Nonlinear Programming Algorithm Research Articles

Design and optimization of reverse salient permanent magnet synchronous motor based on controllable leakage flux

In this paper, a controllable leakage flux reverse salient permanent magnet synchronous motor (CLF-RSPMSM) is designed, which has the advantages of wide speed range and low irreversible demagnetization risk. Firstly, the principle of controllable leakage flux and reverse saliency effect is introduced, and the design of the rotor flux barrier is emphatically discussed. Secondly, multiple design variables are stratified by the comprehensive sensitivity method, and the main variables are screened out. Then the relationship between the main variables and the optimization goal is discussed according to the response surface diagram. Thirdly, a sequential nonlinear programming algorithm (SNP) is used to optimize the three optimization objectives comprehensively. Finally, the electromagnetic performance of the proposed motor is compared with the initial IPM motor, the mechanical strength of the proposed rotor is analyzed, and the results verify the effectiveness of the design and optimization method of the proposed motor.

Research on multi-objective optimal scheduling strategy of photovoltaic and energy storage based on dynamic programming

The multi-objective model of the electric vehicle and wind power in the load control is established, which stabilizes the peak and valley difference of load and electric vehicle charging and discharging cost. Considering the electric vehicle battery available capacity and charge discharge power constraints, as well as the genetic algorithm for nonlinear programming, this paper analyzes the influence of peak load difference on stabilizing the load fluctuation and improving the return of electric vehicle users. Finally, through the example analysis results show that the multi-objective model can be more optimized through the reasonable price in the electric vehicle charging and discharging and genetic algorithm for nonlinear programming and considering the peak and valley load difference, and the results curve is presented.

Improved Algorithm for Nonlinear Programming with Inequality Constraints Based on Big Data Framework

With the development of network technology and electronic information technology, the nonlinear programming problem (NPP) with inequality constraints in the BD framework has become one of the research hotspots and one of the trends that need improvement. Due to the introduction of BD technology, there is still a lack of research on the situation where the objective function is a NPP. The purpose of this article is to use the analysis and computing power of BD technology to simulate and calulate nonlinear programming (NP) with inequality constraints and improve it. In this paper, with the help of stability conditions, matrix splitting and iteration theory, the alternate direction method is used to solve the NPP with inequality constraints, and the principle of compressed mapping is used to finally prove the convergence of the alternate direction method. Matrix splitting techniques and Gauss-Seidel iterative ideas construct an iterative algorithm for solving linear systems. The iterative format of the alternating direction method for solving NPPs with inequality constraints and the equivalent matrix format are given to prepare for further proof of the convergence of the algorithm. Experimental research shows that the NPP model with inequality constraints designed by the dynamic BP technology error correction GPC algorithm used in this article has faster response time and smaller overshoot, and the control effect is better than 20% of the traditional GPC algorithm.

Polyhedral approximation strategies for nonconvex mixed-integer nonlinear programming in SHOT

Different versions of polyhedral outer approximation are used by many algorithms for mixed-integer nonlinear programming (MINLP). While it has been demonstrated that such methods work well for convex MINLP, extending them to solve nonconvex problems has traditionally been challenging. The Supporting Hyperplane Optimization Toolkit (SHOT) is a solver based on polyhedral approximations of the nonlinear feasible set of MINLP problems. SHOT is an open source COIN-OR project, and is currently one of the most efficient global solvers for convex MINLP. In this paper, we discuss some extensions to SHOT that significantly extend its applicability to nonconvex problems. The functionality include utilizing convexity detection for selecting the nonlinearities to linearize, lifting reformulations for special classes of functions, feasibility relaxations for infeasible subproblems and adding objective cuts to force the search for better feasible solutions. This functionality is not unique to SHOT, but can be implemented in other similar methods as well. In addition to discussing the new nonconvex functionality of SHOT, an extensive benchmark of deterministic solvers for nonconvex MINLP is performed that provides a snapshot of the current state of nonconvex MINLP.

