Quadratic Programming Research Articles

A multi-criteria decision-making approach for pressurized water reactor based on hesitant fuzzy-improved cumulative prospect theory and 2-additive fuzzy measure

As one of the world's largest energy consumers, China has paid much attention to the development of non-fossil energy sources. The nuclear power is regarded as the top priority for development due to its remarkable ecological and economic advantages. Given the large investment, long lifecycle, and rigorous quality control, the conceptual design plays a critical role in the pressurized water reactor development. Multitudinous design alternatives are presented at this stage and it is essential to develop an advanced evaluation approach. Hence, this work proposes a multi-criteria decision-making approach for pressurized water reactor based on hesitant fuzzy-improved cumulative prospect theory and 2-additive fuzzy measure. Firstly, considering the inherent uncertainty and cognitive biases of nuclear power experts, cumulative prospect values are calculated for design alternatives by adopting dual prospect reference points and two-tuple entropy measure under a hesitant fuzzy environment. Secondly, a linear programming model based on bidirectional projection measures is constructed to eliminate the discordance between the independent criteria assumption and interdependent evaluation information. This model helps to identify optimal 2-additive fuzzy measures, which serve as the basis for determining the Shapley importance and interaction indices of evaluation criteria. Then, taking Shapley interaction indices modification into account, a quadratic programming model based on the global criterion method is built. Finally, 2-additive Choquet integral-based TOPSIS method is proposed to select the optimal design alternative. A case study on the essential service water system is implemented to demonstrate the reliability and superiority of the proposed approach.

Multi-objective design optimization of polymer spur gears using a hybrid approach

Polymer gears are used in applications requiring small to moderate loads to effectively transmit power and use the limited place available as possible. Various commercial standards have been provided designers with the rating criteria and acquaintance of different polymer material properties for the process of design. However, the result was unsatisfactory in terms of economy, time, and the optimality of the product. Thus, classic and stochastic algorithms have been embraced to reach the best design of polymer gears. Taking advantage of the former and latter algorithm’ methods, optimal design of gears could be attained with an increased gear life span and decreased failure modes. In this study, polyoxymethylene (POM) spur gear set has been optimized combining the mathematical model from plastic standards and hybrid optimization approach of multi-objective genetic algorithm (MOGA) and sequential quadratic programming (SQP). Weight and power loss were the objective functions. Five design variables were optimized with the satisfaction of bending and contact stresses, temperature, wear, and deformation as constraints. Solutions of the problem were formulated as Pareto optimal set. The results of multi-objective were compared with previously published single-objective optimization. The results favored multi-objective optimization (82.67%, 31.39% reduction in weight and power loss respectively) as it gave the best applicable solution fitting in real life situations. The results also went hand in hand with literature confirming the efficiency of the proposed algorithm. With the variation of operating parameters, various optimal designs could be obtained where the designers can choose the design that is suitable for a particular application.

Estimating a Function and Its Derivatives Under a Smoothness Condition

We consider the problem of estimating an unknown function [Formula: see text] and its partial derivatives from a noisy data set of n observations, where we make no assumptions about [Formula: see text] except that it is smooth in the sense that it has square integrable partial derivatives of order m. A natural candidate for the estimator of [Formula: see text] in such a case is the best fit to the data set that satisfies a certain smoothness condition. This estimator can be seen as a least squares estimator subject to an upper bound on some measure of smoothness. Another useful estimator is the one that minimizes the degree of smoothness subject to an upper bound on the average of squared errors. We prove that these two estimators are computable as solutions to quadratic programs, establish the consistency of these estimators and their partial derivatives, and study the convergence rate as [Formula: see text]. The effectiveness of the estimators is illustrated numerically in a setting where the value of a stock option and its second derivative are estimated as functions of the underlying stock price.

