Penalty Methods Research Articles (Page 1)

A stabilized weighted interior penalty method for thermal convection model in heterogeneous porous media

Handling uncertainty in portfolio optimization: A neutrosophic logic adaptive neural network solver for quadratic programming.

Cylinder-plate combined structures (CPCS) are widely used in aerospace, marine engineering, and offshore platform systems. During service, they are frequently subjected to stochastic excitations induced by turbulent boundary layers, acoustic loads, hydrodynamic disturbances, and broadband operational vibrations. Excessive random vibration responses may significantly reduce structural reliability, accelerate fatigue damage, and compromise operational safety. To address these engineering challenges, a unified stochastic dynamic analysis and vibration suppression framework is established for functionally graded graphene platelet-reinforced composites (FG-GPLRC) CPCS equipped with distributed dynamic vibration absorbers (DVAs). Adopting the First-order Shear Deformation Theory (FSDT), a comprehensive energy functional for the CPCS is established, in which the penalty method is implemented to impose boundary conditions and ensure interface continuity. Subsequently, the Pseudo-excitation Method (PEM) is utilized to convert the stochastic vibration analysis into an equivalent deterministic harmonic problem, and the governing equations are spatially discretized by combining the spectral geometric method (SGM) with the Ritz variational procedure, enabling efficient evaluation of power spectral density (PSD) and root-mean-square (RMS) responses. The reliability of the proposed model is verified through a series of numerical validation comparisons. On this basis, comprehensive parametric investigations are conducted to assess how material properties, structural geometries, and critical DVA parameters influence system behavior. The results demonstrate that the incorporation of distributed DVAs can achieve superior vibration suppression performance. This study provides an efficient and reliable theoretical framework for stochastic vibration analysis and damping design of advanced composite plate-shell coupled structures operating in complex random environments, offering important theoretical support for dynamic optimization design in aerospace and marine engineering applications.

During the excavation process of the foundation pit, soil parameters evolve dynamically. In order to improve the accuracy of soil parameter selection in foundation pit engineering and achieve accurate deformation prediction, this paper proposes a displacement inverse analysis method that combines the enhanced starfish optimization algorithm (ESFOA) and the hybrid kernel least squares support vector machine (LSSVM). The ESFOA improves the global search capability and convergence accuracy of the starfish optimization algorithm (SFOA) by optimizing the initial population and introducing a hunting mechanism. On this basis, the ESFOA was used to optimize the RBF kernel function width (σ), polynomial kernel coefficient (q), regularization penalty coefficient (c), and kernel function mixing weight (λ) of the hybrid kernel LSSVM model. Samples were obtained through finite element simulation and orthogonal experiments, and the optimized ESFOA-LSSVM model was used to establish the nonlinear mapping relationship between the horizontal displacement of the foundation pit excavation enclosure and the soil parameters. The horizontal displacement monitoring data of the foundation pit retaining structure is used to invert the soil parameters and predict the deformation of the retaining structure under subsequent conditions. The results show that (1) compared with other algorithms, the ESFOA has good global search capabilities and convergence accuracy; (2) the ESFOA-LSSVM model is tested through test samples, and the model has good accuracy and feasibility; (3) the parameters obtained by the inversion can effectively improve the prediction accuracy of foundation pit deformation, and the prediction results are closer to the actual monitoring values.

