Sequential Linear Programming Research Articles

On mitigating reactive jamming with dynamic resource allocation in optical IRS and UAV-assisted FSO-based networks

Free space optics (FSO) offers a promising opportunity to enhance next-generation network’s capacity with its unlicensed spectrum and wide bandwidth. However, jamming attacks, coupled with inherent anomalies in the FSO-based channel, threaten the performance of these networks. This is especially problematic for security-sensitive applications that demand a resilient communication infrastructure. To address this issue, optical intelligent reflecting surfaces (IRS) and unmanned aerial vehicles (UAVs) can provide promising solutions. This work introduces an efficient approach for mirror element assignment in UAV-assisted FSO-based networks, aimed at mitigating reactive jamming attacks while satisfying users’ quality-of-service (QoS) requirements. To ensure network reliability, we formulate an optimization problem that enhances overall network performance by simultaneously allocating resources such as mirror elements with awareness of jamming attacks. The formulated optimization problem is a binary linear programming problem, which is generally NP-hard. To address this, we introduce a batch-based sequential fixing linear programming procedure called the Reactive Jamming-Aware Mirror Element Allocation (RJA-MEA) scheme. This scheme optimally assigns mirror elements to satisfy the users’ rate demands. In this paper, the performance of the RJA-MEA scheme is compared with reference schemes such as Reactive Jamming Unaware-Mirror Element Allocation (RJU-MEA), Reactive Jamming-Aware Equal Mirror Element Allocation (RJA-EMEA), and Reactive Jamming Unaware-Equal Mirror Element Allocation (RJU-EMEA) schemes. The simulation results reveal that the proposed RJA-MEA scheme surpasses existing reference schemes, thereby significantly improving the overall network sumrate performance.

A topology and sizing optimisation method for lightweight sandwich structures subject to dynamic and static constraints

A static-dynamic topology-sizing optimisation method is presented. The solution is based on a sequential Mixed-Integer Linear Programming solution and aims to minimise the mass of a structure subjected to concurrent constraints on static and dynamic response. It is shown that the classical problem of the dynamics of lightweight sandwich structures may be mitigated through core topology and face sheet thickness combinations, retaining the static load carrying capacity while presenting stringent dynamic properties at a low mass penalty.A numerical example, in the form of a load carrying sandwich beam which is excited at different frequencies, is used to demonstrate the method.

Finite variation sensitivity analysis in the design of isotropic metamaterials through discrete topology optimization

AbstractThis article extends recently developed finite variation sensitivity analysis (FVSA) approaches to an inverse homogenization problem. The design of metamaterials with prescribed mechanical properties is stated as a discrete density‐based topology optimization problem, in which the design variables define the microstructure of the periodic base cell. The FVSA consists in estimating the finite variations of the objective and constraint functions after independently switching the state of each variable. It is used to properly linearize the functions of binary variables so the optimization problem can be solved through sequential integer linear programming. Novel sensitivity expressions were developed and it was shown that they are more accurate than the ones conventionally used in literature. Referred to as the conjugate gradient sensitivity (CGS) approach, the proposed strategy was quantitatively evaluated through numerical examples. In these examples, metamaterials with prescribed homogenized Poisson's ratios and minimal homogenized Young's moduli were obtained. A hexagonal base cell with dihedral symmetry was used to produce only metamaterials with isotropic properties. It was shown that, by using the CGS approach instead of the conventional sensitivity analysis, the sensitivity error was substantially reduced for the considered problem. The proposed developments effectively improved the stability and robustness of the discrete optimization procedures. In all the considered examples, when more accurate sensitivity analyses were performed, the parameters of the topology optimization method could be tuned more easily, yielding effective solutions even if the settings were not ideal.

