Nonlinear Programming Research Articles

Electromagnetic design and analysis of a bell-shaped superconducting magnet for head fMRI using a novel hybrid optimization method

Abstract In task-state functional magnetic resonance imaging (fMRI) scans, it is often necessary for subjects to perform certain task actions, which is difficult to achieve in traditional whole-body MRI systems. In this study, a bell-shaped head magnetic resonance superconducting magnet was designed using a novel hybrid optimization method that combines linear programming (LP), genetic algorithm (GA), and nonlinear programming (NLP). This magnet design offers the following advantages: (1) The small and compact volume of the magnet structure allows for vertical placement of the system, enabling subjects to be in a sitting position during the scan. (2) The off-center DSV (diameter of spherical volume) region expands the subject's field of view. (3) Only the subject's head is positioned inside the scanning system, freeing the subject's torso to cooperate in performing various tasks. This paper provides a detailed description of the entire design process, conducts a comprehensive analysis of the electromagnetic performance and material mechanical properties of the designed magnet, and designs a passive quench protection system for the subsequent manufacturing of the magnet, with simulations and discussions on the magnet's quenching process under the protection of this system.

Nonlinear dynamic analysis and optimization of planar flexible multi-link mechanism with clearance considering the thermal deformation effect of kinematic pair

Nonlinear dynamic analysis and optimization of planar flexible multi-link mechanism with clearance considering the thermal deformation effect of kinematic pair

Drawdown minimization in asset portfolio selection: MINLP models and efficient cross‐entropy algorithm

AbstractPortfolio management is an important research topic in finance and optimization. Drawdown as one of the measures in evaluating portfolios indicates the relative difference between the portfolio value in the current moment and its maximum value during a given time interval in the recent past. In this paper, first, the importance of this measure is discussed and then two mixed‐integer nonlinear programming (MINLP) models with the objectives of minimizing the expected drawdown and the maximum drawdown under real‐world constraints are presented. Due to the NP‐hardness of this problem, by utilizing the problem structure, an efficient cross‐entropy‐based algorithm is presented to solve it. An effective mechanism is suggested to calibrate the algorithm parameters. Computational results confirm the performance of the proposed algorithm from both solution quality and running time in comparison with MINLP solvers.

Particle swarm optimization with local search for height-map surface reconstruction from point clouds in reverse engineering

AbstractSurface reconstruction is a classical process in industrial engineering and manufacturing, particularly in reverse engineering, where the goal is to obtain a digital model from a physical object. For that purpose, the real object is typically scanned or digitized and the resulting point cloud is then fitted to mathematical surfaces through numerical optimization. The choice of the approximating functions is crucial for the accuracy of the process. Real-world objects such as manufactured workpieces often require complex nonlinear approximating functions, which are not well suited for standard numerical methods. In a previous paper presented at the ISMSI 2023 conference, we addressed this issue by using manually selected approximation functions via optimization through the cuckoo search algorithm with Lévy flights. Building upon that work, this paper presents an enhanced and extended method for surface reconstruction by using height-map surfaces obtained through a combination of exponential, polynomial and logarithmic functions. A feasible approach for this goal is to consider continuous bivariate distribution functions, which ensures consistent models along with good mathematical properties for the output shapes, such as smoothness and integrability. However, this approach leads to a difficult multivariate, constrained, multimodal continuous nonlinear optimization problem. To tackle this issue, we apply particle swarm optimization, a popular swarm intelligence technique for continuous optimization. The method is hybridized with a local search procedure for further improvement of the solutions and applied to a benchmark of 15 illustrative examples of point clouds fitted to different surface models. The performance of the method is analyzed through several computational experiments. The numerical and graphical results show that the method is able to recover the shape of the point clouds accurately and automatically. Furthermore, our approach outperforms other alternative methods significantly in terms of the numerical errors. We conclude that our method can be successfully applied to the reconstruction of manufactured workpieces in real industrial settings.

Integrated LI-NSGA-II Approach for Solving the Non-linear Multi-objective Optimization Problem

Real-world engineering projects frequently involve complex, non-linear multi-objective optimization challenges. Traditional methods like PERT/CPM and basic heuristics often fail to provide optimal solutions in such scenarios. Multi-objective evolutionary algorithms, such as genetic algorithms and non-dominated sorting genetic algorithms, are more effective for identifying true Pareto solutions. Among these, the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) is a well-known algorithm for solving multi-objective optimization problems. This study presents an integrated approach, called LI-NSGA-II, which combines Lagrange's Interpolation (LI) with NSGA-II to solve non-linear multi-objective optimization problems in real-world projects. In this LI-NSGA-II approach, LI is used to handle the non-linearity of competing objectives, whereas NSGA-II optimizes these objectives to find optimal solutions. The outcomes achieved through the LI-NSGA-II approach are ideal for real-time monitoring and control of non-linear multi-objective optimization problems.