Methane (CH4) emission quantification in oilfield environments remains challenging due to spatially dispersed sources and complex near-surface atmospheric conditions, creating uncertainties in conventional monitoring approaches and limiting emission mitigation efforts. To address this issue, a UAV–AirCore system was deployed over the Shengli Oilfield in Dongying, China, to obtain high-resolution three-dimensional CH4 concentration observations using a two-stage flight strategy that combined horizontal plume screening with vertical spiral profiling to constrain plume geometry. Based on these observations, an integrated Emission-Partition inversion framework was developed by coupling a multi-source Gaussian dispersion model with a hybrid Particle Swarm Optimization–Interior Point Penalty Function (PSO–IPPF) algorithm, enabling the joint retrieval of emission rates and effective release heights. The proposed framework successfully reconstructed observed concentration fields with a coefficient of determination (R 2 ) of approximately 0.85. For two investigated areas, retrieved emission intensities were 3.22 ± 0.12 g/s and 3.68 ± 0.04 g/s, corresponding to relative uncertainties of 3.7% and 1.1%, respectively, while effective emission heights exhibited uncertainties of approximately 9%. Comparisons with mass balance, nonlinear least-squares fitting (NLSF), OTM 33A, and inventory-based estimates demonstrated consistent emission magnitudes, with the proposed method showing lower dispersion and improved robustness under complex atmospheric conditions. These results indicate that integrating three-dimensional UAV observations with hybrid inversion optimization enhances parameter identifiability and provides a stable and scalable solution for refined methane emission monitoring in industrial regions.

Abstract This paper investigates a novel meshfree approach for transient heat transfer analysis of isotropic material using the Interpolating Moving Least Squares (IMLS). Building upon the strengths of meshless methods, particularly the Element-Free Galerkin (EFG) approach, the proposed method leverages the IMLS technique to construct shape functions that satisfy the Kronecker delta property, thereby allowing essential boundary conditions to be imposed directly without additional transformation or penalty methods. This significantly simplifies the numerical implementation while maintaining the flexibility and adaptability of meshfree formulations. The IMLS-based scheme is integrated within the Galerkin weak form framework to develop a robust and accurate numerical model capable of simulating transient heat transfer behavior. Unlike traditional finite element methods (FEM), which often require complex meshing procedures and suffer from accuracy issues in problems with evolving geometries of sharp gradients, the proposed meshfree method offers enhanced computational precision and geometric flexibility. The implementation is carried out in MATLAB. First, to evaluate the performance and reliability of the method, a convergence study is conducted using various nodal distributions. This analysis identified suitable node densities and support domain sizes that yield optimal accuracy and computational efficiency. The present results are then validated and verified through comparison with benchmark problems and previously published results. The numerical results demonstrate excellent agreement with the reference results, confirming the precision of the proposed IMLS-based approach. Following the validation phase, a detailed parameter sensitivity analysis was performed to investigate the influence of parameters on the temperature distribution of the structure. Finally, the method is applied to a transient heat transfer problem in a complex-shaped isotropic domain to assess its capability to handle real-world engineering problems. These findings establish a valuable benchmark for the ongoing advancement of meshfree methods and provide a solid foundation for future investigations into the applicability of methods to complex and practical engineering problems.

While variable selection has received extensive attention in the literature, its exploration in the presence of response measurement error remains underexplored. In this paper, we investigate this important problem within the context of binary classification with error-prone responses. We present valid variable selection procedures to address the complexities of response errors. Leveraging validation data, we introduce both parametric and semiparametric methodologies to accommodate the mismeasurement effects. By rigorously establishing theoretical results, we offer insights and justifications of the validity of the proposed methods. By properly choosing the penalty function and regularization parameter, we demonstrate that the resulting estimators possess the oracle property. To assess the finite sample properties of the proposed methods, we conduct numerical studies that confirm the effectiveness of our proposed methods.

This article examines the problem of optimizing security policies in software-defined networks (SDN). The authors propose solving this problem using NSGA-II, an efficient algorithm for evolutionary optimization of multiple objectives. The proposed approach aims to achieve a balance between the need to strictly enforce network security and the availability of limited computing resources. Particular attention is paid to factors such as data transmission latency and TCAM table size, which significantly affect the effectiveness of traffic filtering. Based on the model developed in the article, which includes threat probability assessments, objective function normalization methods, and the use of penalty coefficients for rule conflicts, optimization was performed across three key parameters: attack risk, network latency, and TCAM load. The simulation covered three network operation scenarios-normal, mixed, and attack-using Mininet and Ryu packets. A comparison of the proposed method with differential evolution (DE) and a greedy algorithm (Greedy) showed that NSGA-II achieves optimal solution distribution along the Pareto frontier, converges faster, and maintains filtering accuracy. The paper also presents visualization of generational transitions, tradeoff graphs, and load profiles. The conclusion discusses the potential for integrating the proposed model with ONOS and OpenDaylight controllers, and discusses the feasibility of using hybrid solutions based on Deep Reinforcement Learning, Federated Learning, and Explainable AI.