Parameter Estimation Method for Virtual Power Plant Frequency Response Model Based on SLP

In adapting to the double-high development trend of high-voltage direct current (HVDC) receiving-end power systems and solving optimization problems in emergency frequency control (EFC) supporting virtual power plants (VPPs) in large-scale power systems, a parameter estimation method for a VPP frequency response model based on a successive linear programming (SLP) method is proposed. First, a “centralized/decentralized” hierarchical control architecture for VPP participation in EFC is designed. Second, the frequency response characteristics of multiple flexible resources are scientifically analyzed, and the system frequency response (SFR) model and equivalent model of VPP are constructed. Subsequently, parameter estimation of the VPP frequency response model is carried out based on the SLP method, aiming to balance the accuracy and computational efficiency of the model. Finally, the effectiveness of the proposed methodology is verified by using PSD-BPA to simulate and test the three-zone HVDC recipient area grid.

Obtaining the effective number of reinforcements progressively inserted and optimized to reduce the strain energy of cantilever plates with a different relationship between height and length

To achieve more efficient structures, research into material properties is important in mechanical designs. The anisotropy of fiber composites is increasingly being exploited. This is particularly true for curved and continuous composites. The position and orientation of the filaments have a major influence on mechanical properties. So, the application of these fibers at specific paths is very important to obtain excellent structures. When developing components for high-performance applications, it is necessary to use optimization methods to find the best reinforcement paths. To achieve high efficiency, it is necessary to reduce the volume of the reinforcements to improve the strength-to-weight ratio. This reduction not only directly reduces the mass, but also decreases manufacturing costs. The present work aims to gradually add reinforcements to carbon fiber-reinforced polymers (CFRPs). It observes the exact number of fibers required to achieve the greatest possible reduction in strain energy. The results prove that the use of more reinforcements than ideal is unnecessary because it increases the volume of reinforcements but doesn’t improve the properties. Optimization is achieved by parameterizing B-splines using sequential linear programming (SLP). Four cases analyzed concern a cantilevered plate. A force is applied to the free edge, causing bending. The boundary conditions are identical, and only the length of the plate changes. The strain is plotted to observe the strain distribution. Then, the results show that adding three to four reinforcements can reduce the strain energy by 92.6% to 98.0% compared to a structure without reinforcements.

Application of Sequential Linear Goal Programming Method and Modified Simplex Method for Production Planning Optimization

Production planning is an important thing in company management. Every company aims to seek maximum profit in its business activities, so it must be able to utilize its resources as optimally as possible. This study was conducted to determine whether or not any production planning that has been implemented at Istana Roti Hilyah Bakery is optimal. This research aimed to maximize revenue and profit, minimize production costs and raw material usage and optimize production quantities using the sequential linear goal programming method and the simplex modification method with the assistance of LINGO software. Based on the study's results, the revenue increased by IDR 60,000, and the profit increased by IDR 66,679. The minimization value of production costs decreased by IDR 6,679, with the production amount of White Bread as many as 60 pcs, Almond Crumble Bread as many as 45 pcs, Chocolate Crumble Bread as many as 50 pcs, Wheat Bran Bread as many as 55 pcs, Sweet Comb Bread as many as 82 pcs and Jam Comb Bread as many as 84 pcs.

Isogeometric topology optimization of structures using the overweight approach

In this paper, a 2D isogeometric formulation of the material distribution for structural topology optimization considering minimum weight and local stress constraints using the overweight approach is proposed. The aim of this isogeometric formulation is to provide solutions with high spatial definition using a lower number of design variables in comparison with the formulations previously developed to define the material layout. Despite of this, an important number of local stress constraints has to be considered in the solution of the problem. For this purpose, an Overweight Constraint is used to consider all of them. The structural analysis is performed by means of the Isogeometric Analysis (IGA) and the distribution of material is modeled by means of quadratic B-splines. Moreover, the optimization is addressed by means of the Sequential Linear Programming algorithm (SLP) that is driven by the information provided by a full first-order sensitivity analysis extension of the IGA formulation. Finally, the proposed formulation is tested by means of some benchmark problems, and the results show that the isogeometric formulation provides solutions with high spatial definition. A comparison with a Finite Element Method (FEM) topology optimization formulation is included.

