Nonlinear Constrained Optimization Research Articles

A league-knock-out tournament quantum particle swarm optimization algorithm for nonlinear constrained optimization problems and applications

A league-knock-out tournament quantum particle swarm optimization algorithm for nonlinear constrained optimization problems and applications

Constrained Consensus-Based Optimization

In this work we are interested in the construction of numerical methods for high-dimensional constrained nonlinear optimization problems by particle-based gradient-free techniques. A consensus-based optimization (CBO) approach combined with suitable penalization techniques is introduced for this purpose. The method relies on a reformulation of the constrained minimization problem in an unconstrained problem for a penalty function and extends to the constrained settings of the class of CBO methods. Exact penalization is employed and, since the optimal penalty parameter is unknown, an iterative strategy is proposed that successively updates the parameter based on the constrained violation. Using a mean-field description of the many particle limit of the arising CBO dynamics, we are able to show convergence of the proposed method to the minimum for general nonlinear constrained problems. Properties of the new algorithm are analyzed. Several numerical examples, also in high dimensions, illustrate the theoretical findings and the good performance of the new numerical method.

A symmetric splitting sequential quadratic optimization algorithm for two-block nonlinearly constrained nonconvex optimization

In this paper, a double-step-length symmetric splitting sequential quadratic optimization (DSL-SS-SQO) algorithm for solving two-block nonconvex optimization with nonlinear constraints is proposed. First, at each iteration, the idea of symmetric splitting is embedded into solving the quadratic optimization (QO) subproblem approximating the discussed problem. As a result, the QO subproblem is split into two small-scale QOs, which can generate two improved search directions for the two primal variables. Second, the augmented Lagrangian function is used as the merit function, and two step sizes are yielded by performing the Armijo line search along the two improved directions. Third, under mild conditions, the global convergence, strong convergence, iterative complexity, and Maratos effect of the DSL-SS-SQO algorithm are proven. Finally, some numerical results are reported, comparisons with the results obtained by the IPOPT solver are also provided, which preliminarily show that the proposed algorithm is promising.

Modelling and Design Optimization of a Novel Wide‐Body Transport Aircraft to Improve the Structural Integrity

One of the most challenging next‐generation issues is examining a novel and sustainable aircraft to reduce emissions and fuel burn. IATA addressed these issues in collaboration with the EU, GARDEN, and Clean Sky programs to tackle the challenges using retrofit design and upgraded systems. This study aims to create a sustainable aircraft design to solve the fuel burn issue by minimizing the maximum take‐off weight (MTOW). An optimized wide‐body aircraft is established by selecting twelve aerodynamic design variables and fourteen flight mission constraints (retrofit, operational performance, and stability). To develop a sustainable wide body aircraft structure, this study proposes a hybrid design optimization algorithm combined with the multicriteria decision‐making (MCDM) technique. The CRITIC‐WASPAS technique is used to obtain the baseline aircraft, and the optimal design of the baseline aircraft is achieved by solving the proposed nonlinear constrained optimization model. The selected baseline aircraft was compared with the optimized result to validate and determine the robustness of the objective function. The findings reflect that the formulation has improved the MTOW, empty weight fraction, fuel weight, and performance by 3.75%, 28.38%, 2.06%, and 8.63%, respectively.

Optimization of Spacecraft Thrusters Configuration Under Fault Diagnosability and Recoverability Constraints

This paper investigates the problem of optimal placement (position and orientation) of spacecraft thrusters, under fault diagnosability and fault recoverability constraints. Avionics equipment contamination and plume impingement are also considered. The goal is to find the thrusters configuration with the minimal number of thrusters required for a given spacecraft architecture, so that it is guaranteed that it is possible to equip the control unit with a model-based fault diagnosis and fault-tolerant control solution, able to accommodate any single thruster's fault. This includes total loss of controllability of the faulty thruster. The proposed solution is a model-based solution in the sense that it is based on the spacecraft attitude and translational dynamics. With the help of the zonotope concept and its so-called H-representation, it is shown that this problem can be formulated as a nonlinear constrained optimization problem, which can be solved efficiently using hybrid optimization techniques. The proposed solution is assessed on a generic spacecraft architecture that performs a proximity maneuver.

