 97.5% (n=39) had INRG Stage M disease, at diagnosis. 87.5% (95% CI 73.9%, 94.5%) completed 5 cycles of dinutuximab + chemotherapy without PD within 30 weeks, exceeding the feasibility benchmark of 75%. Feasibility and monitoring rules were not triggered. Five pts were removed from protocol therapy prior to Cycle 4 [physician determination (n=2), pt/parent refusal of further therapy (n=2), and PD (n=1)]. No unacceptable toxicities or deaths on protocol therapy were reported. Toxicities of interest are summarized (Table). One-year EFS and OS were 90.0±5.0% and 97.5±2.7%, respectively (median follow-up time for pts without event=1.2 years). Conclusions: Administration of post-consolidation chemoimmunotherapy in pts who underwent tandem ASCT is tolerable and met pre-defined feasibility criteria. The impact of this approach on survival outcomes will be studied in a future COG trial. Clinical trial information: NCT04385277 . [Table: see text]

Optimization of the generalized covariance estimator in noncausal processes

This paper investigates the performance of routinely used optimization algorithms in application to the Generalized Covariance estimator (GCov) for univariate and multivariate mixed causal and noncausal models. The GCov is a semi-parametric estimator with an objective function based on nonlinear autocovariances to identify causal and noncausal orders. When the number and type of nonlinear autocovariances included in the objective function are insufficient/inadequate, or the error density is too close to the Gaussian, identification issues can arise. These issues result in local minima in the objective function, which correspond to parameter values associated with incorrect causal and noncausal orders. Then, depending on the starting point and the optimization algorithm employed, the algorithm can converge to a local minimum. The paper proposes the Simulated Annealing (SA) optimization algorithm as an alternative to conventional numerical optimization methods. The results demonstrate that SA performs well in its application to mixed causal and noncausal models, successfully eliminating the effects of local minima. The proposed approach is illustrated by an empirical study of a bivariate series of commodity prices.

Метод определения эффективности вариантов организации перевозок барже-буксирными составами

A study has been conducted on the method of evaluating options for organizing cargo transportation by barge-tow trains based on determining their effectiveness. Using the methods of the classical theory of transport processes, this problem has no quantitative solution, since it is not possible to take into account the regrouping of the composition during the passage of the route. To overcome this problem, additional mathematical tools have been developed for constructing integral time and velocity matrices, an objective function and graphs of the ratios of the total volume of transported cargo to the time it was en route. The consistent implementation of the proposed tools ensures the coherence of the calculation methods for determining the effectiveness of a flight with and without regrouping on the route, and also makes it possible to select the most appropriate option for organizing transportation. The cumulative result allows us to reflect the method of evaluation, comparison and selection of the most effective option for organizing a flight / group of flights, taking into account the ability to set individual parameters for the movement of the train and cargo. An example of approximation of the coordinate points of the route from the Nizhne-Svirsky shipping lock to Lake Ladoga is illustrated, as well as an example of discretization of an inland waterway section according to a three-level model. The parameters of equalization of the objective function of determining the efficiency of cargo transportation are considered. It is concluded that the optimal transportation option can be carried out on the basis of a combined approach, when several parameters are taken into account or sequentially set in the process of modeling the operation of ships. Graphs have been built that demonstrate the differences between the ways of organizing flights.

A New Approach In Metaheuristic Clustering: Coot Clustering

As a result of technological advancements, the increase in vast amounts of data in today's world has made artificial intelligence and data mining significantly crucial. In this context, the clustering process, which aims to explore hidden patterns and meaningful relationships within complex datasets by grouping similar features to conduct more effective analyses, holds vital importance. As an alternative to classical clustering methods that face challenges such as large volumes of data and computational complexities, a metaheuristic clustering method utilizing Coot Optimization (COOT), a swarm intelligence-based algorithm, has been proposed. COOT, inspired by the hunting stages of eagles and recently introduced into the literature, is a metaheuristic method. Through the proposed COOT metaheuristic clustering method, the aim is to contribute to the literature by leveraging COOT's robust exploration and exploitation processes, utilizing its dynamic and flexible structure. Comprehensive experimental clustering studies were conducted to evaluate the consistency and effectiveness of the COOT-based algorithm using randomly generated synthetic data and the widely used Iris dataset in the literature. The same datasets underwent analysis using the traditional clustering algorithm K-Means, renowned for its simplicity and computational speed, for comparative purposes. The performance of the algorithms was assessed using cluster validity measures such as Silhouette Global, Davies-Bouldin, Krznowski-Lai, and Calinski-Harabasz indices, along with the Total Squared Error (SSE) objective function. Experimental results indicate that the proposed algorithm performs clustering at a competitive level with K-Means and shows potential, especially in multidimensional datasets and real-world problems. Despite not being previously used for clustering purposes, the impressive performance of COOT in some tests compared to the K-Means algorithm showcases its success and potential to pioneer different studies aimed at expanding its usage in the clustering domain.