Convergence of successive linear programming algorithms for noisy functions

AbstractGradient-based methods have been highly successful for solving a variety of both unconstrained and constrained nonlinear optimization problems. In real-world applications, such as optimal control or machine learning, the necessary function and derivative information may be corrupted by noise, however. Sun and Nocedal have recently proposed a remedy for smooth unconstrained problems by means of a stabilization of the acceptance criterion for computed iterates, which leads to convergence of the iterates of a trust-region method to a region of criticality (Sun and Nocedal in Math Program 66:1–28, 2023. https://doi.org/10.1007/s10107-023-01941-9). We extend their analysis to the successive linear programming algorithm (Byrd et al. in Math Program 100(1):27–48, 2003. https://doi.org/10.1007/s10107-003-0485-4, SIAM J Optim 16(2):471–489, 2005. https://doi.org/10.1137/S1052623403426532) for unconstrained optimization problems with objectives that can be characterized as the composition of a polyhedral function with a smooth function, where the latter and its gradient may be corrupted by noise. This gives the flexibility to cover, for example, (sub)problems arising in image reconstruction or constrained optimization algorithms. We provide computational examples that illustrate the findings and point to possible strategies for practical determination of the stabilization parameter that balances the size of the critical region with a relaxation of the acceptance criterion (or descent property) of the algorithm.

An Adaptive Linear Programming Algorithm with Parameter Learning

When dealing with engineering design problems, designers often encounter nonlinear and nonconvex features, multiple objectives, coupled decision making, and various levels of fidelity of sub-systems. To realize the design with limited computational resources, problems with the features above need to be linearized and then solved using solution algorithms for linear programming. The adaptive linear programming (ALP) algorithm is an extension of the Sequential Linear Programming algorithm where a nonlinear compromise decision support problem (cDSP) is iteratively linearized, and the resulting linear programming problem is solved with satisficing solutions returned. The reduced move coefficient (RMC) is used to define how far away from the boundary the next linearization is to be performed, and currently, it is determined based on a heuristic. The choice of RMC significantly affects the efficacy of the linearization process and, hence, the rapidity of finding the solution. In this paper, we propose a rule-based parameter-learning procedure to vary the RMC at each iteration, thereby significantly increasing the speed of determining the ultimate solution. To demonstrate the efficacy of the ALP algorithm with parameter learning (ALPPL), we use an industry-inspired problem, namely, the integrated design of a hot-rolling process chain for the production of a steel rod. Using the proposed ALPPL, we can incorporate domain expertise to identify the most relevant criteria to evaluate the performance of the linearization algorithm, quantify the criteria as evaluation indices, and tune the RMC to return the solutions that fall into the most desired range of each evaluation index. Compared with the old ALP algorithm using the golden section search to update the RMC, the ALPPL improves the algorithm by identifying the RMC values with better linearization performance without adding computational complexity. The insensitive region of the RMC is better explored using the ALPPL—the ALP only explores the insensitive region twice, whereas the ALPPL explores four times throughout the iterations. With ALPPL, we have a more comprehensive definition of linearization performance—given multiple design scenarios, using evaluation indices (EIs) including the statistics of deviations, the numbers of binding (active) constraints and bounds, the numbers of accumulated linear constraints, and the number of iterations. The desired range of evaluation indices (DEI) is also learned during the iterations. The RMC value that brings the most EIs into the DEI is returned as the best RMC, which ensures a balance between the accuracy of the linearization and the robustness of the solutions. For our test problem, the hot-rolling process chain, the ALP returns the best RMC in twelve iterations considering only the deviation as the linearization performance index, whereas the ALPPL returns the best RMC in fourteen iterations considering multiple EIs. The complexity of both the ALP and the ALPPL is O(n2). The parameter-learning steps can be customized to improve the parameter determination of other algorithms.