This article examines proportionate flow-shop scheduling with general earliness/tardiness costs under two due-date assignment models: the common and slack models. The objective is to determine the optimal job sequence and due dates to minimize a total penalty function that includes earliness and tardiness penalties, the number of early and delayed jobs, and the due-date assignment cost. Several optimal structural properties are derived, and two polynomial-time dynamic programming (DP) algorithms are proposed to solve the problems, with a time complexity of O(u 4 ), and u is the number of jobs.

A highly accurate, single-pass, unbiased frictional contact algorithm for higher-order elements based on the concept of midplane is presented. Higher-order elements offer a lucrative choice for contact problems as they can better represent the curvature of original geometries compared to the first-order elements. Compressive and frictional contact constraints are applied over the contact pairs of sub-segments obtained by the subdivision of higher-order segments. The normal traction depends upon the penalisation of true interpenetration, and frictional traction depends upon relative sliding between sub-segments over their shared patches. The midplane constructed by linearised subfacets can be corrected to account for the local curvature of interacting physical surfaces. Demonstrated through multiple tests, the use of higher-order elements surpasses the accuracy of first-order elements for curved geometries. Its versatility extends from static to dynamic conditions for flat and curved interfaces, including frictional contact. The presented examples include contact patch test, Hertzian contact, elastic collision, rotation of concentric surfaces, frictional sliding, self-contact and inelastic collision problems. Here, the contact patch test matches the accuracy of finite elements, and Hertzian contact shows a smoother solution compared to first-order meshes. The elastic collision problem highlights the utility of the algorithm in accurate prediction of configuration changes in multibody systems. The frictional sliding demonstrates the ability to represent the expected nonlinear distribution of nodal forces for the higher-order elements. The large deformation problems, e.g. self-contact and inelastic collision, specifically benefit from the accuracy in surface representation using higher-order discretisation and continuous contact constraint imposition on such surfaces during deformation.

Mathematical distribution Goose algorithm with oscillating dynamic penalty functions for combined economic emission dispatch problem

This paper defines a strong convertible nonconvex (SCN) function for solving the unconstrained optimization problems with the nonconvex or nonsmooth (nondifferentiable) function. First, the concept of SCN function is defined, where the SCN functions are nonconvex or nonsmooth. Second, the operational properties of SCN functions are proved, including addition, multiplication, and compound operations. Third, an SCN optimization with the SCN function and its penalty function is defined. The optimization condition, exactness, and stability of the penalty function for SCN optimization are proved. This paper provides a way for solving unconstrained nonconvex or nonsmooth (nondifferentiable) optimization problems to avoid using subdifferentiation or smoothing techniques.

While reliability-based design optimization (RBDO) significantly improves engineering safety, computational expenses and accuracy concerns restrict its use in complex, high-dimensional, nonlinear, and black-box scenarios. To address this challenge, a Kriging-AMV-MCS reliability optimization method (KAMRO) is proposed in this paper. The algorithm integrates the Kriging surrogate model, an improved advanced mean value (AMV) method, and a Monte-Carlo simulation (MCS) validation mechanism, aiming to achieve efficient and robust design optimization. First, through an adaptive sampling strategy based on the expected feasibility function and space filling criteria, actively constrained regions are intelligently identified and sample distribution is optimized. Second, a two-stage optimization framework is adopted. In the first stage, the penalty function is used to quickly approximate the feasible domain, and in the second stage, explicit constraints are combined for precise optimization. Finally, an MCS-guided post-optimization process is proposed to further optimize and improve the design scheme when the reliability is insufficient. Through validation with engineering cases, including a two-dimensional analytical example, a seven-dimensional gear reducer structural optimization example, and a three-dimensional pressure control head structure design, this RBDO framework significantly reduces computational costs while ensuring design reliability, offering both optimization accuracy and engineering practicality.