Research and analysis of constrained generalized predictive identification algorithm based on the control field of hydropower industry

For GPC with constraints, these shortcomings are made up on the basis of nonlinear programming algorithm. Because of the strong local search ability of nonlinear programming and the strong global search ability of the algorithm, combined with the advantages of the algorithm and introduced into the rolling optimization process of GPC, the optimal control law is obtained. In this paper, a constrained generalized predictive identification algorithm based on the control field of hydropower industry is proposed, and a model of the constrained generalized predictive identification algorithm based on the control field of hydropower industry is established. The simulation results verify the applicability and effectiveness of the combined algorithm in the study of GPC, improve the accuracy and speed of the optimization results, and obtain satisfactory control effect.

Research on the Power Distribution Method for Hybrid Power System in the Fuel Cell Vehicle

The power distribution strategy of hybrid power sources is an important issue for fuel cell vehicles. A good power distribution control strategy can realize the optimal control of the vehicle energy, which can save energy and improve the operating conditions of the power source. Therefore, this article proposes a power distribution strategy. First, in order to solve the problems existing in the existing fuel cell model and the lithium-ion battery model, an improved hybrid power system model with better dynamic performance was established in the Simulink. Second, in order to ensure the durability of the power system, operation constraints are added to the distribution strategy. Finally, the power allocation is regarded as a nonlinear programming optimization problem and solved by a nonlinear programming algorithm. The nonlinear programming algorithm selects the BFGS algorithm. The simulation results of other control strategies in MATLAB show that the proposed power distribution strategy greatly improves the durability of the vehicle and has good adaptability under urban conditions. This distribution method can provide support for the actual application of offline control strategies.

Nonlinear management programming for grid connected hybrid system combined to e-mobility facility

The integration of renewable energy sources is a very essential point in the strategic list that has to be met by the different countries' governments to combat the constraints of the 21st century that the increased electricity demand in the residential sector represents the front-line constraints. However, the problem of intermittency inevitably arises. As a result, an optimal energy management represents the most intelligent solution to smoothen the energy profile during cases of extreme renewable production or critical energy shortages. Furthermore, in the second row the transport sector with major consumption of energy in a given country is regarded. For this reason, in a sense, to reduce greenhouse gas emissions that threatens the environmental climate, the development of transportation electrification combined to households equipped with a grid connected PV-wind-battery hybrid system is investigated in this paper. In fact, to take advantage of the integration of renewable energy systems to residential sector as well as the notion of transport electrification, the two notions are combined for electric vehicles with renewable energy charging. Indeed, the energy management of the global hybrid architecture is proposed via a nonlinear programming algorithm and validated with MATLAB simulation.

Sharp formulations of nonconvex piecewise linear functions to solve the economic dispatch problem with valve-point effects

Wire drawing effects in a unit with several steam admission valves produce some ripples in the unit cost characteristic. Representing the ripples as sinusoidal terms gives rise to a nonconvex cost characteristic. This paper focuses on the solution of the economic dispatch (ED) problem with the nonconvex cost functions. To this end, this work presents a new framework in which, firstly, the complex problem is tightly transformed into a set of linear programming (LP) problems using an iterative piecewise linear function (PLF) approximation especially developed for the nonconvex terms. Subsequently, five strong models including convex combination, disaggregated convex combination, multiple choice, incremental, and logarithmic techniques are proposed to represent the set of built LP problems as a mixed-integer programming (MIP) problem which efficiently can be solved by a robust powerful algorithm. Then, the obtained solution from the MIP algorithm is used to warm-start an enhanced nonlinear programming (NLP) model and to further improve the solution. In extensive experiments, we compare the performance of the presented methods in terms of solution quality, computational efficiency, and consistency with other approaches in the literature of the nonconvex ED. The tight PLF approximation and the five sharp and generally locally ideal MIP formulation techniques in conjunction with the existing efficient MIP and NLP algorithms result in the strong solution framework which can find a global or a virtually global solution and surpass the state-of-the-art methods in the area of the nonconvex ED in all considered case studies.

