Search Results (636)

The transition toward renewable-dominated power systems introduces significant complexity and nonlinearity, rendering traditional mechanism-based modeling computationally prohibitive for real-time security assessment. While data-driven approaches offer computational efficiency, they fundamentally lack physical interpretability and often exhibit generalization failures under rare, large-signal disturbances due to the absence of intrinsic physical constraints. To bridge this gap, this paper proposes a Physics-Guided Symbolic Regression (PGSR) framework for constructing interpretable and robust dynamic equivalent models. The methodology embeds domain knowledge via topological masks and dimensional consistency rules to restrict the evolutionary search space to physically admissible manifolds. A multi-resolution extraction strategy based on the Pareto frontier is developed to autonomously identify both linear small-signal models and nonlinear large-signal formulations adaptable to varying analytical requirements. Furthermore, a post hoc verification stage based on Lyapunov stability theory ensures the dynamic validity and energy dissipation properties of the generated equations. A case study on the WSCC 9-bus system demonstrates that the proposed method accurately recovers the underlying Taylor-series structure of swing equations and significantly outperforms four data-driven baselines—including polynomial, kernel, and neural network models—in out-of-distribution generalization, achieving 12–42× lower trajectory error under unseen large perturbations. Full article

Objectives: An integrated methodological framework was developed for modeling and multiobjective optimization of sustained-release drug delivery systems. Methods: The cumulative release percentage was fitted as a function curve, and functional principal component analysis was subsequently used to transform the function curves into functional principal component scores (FPCs). FPCs were then treated as dependent variables, while the proportions of the formulation factors were used as independent variables to construct Scheffé polynomial regression models. Finally, Non-dominated Sorting Genetic Algorithm III (NSGA-III) was applied to perform multi-objective optimization. Results: FPC1, FPC2, and FPC3 captured 95.18%, 4.39%, and 0.32% of the total variation, respectively. Corresponding Scheffé polynomial regression models were established, including quadratic models for FPC1 (adjusted R² = 0.751, AIC = 168.557) and FPC2 (adjusted R² = 0.592, AIC = 119.302), and a special cubic model for FPC3 (adjusted R² = 0.597, AIC = 64.574). The NSGA-III algorithm generated a Pareto optimal set, yielding stable formulation compositions with mean (SD) values of X₁ = 0.123 (0.015), X₂ = 0.821 (0.032), X₃ = 0.012 (0.017), and X₄ = 0.045 (0.015). The corresponding FPCs were −41.787 (2.544), 10.009 (0.168), and 8.264 (0.010) for FPCs1–FPCs3, respectively. The reconstructed cumulative release percentages were 42.471 (1.661), 52.623 (2.868), 69.942 (1.200), 84.275 (1.010), and 93.330 (0.832), demonstrating good agreement with the target release profiles. Conclusions: The integrated FDA–Scheffé–NSGA-III framework provides a robust and effective approach for accurately modeling release behavior and optimizing sustained-release formulations. Full article

Permutation flow shop scheduling is an important production planning problem handled in different contexts. Just-in-time measures have been significant in the optimization of real problems and one is specifically addressed here: the total earliness and tardiness of jobs. The most used approach in the literature to mathematically express this measure is to sum them up using unit weights thus obtainning a mono-objective function. In this paper it is shown that this is a simplification of a problem that is inherently multi-objective, highlighting how a more comprehensive approach can better support decision-making. A bi-objective mathematical optimization model and tools capable of analyzing the mono-objective solution within the multi-objective perspective are proposed. A computational study to analyze the benefits and difficulties of the solution using the bi-objective approach is presented. The results show that for large-scale instances in which the tardiness factor is small, the conflict between the objectives of minimizing the total earliness and minimizing the total tardiness of jobs increases significantly. Specifically, the mono-objective solution is unbalanced in 50.00% of the analyzed instance structures. However, in 48.12% of the instances, alternative Pareto-optimal trade-offs can be achieved with zero increase to the mono-objective optimal value. Therefore, the multi-objective approach has a greater potential to support decision-makers. Furthermore, we show that the choice of the solution method must be carefully considered, since the Pareto frontier associated with most instances has many non-supported points, representing up to 66.71% of the non-dominated set. Full article