Unveiling optimal half-cell potentials in RCC slabs through cutting-edge ANFIS, ANN and genetic algorithm integration

Purpose The purpose of this study is to compare the prediction models for half-cell potential (HCP) of RCC slabs cathodically protected using pure magnesium anodes and subjected to chloride ingress.The models for HCP using 1,134 data set values based on experimentation are developed and compared using ANFIS, artificial neural network (ANN) and integrated ANN-GA algorithms. Design/methodology/approach In this study, RCC slabs, 1000 mm × 1000 mm × 100 mm were cast. Five slabs were cast with 3.5% NaCl by weight of cement, and five more were cast without NaCl. The distance of the point under consideration from the anode in the x- and y-axes, temperature, relative humidity and age of the slab in days were the input parameters, while the HCP values with reference to the Standard Calomel Electrode were the output. Experimental values consisting of 80 HCP values per slab per day were collected for 270 days and were averaged for both cases to generate the prediction model. Findings In this study, the premise and consequent parameters are trained, validated and tested using ANFIS, ANN and by using ANN as fitness function of GA. The MAPE, RMSE and MAE of the ANFIS model were 24.57, 1702.601 and 871.762, respectively. Amongst the ANN algorithms, Levenberg−Marquardt (LM) algorithm outperforms the other methods, with an overall R-value of 0.983. GA with ANN as the objective function proves to be the best means for the development of prediction model. Originality/value Based on the original experimental values, the performance of ANFIS, ANN and GA with ANN as objective function provides excellent results.

Multivariate Singular Spectrum Analysis by Robust Diagonalwise Low-Rank Approximation

Multivariate Singular Spectrum Analysis (MSSA) is a powerful and widely used nonparametric method for multivariate time series, which allows the analysis of complex temporal data from diverse fields such as finance, healthcare, ecology, and engineering. However, MSSA lacks robustness against outliers because it relies on the singular value decomposition, which is very sensitive to the presence of anomalous values. MSSA can then give biased results and lead to erroneous conclusions. In this paper a new MSSA method is proposed, named RObust Diagonalwise Estimation of SSA (RODESSA), which is robust against the presence of cellwise and casewise outliers. In particular, the decomposition step of MSSA is replaced by a new robust low-rank approximation of the trajectory matrix that takes its special structure into account. A fast algorithm is constructed, and it is proved that each iteration step decreases the objective function. In order to visualize different types of outliers, a new graphical display is introduced, called an enhanced time series plot. An extensive Monte Carlo simulation study is performed to compare RODESSA with competing approaches in the literature. A real data example about temperature analysis in passenger railway vehicles demonstrates the practical utility of the proposed approach.

The economic impact of crowd-shipping based on public transport in Egypt: a GA approach.

The last-mile delivery challenges and complexity are increasing simultaneously with the e-commerce growth, the e-commerce growth constitutes a threat to urban transport, especially for big cities and developing countries. This paper examines the economic impact of crowd-shipping based on public transport collaborated with the automated parcel locker and the impact of traditional delivery, as two different methods of last-mile delivery under the same circumstances. This paper aims to assess crowd-shipping as an alternative solution for last-mile delivery compared to traditional delivery. Data has been simulated based on Cairo reality, one of the largest cities in the world. The mathematical models were formulated for the problem, where the first model objective function minimizes the costs of vehicle possession and vehicle kilometers traveled, while the second model objective function minimizes the costs of establishing lockers, vehicle possession, and vehicle kilometers traveled. A genetic algorithm has been used due to the complexity of the problem. The results show that the economic impact of the crowd-shipping delivery system is better than the traditional delivery system under the conditions of large-sized and medium-sized demand, while the economic impact of traditional delivery is better than the crowd-shipping delivery system under the conditions of small-sized demand.