Regularized Interior Point Methods for Constrained Optimization and Control

Regularization and interior point approaches offer valuable perspectives to address constrained nonlinear optimization problems in view of control applications. This paper discusses the interactions between these techniques and proposes an algorithm that synergistically combines them. Building a sequence of closely related subproblems and approximately solving each of them, this approach inherently exploits warm-starting, early termination, and the possibility to adopt subsolvers tailored to specific problem structures. Moreover, by relaxing the equality constraints with a proximal penalty, the regularized subproblems are feasible and satisfy a strong constraint qualification by construction, allowing the safe use of efficient solvers. We show how regularization benefits the underlying linear algebra and a detailed convergence analysis indicates that limit points tend to minimize constraint violation and satisfy suitable optimality conditions. Finally, numerical results indicate that the combined approach compares favorably, in terms of robustness, against both interior point and augmented Lagrangian codes.

Semi-active Groundhook Control of Offshore Tension Leg Platforms Using TMD with Optimized Parameters and MR Damper Under Regular waves

The motivation and objective of the present study are to propose a semi-active control system for offshore tension leg platforms (TLPs) to mitigate the vibrations induced by regular wave loads. State-of-the-art indicates that not much work is reported on semi-active control of offshore TLPs considering potential nonlinearities for multiple hazards using a control algorithm, which is robust against uncertainties. A displacement based groundhook (DB-GH) control algorithm using tuned mass damper (TMD) and magneto-rheological (MR) damper is employed for the semi-active controller because of its robustness against parametric uncertainties and reliability. Optimized parameters of the semi-active TMD (SATMD) are obtained using constrained nonlinear optimization to achieve the best control performance. The flexibility of the groundhook control lies in its simplicity of implementation, computational efficiency and its demand for only two sensors in order to achieve the calculations of control forces. The scope of the present study is to demonstrate the efficiency of the proposed controller and investigate the effects of different influencing parameters. A TLP, reported in literature, is taken as an illustrative example. The non-linearly coupled dynamic responses of the structure-damper system is analysed and solved in time domain using MATLAB SIMULINK. The results show the SATMD performs quite satisfactorily in reducing the responses of the TLP in different critical conditions.

Online Feedback Optimization of Compressor Stations with Model Adaptation using Gaussian Process Regression

Online Feedback Optimization is a method used to steer the operation of a process plant to its optimal operating point without explicitly solving a nonlinear constrained optimization problem. This is achieved by leveraging a linear plant model and feedback from measurements. However the presence of plant-model mismatch leads to suboptimal results when using this approach. Learning the plant-model mismatch enables Online Feedback Optimization to overcome this shortcoming. In this work we present a novel application of Online Feedback Optimization with online model adaptation using Gaussian process regression. We demonstrate our approach with a realistic load sharing problem in a compressor station with parametric and structural plant-model mismatch. We assume imperfect knowledge of the compressor maps and design an Online Feedback Optimization controller that minimizes the compressor station power consumption. In the evaluated scenario, imperfect knowledge of the plant leads to a 5% increase in power consumption compared to the case with perfect knowledge. We demonstrate that Online Feedback Optimization with model adaptation reduces this increase to only 0.8%, closely approximating the case of perfect knowledge of the plant, regardless of the type of mismatch.