Optimal sizing of hybrid renewable energy systems for desert camps is a multi-objective problem that must account for cost, reliability, component degradation, and uncertainty. This paper introduces an improved multi-objective neural architecture search (IMONAS) framework for hybrid nanogrid sizing in the desert environment of Hafr Al-Batin, Saudi Arabia. The framework combines neural optimization, stochastic uncertainty modeling, and explicit battery degradation modeling, a combination not addressed in the reviewed studies for this application. Six test cases are examined by varying uncertainty assumptions, battery degradation, and the annual duration of uncertain operation. For each case, IMONAS provides Pareto-front solutions that specify the photovoltaic, diesel generator, battery autonomy, and inverter choices while minimizing the cost of energy (COE) and the loss of power supply probability (LPSP). IMONAS is compared with the original MONAS and five other multi-objective optimization methods. In addition to visual Pareto-front comparisons, the assessment uses Pareto-dominance indicators, namely the C-metric and an aggregated score derived from pairwise C-metric comparisons across the algorithms and cases. The results provide a validated sizing framework for remote arid-region nanogrids under uncertainty and battery degradation. Full article

Weak grid infrastructure and the absence of flexible storage are among the principal barriers to reliable, low-carbon energy access in sub-Saharan transmission systems. This paper proposes a hierarchical multi-objective framework for the optimal siting and sizing of battery energy storage systems (BESSs), applied to the 130-bus Mali transmission network within the EMERGE project. The upper level employs NSGA-II to simultaneously maximize daily price arbitrage revenue and minimize active power losses; the lower level solves a network-constrained DC optimal power flow with thermal branch limits enforced as hard linear inequalities via the Power Transfer Distribution Factor (PTDF) matrix. Over 500 generations, the framework identifies Bus 91 (SIRAKORO II, 150 kV) as the dominant storage location, achieving a maximum daily revenue of approximately €10,033 at a marginal loss increment of $6.7\times {10}^{-3}$ MWh. The resulting Pareto front gives Mali system planners a quantitative tool for trading off private investment returns against grid-level environmental impact, demonstrating that rigorous network-constrained BESS planning is technically tractable and economically viable in the resource-constrained context of sub-Saharan energy transitions. Full article

Background: Egypt is one of the top steel producers in the Middle East and Africa, yet it faces acute water scarcity and rising energy costs, making it a critical context for studying trade-offs among carbon emissions, water ecological effects, and operational cost in steel supply chain. Methods: Using a multi-objective optimization model based on real data from a major Egyptian steel manufacturer, this study evaluates trade-offs among cost, tardiness, and environmental impact measured by carbon emissions and water ecological effects. Unlike prior studies, this study demonstrates that dedicated warehousing enables batch-level traceability of returned scrap while reducing material handling travel time and carbon emissions. The AUGMECON method generates Pareto-optimal solutions, and sensitivity analysis is conducted on six parameters: scrap take-back rate, demand variability, raw material price, energy cost, production capacity, and carbon tax. Results: Demand and raw material prices dominate performance: a 5% demand increase raises cost by 8.6%, and a 15% raw material price increase raises cost by 32.7%. The knee-point solution achieves 58.18 billion EGP, 0.99 months tardiness, and 2096 million kg CO₂ over nine months. Conclusions: This study quantifies the impact of the circular economy and operational parameters on steel supply chain performance under a dedicated warehousing policy. Full article

The evolution of 193 nm deep-ultraviolet (DUV) lithography toward high numerical aperture (NA > 1.35) presents challenges approaching physical limits for antireflective (AR) coatings on strongly curved lens elements. In this study, a full-stack multi-objective optimization framework is developed by coupling the Non-dominated Sorting Genetic Algorithm II (NSGA-II) with the Transfer Matrix Method (TMM) to optimize a 7-layer LaF₃/MgF₂ system on strongly curved substrates ($R=150$ mm). The model integrates material dispersion, thermo-optic effects, deposition flux deviations, and manufacturing thickness constraints. Following 1500 generations of optimization and TOPSIS-based decision-making, the selected Pareto optimal solution achieves a full-aperture average reflectance of 1.3633% and a radial uniformity of 9.5037%. The design further exhibits high environmental robustness with a thermal drift of 0.0019% and a residual stress of 39.23 MPa. These results demonstrate that the proposed method overcomes the critical process bottleneck of achieving full-aperture uniformity below 10% on strongly curved optics. This framework provides a general paradigm for the robust design of next-generation ultra-precision DUV optical systems, effectively balancing theoretical depth with engineering feasibility. Full article