Issues on a 2–Dimensional Quadratic Sub–Problem and Its Applications in Nonlinear Programming: Trust–Region Methods (TRMs) and Linesearch Based Methods (LBMs)

This paper analyses the solution of a specific quadratic sub-problem, along with its possible applications, within both constrained and unconstrained Nonlinear Programming frameworks. We give evidence that this sub–problem may appear in a number of Linesearch Based Methods (LBM) schemes, and to some extent it reveals a close analogy with the solution of trust–region sub–problems. Namely, we refer to a two-dimensional structured quadratic problem, where five linear inequality constraints are included. Finally, we detail how to compute an exact global solution of our two-dimensional quadratic sub-problem, exploiting first order Karush-Khun-Tucker (KKT) conditions.

A sound insulation cooling fin for broadband noise control and ventilation

Abstract The noise generated by the ultrathin centrifugal fan in a laptop can significantly impact user comfort. While optimizing the fan itself for noise control is important, addressing noise propagation is also crucial. Due to space limitations inside a laptop, adding an extra component for noise control is nearly impossible. Therefore, modifying the cooling fin outside of the fan outlet for sound insulation can be an effective solution. A sound insulation cooling fin is proposed to provide broad noise insulation while maintaining proper ventilation. Through the introduction of a coupled area change passage, noise at specific frequencies at the passage outlet can be managed to be insulated due to the destructive interference. The effectiveness of the unit's sound insulation is verified through an impedance tube measurement. Moreover, combining different units can create a multi-peak sound insulation effect which is suitable for various noise conditions. To meet the demand of real situations, a reversal design flow combining neural network and nonlinear constrained optimization algorithm is developed. As a result, a sound cooling fin combing 2 sound insulation units featuring 4013 Hz and 6000 Hz is fabricated and the actual insulation performance is measured in an anechoic chamber. The sound transmission loss at the designed frequency range reaches 5 dB, aligning well with the simulation results. The sound insulation cooling fin has the potential to be widely used for noise control in small-scale electronic devices.

Modeling a Green and Reliable Intermodal Routing Problem for Food Grain Transportation Under Carbon Tax and Trading Regulations and Multi-Source Uncertainty

This study addresses an intermodal routing problem encountered by an intermodal transportation operator fulfilling the food grain transportation order of an agri-food company. To enhance the environmental sustainability of food logistics, carbon tax and trading regulations have been employed to reduce the carbon emissions associated with transportation. Multi-source uncertainties, including the company’s demand for food grains and various parameters related to the intermodal transportation activities, are modeled via trapezoidal fuzzy numbers to optimize the comprehensive reliability of the solution. This work incorporates wastage reduction by lowering the wastage costs and formulating a wastage threshold constraint in intermodal routing. Accordingly, a fuzzy mixed-integer nonlinear programming model for a green and reliable intermodal routing problem for food grain transportation is proposed. To overcome the model’s insolvability and the difficulty in finding the global optimum solution to a nonlinear optimization model, a two-stage solution method is developed, employing chance-constrained programming and linearization technique to reformulate the initial model. A numerical case study is given to verify the feasibility of the proposed methods. Sensitivity analysis reveals the influence of confidence levels and wastage threshold, providing insights for the agri-food company to balance economics, reliability, and wastage reduction in food grain transportation. The numerical case study also analyzes the feasibility of carbon tax and trading regulations in reducing carbon emissions, concluding that carbon tax regulations consistently achieve greater reductions and are universally feasible. In contrast, the feasibility of carbon trading regulations depends on confidence levels and wastage threshold. The findings of this work could provide strong quantitative support for intermodal transportation operators and agri-food companies seeking to implement sustainable food grain transportation.

A speed optimization model for connected and autonomous vehicles at expressway tunnel entrance under mixed traffic environment.

