Nonlinear Optimization Problem Research Articles

A branch-and-bound algorithm for parametric mixed-binary nonlinear programs

AbstractAs rapid response to changes becomes more imperative, optimization under uncertainty has continued to grow in both the continuous and mixed-integer fields. We design a branch-and-bound (BB) algorithm for mixed-binary nonlinear optimization problems with parameters in general locations. At every node of the BB tree we apply a state-of-the-art algorithm we have recently developed to approximately optimize parametric programs containing objectives and constraints biconvex in the variables and parameters. Numerical results are included.

Designing employee benefits to optimize turnover: A prescriptive analytics approach

Employee turnover significantly impacts organizations, particularly those with substantial investments in training their workforce. To mitigate these effects, we propose a Prescriptive Human Resources Analytics approach that optimizes employee benefits to minimize total costs, focusing on turnover management The methodology models employee decision-making using a discrete choice model, with parameters estimated through maximum likelihood. We solve the resulting nonlinear optimization problem with a heuristic tailored to the problem’s complexity. We applied this methodology to a hospital case study, which was used to enhance the transportation system as an employee benefit, considering the associated turnover costs. The results demonstrate that our approach can reduce total costs, optimize the usage level of the designed benefits, and increase employee satisfaction. This research provides a robust framework for data-driven decision-making in HR, offering practical tools for improving employee retention strategies.

Two-Stage Optimal Scheduling Strategy of Microgrid Distribution Network Considering Multi-Source Agricultural Load Aggregation

With the proposed “double carbon” target for the power system, large-scale distributed energy access poses a major challenge to the way the distribution grid operates. The rural distribution network (DN) will transform into a new local power system primarily driven by distributed renewable energy sources and energy storage, while also being interconnected with the larger power grid. The development of the rural DN will heavily rely on the construction and efficient planning of the microgrid (MG) within the agricultural park. Based on this, this paper proposes a two-stage optimal scheduling model and solution strategy for the microgrid distribution network with multi-source agricultural load aggregation. First, in the first stage, considering the flexible agricultural load and the market time-of-use electricity price, the economic optimization is realized by optimizing the operation of the schedulable resources of the park. The linear model in this stage is solved by the Lingo algorithm with fast solution speed and high accuracy. In the second stage, the power interaction between the MG and the DN in the agricultural park is considered. By optimising the output of the reactive power compensation device, the operating state of the DN is optimised. At this stage, the non-linear and convex optimization problems are solved by the particle swarm optimization algorithm. Finally, the example analysis shows that the proposed method can effectively improve the feasible region of safe operation of the distribution network in rural areas and improve the operating income of a multi-source agricultural load aggregation agricultural park.

Tridiagonal Weighting‐Based Interference Cancellation Method in High‐Mobility OFDM Systems

ABSTRACTIn orthogonal frequency division multiplexing (OFDM) systems, the time‐selective fading channel causes the signal Doppler expansion in high‐mobility scenarios, leading to intercarrier interference (ICI) in the received signals. People had employed a full‐dimensional weighting matrix method to reduce the Doppler‐assisted ICI, though it required a high implementation complexity. In order to reduce the ICI and produce lower complexities, this paper proposes to exploit the tridiagonal weighting matrix to suppress ICIs, in which an optimization problem is constructed to design the tridiagonal weighting matrix, and the nonzero coefficients within the tridiagonal matrix denote optimization variables. Moreover, the optimization objective exploits the system bit error rate (BER) instead of the conventional signal to interference plus noise ratio (SINR), which results in a highly nonlinear optimization problem. Therefore, an iterative solving approach is proposed according to the successive convex approximation (SCA). Simulations show that the proposed method can achieve a good balance between the complexity and BER degradation, especially in the scenario with moderate Doppler spreads.

Distillation column optimization: A formal method using stage-to stage computations and distributed streams

This work addresses the complexities of optimizing the number of stages in a distillation column, which typically lead to challenging non-linear mixed-integer optimization problems. To simplify this, we employ distributed streams, thereby eliminating discrete degrees of freedom. To avoid sophisticated initialization procedures, the optimization problem is reformulated by employing a sequence of stage-to-stage calculations, each reduced to maintaining only the MESH (mass, equilibrium, summation, heat) equations for a single stage.Our numerical experiments show the efficiency and stability of solving the simplified optimization problem in various scenarios, including single and multiple distillation columns. For a single column scenario, we compare the accuracy of our optimization method with a full enumeration approach. Additionally, for a pressure swing flowsheet designed to separate an azeotropic mixture, we illustrate potential energy savings by optimizing a stage distribution versus using a predetermined stage distribution.