Hurdle-Hop Simulation of Tilt-Rotor Aircraft Based on Optimal Control Theory

Aiming at simulating the hurdle-hop of tilt-rotor aircraft in forward flight near the ground, two models of numerical simulation and analysis based on optimal control theory were proposed. Firstly, Longitudinal flight dynamic model for tilt-rotor was modified considering the influence of ground effect. Secondly, the first model is combined with predicted trajectory from inverse simulation method, the inverse model of hurdle-hop of tilt-rotor is established based on optimal trajectory, and the second model is the optimal control model of unpredicted trajectory, which is formulated from the reasonable function of objective, path and boundary constraints for hurdle-hop with detailed analysis, solved two models by direct multiple shooting method and nonlinear programming algorithm. Finally, XV-15 as the sample vehicle. Two models for hurdle-hop based on optimal control theory was calculated, the history of optimal flight trajectory and control are given.

Accelerating Generalized Benders Decomposition for Wireless Resource Allocation

Generalized Benders decomposition (GBD) is a globally optimal algorithm for mixed integer nonlinear programming (MINLP) problems, which are NP-hard and can be widely found in the area of wireless resource allocation. The main idea of GBD is decomposing an MINLP problem into a primal problem and a master problem, which are iteratively solved until their solutions converge. However, a direct implementation of GBD is time- and memory-consuming. The main bottleneck is the high complexity of the master problem, which increases over the iterations. Therefore, we propose to leverage machine learning (ML) techniques to accelerate GBD aiming at decreasing the complexity of the master problem. Specifically, we utilize two different ML techniques, classification and regression, to deal with this acceleration task. In this way, a cut classifier and a cut regressor are learned, respectively, to distinguish between useful and useless cuts. Only useful cuts are added to the master problem and thus the complexity of the master problem is reduced. By using a resource allocation problem in device-to-device communication networks as an example, we validate that the proposed method can reduce the computational complexity of GBD without loss of optimality and has good generalization ability. The proposed method is applicable for solving various MINLP problems in wireless networks since the designs are invariant for different problems.

Distance to the stochastic part of phylogenetic varieties

Modelling the substitution of nucleotides along a phylogenetic tree is usually done by a hidden Markov process. This allows to define a distribution of characters at the leaves of the trees and one might be able to obtain polynomial relationships among the probabilities of different characters. The study of these polynomials and the geometry of the algebraic varieties defined by them can be used to reconstruct phylogenetic trees. However, not all points in these algebraic varieties have biological sense. In this paper, we explore the extent to which adding semi-algebraic conditions arising from the restriction to parameters with statistical meaning can improve existing methods of phylogenetic reconstruction. To this end, our aim is to compute the distance of data points to algebraic varieties and to the stochastic part of these varieties. Computing these distances involves optimization by nonlinear programming algorithms. We use analytical methods to find some of these distances for quartet trees evolving under the Kimura 3-parameter or the Jukes-Cantor models. Numerical algebraic geometry and computational algebra play also a fundamental role in this paper.

Simultaneous material, shape and topology optimization

Using three design fields we develop an optimization environment that can simultaneously optimize material, shape and topology. We use the implicit representation of the boundaries with level-set functions that define the shape and topology. Differentiable R-functions allow us to combine these shapes and topology descriptions with Boolean operations. Additionally, we incorporate design dependent-stiffness materials with another design field. Notably, this framework accommodates design dependent loads, has the ability to introduce holes, and ensures the satisfaction of optimality criteria. It builds upon the fictitious domain, ersatz material, material interpolation and level-set methods. It also borrows from parameterized density-based topology optimization methods. Since analytical sensitivities can be computed, we use efficient nonlinear programming algorithms to update the design instead of the Hamilton–Jacobi’s scheme of level-set methods. We illustrate the features of our framework by designing a cantilever beam with octet truss microlattice, a dam with design-dependent loads, and a composite clevis plate.