Adaptive control algorithm for quadruped robots in unknown high-slope terrain

The capability to navigate high-slope terrains is crucial for quadruped robots engaged in field operations. We propose a novel terrain estimation and adaptation strategy tailored for facilitating quadruped robot locomotion on complex slope terrains. Our approach involves predicting terrain slopes by analyzing foot positions and IMU data, subsequently adjusting the robot’s body orientation and height in real-time to accommodate varying slope conditions. To effectively control the motion of quadruped robots on such challenging terrains, we introduce a multimodal motion control algorithm that integrates Model Predictive Control (MPC) with Quadratic Programming (QP) torque control. This combined approach ensures stable and efficient locomotion even on steep slopes. Furthermore, we present a state estimation method based on Kalman filtering, enabling accurate self-assessment by the robot without heavy reliance on visual sensors. In simulation validation, our quadruped robot achieved notable performance metrics. It achieved a forward speed of 0.7 m/s on slopes with angles up to 43∘ and demonstrated stable rotational capability at a speed of 2 rad/s on a 32∘ slope. When subjected to external force interference, the robot exhibited resilience, withstanding constant external forces of up to 60Nm and external torques of up to 35Nm on flat ground. Moreover, on a 30∘ slope, the robot maintained stable locomotion in the face of impulses reaching 64Nm ⋅ s along the x and y directions of its body coordinate system and 7Nm ⋅ s along the z-axis. This comprehensive strategy and experimental validation highlight the efficacy and robustness of our adaptive control algorithm, paving the way for enhanced performance of quadruped robots navigating high-slope terrains with unpredictable characteristics.

Adaptive Nonsingular Fast Terminal Sliding Mode-Based Direct Yaw Moment Control for DDEV under Emergency Conditions

Adaptive Nonsingular Fast Terminal Sliding Mode-Based Direct Yaw Moment Control for DDEV under Emergency Conditions

Sequential Quadratic Programming (SQP) Based Optimal Power Flow Methodologies for Electric Distribution System With High Penetration of DERs

Sequential Quadratic Programming (SQP) Based Optimal Power Flow Methodologies for Electric Distribution System With High Penetration of DERs

A Simulation-Based Method for Optimizing Remote Park-and-Ride Schemes

Urbanization places greater demand on the link between downtown areas and suburbs, due to commuters’ long-distance and diverse trips. As an emerging form of park-and-ride (PNR) services, remote PNR (RPR) facilities have proved to be more economical and environmentally friendly, allowing travelers to park in a suburban area and travel to a rail station via bus. In this regard, a generalized simulation-based bilevel model for optimizing the locations and capacities of RPR facilities is developed in this article. A hybrid algorithm integrating Bayesian optimization, branch and bound, and trust region sequential quadratic programming is proposed to achieve an optimal solution. The proposed integrated method balances the desired efficiency and accuracy through the combination of machine learning-based technology and mathematical optimization methodology. The validity of the proposed model is tested on a large-scale real-world transportation network in Halle, Germany. Modeling and analyzing RPR schemes using the proposed framework may provide new insights into improving social welfare.

1-bit Massive MIMO Signal Detector Based on Convex Integral Quadratic Programming

1-bit Massive MIMO Signal Detector Based on Convex Integral Quadratic Programming

이차계획법에 기반한 소파 이동 문제의 상한선 개선

The moving sofa problem is a problem in discrete geometry that involves finding a shape with the maximum area that can pass through a right-angled corner in a hallway with unit width, and has remained an open problem since it was posed by Moser in 1966. The largest lower bound on the maximum area known to date is 2.2195..., found by Gerver in 1992, and the smallest upper bound is 2.37, proved by Kallus and Romik in 2018. While the minimum upper bound of 2.37 appears to be somewhat loose, experimental evidence suggests that there is little room for improvement in the largest lower bound of 2.2195.... In this study, we aim to lower the upper bound to be closer to Gerver’s maximum lower bound. For this purpose, we construct an optimization algorithm based on geometric branch-and-bound and quadratic programming, and prove various geometric properties for efficient search of the algorithm. Under a reasonable geometric assumption, the proposed optimization algorithm obtains an improved upper bound of 2.3361 with much shorter computation time than Kallus and Romik.