Reducing flow heterogeneity in drip irrigation networks using genetic algorithms

AbstractIrrigation based on non‐compensated drip emitters is extremely common in agriculture, especially due to its simplicity, robustness and competitive cost. Nevertheless, because of friction losses in the pipe, together with irregular terrain, these systems often suffer from uneven water distribution in the drip emitters, which not only results in inefficient use of water resources but also might lead to inadequate irrigation in certain parts of the field. This work proposes to design the topology of the irrigation network to compensate for these discharge differences. To this end, a graph‐based mathematical model is developed to determine the discharge flows at different emitters for any network topology. This model is employed to formulate an integer nonlinear optimization problem, for which a messy genetic algorithm is proposed. The methodology is validated on an example problem, which is based on a rectangular agricultural crop of 49 fruit trees. The results revealed a 70% reduction in the coefficient of variation of the irrigation discharge rates, which was employed as a metric of irrigation uniformity. This caused a 75% reduction in the water excess. The results demonstrate that the uniformity can be improved simply by choosing a proper connectivity layout to build the pipe network.

Adjoint-Based Calibration of Nonlinear Stochastic Differential Equations

To study the nonlinear properties of complex natural phenomena, the evolution of the quantity of interest can be often represented by systems of coupled nonlinear stochastic differential equations (SDEs). These SDEs typically contain several parameters which have to be chosen carefully to match the experimental data and to validate the effectiveness of the model. In the present paper the calibration of these parameters is described by nonlinear SDE-constrained optimization problems. In the optimize-before-discretize setting a rigorous analysis is carried out to ensure the existence of optimal solutions and to derive necessary first-order optimality conditions. For the numerical solution a Monte–Carlo method is applied using parallelization strategies to compensate for the high computational time. In the numerical examples an Ornstein–Uhlenbeck and a stochastic Prandtl–Tomlinson bath model are considered.

Method for prediction magnetic silencing of uncertain energy-saturated extended technical objects in prolate spheroidal coordinate system

Aim. Development of method for prediction by energy-saturated extended technical objects magnetic silencing based on magnetostatics geometric inverse problems solution and magnetic field spatial spheroidal harmonics calculated in prolate spheroidal coordinate system taking into account of technical objects magnetic characteristics uncertainties. Methodology. Spatial prolate spheroidal harmonics of extended technical objects magnetic field model calculated as magnetostatics geometric inverse problems solution in the form of nonlinear minimax optimization problem based on near field measurements for prediction far extended technical objects magnetic field magnitude. Nonlinear objective function calculated as the weighted sum of squared residuals between the measured and predicted magnetic field COMSOL Multiphysics software package used. Nonlinear minimax optimization problems solutions calculated based on particle swarm nonlinear optimization algorithms. Results. Results of prediction extended technical objects far magnetic field magnitude based on extended technical objects spatial prolate spheroidal harmonics of the magnetic field model in the prolate spheroidal coordinate system using near field measurements with consideration of extended technical objects magnetic characteristics uncertainty. Originality. The method for prediction by extended technical objects magnetic cleanliness based on spatial prolate spheroidal harmonics of the magnetic field model in the prolate spheroidal coordinate system with consideration of magnetic characteristics uncertainty is developed. Practical value. The important practical problem of prediction extended technical objects magnetic silencing based on the spatial prolate spheroidal harmonics of the magnetic field model in the prolate spheroidal coordinate system with consideration of extended technical objects magnetic characteristics uncertainty solved. References 48, figures 2.

