Metaheuristic algorithms play a vital role in addressing complex and nonlinear optimization problems. This study proposes an enhanced variant of the Black-winged Kite Algorithm (BKA), termed Adaptive Memory-based Opposition and Midpoint Mutation in BKA (AMOMM-BKA), developed to improve population diversity and convergence accuracy, particularly for complex optimization problems. The proposed framework integrates four complementary strategies to balance exploration and exploitation effectively. Blended Opposition-Based Learning (BOBL) combines classical opposition with population-mean guidance to adaptively expand the search space, while historical reflective opposition exploits individual memory to guide the search toward promising regions. Random opposition introduces controlled randomness to preserve population diversity and prevent premature convergence, and midpoint-based mutation directs individuals toward the midpoint between elite and peer solutions, enhancing focused exploration and convergence precision. AMOMM-BKA was evaluated using three CEC benchmark suites (CEC2005, CEC2019, and CEC2022), and its performance was compared with four categories of existing optimization algorithms:(i) widely cited classical optimizers, such as PSO and GWO; (ii) recently developed algorithms, including GJO, SO, SCSO, and AVOA; (iii) high-performance optimizers, such as CMAES and SHADE; and (iv) improved variants of BKA, including CBKA, IBKA, and QOBLBKA. Moreover, its successful application to four mechanical and structural engineering design problems further validates the algorithm's effectiveness and practical relevance. The statistical analysis, including the Friedman rank test and Wilcoxon test, were conducted on the experimental results to verify the robustness and significance of the findings. AMOMM-BKA consistently demonstrated superior performance, achieving the top rank with an average score of 1.78 approximately 56.18% better than the second-best algorithm, SHADE (average rank: 4.56) highlighting its remarkable convergence rate, solution accuracy, and robustness across diverse optimization.

This paper addresses concurrent scheduling of machines, automated guided vehicles (AGVs), tools, and Tool Transporter (TT) in a multi-machine Flexible Manufacturing System (FMS), considering tool and job transport times to minimize makespan (MKSN). However, due to financial constraints, only one copy of each tool type is offered. These tools are placed in a Central Tool Magazine (CTM), which is shared with numerous machines. The problem is the allocation of machines, tool assignment, job-operation sequencing, and trip operations, including TT and AGVs' empty and laden trip times for MKSN minimization. This study introduces a mixed nonlinear integer programing to model the problem, and a Crow Search Algorithm (CSA) based on the clever behavior of crows is used to solve it. Results are tabulated, examined, and compared to current algorithms.

Many real-world problems feature nonlinear dynamic processes. Classical mathematical models may be adequate to describe a single dynamic process in isolation, but can be easily undermined by two natural and simple kinds of phenomenological variations: the emergence (or activation) of an additional dynamic process, and events that affect the parameters of an active process. COVID-19 data offers an important case study expressing these phenomenological variations that deeply challenge the classical SIR epidemiological model, and call for novel mathematical methods to detect and adapt to these critical variations. We address the modeling issues with a novel mathematical framework that reenvisions data as a mixture of multiple causal generating processes, each subject to possible parameter change-points. The new viewpoint extends nonlinear classical models in a manner that overcomes many of these types of phenomenological variations and enables a highly adaptive modeling closely linked to causal events. The new model space unifies a wider class of dynamics and is particularly effective at fitting multi-surge data and explaining key causal events related to surge origination. To demonstrate, we construct a mixture of logistic models termed the Adaptive Logistic Model (ALM), and then formulate appropriate nonlinear least squares optimization and regularization goals, and then apply ALMto data. To validate the approach, we return to COVID-19 forecasting (for case count), and compare ALM directly to other forecasting methods. ALM forecast accuracy is competitive with all leading forecast methods, but its greatest utility may be in how it detects changing dynamics (change-points) and retains far fewer but more interpretable parameters relating naturally to cause and intervening change. The method can be applied more generally as it adapts well to the multi-generative nature of many time series data problems. We demonstrate ALM robustness through data experiments in hydrology, economics, cybersecurity, and social media.