Topology optimization for stationary fluid–structure interaction problems with turbulent flow via sequential integer linear programming and smooth explicit boundaries

Topology optimization methods face serious challenges when applied to structural design with fluid–structure interaction (FSI) loads, especially for high Reynolds fluid flow, i.e., considering turbulence. In this problem, the information at the fluid–structure interface is crucial for the modeling and convergence of the turbulent fluid flow analysis. This paper devises a new explicit boundary method that generates two- and three-dimensional smooth surfaces to be used in topology optimization with binary {0,1} design variables. A phase-field function is obtained after nodal spatial filtering of the design variables. The 0.5 isoline defines a smooth surface to construct the topology. The FSI problem can then be modeled with accurate physics and explicitly defined regions. The Finite Element Method is used to solve the fluid and structural domains. This is the first work to consider a turbulent flow in the fluid–structure topology optimization framework. The fluid flow is solved considering the k−ɛ turbulence model including standard wall functions at the fluid and fluid–structure boundaries. The structure is considered to be linearly elastic. Semi-automatic differentiation is employed to compute sensitivities and the optimization problem is solved via sequential integer linear programming. Results show that the proposed methodology is able to provide structural designs with smooth boundaries considering loads from low and high Reynolds flow.

Comparing single and multiple objective constrained optimization algorithms for tuning a groundwater remediation system

Groundwater flow and particle tracking models are critical tools to simulate the natural system, contaminant fate and transport, and effects of remediation. Constrained optimization uses models to systematically explore the interplay between remedial design and contaminant fate, considering uncertainty. Sequential Linear Programming (SLP) provides a design alternative addressing a single goal (e.g. maximum hydraulic containment, maximum mass removal). Multi-objective algorithms like Nondominated Sorting Genetic Algorithm (NSGA-II) explore the tradeoffs among such objectives and more (e.g. cost, public-supply well contamination). We explore both approaches at a contaminated site in Long Island, New York USA. We compare the algorithms and ramifications on results. NSGA-II explores, at additional computational cost, explicit tradeoffs among multiple objectives, providing additional insights relative to SLP. The NGSA-II algorithm allows for graphical consideration of three objectives. SLP decision variables often settle at predetermined bounds. Bounds assignment thus differs from parameter estimation; bounds must be acceptable rather than safeguards.

Incentive Compatible Pricing for Enhancing the Controllability of Price-Based Demand Response

Price-based demand response is widely implemented by the load aggregators (LAs) to exploit the flexibility of massive demand-side resources. However, a key problem in real-life implementation is the controllability of price-based demand response, viz, whether the price can guide the demand to the desired value. To bridge this gap, this paper proposes a close-loop reverse Stackelberg game-based pricing method to better regulate the demand response. In the hierarchical game structure, the non-cooperative competition of heterogeneous demand-side resources in participating demand response constitutes the lower-level, while the determination of pricing policy by LA makes the upper-level. Towards a computationally efficient solution, the mean-field game is adopted to approximate the Nash equilibrium of the large-scale lower level competition, and the indirect formulation of close-loop reverse Stackelberg game is adopted. The accuracy of the approximation is proved to be the (1,2) -hierarchical equilibrium of the original game. Finally, a decentralized solution algorithm with sequential linear programming as outer-loop and mean-field iteration as inner-loop is proposed to price the demand response. Numerical tests on a retail electricity market containing 15,000 heterogeneous demand-side flexible resources validate the effectiveness of the proposed pricing scheme.