Investigation of longitudinal dynamics of vehicles in disordered traffic

Vehicles in developing countries have wide variations in their static and dynamic characteristics, and drivers tend to not follow lane discipline. Models for driving behavior under such disordered traffic conditions need to include the vehicle dynamics and their interactions with the surrounding environment. Calibration of those models is necessary to evaluate their predictive power and suitability for analyzing traffic flow under disordered traffic. The present study aims to calibrate a longitudinal dynamics model, the High-Speed Social-Force Model (HSFM) using a vehicle trajectory dataset collected from Chennai city. The HSFM was calibrated by minimizing the deviations between the simulated and observed longitudinal coordinates of vehicles using a genetic algorithm. The observed and simulated vehicle trajectories were compared using a goodness of fit function of the positions. The convergence of the objective function has been illustrated with the help of fitness landscapes. The calibration errors were found to be within the acceptable range and the optimal parameter values were found to be consistent. The outcomes of the study indicate that the model can capture the influence of non-overlapping leaders under disordered traffic conditions.

Hybrid minigrid system comprising energy storage systems with optimal frequency control empowering the new Egypt large optical telescope site

Proposed hybrid minigrid two area system simulation model encompassing Photo Voltaic (PV) system, Wind Turbines (WT), diesel generators and Energy Storage Systems with intelligent based optimal Frequency Controllers (FCs) empowering the new Egypt large optical telescope (ELOT) site is presented in this research. Technical study and specifications for a PV solar system of 1000 Kw is introduced. Intelligent fine optimized Proportional Integral Derivative (PID) and Fuzzy self-tuned PID (FSTPID) controllers are designed through applying Harris Hawk optimizer (HHO). The proposed HHO employed method performance is validated under number of eventualities which include vacillations of load, sun radiation and wind speed. The objective function and control parameters are the integral time summation of absolute deviations and the parameters of controllers, consecutively. The system dynamic response and simulation results show that the proposed HHO based FSTPID type FCs are effective in reducing frequency and tie line power signals’ deviations in a diminutive time for such minigrid hybrid system. For supplemental validations, simulation results obtained are compared with genetic algorithm to get the proposed controllers’ gains.

Coordinated torque control for enhanced steering and stability of independently driven mobile robots

Purpose Mobile robots with independent wheel control face challenges in steering precision, motion stability and robustness across various wheel and steering system types. This paper aims to propose a coordinated torque distribution control approach that compensates for tracking deviations using the longitudinal moment generated by active steering. Design/methodology/approach Building upon a two-degree-of-freedom robot model, an adaptive robust controller is used to compute the total longitudinal moment, while the robot actuator is regulated based on the difference between autonomous steering and the longitudinal moment. An adaptive robust control scheme is developed to achieve accurate and stable generation of the desired total moment value. Furthermore, quadratic programming is used for torque allocation, optimizing maneuverability and tracking precision by considering the robot’s dynamic model, tire load rate and maximum motor torque output. Findings Comparative evaluations with autonomous steering Ackermann speed control and the average torque method validate the superior performance of the proposed control strategy, demonstrating improved tracking accuracy and robot stability under diverse driving conditions. Research limitations/implications When designing adaptive algorithms, using models with higher degrees of freedom can enhance accuracy. Furthermore, incorporating additional objective functions in moment distribution can be explored to enhance adaptability, particularly in extreme environments. Originality/value By combining this method with the path-tracking algorithm, the robot’s structural path-tracking capabilities and ability to navigate a variety of difficult terrains can be optimized and improved.

An improved gain-scheduling robust MPC for path following of autonomous independent-drive electric vehicles with time-varying and uncertainties

This paper proposes a gain-scheduling robust model predictive control (GS-RMPC) algorithm for the path-following problem of autonomous independent-drive electric vehicles (AIDEVs) with consideration of time-varying and uncertainties. Firstly, the polytopic uncertainty method and norm-bounded uncertainty method are introduced to characterise the vehicle dynamics model. Secondly, the infinite predict horizon optimisation process of online GS-RMPC is transformed into a series of linear matrix inequalities (LMIs) by minimising the worst-case objective function while considering all scheduling states in the polytope. Thirdly, an offline solution is also proposed to reduce the computational burden based on asymptotically stable invariant ellipse sets. Then, a hierarchical control structure is proposed to distribute the additional yaw moment, and a multi-step predictor is designed to compensate for the actuator time delay. Finally, the hardware-in-the-loop (HIL) testing is conducted to verify the efficacy of the proposed strategy.