Abstract Unmanned Aerial Vehicles (UAVs) can be used to track growing and moving boundaries such as those of wildfires where the boundary cannot be prespecified. Towards this, we first present a Model Predictive Control (MPC) formulation for this task, which systematically incorporates vehicle dynamics, evolving boundary models, and input constraints to enable precise tracking. While effective, solving the nonlinear optimization online incurs high computational cost, limiting real-time deployment. To address this, we propose a novel receding-horizon guidance law that replaces the optimization step with a closed-form solution based on steady-turn motion primitives embedded in a receding-horizon framework. This approach generates circular-arc trajectories in lieu of the computationally expensive optimization routine, while preserving the predictive nature of the formulation and enabling real-time onboard implementation. Simulation studies validate the method across varying UAV initial conditions, prediction horizons, and fire model parameters, demonstrating that it achieves tracking performance comparable to MPC while reducing computation time by several orders of magnitude.

Ensuring safe driving while maintaining travel efficiency for autonomous vehicles (AVs) in dynamic and occluded environments is a critical challenge. This article proposes an occlusion-aware contingency safety-critical planning approach for real-time autonomous driving. Leveraging reachability analysis for risk assessment, forward reachable sets (FRSs) of phantom vehicles (PVs) are used to derive risk-aware dynamic velocity boundaries. These velocity boundaries are incorporated into a biconvex nonlinear programming (NLP) formulation that formally enforces safety using spatiotemporal barrier constraints, while simultaneously optimizing exploration and fallback trajectories within a receding horizon planning framework. To enable real-time computation and coordination between trajectories, we employ the consensus alternating direction method of multipliers (ADMMs) to decompose the biconvex NLP problem into low-dimensional convex subproblems. The effectiveness of the proposed approach is validated through simulations and real-world experiments in occluded intersections. Experimental results demonstrate enhanced safety and improved travel efficiency, enabling real-time safe trajectory generation in dynamic occluded intersections under varying obstacle conditions. The project page is available at: https://zack4417.github.io/oacp-website/.

The inverse finite element method (iFEM) reconstructs full-field displacements from strain data without prior knowledge of loads or material properties. However, unknown or time-varying boundary conditions can degrade shape-sensing accuracy. This work advances smart sensing and structural health monitoring for beam-like structures by coupling iFEM with an online identification of boundary-condition degradation. An aluminum beam instrumented with an fiber Bragg grating sensor network is tested under controlled degradations—rotational stiffness reduction and vertical support settlement—each modeled as a virtual spring with unknown stiffness. A nonlinear optimization routine estimates the spring parameters while iFEM performs real-time shape reconstruction. Results show high-accuracy displacement fields and reliable quantification of support degradation, with a maximum deviation of about 10% from ground truth for both rotational and vertical cases. The framework demonstrates practical feasibility for simultaneous shape sensing and boundary-condition assessment in operational environments.

This study incorporates the application of non-linear programming in which there is more than one objective function. In the planning of agriculture, activities play an important part in optimization techniques of the objective values for the composition of mix-type crop production in different land allocations in a particular area. Designing the best production of crops by implementations of land allocation was the main goal of this study. In this article, we considered a multi-objective crop planning model in an area with Shannon’s measure of entropy objective function where coefficient parameters of objective functions are taken as trapezoidal fuzzy numbers. Then the said problem is formulated into fuzzy multi objective model and uses a fuzzy decision-making method to solve this problem. Finally, a numerical example has been provided to support the given crop production planning problem.

A well-coordinated post-disaster relief supply chain is essential for delivering timely assistance to affected regions under uncertainty. This study addresses network planning in the post-disaster phase by explicitly considering supply capacity and demand uncertainty within a robust optimisation framework. We propose a mixed-integer nonlinear programming model that integrates procurement, facility location, processing, and distribution decisions, while accounting for social costs such as deprivation and logistics. To efficiently solve this complex model, we develop a two-phase heuristic that combines nonlinear programming relaxation with a structure-preserving approach. Computational experiments evaluate the algorithm’s performance across different network sizes, service levels, demand variability, and social cost scenarios. A case study based on the 2008 Sichuan earthquake demonstrates real-world applicability. Benchmark comparisons with Genetic Algorithm and Particle Swarm Optimisation show that our approach provides superior solution quality and computational efficiency, especially for large-scale, uncertain supply chains. These results highlight the potential of robust optimisation and the proposed heuristic to improve disaster response planning.