In this paper, a multi-objective optimisation method based on the Non-dominated sorting genetic algorithm II (NSGA-II) is proposed, which proves to be effective in solving the computer-aided molecular design (CAMD) problem in the design of solvents for cooling crystallisation. A multi-objective optimisation model has been developed for the CAMD problem of solvents in the crystallisation process with the toxicity, solubility parameters, and potential recovery of the solvents as objective functions and the feasibility of the molecular structure as constraints. The properties involved are to be calculated by the group contribution method, and the solubility parameters of the solute in the solvent are calculated based on the Universal Quasichemical Functional-group Activity Coefficients (UNIFAC) model. Based on this method, cooling crystallisation solvents for 2-mercaptobenzothiazole (MBT) and sebacic acid were designed. The results indicate that the proposed multi-objective CAMD framework exhibits a certain degree of generality. Even when the optimisation parameters and methods differ from those of other existing frameworks, it does not overlook the optimal solutions under specific design conditions. Furthermore, clustering of the Pareto front for MBT revealed that, since multi-objective optimisation does not aim to obtain a single optimal solution, it can identify multiple candidate solvents that balance potential yield and toxicity. This approach avoids the issue of single-objective optimisation, which tends to overemphasise potential yield at the expense of toxicity. Full article

The growing penetration of electric vehicles (EVs) and distributed photovoltaic (PV) generation is increasing operational uncertainty in distribution networks and intensifying long-standing challenges such as higher power losses, rising peak demand, and voltage instability. To address these issues, this paper proposes a multi-objective optimization framework for the strategic placement of smart meters equipped with demand response (DR) capability in radial distribution systems. Unlike conventional placement approaches that mainly focus on monitoring or reducing non-technical losses, the proposed method integrates active load control into the planning stage and explicitly considers the stochastic behavior of loads, PV generation, and electric vehicle charging stations (EVCSs). The problem is formulated with four objectives: minimizing total power losses, substation peak demand, voltage deviation penalty, and installation cost. A scenario-based stochastic model is employed to represent operational variability across the network. The resulting nonlinear mixed discrete optimization problem is solved using the Non-dominated Sorting Genetic Algorithm II (NSGA-II), an evolutionary multi-objective optimization technique that generates a set of Pareto-optimal solutions representing trade-offs among conflicting objectives. Smart meters are allowed to curtail a portion of controllable demand during critical loading conditions, which helps reduce feeder loading and improve voltage profiles. The proposed approach is evaluated on the IEEE 33-bus and IEEE 69-bus distribution systems. Simulation results demonstrate significant reductions in power losses and peak demand, with the IEEE 33-bus system achieving up to a 26.2% reduction in power losses and 52.5% reduction in substation peak demand compared with existing metaheuristic approaches. The results also indicate improved voltage stability and effective performance in the IEEE 69-bus system, confirming the importance of topology-aware DR-enabled planning. Overall, the findings show that embedding demand response capability within smart meter allocation can significantly enhance the resilience and operational efficiency of modern distribution networks with high EV and PV penetration. Full article