On the multi-objective perspective of discrete topology optimization in fluid-structure interaction problems

Fluid-structure interaction is a challenging topic that addresses fluid and solid physics, as well as the stress coupling between them. Traditional topology optimization methods are performed with coupling load interpolation schemes in order to have some information on fluid flow sensitivity analysis and improve compliance minimization into design-dependent problems. In this paper, we propose a strategy to design fluid-structure systems by combining solid and fluid objectives without the need for the coupling load interpolation scheme. Therefore, we investigate topology optimization applied to fluid-structure interaction problems via a multi-objective formulation. We combine structural compliance with some fluid flow objective functions (energy dissipation, downforce, and drag) subject to a volume constraint. We assume linear elasticity for the solid and the steady incompressible Navier-Stokes equations for the fluid. The optimization problem is solved by using sequential integer linear programming via the TOBS (Topology Optimization of Binary Structures) method with a geometry trimming (GT) technique. It is a gradient-based method that produces explicit (discrete) boundaries that are convenient for coupled physics problems. Numerical results are presented for two and three-dimensional problems considering low to moderate Reynolds numbers. We demonstrate that the proposed multi-objective approach yields physically meaningful designs with improved performance, highlighting that the incorporation of coupling load interpolation into fluid-structure interaction optimization is redundant.

A novel day-ahead scheduling model to unlock hydropower flexibility limited by vibration zones in hydropower-variable renewable energy hybrid system

Giving full play to the flexibility of hydropower and integrating more variable renewable energy (VRE) is of great significance for accelerating the transformation of China's power energy system. For middle- to large-sized hydropower units, its irregular vibration zone (VZ) is a major factor affecting its flexibility, because VZs limits the power output and adjustment range. In the existing studies on hydropower unit commitment and flexibility scheduling, VZs only limits the output of hydropower units, while the impact on the flexibility adjustment ability of units is ignored. The hydropower flexibility in day-ahead scheme is overestimated, which increases the risk of system flexibility shortage causing power curtailment and load loss. In this study, a novel day-ahead scheduling model considering the flexibility limited by the VZs and the probability of flexibility shortage is constructed for the day-ahead generation scheme of hydropower-VRE hybrid generation system (HVHGS) to optimize the target load, VRE output and hydropower unit commitments. The impaction of the VZs on hydropower flexibility is firstly modeled by chance constraints and stochastic programming method. Moreover, a data-driven model based on machine learning and an efficient solving approach based on successive linear programming is carry out to describe the uncertainty of VRE output more realistically and ensure the timeliness of optimization scheme, respectively. The proposed model is applied to a real hydropower station in the Hongshui River Basin in China. In 16 representative scenarios, the proposed model can complete the optimization in an acceptable time, with a maximum of 444.57 s. Compared with the traditional interval optimization model, the proposed model effectively improves the flexibility supply capacity of hydropower in the day-ahead scheme. The maximum reduction value of flexibility shortage probability and expectation reach 98.77% and 442.66 MW, respectively. In particular, the flexibility of the model is most obvious under heavy load demand in flood season, and it is almost not at the cost of daily target load adjustment, which provides practical reference for decision makers.

Implementation of nonlinear variable-cost network optimization models for technology assessment in the petrochemicals industry

Innovation in petrochemical technology is ongoing, whether to exploit opportunities, such as increased natural gas liquid supplies, or to face new challenges, including the need to decarbonize and to adapt to a future circular economy. Thus, there is a continuing need for petrochemical technology assessment. We consider methods for implementing optimization-based, superstructure models that assess new technology in the context of the entire hydrocarbon ecosystem, thereby capturing not just first-order, local impacts, but also higher-order, industry-wide impacts. These models are nonlinear, variable-cost, network representations of the industry, incorporating a dominant-producer price leadership approach. They are formulated either as a mixed-integer nonlinear programming problem or as a special-purpose successive linear programming problem. The performance of the different approaches is evaluated based on quality of results and computational efficiency. The comparisons initially use small prototype networks that feature structural properties of the industrial network, followed by application to full-scale, industry-wide problems.

A sequential linear programming (SLP) approach for uncertainty analysis-based data-driven computational mechanics

A sequential linear programming (SLP) approach for uncertainty analysis-based data-driven computational mechanics

SLEQP: An open‐source package for nonlinear programming

AbstractWe present SLEQP, an open source C‐package consisting of an active‐set method capable of solving large‐scale nonlinear programming (NLP) problems based on successive linear programming and equality constrained quadratic programming techniques. The method includes a feasibility restoration phase and second‐order corrections (SOCs), achieving robust practical performance. It has also been adapted for the special cases of unconstrained optimization, box‐constrained problems, and nonlinear least squares problems and contains interfaces to both Python and MATLAB. To demonstrate the performance of the package, we perform a computational study based on the well‐known CUTest suite of NLP problems.