Nonparametric Modelling of Ship Dynamics Using Puma Optimizer Algorithm-Optimized Twin Support Vector Regression

Ship dynamic models serve as the foundation for designing ship controllers, trajectory planning, and obstacle avoidance. Support vector regression (SVR) is a commonly used nonparametric modelling method for ship dynamics. Achieving high accuracy SVR models requires a substantial amount of training samples. Additionally, as the number of training samples increases, the computational efficiency for solving the quadratic programming problem (QPP) of SVR decreases. Ship controllers demand dynamic models with both high accuracy and computational efficiency. Therefore, to enhance the prediction accuracy and computational efficiency of SVR, this paper proposes a nonparametric modelling method based on twin SVR (TSVR). TSVR replaces a large QPP with a set of smaller QPPs, significantly enhancing generalizability and computational efficiency. To further improve the predictive accuracy of TSVR, the puma optimizer algorithm is employed to determine the optimal hyperparameters. The performance of the proposed method is validated using a Mariner class vessel. Gaussian white noise is introduced into the modelling data to simulate measurement error. The TSVR model accurately predicts various zigzag and turning circle manoeuvring motions under disturbance conditions, demonstrating its robustness and generalizability. Compared to the SVR model, the TSVR model achieves lower root mean square error and computational time, confirming its superior predictive accuracy and computational efficiency.

Uncertainty relation and the constrained quadratic programming

The uncertainty relation is a fundamental concept in quantum theory, plays a pivotal role in various quantum information processing tasks. In this study, we explore the additive uncertainty relation pertaining to two or more observables, in terms of their variance, by utilizing the generalized Gell-Mann representation in qudit systems. We find that the tight state-independent lower bound of the variance sum can be characterized as a quadratic programming problem with nonlinear constraints in optimization theory. As illustrative examples, we derive analytical solutions for these quadratic programming problems in lower-dimensional systems, which align with the state-independent lower bounds. Additionally, we introduce a numerical algorithm tailored for solving these quadratic programming instances, highlighting its efficiency and accuracy. The advantage of our approach lies in its potential ability to simultaneously achieve the optimal value of the quadratic programming problem with nonlinear constraints but also precisely identify the extremal state where this optimal value is attained. This enables us to establish a tight state-independent lower bound for the sum of variances, and further identify the extremal state at which this lower bound is realized.

Convex distributed robust model predictive control for collision and obstacle avoidance

AbstractThe article proposes a convex distributed robust model predictive control algorithm for collision avoidance in multi‐agent systems with additive disturbances, which utilizes the concept of tube model predictive control to address the disturbances. To tackle the coupled collision avoidance constraints, each agent integrates assumed nominal position and input trajectories from its neighbors, rather than relying on actual ones. Compatibility constraints are then designed using the normal vector of the constructed separating hyperplanes for collision avoidance and the residual collision avoidance margin of the optimal solutions at the last time step to restrict deviations between assumed and actual trajectories and ensure consistency among the agents. The nonconvex collision and obstacle avoidance constraints are convexified using the concept of safe sets, transforming them into time‐varying closed polyhedral constraints while accounting for the impact of disturbances. Particularly, the residual collision avoidance margin is incorporated into the construction of safe sets for the satisfaction of coupled collision avoidance constraints. Consequently, the original collision avoidance optimal control problems can be efficiently and simultaneously solved for all agents using standard quadratic programming techniques. Under the design of local terminal constraint sets for each agent, the proposed algorithm ensures a rigorous analysis of robust constraint satisfaction for collision avoidance constraints, as well as an assessment of recursive feasibility and closed‐loop stability. The effectiveness of the algorithm is demonstrated through an illustrative example, and simulation results validate its ability to successfully achieve collision and obstacle avoidance even in the presence of disturbances.

A Reentry Trajectory Planning Algorithm via Pseudo-Spectral Convexification and Method of Multipliers

The reentry trajectory planning problem of hypersonic vehicles is generally a continuous and nonconvex optimization problem, and it constitutes a critical challenge within the field of aerospace engineering. In this paper, an improved sequential convexification algorithm is proposed to solve it and achieve online trajectory planning. In the proposed algorithm, the Chebyshev pseudo-spectral method with high-accuracy approximation performance is first employed to discretize the continuous dynamic equations. Subsequently, based on the multipliers and linearization methods, the original nonconvex trajectory planning problem is transformed into a series of relaxed convex subproblems in the form of an augmented Lagrange function. Then, the interior point method is utilized to iteratively solve the relaxed convex subproblem until the expected convergence precision is achieved. The convex-optimization-based and multipliers methods guarantee the promotion of fast convergence precision, making it suitable for online trajectory planning applications. Finally, numerical simulations are conducted to verify the performance of the proposed algorithm. The simulation results show that the algorithm possesses better convergence performance, and the solution time can reach the level of seconds, which is more than 97% less than nonlinear programming algorithms, such as the sequential quadratic programming algorithm.