Many deterministic multi-objective optimization methods generate Pareto outcomes by repeatedly solving scalarized subproblems for different preference or reference vectors. When the number of objectives is $m\ge 3$, the resulting samples lie on an $(m-1)$-dimensional Pareto surface in objective space. For tasks such as visualization, trade-off exploration, interactive decision making, and sensitivity analysis, a finite cloud of non-dominated points may be insufficient; one often needs a continuous surrogate of the Pareto surface together with a quantitative control of its reconstruction error. This paper studies the corresponding outer-loop reconstruction problem: how should new reference vectors be selected so as to reconstruct the Pareto surface to a prescribed uniform accuracy while using as few scalarized solves as possible? We propose Certified Adaptive Triangulation Sampling (CATS), a curvature-aware adaptive triangulation method for reconstructing a Pareto surface from an oracle $u\mapsto z\left(u\right)$, $u\in {\Delta }_d$, where $d=m-1$. CATS builds a simplicial mesh over the reference simplex and refines the cell with the largest local interpolation quantity $\eta \left(\tau \right)=\frac{1}{2}\left({max}_k{M}_{\tau ,k}\right)\mathrm{diam}{\left(\tau \right)}^2$, where $M_{\tau ,k}$ is an upper bound on the Hessian norm of the kth component of the oracle-induced map over $\tau$. This quantity matches the natural error scale of affine interpolation for $C^2$ maps. The rigorous certified interpretation of CATS applies when the preference-to-Pareto map is single-valued, $C^2$, and equipped with reliable local Hessian-norm upper bounds. If such bounds are replaced by numerical curvature estimates, the same rule can still be used as an adaptive refinement indicator, but the resulting stopping test is not a formal certificate unless those estimates are themselves validated. Under the certified assumptions, we prove that the stopping condition ${max}_{\tau }\eta \left(\tau \right)\le \epsilon$ guarantees ${sup}_{u\in {\Delta }_d}{\parallel z\left(u\right)-\widehat{z}\left(u\right)\parallel }_{\infty }\le \epsilon$, and that the oracle complexity of certified simplicial piecewise-affine reconstruction is $\mathsf{\Theta }\left({\epsilon }^{-d/2}\right)$. On the rigorously certified core tests, CATS uses $2.7\times$–$3.8\times$ fewer oracle calls than uniform reference-direction sampling and $1.2\times$–$1.6\times$ fewer than an AWS-inspired patch-area refinement rule. Additional benchmark studies, evaluated with the same interpolation quantity as a practical stopping indicator, show the same qualitative advantage, especially on anisotropic and localized surface geometries. Full article

Empty-vehicle repositioning is a persistent challenge in long-haul road freight because carriers must reduce empty mileage without sacrificing service reliability under lead times, appointment windows, and uncertain load realization. This paper formulates empty-vehicle repositioning on freight corridors as a stochastic control problem with explicit space–time feasibility and a stated within-epoch event order. Lead times couple current dispatch decisions to future capacity, pickup windows impose reachability constraints, and stochastic match feasibility captures information and market frictions. We develop dynamic lower bounds from time-expanded relaxations, showing that dual prices of inventory-balance constraints can be interpreted as space–time scarcity values. We further introduce an order-dependent nested friction decomposition that separates excess empty movement into spatial imbalance, temporal mismatch induced by lead times and time windows, and information frictions. Guided by this structure, we propose price-guided rolling-horizon and generalized-cost policies and evaluate them on synthetic corridor experiments organized around the three friction families. The results reveal service–empty-mileage trade-offs, a pronounced knee in the Pareto frontier, lower service loss under widened tight pickup windows, and strong sensitivity to match feasibility. The PG-RH policy reduces empty-distance exposure and total cost relative to static balancing in the main scenarios while maintaining comparable, but not uniformly dominant, service performance. The framework provides a diagnostic basis for identifying the sources of deadhead and for designing operational interventions that reduce empty mileage without undermining reliability. Full article

This study aims to optimize the performance of cyclone separators by simultaneously maximizing separation efficiency and minimizing pressure drop through a CFD-based multi-objective optimization framework. The research objectives are explicitly focused on (i) developing accurate predictive surrogate models for cyclone behavior and (ii) identifying optimal geometric configurations that balance both performance criteria. The methodology integrates Design of Experiments (DOE), Response Surface Methodology (RSM), and the Non-dominated Sorting Genetic Algorithm II (NSGA-II), using a full factorial design of 25 simulations to construct fourth-order surrogate models. This formulation was strictly necessary to capture the severe non-linearities observed in preliminary CFD runs. These models exhibited high predictive capability, with coefficients of determination (R²) above 0.94. The NSGA-II optimization generated a Pareto-optimal front that clearly describes the trade-off between separation efficiency and pressure drop, enabling systematic decision-making. The selected optimal configuration achieved a separation efficiency of 94.5% and a pressure drop of 194.78 Pa. CFD validation confirmed the robustness of the surrogate models, with relative errors below 1% for efficiency and below 5% for pressure drop. Overall, the results demonstrate that integrating CFD, surrogate modeling, and evolutionary optimization provides a reliable and computationally efficient strategy for cyclone separator design optimization. Full article