An adaptive snow ablation-inspired particle swarm optimization with its application in geometric optimization

In response to the shortcomings of particle swarm optimization (PSO), such as low execution efficiency and difficulty in overcoming local optima, this paper proposes a multi-strategy PSO method incorporating snow ablation operation (SAO), known as SAO-MPSO. Firstly, Cubic initialization is performed on particles to obtain a good initial environment. Subsequently, SAO and PSO are combined in parallel, and a balanced search mechanism led by multiple sub-populations is devised, significantly improving the search efficiency of overall population. Finally, the degree day method of SAO is introduced, and particles are endowed with memory of environmental changes to prevent premature convergence of PSO, while balancing the exploration and exploitation (ENE) capabilities in later phases. All adaptive parameters are used throughout this method in place of fixed parameters to improve the robustness and adaptability. For a comprehensive analysis of SAO-MPSO, its good ENE ability is verified on CEC 2020 and CEC 2022 and this method is compared with existing improved PSO versions on both test sets. The results show that SAO-MPSO has certain advantages in the comparison of similar improved algorithms. In order to further validate the strength of SAO-MPSO in dealing with nonlinear optimization problems (OPs) with strong constraints, firstly, based on the ball Wang-Ball (BWB) curve, a combined BWB (CBWB) curve is constructed, and a construction method for CBWB curves that satisfy G1 and G2 continuity is derived. Then, with the energy minimization and scale parameters of the CBWB curve as the optimization objective and variables respectively, a shape optimization model that satisfies G2 continuity is established. Finally, three numerical optimization examples based on this model are solved using SAO-MPSO and compared with 10 other methods. The results show that the energy obtained by SAO-MPSO is the smallest, which verifies the effectiveness of this method applied to shape OPs of CBWB curve.

Non-linear programming model proposal for mutual support distance of air defence systems

With the advancements in technology, the deployment of air defence systems required for the defence of a country after procurement is considered as an important problem in terms of defence effectiveness. It is seen that criteria such as coverage, strike effectiveness and logistics network are taken into account while deploying. In addition, principles such as remote countermeasures, defence in depth and all-round defence are also taken into account. In this study, two different deployment models are proposed for point and area air defence. In this model, the optimum deployment distance at which other systems can support each other in addition to a deployed air defence system is determined. In the nonlinear target programming model proposed for point air defence, the number of missiles is considered to be reasonably balanced for perimeter defence, while for area defence, the nonlinear optimization problem is addressed by calculating the equally important coverage and strike effectiveness criteria values. In this study, it is observed that the approach based on mutual support distance has been used for the first time in the defence literature. According to the results obtained, it is observed that this proposed model for determining the mutual support distance solves the deployment problem optimally.

On the inverse problem of parameter identification in the steady Oseen model with unilateral and frictional‐type boundary conditions

AbstractRecently, Migórski‐Dudek investigated a steady Oseen flow for a generalized Newtonian incompressible fluid with unilateral and frictional‐type boundary conditions. They established an existence theorem for the steady Oseen model when the divergence‐free convection field and acting volume force are known. However, prior knowledge of and is often impossible in practical engineering applications. This leads to the question of whether the divergence‐free convection field and acting volume force can be determined. The main objective of this paper is to provide a positive response to this challenging and intriguing question. Specifically, we aim to formulate an inverse problem for identifying and , characterized by a nonlinear and nonsmooth regularized optimization problem. Initially, we introduce a variational selection mapping for the steady Oseen model. We then establish the boundedness and generalized continuity of this variational selection. Finally, by leveraging optimization theory, convex analysis, and nonsmooth analysis, we develop an abstract regularization framework for the considered inverse problem and establish the existence of a solution.

A fault-tolerant algorithm of AUV formation based on reconfiguration map

Aiming at the fault occurrence of AUV formation members during sailing, a fault tolerance algorithm of AUV formation based on reconfiguration was proposed. Firstly, the cost matrix is designed based on the reconfiguration and Hungarian algorithm to solve the problem of assigning target points under the fault condition. Then, based on Bezier curves, the dynamic constraints of AUV are designed parametrically. The nonlinear optimization problem satisfies the constraints through the characteristics of spline curves, and the adaptive particle swarm optimization algorithm is used to solve the tracking trajectory. The comparison and simulation experiment of a particle swarm algorithm based on a reconfiguration map (RMPSO) was carried out. The simulation results show that under the same planned path, the total tracking path of the following AUV is shorter, the turning radius is smaller, and the heading Angle is more stable. Finally, field tests are carried out in Qiandao Lake to verify the effectiveness of the algorithm for formation faults.

Variable Splitting and Fusing for Image Phase Retrieval.