The sustained growth of electricity demand and the global transition toward low-carbon energy systems have intensified the need for efficient, flexible, and reliable operation of electrical distribution networks. In this context, the coordinated integration of distributed renewable energy resources and demand-side flexibility has emerged as a key strategy to improve technical performance and economic efficiency. This work proposes an integrated optimization framework for active power supply in a radial, distribution-like network through the optimal siting and sizing of photovoltaic (PV) units and wind turbines (WTs), combined with a real-time pricing (RTP)-based demand-side response (DSR) program. The problem is formulated using the branch-flow (DistFlow) model, which explicitly represents voltage drops, branch power flows, and thermal limits in radial feeders. A multiobjective function is defined to jointly minimize annual operating costs, active power losses, and voltage deviations, subject to network operating constraints and inverter capability limits. Uncertainty associated with solar irradiance, wind speed, ambient temperature, load demand, and electricity prices is captured through probabilistic modeling and scenario-based analysis. To solve the resulting nonlinear and constrained optimization problem, an Improved Whale Optimization Algorithm (I-WaOA) is employed. The proposed algorithm enhances the classical Whale Optimization Algorithm by incorporating diversification and feasibility-oriented mechanisms, including Cauchy mutation, Fitness–Distance Balance (FDB), quasi-oppositional-based learning (QOBL), and quadratic penalty functions for constraint handling. These features promote robust convergence toward admissible solutions under stochastic operating conditions. The methodology is validated on a large-scale radialized network derived from the IEEE 118-bus benchmark, enabling a DistFlow-consistent assessment of technical and economic performance under realistic operating scenarios. The results demonstrate that the coordinated integration of PV, WT, and RTP-driven demand response leads to a reduction in feeder losses, an improvement in voltage profiles, and an enhanced voltage stability margin, as quantified through standard voltage deviation and fast voltage stability indices. Overall, the proposed framework provides a practical and scalable tool for supporting planning and operational decisions in modern power distribution networks with high renewable penetration and demand flexibility.

The efficient management of reverse supply chains, particularly the collection and remanufacturing of defective products, plays a critical role in reducing production costs and determining the final pricing of remanufactured products. While existing research extensively explores warranty policies and maintenance services to enhance customer satisfaction and profitability, the integration of vehicle routing for product collection and sustainability advertising strategies remains underexplored. Addressing this gap, this study introduces a comprehensive two-stage reverse supply chain model that captures the interactions between manufacturers (MFRs) and remanufacturers (RMFRs) through a Stackelberg game framework. Methods: The proposed model incorporates interactive production constraints, vehicle routing problem (VRP) for optimizing collection logistics, and sustainability advertising to influence consumer behavior towards remanufactured products. Utilizing mixed nonlinear programming (MINLP) and nonlinear programming (NLP) techniques, the model simultaneously optimizes pricing strategies, collection efforts, and advertising investments for both MFRs and RMFRs. Numerical analyses are conducted to solve the optimization problems, accompanied by sensitivity analyses to evaluate the impact of key parameters such as production costs, defect rates, and routing constraints. The numerical results demonstrate that increases in production costs for MFRs lead to higher selling prices, thereby reducing their profit margins and negatively impacting RMFR profitability due to decreased demand for remanufactured products. Sensitivity analysis reveals that higher defect rates (α ≥ 0.8) significantly diminish overall supply chain profitability by lowering customer acceptance of RMPs. Additionally, expanding the allowable vehicle routing distance L effectively reduces collection costs, enhancing RMFR profits and enabling greater investment in sustainability advertising. The study shows that the integration of VRP and advertising strategies proves crucial in balancing cost efficiencies and market competitiveness, ultimately fostering a more sustainable and profitable reverse supply chain.