This study proposes a multi-objective optimization strategy for the structural design of liquid-cooled channels in battery systems, aiming to identify liquid-cooled plate design schemes with better cooling performance and acceptable flow resistance. Optimal Latin hypercube sampling (OLHS) was combined with computational fluid dynamics (CFD) simulations to construct a CFD-generated dataset that includes the maximum temperature and system pressure drop. Then, modeFRONTIER was employed to integrate surrogate-model training, rapid prediction, and non-dominated sorting genetic algorithm II (NSGA-II) optimization, thereby obtaining the Pareto optimal set. The technique for order preference by similarity to ideal solution (TOPSIS) decision method was further introduced to determine the final optimal design. Results indicate that the optimized liquid-cooling system exhibits outstanding comprehensive performance in terms of balancing heat dissipation and flow resistance at a 5 C discharge rate. Remarkably, sensitivity analysis shows that inlet velocity is the dominant factor affecting the maximum battery temperature, with a correlation coefficient of −0.789. The maximum temperature of the battery module is effectively limited to 30.07 °C, while the flow pressure drop is only 799.58 Pa, achieving an excellent balance between heat dissipation efficiency and energy consumption. Full article

This paper presents a control design framework that systematically translates nonlinear equilibrium operability analysis into frequency-domain robust synthesis for continuous microbial electrolysis cells (MEC). Since MEC operation is threatened by washout and highly variable influent conditions, analytical local conditions for the existence and local stability of normal operating conditions (NOC) and washout equilibria are first established. Departing from these nonlinear properties, the model is linearized within the locally validated NOC region, and a parametric sensitivity screening is used to identify dominant uncertainty sources ($\alpha$, ${\mu }_{max}$, $K_d$). These are embedded into an unstructured multiplicative uncertainty weight, enabling the synthesis of nominal and robust $H_{\infty }$ controllers that explicitly account for actuator effort, disturbance rejection, and measurement noise. Controller order reduction via balanced truncation is performed while preserving closed-loop local robustness properties. As a benchmark, an internal model control proportional–integral (IMC-PI) controller is derived, and its single tuning parameter is selected by solving a univariate multi-objective optimization that balances integral absolute error and maximum control effort, yielding a Pareto-optimal compromise. Numerical simulations under simultaneous inlet disturbances, parametric variations, measurement noise, and actuator saturation show that the reduced-order robust $H_{\infty }$ controller outperforms the optimized IMC-PI in the tracking–effort trade-off, while the nominal $H_{\infty }$ controller satisfies an a posteriori robust stability test for the linearized dynamics. The proposed framework provides a systematic path from nonlinear operability analysis to implementable robust control, demonstrating that high-order $H_{\infty }$ designs can be reduced to low-order transfer functions suitable for standard industrial control hardware while preserving local stability properties against realistic process perturbations. Full article

Aiming at the problem that the loss and temperature rise of the pole-suspended rotor low-speed high-torque permanent magnet synchronous motor (LHPMSM) increase in the pursuit of high torque density, and the design cycle is prolonged due to the dependence on thermal post-verification. In this paper, a multi-physics trade-off design method based on weighted heating rate combined with a surrogate model and a multi-objective evolutionary algorithm is proposed. Firstly, the rationality of introducing a weighted heating rate is proved by mathematical proof and thermal network calculation. Secondly, the two-dimensional sensitivity analysis of the key structural parameters of the motor is carried out to identify the most influential structural variables, which are then used to construct a high-precision surrogate model based on gradient boosting regression tree (GBRT). Then, in order to effectively obtain the Pareto solution set of balanced torque performance and heat dissipation performance, the non-dominated sorting genetic algorithm (NSGA-II) is used for multi-objective optimization. Finally, the multi-physical field finite-element simulation verification and a 356kW prototype experimental analysis show that the optimized design significantly improves the torque performance while effectively controlling the temperature rise and realizes the fast compromise design of the multi-physical field of the motor. The effectiveness and advancement of the proposed method to achieve coordinated improvement of high power density and high steady-state thermal margin in motor design are verified. Full article