High-throughput functional mapping of variants in an arrhythmia gene, KCNE1, reveals novel biology

BackgroundKCNE1 encodes a 129-residue cardiac potassium channel (IKs) subunit. KCNE1 variants are associated with long QT syndrome and atrial fibrillation. However, most variants have insufficient evidence of clinical consequences and thus limited clinical utility.MethodsIn this study, we leveraged the power of variant effect mapping, which couples saturation mutagenesis with high-throughput sequencing, to ascertain the function of thousands of protein-coding KCNE1 variants.ResultsWe comprehensively assayed KCNE1 variant cell surface expression (2554/2709 possible single-amino-acid variants) and function (2534 variants). Our study identified 470 loss- or partial loss-of-surface expression and 574 loss- or partial loss-of-function variants. Of the 574 loss- or partial loss-of-function variants, 152 (26.5%) had reduced cell surface expression, indicating that most functionally deleterious variants affect channel gating. Nonsense variants at residues 56–104 generally had WT-like trafficking scores but decreased functional scores, indicating that the latter half of the protein is dispensable for protein trafficking but essential for channel function. 22 of the 30 KCNE1 residues (73%) highly intolerant of variation (with > 70% loss-of-function variants) were in predicted close contact with binding partners KCNQ1 or calmodulin. Our functional assay data were consistent with gold standard electrophysiological data (ρ = − 0.64), population and patient cohorts (32/38 presumed benign or pathogenic variants with consistent scores), and computational predictors (ρ = − 0.62). Our data provide moderate-strength evidence for the American College of Medical Genetics/Association of Molecular Pathology functional criteria for benign and pathogenic variants.ConclusionsComprehensive variant effect maps of KCNE1 can both provide insight into IKs channel biology and help reclassify variants of uncertain significance.

A Set Covering Approach to Design Maximally Permissive Supervisors for Flexible Manufacturing Systems

The supervisory control of Petri nets aims to enforce the undesired behavior as unreachable by designing a set of control places. This work presents a set cover approach to design maximally permissive supervisors. For each first-met bad marking, an integer linear programming problem is developed to obtain a control place to prohibit it. An objective function is formulated to make the maximal number of first-met bad markings forbidden. Then, we develop a set covering approach to minimize the number of selected control places. The proposed approach can guarantee the maximal permissiveness of the obtained supervisor and provide a trade-off between structural complexity and computational cost. Several examples are considered to validate the proposed method.

Integrating Sustainable Energy Technologies into District Cooling Systems: A Review of Modelling and Optimisation Approaches

With the rising cooling demand and prevalent energy crisis, District cooling (DC) is evolving as one of the sustainable energy solution worldwide. As per ‘EHP DHC Outlook, May 2023’, the sales in DC sector reached 3 TWh, covering more than 150 European cities. The centralised nature of the DC system offer benefits such as energy efficient operations, sector coupling, peak load management. Further, the feasibility of integrating renewable technologies (eg. solar energy), free cooling sources (eg. seawater heatpumps) and thermal energy storage (eg. ice slurry) is also explored. These developments make the futuristic DC system quite complex, as it involves multiple energy transformations. In this regard, utilising computation tools for decision-making has become increasingly relevant. However, choosing the appropriate approach among the existing ones in this evolving field is a curb some task for energy practitioners. The aim of the study is to review the modelling and optimisation approaches in the context of innovative DC systems. Data collection and analysis is based on desk-review of scientific literature published in the recent past. Firstly, various possibilities of integrating sustainable energy technologies for DC applications are explored. Then, relevant modelling and simulation approaches are studied, focussing on the similarities and limitations. Finally, different optimisation methods are examined in terms of parameters such as objective functions, control variables, solving techniques. The contribution of the study involve overview of different integration pathways, identifying the strength and weakness of modelling approaches and insights into suitability of optimisation techniques. It is expected that this study will be a reference material, while performing feasibility studies as well as developing digital-twins in DC context.

A surrogate-assisted a priori multiobjective evolutionary algorithm for constrained multiobjective optimization problems

AbstractWe consider multiobjective optimization problems with at least one computationally expensive constraint function and propose a novel surrogate-assisted evolutionary algorithm that can incorporate preference information given a priori. We employ Kriging models to approximate expensive objective and constraint functions, enabling us to introduce a new selection strategy that emphasizes the generation of feasible solutions throughout the optimization process. In our innovative model management, we perform expensive function evaluations to identify feasible solutions that best reflect the decision maker’s preferences provided before the process. To assess the performance of our proposed algorithm, we utilize two distinct parameterless performance indicators and compare them against existing algorithms from the literature using various real-world engineering and benchmark problems. Furthermore, we assemble new algorithms to analyze the effects of the selection strategy and the model management on the performance of the proposed algorithm. The results show that in most cases, our algorithm has a better performance than the assembled algorithms, especially when there is a restricted budget for expensive function evaluations.