This paper introduces a two-stage optimization framework for base station placement in heterogeneous networks, addressing the dual challenge of maximizing network quality while achieving cost-effective deployment. The initial stage leverages Binary Integer Programming (BIP) on a discretized hexagonal grid to find the least expensive combination of macro and micro stations that guarantees full coverage. This BIP formulation ensures cost optimality for the defined discrete problem, surpassing conventional heuristic approaches. The second stage employs Differential Evolution (DE), a meta-heuristic, to refine these positions using continuous coordinates, maximizing the network-wide Signal-to-Interference-plus-Noise Ratio (SINR) while coverage is enforced via a penalty-based objective function. This decomposition facilitates a more scalable approach, yielding high-quality solutions where the first stage guarantees full coverage, while the second stage employs an adjustable penalty function to allow for maintaining this coverage during refinement. Although the general problem is NP-hard, the two-stage approach effectively tackles complexity, leading to superior solutions compared to competing methods, primarily by combining the guarantee of cost optimality in the first phase with the continuous refinement of network quality in the second.

Hose-drawn traveler (HDT) is a significant type of sprinkler irrigation equipment in China. In arid and remote areas, where grid power is unreliable or unavailable, the water pumping system of the HDT typically depends on a complementary power supply (CPS) system integrating batteries, photovoltaic (PV) panels, and gasoline generators. However, the configuration of the CPS system is often determined empirically, which can lead to increased costs and compromised operational reliability. This paper aims to optimize the configuration of the CPS system based on the power demand of the water pumping system in HDT. We propose an optimization model for component sizing that considers both the annual costs and reliability of the power supply system. An improved particle swarm optimization (PSO) algorithm, incorporating a penalty function, is employed to determine the optimal configuration of the CPS system. The proposed optimization approach is then applied to an HDT operating in three typical regions in China: Golmud, Beijing, and Harbin. Finally, a comparative analysis of the configurations and annual cost of two CPS systems, PV-battery (PVB) and PV-battery-gasoline (PVBG), is conducted. Results show that for a given region, season, and power of water pump, the PVBG system needs a smaller PV panel area and lower battery capacity than the PVB system. For a fixed region and season, increasing power of water pump leads to a more significant rise in the annual cost of the PVB system than in that of the PVBG system. At high pump power levels, the PVBG system is more cost-effective, resulting in a lower annual cost than the PVB system. In Golmud, under identical seasonal and pump power conditions, both systems have lower annual cost than in Beijing and Harbin, suggesting that Golmud is a more suitable region for deploying CPS systems. The proposed method provides a reference for designing power supply systems of HDT irrigation.

In constrained nonlinear optimization, we aim to achieve two goals: one is to minimize the objective function, and the other is to satisfy the constraints. A common way to balance these competing targets is to use penalty functions. Suppose that an algorithm generates a descent direction and produces a step that decreases the objective function value but increases the constraint violation—a phenomenon known as the Maratos effect. This leads to the rejection of the full step by the non-smooth penalty function; therefore, superlinear convergence is not preserved. This work leverages a piecewise convexity model to solve the optimal PMU placement. A quadratic objective function is minimized subject to a non-convex equality constraint within box constraints [0, 1] × [0, 1] ⊂ R2. The initial non-convex region is reconsidered as a union of piecewise line segments. This decomposition enables algorithms to converge to a local optimum while preserving superlinear convergence near the solution. An analytical solution is presented using the Karush–Kuhn–Tucker conditions. First-and-second-order optimality conditions are applied to find the local minimum. We show how the Maratos effect is avoided by adopting the piecewise convexity without needing a non-smooth penalty function, second-order corrections or employing the watchdog methods. Simulations demonstrate that the algorithms partially search the space along the line segments—avoiding zig-zag trajectories—and reach (0, 1) or (1, 0), where both feasibility and optimality are satisfied at once.