A non-overlapping optimization-based domain decomposition approach to component-based model reduction of incompressible flows

We present a component-based model order reduction procedure to efficiently and accurately solve parameterized incompressible flows governed by the Navier-Stokes equations. Our approach leverages a non-overlapping optimization-based domain decomposition technique to determine the control variable that minimizes jumps across the interfaces between sub-domains. To solve the resulting constrained optimization problem, we propose both Gauss-Newton and sequential quadratic programming methods, which effectively transform the constrained problem into an unconstrained formulation. Furthermore, we integrate model order reduction techniques into the optimization framework, to speed up computations. In particular, we incorporate localized training and adaptive enrichment to reduce the burden associated with the training of the local reduced-order models. Numerical results are presented to demonstrate the validity and effectiveness of the overall methodology.

Remark on Algorithm 1012: Computing projections with large data sets

In ACM TOMS Algorithm 1012, the DELAUNAYSPARSE software is given for performing Delaunay interpolation in medium to high dimensions. When extrapolating outside the convex hull of the training set, DELAUNAYSPARSE calls the nonnegative least squares solver DWNNLS to compute projections onto the convex hull. However, DWNNLS and many other available sum of squares optimization solvers were not intended for usage with many variable problems, which result from the large training sets that are typical in machine learning applications. Thus, a new PROJECT subroutine is given, based on the highly customizable quadratic program solver BQPD . This solution is shown to be as robust as DELAUNAYSPARSE for projection onto both synthetic and real-world data sets, where other available solvers frequently fail. Although it is intended as an update for DELAUNAYSPARSE , due to the difficulty and prevalence of the problem, this solution is likely to be of external interest as well.

Novel solution strategies for multiparametric nonlinear optimization problems with convex objective function and linear constraints

AbstractThis paper expands the multiparametric quadratic programming (mp-QP) framework presented in Narciso et al. (Comput Chem Eng 164:107882, 2022. https://doi.org/10.1016/j.compchemeng.2022.107882) to the more general multiparametric nonlinear programming (mp-NLP) case. First, the vector of parameters in mp-NLP problems is recast so that a unique transformed parameter is implicitly assigned to each of the inequality constraints. Maps of critical regions in this transformed space of parameters feature a set of 1-dimensional parametric edges (two per inequality constraint), which then greatly facilitate solution calculation. In the mp-NLP case, however, parametric edges define nonlinear semi-infinite lines; this requires an adaptation to the mp-QP algorithm (deals with linear parametric edges only), to enable a suitable calculation path to the more general nonlinear case. Three routes are proposed to mp-NLPs: the first route delivers solutions in compact form (same format as in mp-QP) using a single reference point per edge; the second route delivers explicit solutions using a hybrid approach for critical region construction, where all active sets not detected in the parameters space are excluded from the solution (equivalent to first route concerning accuracy); the third route builds on the initial explicit solution and further partitions the parameters space until all solution fragments satisfy an error check. Five algorithms were coded for these routes, and tested in a large range of mp-NLP problems. These strategies enable significant improvements in terms of solution accuracy, algorithm efficiency, and interpretability when compared to the state-of-the-art mp-NLP algorithms.

Structure optimization of linear shaped charge based on different explosives

AbstractIn order to improve the damage ability of traditional shaped charge, a special linear shaped charge is designed. The driving characteristics of B explosive, HMX based explosive (JO‐8) and CL‐20 based explosive on linear explosively formed projectile (LEFP) are compared. The forming effect of LEFP is analyzed, the structural parameters of LEFP are designed, and the structure of shaped charge is optimized by combining genetic algorithm (NSGA‐II) and sequence quadratic programming (NLPQL). The Pulsed X‐ray experiment of scale LEFP is carried out. The results show that: (1) under the same structure, the LEFP formed by the shaped charge using CL‐20 explosive has better performance; (2) the LEFP formed by optimized B explosive is superior to that formed by unoptimized JO‐8 explosive, while LEFP formed by optimized JO‐8 explosive is superior to that formed by CL‐20 explosive, which indicates that explosives with lower energy density can also produce better LEFP after optimization; (3) The experimental results are consistent with the numerical results, which verifies the reliability of the numerical simulation and the effectiveness of the optimization method.