Rear-end collisions frequently occurred in the entrance zone of expressway tunnel, necessitating enhanced traffic safety through speed guidance. However, existing speed optimization models mainly focus on urban signal-controlled intersections or expressway weaving zones, neglecting research on speed optimization in expressway tunnel entrances. This paper addresses this gap by proposing a framework for a speed guidance model in the entrance zone of expressway tunnels under a mixed traffic environment, comprising both Connected and Autonomous Vehicles (CAVs) and Human-driven Vehicles (HVs). Firstly, a CAV speed optimization model is established based on a shooting heuristic algorithm. The model targets the minimization of the weighted sum of the speed difference between adjacent vehicles and the time taken to reach the tunnel entrance. The model's constraints incorporate safe following distances, speed, and acceleration limits. For HVs, speed trajectories are determined using the Intelligent Driver Model (IDM). The CAV speed optimization model, represented as a mixed-integer nonlinear optimization problem, is solved using A Mathematical Programming Language (AMPL) and the BONMIN solver. Safety performance is evaluated using Time-to-Collision (TTC) and speed standard deviation (SD) metrics. Case study results show a significant decrease in SD as the CAV penetration rate increases, with a 58.38% reduction from 0% to 100%. The impact on SD and mean TTC is most pronounced when the CAV penetration rate is between 0% and 40%, compared to rates above 40%. The minimum TTC values at different CAV penetration rates consistently exceed the safety threshold TTC*, confirming the effectiveness of the proposed control method in enhanced safety. Sensitivity analysis further supports these findings.

Fatigue-Induced Failure of Polysilicon MEMS: Nonlinear Reduced-Order Modeling and Geometry Optimization of On-Chip Testing Device

In the case of repeated loadings, the reliability of inertial microelectromechanical systems (MEMS) can be linked to failure processes occurring within the movable structure or at the anchors. In this work, possible debonding mechanisms taking place at the interface between the polycrystalline silicon film constituting the movable part of the device and the silicon dioxide at the anchor points are considered. In dealing with cyclic loadings possibly inducing fatigue failure, a strategy is proposed to optimize the geometry of an on-chip testing device designed to characterize the strength of the aforementioned interface. Dynamic analyses are carried out to assess the deformation mode of the device and maximize the stress field leading to interface debonding. To cope with the computational costs of numerical simulations within the structural optimization framework, a reduced-order modeling procedure for nonlinear systems is discussed, based on the direct parametrization of invariant manifolds (DPIM). The results are reported in terms of maximum stress intensification for varying geometry of the testing device and actuation frequency to demonstrate the accuracy and computational efficiency of the proposed methodology.

Optimization of cargo distribution for high-speed freight trains to overcome strong wind conditions

The high-speed freight train (HSFT) is an emerging freight transportation mode that can play a significant role in the development of remote cities. In this study, we propose an optimization method for cargo distribution to prevent HSFT from overturning in strong winds. The multibody dynamics (MBD) HSFT model is built and imposed with aerodynamic loads derived through the computational fluid dynamics method. Based on the MBD simulation results, the prediction model of overturning safety for HSFT is established using gradient-boosting decision tree to make the value of cargo height continuous. Consequently, a nonlinear programming model for the cargo distribution problem is built and solved. The MBD simulation results reveal that the outer side crosswind is good for large vehicle velocity and the vehicle in the rear position of HSFT is safer. The case study demonstrates that the proposed optimization method can decrease the overturning risk for HSFT by more than 10% compared with the even distribution scheme. This research will contribute to making the loading plan for the rail company, ensuring the operational safety of HSFT in the windy area.

Optimal structural and functional assemblies in additive manufacturing using the African buffalo-inspired part segregation algorithm

In multilevel or additive production, reduction of the total manufacturing duration is crucial. This may be achieved by harmonizing assembly and production time and by simultaneous collaboration with component manufacturers, thus incurring fewer delays. Here, a novel approach, the African buffalo-inspired part segregation algorithm, is proposed for optimal structural and functional assemblies in additive manufacturing. A mixed-integer nonlinear programming model is developed to assess the near-term optimum criteria area and dispersed materials in a computational manufacturing context. The number of support substances, total production period and total assembly costs are reduced in the time-reduction approach. A specific swarm intelligence-part-based segregation strategy is used to choose the appropriate number of element assemblages, and a part division strategy that complies with the criteria for transverse effect, dimensions and elevations is applied. The proposed approach is evaluated for structures with conventional and free-form borders using two real-size three-dimensional representations. The results indicate that this method may reduce overall production time compared to the time spent constructing one component, under all investigated circumstances.