Nonlinear dynamic analysis and optimization of sandwich plate and shell panels with auxetic core and functionally graded Zr-MgO/Al facesheets

A water supply pipe leakage localization method based on pressure-flow fused signal analysis and adaptive dynamic programming.

Non-linear restoration and optimization for camera calibration in low-light conditions

Neural network-driven predictive control and fractional-order nonlinear filter optimization for helicopter active vibration control

Great Deluge-based metaheuristic incorporating integer nonlinear programming for modeling and solving dynamic capability-based machine layout problem

Optimizing the deployment of fast-charging stations for electric vehicles: A mixed-integer nonlinear programming approach with particle swarm optimization

Transmission expansion planning for hybrid AC/DC grids using a mixed-integer non-linear programming approach

Abstract Integrated sustainable supply chain scheduling (ISSCS) is essential for minimizing distribution costs, reducing environmental impacts, and improving customer service. This study develops a bi-objective mixed-integer nonlinear programming (MINLP) model that simultaneously optimizes single-machine production scheduling, due-date assignment, batch delivery decisions, and heterogeneous-fleet vehicle routing with customer-specific time windows. The objectives are to reduce freight transportation and emission costs while minimizing delivery tardiness. Numerical experiments based on real operational data validate the model using the $$\varepsilon $$ -constraint method, which produces Pareto-optimal solutions with relative gaps below 0.8%. For large-scale instances, two multi-objective metaheuristics, Non-Dominated Sorting Genetic Algorithm II (NSGA-II) and Multi-objective Particle Swarm Optimization (MOPSO), are designed, tuned using Taguchi analysis, and evaluated using generational distance, mean ideal distance, spacing, diversity, and computational time. Experimental results show that NSGA-II delivers superior convergence and solution quality: within 50 iterations, it reduces average distribution cost from 126.2 to 69.3 million LCU (a 45% reduction) and decreases tardiness from 23,950 to 858 h (a 96% reduction). MOPSO achieves 32% cost reduction (108.4–68.1 million LCU) and 96% tardiness reduction (29,595–1047 h), but with less diversity and slower convergence. Pareto-front and convergence analyses confirm that NSGA-II consistently provides better-distributed and more stable non-dominated solutions. Overall, the proposed integrated model effectively reduces transportation, emission, and customer-dissatisfaction costs; the batch-delivery formulation ensures timely service across multiple time windows; and the metaheuristic frameworks especially NSGA-II demonstrate strong capability for solving large-scale sustainable supply-chain scheduling and environmentally friendly freight transportation problems.

This paper presents a robust, decoupled approach to camera distortion correction using a rational function model (RFM), designed to address challenges in accuracy and flexibility within precision-critical applications. Camera distortion is a pervasive issue in fields such as medical imaging, robotics, and 3D reconstruction, where high fidelity and geometric accuracy are crucial. Traditional distortion correction methods rely on radial-symmetry-based models, which have limited precision under tangential distortion and require nonlinear optimization. In contrast, general models do not rely on radial symmetry geometry and are theoretically generalizable to various sources of distortion. There exists a gap between the theoretical precision advantage of the Rational Function Model (RFM) and its practical applicability in real-world scenarios. This gap arises from uncertainties regarding the model's robustness to noise, the impact of sparse sample distributions, and its generalizability out of the training sample range. In this paper, we provide a mathematical interpretation of how RFM is suitable for the distortion correction problem through sensitivity analysis. The precision and robustness of RFM are evaluated through synthetic and real-world experiments, considering distortion level, noise level, and sample distribution. Moreover, a practical and accurate decoupled distortion correction method is proposed using just a single captured image of a chessboard pattern. The correction performance is compared with the current state-of-the-art using camera calibration, and experimental results indicate that more precise distortion correction can enhance the overall accuracy of camera calibration. In summary, this decoupled RFM-based distortion correction approach provides a flexible, high-precision solution for applications requiring minimal calibration steps and reliable geometric accuracy, establishing a foundation for distortion-free imaging and simplified camera models in precision-driven computer vision tasks.

Picometer-Level Vortex Beam Interferometry via Nonlinear Optimization Self-Calibration