Phase Retrieval is defined as the recovery of a signal when only the intensity of its Fourier Transform is known. It is a non-linear and non-convex optimization problem with a multitude of applications including X-ray crystallography, microscopy and blind deconvolution. In this study, we address the problem of Phase Retrieval from the perspective of variable splitting and alternating minimization for real signals and seek to develop algorithms with improved convergence properties. An exploration of the underlying geometric relations led to the conceptualization of an algorithmic step aiming to refine the estimate at each iteration via recombination of the separated variables. Following this, a theoretical analysis to study the convergence properties of the proposed method and justify the inclusion of the recombination step was developed. Our experiments showed that the proposed method converges substantially faster compared to other state-of-the-art analytical methods while demonstrating equivalent or superior performance in terms of quality of reconstruction and ability to converge under various setups.

Control charts for monitoring the capability of unstable process

Stability is an important criterion to be investigated at the early stage of any industrial process and stable processes are usually preferred over unstable ones. But a process can be unstable and nevertheless capable and, therefore, there is a clear need to monitor such situations to ensure an acceptable capability. In this study we introduce, in a first step, a new Shewhart-type control chart for normal processes based on the yield index S pk to monitor the capability of potentially unstable processes and then, in a second step, we extend it using an Exponentially Weighted Moving Average (EWMA) scheme. Moreover, the optimal values of the control parameters are obtained using a nonlinear optimization problem for which the out-of-control average run length is the objective function. The introduced charts’ sensitivity is examined for deterministic shift sizes. Numerical and graphical analyses are given to display the features of the proposed charts. A simulation study shows, how in such a situation, the introduced tool is successful to recognize changes in the process capability.

Historical knowledge transfer driven self-adaptive evolutionary multitasking algorithm with hybrid resource release for solving nonlinear equation systems

In reality, there are many extremely complex nonlinear optimization problems. How to locate the roots of nonlinear equation systems (NESs) more accurately and efficiently has always been a major numerical challenge. Although there are many excellent algorithms to solve NESs, which are all limited by the fact that the algorithm can solve at most one NES in a single run. Therefore, this paper proposes a historical knowledge transfer driven self-adaptive evolutionary multitasking algorithm framework (EMSaRNES) with hybrid resource release to solve NESs. Its core is that in one run, EMSaRNES can efficiently and accurately locate the roots of multiple NESs. In EMSaRNES, self-adaptive parameter method is proposed to dynamically adjust parameters of the algorithm. Secondly, adaptive selection mutation mechanism with historical knowledge transfer is designed, which dynamically adjusts the evolution of populations with or without knowledge sharing according to changes in the current population diversity, thereby balancing population diversity and convergence. Finally, hybrid resource release strategy is developed, which archives the roots that meet the accuracy requirements, and then three distributions are selected to generate new populations, thus ensuring that the population diversity is maintained at high level. After a variety of experiments, it has been proven that compared to comparative algorithms EMSaRNES has superior performance on 30 general NESs test sets. In addition, the results on 18 extremely complex NESs test sets and two real-life application problems further prove that EMSaRNES finds more roots in the face of complex problems and real-life problems.

Nonlinear model predictive control for maximum wind energy extraction of semi-submersible floating offshore wind turbine based on simplified dynamics model

The application of floating offshore wind turbines means better exploitation of offshore wind resources. However, the six-degree of freedom motion characteristics of floating platforms bring greater challenges to control system design. Based on the dynamic characteristics of semi-submersible floating offshore wind turbines, this paper establishes a simplified nonlinear dynamic model for control system design. On this basis, a complete framework for nonlinear model predictive control of maximum wind energy extraction for semi-submersible floating offshore wind turbines considering wind and wave disturbances is developed. Based on the previewed wind and wave, a dynamic optimization problem with both state and control constraints is constructed, considering maximum wind energy extraction and torque fluctuation. Then, an improved equilibrium optimizer is proposed to address the nonlinear non-convex dynamic optimization problems, which achieves a better trade-off between exploitation and exploration. Simulation results verify the superiority of the proposed nonlinear model predictive control framework via the improved equilibrium optimizer, and the influences of different control algorithms on the platform motion state, power coefficient, and equivalent wind speed are analyzed.