Abstract We construct an <i>N</i>-person snowdrift game with dynamic punishment and delayed reciprocity. The resulting dynamic replicator equation are established and the stability of its equilibriums and the critical value for the Hopf bifurcation are obtained. Additionally, multiple performed numerical simulations are in good agreement with the theoretical ones. Compared with the classical N -person snowdrift game, our model is conducive to the enhancement of cooperation as the benefit-cost ratio, penalty coefficient and group size increase. Precisely, the proportion of cooperators in our model is higher than that in the classical game. Moreover, the critical value for the Hopf bifurcation under payoff delay is also greater, this indicates that our model has higher tolerance for time delays. These results provide new insights for the classical N -person snowdrift games.

Multiple-site-type (MST) catalysts, such as heterogeneous Ziegler–Natta, Phillips, and some supported metallocenes, make polyolefins with broad molecular weight distributions (MWDs) that cannot be described with a single fundamental equation. Since polyolefin properties depend on their MWDs, accurate mathematical models for these distributions are essential in polymer reaction engineering. A popular modeling approach is to deconvolute their MWDs into several Flory most probable distributions (MPD). All previous deconvolution algorithms start by fitting an experimental MWD with a few Flory MPDs and then increase their number until the deviation between measured and predicted MWDs stops decreasing (forward deconvolution). This article reverses this approach, initially fitting experimental MWDs with multiple Flory MPDs and then decreasing their number with the assistance of a penalty function based on Shannon entropy (reverse deconvolution). The reverse method is easier to implement than the traditional forward methods and simplifies the automation of MWD deconvolution methods.

ABSTRACT Multi‐point constraints are essential in modeling various engineering problems, for example, in the context of joints undergoing large rotations or coupling of different element types in finite element analysis. The master–slave elimination is an efficient method for the numerical treatment of such constraints because it reduces the dimension of the resulting linear system. However, the method requires the computation of the reduced row echelon form of a submatrix of the constraint Jacobian. For nonlinear constraints, this computation has to be performed at every iteration step of the Newton–Raphson scheme. Although this process is computationally expensive for large systems, the method exhibits a reduced computational complexity compared to multiplier and the penalty methods, nevertheless. Therefore, a method for drastically increasing the computational efficiency of this already efficient method is presented. It is based on the exploitation of the specific structure of the constraint Jacobian as it appears in typical engineering applications. The analysis of this structure is based on the identification of constraint clusters, which can be performed in a preprocessing step without significant computational effort. All matrix operations required for this calculation are performed using the compressed sparse row (CSR) technique for storing sparse matrices, which is also particularly advantageous because all the matrices required for this are already stored in this format. Finally, the master–slave elimination is extended by the exploitation of the structure of the constraint Jacobian, which reduces the computational costs. The speed‐up of the improved master–slave elimination over the previous master–slave elimination is demonstrated using a numerical example.

In today’s online world, cyberbullying is an escalating problem that can trigger deep emotional pain and isolation from others. There is an increasing necessity to regulate content shared on online platforms. Cyberbullying material can spread quickly across online platforms and may remain visible for a long time, sometimes without ever being removed. Such persistent exposure to harmful content can take a serious toll on the mental, emotional, and psychological health of young people. In extreme situations, ongoing harassment in digital spaces can contribute to thoughts of self-harm or suicide. The proposed system utilizes Long Short-Term Memory (LSTM) networks to assess user-generated text and compute a bullying likelihood for every sentence. This system monitors user activity in real time and decreases a reputation score whenever harmful or bullying content is identified. Once the score falls below a set limit, the user is automatically prevented from continuing interactions on the platform. By merging deep learning with a reputation- based penalty method, the design works to curb cyberbullying while ensuring moderation remains both fair and proactive. The approach is adaptable, efficient, and capable of supporting healthier online spaces.