Solving continuous and discrete nonlinear programs with BARON

Solving continuous and discrete nonlinear programs with BARON

Mixed‐Integer Motion Planning for Nonholonomic Robots Under Visible Light Communication Constraints

ABSTRACTThis work is concerned with the problem of motion planning for a group of nonholonomic robots under Visible Light Communication (VLC) connectivity requirements. Recently, multi‐robot systems operating with VLC networks have been demonstrated as an attractive solution for inspection tasks in pipelines and underground facilities. However, there are still no established methodologies to automate their operation. We address this problem with an optimization framework based on Mixed‐Integer Linear Programming (MILP) to design a motion planner that safely coordinates the robot team while jointly addressing the nonlinearity of the robots' dynamics, the directed line‐of‐sight requirement for VLC connections, and the connectivity maintenance of the ensuing directed networks. We propose a novel method to encode the nonlinear dynamics of nonholonomic robots into the MILP formulation and demonstrate through comparative trials that, although the resulting optimization search space is more restricted, the approach still outperforms mixed‐integer nonlinear programming in terms of optimization time and solution quality. The efficacy of the proposal is also demonstrated through realistic simulations of the Turtlebot3 robot platform.

Effect of Propeller Face Camber Ratio on the Reduction of Fuel Consumption

This paper presents the effect of the face camber ratio (FCR) on propeller performance, cavitation, and fuel consumption of a bulk carrier in calm water. First, using a developed propeller optimization model coupling a ship performance prediction tool (NavCad) and a nonlinear optimizer in MATLAB, an optimized propeller design at the optimal engine operating point with minimum fuel consumption is selected. This optimized propeller demonstrates superior fuel efficiency compared to the one selected by using the traditional selection methods that prioritize only higher propeller efficiency. Afterward, the FCR is applied to the propeller geometry to evaluate the effect on propeller performance. The open water curves of propellers with different FCRs ranging from 0% to 1.5% are computed based on empirical formulas and computational fluid dynamics (CFD) simulations. Between the two techniques, a good agreement is noted in verifying the predictions. Then, the open water curves from CFD models are implemented into NavCad to evaluate the overall hydrodynamic performance of the propeller at the design point in terms of efficiency, quantify reductions in fuel consumption, and analyze changes in cavitation and noise criteria. The computed results show a reduction in fuel consumption by 3% with a higher FCR. This work offers a preliminary evaluation of propeller performance-based FCR and shows its benefits. This technique offers a promising solution for improving the energy efficiency of the ship and lowering the level of fuel consumption and exhaust emissions.

A joint work package sizing and scheduling problem considering resource constraints with a look-ahead heterogeneous reinforcement learning method

Effective work package sizing and project scheduling are crucial for construction project management. However, existing studies often address them as separate optimisation problems, neglecting the interactive nature of these processes. In practical scenarios with limited resources, there is an increasing demand for integrating work package sizing and project scheduling to enhance project management efficiency. This research aims to bridge this gap by developing an integer non-linear programming model that incorporates work package sizing and project scheduling while considering their interaction within a resource-constrained environment. Moreover, we introduce a novel look-ahead heterogeneous reinforcement learning approach that dynamically adjusts work package sizes and project schedules based on observed information at each decision step. A look-ahead sequential decision mechanism is proposed to effectively address the interdependencies and constraints inherent in the joint model. We extend the heterogeneous agent mirror learning technique to our problem to improve sample efficiency and ensure progressive enhancement of the joint policy. To evaluate our approach's effectiveness, we conduct experiments using datasets of 15, 30, 60, 90, and 120 tasks from Rangen and PSPLIB and validate our method in a real-world modular integrated construction project. The experimental results reveal that a joint model integrating work package sizing and project scheduling offers a more comprehensive understanding of their interplay, leading to better resource utilisation and improved project schedules. A comparative analysis against existing state-of-the-art reinforcement learning and priority rule-based methods further substantiates the superior effectiveness of our proposed approach, yielding an approximate 5% reduction in total project cost.