Non-Axisymmetric Buckling Stress of Axially Compressed Circular Cylindrical Shells: Closed-Form and Simplified Formulae

AbstractDue to their thin-walled characteristics, axially loaded circular cylindrical shells (CCSs) commonly undergo buckling failure. The limiting buckling stress of such shells has not yet been fully developed due to a wide range of influencing parameters such as sensitivity to imperfections, nonlinearity, and buckling mode. It has been proved early, and in this study, that the nonaxisymmetric buckling stress can be one of the remedies that casts into eliminating the overestimation caused by the classical axisymmetric buckling formula. However, the complex nonlinear constrained optimization required to obtain the nonaxisymmetric buckling stress and mode remains to be the main obstacle for practicing engineers to approach the nonaxisymmetric buckling. In this study, the nonaxisymmetric buckling formula has been cast in a compact form and possible approaches to utilize it have been discussed considering the degree of user knowledge and availability of computational tools. Moreover, it has been used to derive a closed-form buckling stress formula that considers the effect of all geometric and material properties. The proposed closed-form formula predicts buckling stress that is always less than that of the classical formula for L/R greater than 0.91 and the amount of reduction increases with the increase of L/R ratio. In comparison with the exact nonaxisymmetric buckling formula, the proposed closed-form formula yields buckling stress within ± 4%. Thus, it shares the simplicity of the classical axisymmetric buckling formula and the accuracy of the nonaxisymmetric buckling formula.

A particle swarm optimization algorithm based on an improved deb criterion for constrained optimization problems.

To solve the nonlinear constrained optimization problem, a particle swarm optimization algorithm based on the improved Deb criterion (CPSO) is proposed. Based on the Deb criterion, the algorithm retains the information of 'excellent' infeasible solutions. The algorithm uses this information to escape from the local best solution and quickly converge to the global best solution. Additionally, to further improve the global search ability of the algorithm, the DE strategy is used to optimize the personal best position of the particle, which speeds up the convergence speed of the algorithm. The performance of our method was tested on 24 benchmark problems from IEEE CEC2006 and three real-world constraint optimization problems from CEC2020. The simulation results show that the CPSO algorithm is effective.

A filter sequential adaptive cubic regularization algorithm for nonlinear constrained optimization

A filter sequential adaptive cubic regularization algorithm for nonlinear constrained optimization

Double-track particle swarm optimizer for nonlinear constrained optimization problems

Particle swarm optimization (PSO) is a popular stochastic algorithm for solving nonlinear optimization problems. It has been used in various industrial applications because of its few parameters and ease of implementation. Various optimal problems must be frequently formed as nonlinear constrained optimization (NCO) problems because of global resource limitations. These problem-specific nonlinear constraints can result in many infeasible regions in the search space. Current PSO-based approaches are inherently designed for unconstrained optimization problems and cannot directly handle the constraint issue; therefore, they add the constraint handling technique (CHT) to account for NCO problems. This study proposes a double-track schema inside PSO called double-track PSO (DTPSO) to address the NCO problem. When an infeasible region blocks a particle, the DTPSO creates a copy of the particle. The original and copied particles utilize different search strategies to move to feasible and infeasible regions. The results indicate that the proposed DTPSO outperforms the seven referenced PSO-based methods in all 33 NCO problems and five recent strong methods in 19 mechanical design problems belonging to the IEEE CEC 2020 competition on real-world single-objective constrained optimization problems. Furthermore, the experiment results demonstrate the quality of the solution and the effective computation of the proposed DTPSO.

Densest plane group packings of regular polygons.

Packings of regular convex polygons (n-gons) that are sufficiently dense have been studied extensively in the context of modeling physical and biological systems as well as discrete and computational geometry. Former results were mainly regarding densest lattice or double-lattice configurations. Here we consider all two-dimensional crystallographic symmetry groups (plane groups) by restricting the configuration space of the general packing problem of congruent copies of a compact subset of the two-dimensional Euclidean space to particular isomorphism classes of the discrete group of isometries. We formulate the plane group packing problem as a nonlinear constrained optimization problem. By means of the Entropic Trust Region Packing Algorithm that approximately solves this problem, we examine some known and unknown densest packings of various n-gons in all 17 plane groups and state conjectures about common symmetries of the densest plane group packings for every n-gon.