Efficient data-driven nonlinear system identification for structural health monitoring: A proof-of-principle study

Structural health monitoring (SHM) is the process of detecting damage in structures. Typically, the damage-sensitive feature identification is based on fitting some models to the measured system response data. The parameters of these models or the prediction errors associated with these models then become the desired damage-sensitive features. Real-world structures usually exhibit significant nonlinear behaviors. Data-driven nonlinear system identification (NSI) is essential to obtain accurate models of structural dynamics for reliable damage detection. However, on the one hand, the data acquisition of real-world structures for damage detection is usually difficult or scarce. On the other hand, NSI generally needs to solve a nonlinear optimization problem that requires more computational time for convergence than linear system identification. Data efficiency and computational efficiency become two critical challenges in data-driven NSI. To address these challenges, this work presents a proof-of-principle study on developing a meta learning-based method for efficient data-driven NSI. Specifically, the meta learning algorithm leverages a previously collected database of similar but different systems to learn the meta-knowledge about how to identify a new system, enabling a fast identification/modeling with limited data. Numerical simulations are performed to validate the method on fundamental nonlinear dynamical systems widely seen in civil engineering. It is observed that the presented meta learning-based method outperforms the conventional method in terms of both data and computational efficiency. Limitations of this work are further discussed.

Heat-Equation-Based Smoothing Homotopy Method for Nonlinear Optimal Control Problems

This paper presents a new heat-equation-based smoothing homotopy method for solving nonlinear optimal control problems with the indirect method. The surrogates, derived from the heat equation solution, are first incorporated into the necessary conditions as replacement of the terminal state and costate variables. The homotopy process is then applied to the heat conduction time: a longer time results in a more uniform temperature distribution and greater stability against initial temperature variations, thereby making the corresponding homotopy problem much easier to solve; zero time implies no heat conduction and reverts to the original problem. Furthermore, capitalizing on the heat equation’s boundedness characteristic, an efficient approach for determining the hypersensitive parameters is proposed, thus obviating the necessity of manual tuning. Challenging numerical examples are provided to demonstrate the superior performance of the proposed method, indicating that its convergence and efficiency are significantly enhanced compared to the original smoothing homotopy methods.

Pareto-critical equilibrium condition for non-linear multiobjective optimization problems with applications

The new (necessary) Pareto-critical equilibrium condition (PCEC) discussed in this study is based on the Pareto-critical condition for non-linear optimization problems. The proposed condition is evaluated by defining a multiobjective optimization problems (MOOPs) subject to a set of constraints. Then this MOOPs is converted to a single objective optimization problem by using the available optimization techniques, for instance, the weighted sum method, and solved by the non-linear Nelder-Mead simplex method. The obtained solution points satisfy the proposed PCEC of an unconstrained multiobjective optimization problem (MOOPs) under the convexity assumption. This PCEC is evaluated in a search that either results in a point inside the feasible region or a point for which the PCEC holds. The resulting Pareto-critical equilibrium condition is globally valid for convex problems. Numerical experiments are carried out in order to clarify the proposed condition's validity. Moreover, the proposed PCEC is used to place a downlink transmit beamforming system base station in an ideal position as a first application and is also employed in situations where there are multiple agents working towards a common goal as a second application.

An Improved Grey Wolf Optimizer(IGWO) algorithm for optimization of centrifugal pump with guide vane

Abstract To improve the hydraulic performance of a centrifugal pump with guide vane, an improved grey wolf optimizer (IGWO) algorithm is proposed. First, the IGWO algorithm enhances the diversity and global exploration of the initial population with optimal Latin hypercube sampling. Then, the convergence factor is improved by combining the Tanh function to meet the needs of complex non-linear optimization problems. Finally, a search mechanism that enhances population communication is constructed and combined with a mutation-driven search scheme to improve the ability to avoids the local optima traps. The results show that IGWO algorithm has obvious advantages in convergence speed and robustness when dealing with complex non-linear optimization problems. Additionally, satisfactory results are achieved in the application of centrifugal pump optimization. The efficiency of optimized pump reaches 87.8%, which is 1.2% higher than that of the original pump. The anti-cavitation performance of the centrifugal pump is enhanced by improving the distribution of blade inlet attack angles. The vortex area inside the optimized pump impeller is reduced over a large area, and the operating stability of the pump, the matching between the impeller and the guide vane, and the flow characteristics in the guide vane domain are all improved.