A Hilbertian projection method for constrained level set-based topology optimisation

We present an extension of the projection method proposed by Challis et al. (Int J Solids Struct 45(14–15):4130–4146, 2008) for constrained level set-based topology optimisation that harnesses the Hilbertian velocity extension-regularisation framework. Our Hilbertian projection method chooses a normal velocity for the level set function as a linear combination of (1) an orthogonal projection operator applied to the extended optimisation objective shape sensitivity and (2) a weighted sum of orthogonal basis functions for the extended constraint shape sensitivities. This combination aims for the best possible first-order improvement of the optimisation objective in addition to first-order improvement of the constraints. Our formulation utilising basis orthogonalisation naturally handles linearly dependent constraint shape sensitivities. Furthermore, use of the Hilbertian extension-regularisation framework ensures that the resulting normal velocity is extended away from the boundary and enriched with additional regularity. Our approach is generally applicable to any topology optimisation problem to be solved in the level set framework. We consider several benchmark constrained microstructure optimisation problems and demonstrate that our method is effective with little-to-no parameter tuning. We also find that our method performs well when compared to a Hilbertian sequential linear programming method.

Static Output Feedback Control for Positive Takagi–Sugeno Fuzzy Systems: A Successive Linear Programming Approach

This article considers the control synthesis for positive nonlinear systems modeled by Takagi–Sugeno (T–S) fuzzy characterizations. A fuzzy static output feedback (SOF) controller is sought to assure the closed-loop stability and positivity with a guaranteed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal{l}_{1}$</tex-math> </inline-formula> performance level. The favorable positivity enables us to adopt a linear co-positive function as the Lyapunov candidate, and we construct the essential conditions for the existence of fuzzy SOF controllers in the form of bilinear programming (BP) problem. To provide a direct and generic algorithm for solving the BP problem, we propose a vital approximation strategy by which the general bilinear constraints are replaced with a sequence of convex surrogate ones. Recognizing the fact that a fundamental promise of the proposed successive linear programming algorithm is a feasible initial solution, we also develop an iterative procedure to calculate an initial controller gain. Finally, we clarify the applicability of the developed scheme with two examples.

Topology Optimization Design of Resonant Structures Based on Antiresonance Eigenfrequency Matching Informed by Harmonic Analysis

Abstract In this article, we present a design methodology for resonant structures exhibiting particular dynamic responses by combining an eigenfrequency matching approach and a harmonic analysis-informed eigenmode identification strategy. This systematic design methodology, based on topology optimization, introduces a novel computationally efficient approach for 3D dynamic problems requiring antiresonances at specific target frequencies subject to specific harmonic loads. The optimization’s objective function minimizes the error between target antiresonance frequencies and the actual structure’s antiresonance eigenfrequencies, while the harmonic analysis-informed identification strategy compares harmonic displacement responses against eigenvectors using a modal assurance criterion, therefore ensuring an accurate recognition and selection of appropriate antiresonance eigenmodes used during the optimization process. At the same time, this method effectively prevents well-known problems in topology optimization of eigenfrequencies such as localized eigenmodes in low-density regions, eigenmodes switching order, and repeated eigenfrequencies. Additionally, our proposed localized eigenmode identification approach completely removes the spurious eigenmodes from the optimization problem by analyzing the eigenvectors’ response in low-density regions compared to high-density regions. The topology optimization problem is formulated with a density-based parametrization and solved with a gradient-based sequential linear programming method, including material interpolation models and topological filters. Two case studies demonstrate that the proposed design methodology successfully generates antiresonances at the desired target frequency subject to different harmonic loads, design domain dimensions, mesh discretization, or material properties.