Research and application of a new multilevel fuzzy comprehensive evaluation method for cold stress in dairy cows.

Effective and comprehensive evaluation of cold stress is critical for healthy dairy cow breeding in the winter. Previous studies on dairy cow cold stress have considered thermal environmental factors but not physiological factors or air quality. Therefore, this study aimed to propose a multilevel fuzzy comprehensive evaluation (FCE) method for cold stress in dairy cows based on the analytic hierarchy process (AHP) and a genetic algorithm (GA). First, the AHP was used to construct an evaluation index system for cold stress in dairy cows from 3 dimensions: thermal environment (temperature, relative humidity, wind speed, and illumination), physiological factors (respiratory rate, body surface temperature), and air quality [NH3, CO2, inhalable particulate matter (PM10)]. Second, the consistency test of the judgment matrix was transformed into a nonlinear constrained optimization problem and solved using the GA. Next, based on fuzzy set theory, the comment set and membership function were established to classify the degree of cold stress into 5 levels: none, mild, moderate, high, and extreme. Then, the degree of cold stress in cows was obtained using multilevel fuzzy comprehensive judgment. To investigate the effect of illumination indicators on cold stress in dairy cows, 24 prelactation cows from the south and north sides were selected for a 117-d comprehensive cold stress evaluation. The results showed that the mean mild cold stress durations were 605.3 h (25.22 d) and 725.5 h (30.23 d) and the moderate cold stress durations were 67.2 h (2.8 d) and 96 h (4.0 d) on the south and north sides, respectively. Simultaneously, generalized linear mixed model showed that there were significant correlations between the daily cold stress duration and milk yield, feeding time, lying time, and active steps in the cows on both sides. This method can reasonably indicate cow cold stress conditions and better guide cold protection practices in actual production.

Optimal coordination of directional overcurrent relay based on combination of Firefly Algorithm and Linear Programming

Optimal coordination and settings of directional overcurrent relays (DOCRs) are crucial task to ensure reliable and effective protection in power system networks. The settings of DOCRs are plug setting current (PSC) and time multiplier setting (TMS). The DOCRs coordination is well-known as a highly constrained nonlinear optimization problem. Its complexity in terms of non-linearity increases along with the network size increment. This paper proposes a hybrid optimization algorithm which consists of Firefly Algorithm and Linear Programming (FA-LP) to relax the search space by linearizing the equation of the DOCRs coordination to attain an optimal solution. Furthermore, this paper also considers a mixed type of IEC relay characteristics to attain effective relay operation. The proposed method is tested on the IEEE 8-, 15- and 30-bus test systems. The results show the reduction of total relay operating time between 15.6% and 85.5% as compared to other techniques in the literature and also being verified using the ETAP software.

Magnetic particle tracking: A semi-algebraic solution

Magnetic Particle Tracking (MPT) is a relatively new non-invasive measurement technique which is often used to study dense granular flow. Its basic principle relies on tracking the movement of a single magnetic tracer by means of measuring the magnetic field strength at a suitable distance from the tracer. By assumption of a magnetic dipole and the use of minimization techniques, both location and orientation of the tracer can be determined. MPT is therefore uniquely suited for the study of non-spherical particles. The performance of the localization is largely dependent on the signal-to-noise ratio and very often relies on nonlinear optimization techniques, as the definition of the magnetic field generated by a dipole is highly nonlinear and has five degrees of freedom. In this paper, we present a semi-algebraic solution by decoupling the estimation of the position and orientation in separate algebraic solutions. The two estimates are mutually dependent, necessitating an iterative approach between the two. The main benefits of this new approach is in the speed and robustness of the algorithm, which are much higher than for the classical constrained nonlinear optimization techniques.