Energy management for scalable battery swapping stations: A deep reinforcement learning and mathematical optimization cascade approach

The rapid growth of electric vehicles is driving the expansion of scalable Battery Swapping Stations (BSSs) to meet the demand for fast charging. However, existing BSS energy management struggles to adapt to the changes in battery counts online, the uncertainty of electricity prices and battery demand, as well as the complexity of demand response (DR). To address these issues, we propose a cascading approach that combines Deep Reinforcement Learning (DRL) with Mathematical Optimization (MO). Firstly, our method employs a two-layer optimization framework and establishes a BSS model. The upper controller uses DRL to make sequential decisions on total power for each time slot, addressing sequential decision-making under uncertainty. The lower controller uses MO to allocate total power to each charging bay for a single time slot, addressing space complexity. Secondly, we tailor proximal policy optimization algorithms and mixed-integer quadratic programming algorithms for BSS DR. The DRL is universally adaptable to scalable BSS, while the MO automatically generates and solves optimization models based on the working charging bay count. The proposed method is at least 33 times faster than existing methods and performs well in scalable BSSs under uncertain conditions. It can converge within a typical BSS DR scheduling slot of 15 min based on an i7-8950H CPU, even for a BSS with 3200 charging bays.

Design of distributed trading mechanism for prosumers considering the psychological gap effect in community electricity markets

With the large-scale customer-side development of distributed energy and continuous advancements in power market reform, the market-oriented trading of distributed power generation with the participation of prosumers has gradually become an important solution to promote the consumption of distributed energy. In addition, prosumers exhibit obvious bounded rationality characteristics; therefore, the design of efficient and reasonable trading mechanisms determines the efficiency of the market. From this perspective, a distributed electricity market trading mechanism based on the Stackelberg game is proposed for the community electricity trading market, with multiple prosumers participating in the distribution side. Firstly, the trading architecture of the community electricity market was established under the distribution network level. Secondly, the pricing strategy of the distribution network operator and the quantitative strategy of community prosumers were analysed; on this basis, the characteristics of the bounded rationality of prosumers were considered, and the impact of the psychological gap effect of prosumers on their energy utility was introduced into the objective function of prosumers. This facilitated the construction of a Stackelberg game model in which distribution network operators lead and community prosumers follow. Thirdly, the Stackelberg equilibrium was proven to exist and be unique, which was then solved by the distributed algorithm – combining the evolutionary algorithm and quadratic programming – which improves the solution efficiency and effectively protects the privacy of prosumers. Finally, the effectiveness and feasibility of the proposed trading mechanism were verified through numerical examples.

Energy-based modeling of rate-independent hysteresis and viscoelastic effects in dielectric elastomer actuators

Dielectric elastomer (DE) transducers are known to exhibit a rate-dependent hysteresis in their force-displacement response, which is commonly attributed to the viscoelastic behavior of elastomer materials and compliant electrodes. In the case of DE materials characterized by low mechanical losses, such as silicone, the mechanical hysteresis often turns out to be practically rate-independent in the low frequency range (sub-Hz), whereas rate-dependent hysteretic effects only become relevant at higher deformation rates. Most of the existing literature focuses on describing DE hysteretic losses using viscoelasticity theory. This approach results in relatively simple dynamic models, which are not capable of describing rate-independent hysteretic behaviors. In this work, we propose a control-oriented modeling framework for both rate-dependent and rate-dependent hysteresis occurring in uniaxially loaded DE actuators. To this end, classic thermodinamically-consistent modeling approaches for DEs are combined with a new energy-based Maxwell-Lion formalization of the hysteretic losses. The resulting dynamic model comprises a set of nonlinear ordinary differential equations, and is capable of simultaneously describe geometric dependencies, large deformation nonlinearities, electro-mechanical coupling, and rate-independent and rate-dependent hysteretic effects. To deal with the large number of involved parameters, a novel systematic identification algorithm based on quadratic programming is also proposed. After presenting the theory, the model is validated based on experiments conducted on a silicone-based rolled DE actuator. Its superiority compared to classic DE viscoelastic models is quantitatively assessed.