An Integrated Algorithm Fusing UWB Ranging Positioning and Visual–Inertial Information for Unmanned Vehicles

During the execution of autonomous tasks within sheltered space environments, unmanned vehicles demand highly precise and seamless continuous positioning capabilities. While the existing visual–inertial-based positioning methods can provide accurate poses over short distances, they are prone to error accumulation. Conversely, radio-based positioning techniques could offer absolute position information, yet they encountered difficulties in sheltered space scenarios. Usually, three or more base stations were required for localization. To address these issues, a binocular vision/inertia/ultra-wideband (UWB) combined positioning method based on factor graph optimization was proposed. This approach incorporated UWB ranging and positioning information into the visual–inertia system. Based on a sliding window, the joint nonlinear optimization of multi-source data, including IMU measurements, visual features, as well as UWB ranging and positioning information, was accomplished. Relying on visual inertial odometry, this methodology enabled autonomous positioning without the prerequisite for prior scene knowledge. When UWB base stations were available in the environment, their distance measurements or positioning information could be employed to institute global pose constraints in combination with visual–inertial odometry data. Through the joint optimization of UWB distance or positioning measurements and visual–inertial odometry data, the proposed method precisely ascertained the vehicle’s position and effectively mitigated accumulated errors. The experimental results indicated that the positioning error of the proposed method was reduced by 51.4% compared to the traditional method, thereby fulfilling the requirements for the precise autonomous navigation of unmanned vehicles in sheltered space.

Optimal configuration strategy of energy storage for enhancing the comprehensive resilience and power quality of distribution networks

Resilience assessment and enhancement in distribution networks primarily focus on the ability to support and recover critical loads after extreme events. With the increasing integration of new energy sources and power electronics, distribution networks have gained a degree of resilience. However, the impact of power quality issues on these networks has become more severe. In some cases, even networks assessed as highly resilient by users suffer equipment damage and substantial economic losses due to power quality issues. To address this issue, this paper builds upon conventional distribution network resilience assessment methods by supplementing and modifying indices in the dimensions of resistance and recovery to account for power quality issues. Furthermore, an optimized energy storage system (ESS) configuration model is proposed as a technical means to minimize the total operational cost of the distribution network while enhancing comprehensive resilience indices. The proposed nonlinear optimization model is solved using second-order cone relaxation techniques. Finally, the proposed strategy is simulated on the IEEE 33-node distribution network. The simulation results demonstrate that the proposed strategy effectively improves the comprehensive resilience indices of the distribution network and reduces the total operational cost.

An Effective Hybrid Metaheuristic Approach Based on the Genetic Algorithm

This paper presents an effective hybrid metaheuristic algorithm combining the genetic algorithm (GA) and a simple algorithm based on evolutionary computation. The evolutionary approach (EA) is applied to form the initial population of the GA, thus improving the algorithm’s performance, especially its convergence speed. To assess its effectiveness, the proposed hybrid algorithm, the EAGA, is evaluated on selected benchmark functions, as well as on a real optimisation process. The EAGA is used to identify parameters in a nonlinear system of differential equations modelling an E. coli fed-batch fermentation process. The obtained results are compared against published results from hybrid metaheuristic algorithms applied to the selected optimisation problems. The EAGA hybrid outperforms the competing algorithms due to its effective initial population generation strategy. The risk of premature convergence is reduced. Better numerical outcomes are achieved. The investigations validate the potential of the proposed hybrid metaheuristic EAGA for solving real complex nonlinear optimisation tasks.

Train assignment and handling capacity arrangement in multi-yard railway container terminals: An enhanced adaptive large neighborhood search heuristic approach

Expanding terminal scale and constructing multiple railway handling yards have become popular strategies for leading railway container terminals globally to cope with the ever-increasing handling volume. Although such an approach greatly enhances the terminal’s productivity, it also intensifies handling operations and introduces additional inter-yard interactions, complicating terminal management. To address these challenges, this paper investigates an integrated optimization approach for multi-yard railway container terminals, which feature both rail-road and rail-rail container transshipment operations. The train assignment plan for each yard and the handling capacity arrangement for each train are jointly optimized while considering inter-yard container transits, workload allocation for yards, and safety requirements in train shunting. This problem is formulated as a nonlinear programming model, with the objective to minimize operational delay and service time for each incoming train, and to minimize workload differences and container transit volume among yards. To efficiently solve this problem, this research develops an enhanced adaptive large neighborhood search (EALNS) heuristic, which includes several customized operators and feasibility repair methods, and is further enhanced with a local search method and backtracking mechanism compared to the standard ALNS framework. Computational experiments with different data scales and problem settings demonstrate the superiority of the EALNS in terms of solution quality and stability compared with three other solution methods. Additionally, practical insights for terminal operations are drawn through detailed analysis of different infrastructure configurations, transshipment train characteristics, and unit cost settings.