A NSGA-II variant for the dynamic economic emission dispatch considering plug-in electric vehicles

The dynamic economic emission dispatch considering plug-in electric vehicles (DEED-PEV) belongs to a nonlinear constrained optimization problem and has the multimodal and discontinuity characteristics. The first characteristic mainly comes from the cost function with valve-point effects, and the second one is associated with the constraints of prohibited operating zones. In this paper, a novel NSGA-II (NNSGA-II) is proposed to deal with DEED-PEV. NNSGA-II replaces the simulated binary crossover operator by the one based on Gaussian distribution, and adaptively adjusts the crossover rate of each individual according to its rank in population. Also, it incorporates a rewarding coefficient into the crowding distance in density estimation, which gives considerations to both density and evenness of solutions. Accordingly, NNSGA-II is able to perform extensive searches in solution space and achieve a series of individuals with high diversity and good evenness. Experimental results suggest that NNSGA-II outperforms the other seven MOEAs for nine DEED-PEV problems with different charging and discharging scenarios of plug-in electric vehicles, and its obtained solutions are superior to those of the other seven MOEAs according to the hypervolume and coverage indicators. In short, NNSGA-II is a potential alternative for minimizing the generation cost and pollutant emission of DEED-PEV.

Studying the Efficiency of Parallelization in Optimal Control of Multistage Chemical Reactions

In this paper, we investigate the problem of optimal control of complex multistage chemical reactions, which is considered a nonlinear global constrained optimization problem. This class of problems is computationally expensive due to the inclusion of multiple parameters and requires parallel computing systems and algorithms to obtain a solution within a reasonable time. However, the efficiency of parallel algorithms can differ depending on the architecture of the computing system. One available approach to deal with this is the development of specialized optimization algorithms that consider not only problem-specific features but also peculiarities of a computing system in which the algorithms are launched. In this work, we developed a novel parallel population algorithm based on the mind evolutionary computation method. This algorithm is designed for desktop girds and works in synchronous and asynchronous modes. The algorithm and its software implementation were used to solve the problem of the catalytic reforming of gasoline and to study the parallelization efficiency. Results of the numerical experiments are presented in this paper.

Optimizing the amount of concrete for the construction of wastewater stabilization ponds: A case study of Ayvadere, Trabzon, Türkiye

Natural systems are a cost-effective way to clean wastewater from small communities. This paper aims to use an optimization technique to minimize the volume of concrete needed to construct a facultative pond provided within a series of three ponds. A nonlinear constrained optimization model was written and then solved using one of the Add-Ins of MS office. The add-in used was Excel Solver, and the algorithm was generalized reduced gradient (GRG). Before applying the optimization model, wastewater stabilization ponds (WSPs) were de-signed using various configurations and arrangements. The best possible configuration that gave minimum area and hydraulic detention time was selected for the study area. Afterward, the optimization model was applied that further reduced the area by 11.46 %, hydraulic detention time by 11.47%, and concrete volume by 6.94% compared to the traditional approach. In both methods, effluents satisfy the Turkish class-B stand-ards for irrigation. It is recommended that a small-scale application of the model be made to compare the results before applying it on a large scale.

Computational Neural Dynamics Model for Time-Variant Constrained Nonlinear Optimization Applied to Winner-Take-All Operation

Although time-variant nonlinear optimization with equality and inequality constraints (TVNOEIC) is a widespread problem in real life, the research on this issue is much less than the time-invariant one. Large lagging errors may not be inevitable if the traditional models designed for time-invariant optimizations are exploited to time-variant ones. To eliminate the lagging errors, models for handling time-variant optimization problems are urgently required. Recently, neural networks and the related neural dynamics approaches have witnessed rapid developments and made significant contributions to the online solution of various problems. On this basis, a noise-suppressing discrete-time neural dynamics (NSDTND) model is proposed in this article for solving the TVNOEIC problem. Theoretical analysis is presented to prove that the residual error of the proposed model is tiny enough to estimate the actual solution even in the presence of noise perturbation. In addition, numerical simulations, including an application on winner-take-all operation, are provided to further demonstrate the effectiveness and robustness of the proposed NSDTND model.