Weight Saliency search with Semantic Constraint for Neural Machine Translation attacks

Text adversarial attack is an effective way to improve the robustness of Neural Machine Translation (NMT) models. Existing NMT attack tasks are often completed by replacing words. However, most of previous works pursue a high attack success rate but produce semantic inconsistency sentences, leading to wrong translations even for humans. In this paper, we propose a Weight Saliency search with Semantic Constraint (WSSC) algorithm to make semantic consistency word modifications to the input sentence for black-box NMT attacks. Specifically, our WSSC has two major merits. First, it optimizes the word substitution with a word saliency method, which is helpful to reduce word replacement rate. Second, it constrains the objective function with a semantic similarity loss, ensuring every modification does not lead to significant semantic changes. We evaluate the effectiveness of the proposed WSSC by attacking three popular NMT models, i.e., T5, Marian, and BART, on three widely used datasets, i.e., WMT14, WMT16, and TED. Experimental results validate that our WSSC improves Attack Success Rate (ASR) by 4.02% and Semantic Similarity score (USE) by 1.28% on average. Besides, our WSSC also shows good properties in keeping grammar correctness and transfer attack.

A multi-objective fuzzy mathematical model for circular economy with leasing as a strategy

PurposeThis paper aims at developing a multi-objective mathematical model of circular economy that integrates key concept of leasing as a strategy in addition to reuse, refurbishing, primary recycling, secondary recycling and disposal.Design/methodology/approachThis paper proposes multi-objective fuzzy mixed integer linear programming mathematical model considering multi-product, multi-echelon and multi-capacitated concepts of the circular economy. The three objectives of the proposed model, namely, economic, environmental and social are solved simultaneously using constraint approach to obtain balanced trade-off between the objective functions. The model is validated by solving a case study from the literature. The proposed model is made pragmatic for industrial application by considering multi-external suppliers multi-customer zones, multi-disassembly centers, multi-collection centers and multi-refurbishing centers and accounting for purchasing, processing, transportation, set-up costs and capacity constraints at the same time.FindingsThe results show that the leasing of the products improves the economic function in addition to the known environmental improvements. The proposed model also shows that the circular economy can generate the jobs for the unskilled people at different locations.Research limitations/implicationsThe proposed model can be further improved by considering the non-linearity due to economy of scale at various centers and in transportation. The model can be further extended to make it multi-period model.Practical implicationsThe proposed model of circular economy can be used by the organizations as a policy tool to decide the optimum number of collection centers, disassembly centers, refurbishing centers, recycling centers and disposal centers and their optimum locations and allocations. The organizations can also trade-off among economic, environmental and social benefits of their proposed decisions in circular economy.Originality/valueThe originality of the proposed mathematical model is consideration of leasing as a strategy to have better control over the supply chain for circularity; considering the training of unskilled people for backward supply chain jobs and accounting for primary recycling and secondary recycling separately for economical computation.

Novel Hierarchical Energy Management System for Enhanced Black Start Capabilities at Distribution and Transmission Networks

A novel energy management system featuring a unique framework involving multiple hierarchical controllers at the distribution and transmission network levels is proposed. The unique objective function of this energy management system is designed to enhance system inertia during black start and optimise load shedding. The objective function further aims to increase reliance on renewable energy sources, prioritising solar power along with battery and fuel cell technologies. This work delves deeply into the dynamics of multi-area power networks, where some areas possess black start capabilities (BSAs) while others do not (NBSAs). The proposed energy management system specifically explores the complex interplay between these black start capabilities and the hierarchical load restoration order. During grid blackouts, the systems located in BSA areas are tasked with first restoring essential loads in their own regions before extending aid to the adjacent NBSA areas, taking into account factors such as their available reserved power and geographical proximity. This work is extended to analyse complex multi-area power network architectures. This extended analysis provides invaluable insights for enhancing power restoration processes and facilitating the large-scale integration of sustainable energy solutions in complex systems. The proposed energy management system is validated using the IEEE 39-Bus network, which consists of ten distinct areas, each differing in their black start capabilities. The results demonstrate the superiority of the proposed system.