Improved Superstructural Optimisation of an Industrial Water System with Multiple Water Resources

Most of the previous industrial water network models use freshwater as a vital water supply source without defining the origin of freshwater. However, in practice, the freshwater can be obtained from many water resources (e.g., municipal water, groundwater, surface water, municipally treated water, and seawater), after necessary Pre-treatment. Also, the effluents from the desalted water station, power station, and cooling water station can be used in other water using processes by satisfying the contaminant limits. Nevertheless, the existing water system design model does not apply directly to the design of effective industrial water systems. In order to overcome the above limitation, this paper proposed an innovative property based mathematical superstructure model for the industrial water network, consisting of water pre-treatment, water utility, water-using, and wastewater treatment systems. The proposed mathematical model provides appropriate water resource selection to acquire freshwater for the industrial water network and integrates all possible functional designs for water treatment, reuse, and recycling. The design model comprises the related equations, flow rate, and property constraints between the different water sources and sinks. The proposed model is framed as a nonlinear programming (NLP) algorithm and resolved using commercial software GAMS. The proposed model is validated by a case study of the simplified water system of the Chinese industrial chemical complex. Results show a substantial reduction of 8.39 % and 21.75 % in the total annualised cost and freshwater demand.

Topology optimization of multiple deformable bodies in contact with large deformations

Previous works in topology optimization of structures with contact boundary conditions have concentrated on the two-dimensional rigid obstacle problem. This is because the contact analysis of multiple three-dimensional deformable bodies with meshes that are non-matching across the contact interface requires computationally complex contact algorithms beyond the scope of previous optimization investigations. Our research is devoted to addressing topology design problems with multiple deformable three-dimensional components in contact using state-of-the-art contact algorithms.We formulate and resolve the design simulation problem using large deformation continuum mechanics and the finite element method. To account for large sliding that can occur during the design optimization process here, the mortar segment-to-segment approach was used to discretize the contact surface due to its numerical robustness in this regime. Since, mortar integrals provide smooth contact forces as nodes slide on/off the surface, solution convergence is well behaved. Considering the contact problem is computationally expensive to solve, we solve the optimization problem using efficient nonlinear programming algorithms which require the sensitivities of the cost and constraint functions. To this end, we formulate analytical adjoint sensitivity expressions to compute the gradients of general functionals. As expected and corroborated in this work, the adjoint method is computationally efficient. Additionally, we use a B-spline design parameterization to regularize the topology optimization problem. We show that this parameterization reduces the number of design variables compared to usual element-wise parameterizations and provides a precise and smooth description of the design boundary. We present numerical example problems of multiple deformable three-dimensional bodies in contact with large deformations and find optimal topologies that maximize the total contact force, maximize the strain energy, and minimize the compliance.

Two linear approximation algorithms for convex mixed integer nonlinear programming

We present two new algorithms for convex Mixed Integer Nonlinear Programming (MINLP), both based on the well known Extended Cutting Plane (ECP) algorithm proposed by Weterlund and Petersson. Our first algorithm, Refined Extended Cutting Plane (RECP), incorporates additional cuts to the MILP relaxation of the original problem, obtained by solving linear relaxations of NLP problems considered in the Outer Approximation algorithm. Our second algorithm, Linear Programming based Branch-and-Bound (LP-BB), applies the strategy of generating cuts that is used in RECP, to the linear approximation scheme used by the LP/NLP based Branch-and-Bound algorithm. Our computational results show that RECP and LP-BB are highly competitive with the most popular MINLP algorithms from the literature, while keeping the nice and desirable characteristic of ECP, of being a first-order method.

Nested optimization design for combined cooling, heating, and power system coupled with solar and biomass energy

Renewable energy source integration in combined cooling, heating, and power (RES-CCHP) systems can improve energy efficiency and foster renewable energy consumption, which is a promising solution to the current energy and environmental crisis. This paper studies the off-design characteristics of these systems, establishes a two-way interaction mechanism between the system capacity and operation strategy, and proposes a two-stage nested optimization design method for the RES-CCHP. In the first stage, the capacity of each system component is obtained by the genetic algorithm and then used as the constraint for the operation optimization. In the second stage, the nonlinear programming algorithm is employed to optimize the operational energy consumption, costs, and CO2 emissions taking the off-design characteristics of core devices into consideration. Several case studies are conducted to verify the feasibility of the two-stage optimal design method. It was found that the two-stage nested optimization design increases the primary energy saving ratio, cost saving ratio, and carbon dioxide emission reduction ratio by 4.5%, 4.32%, and 3.27% compared with the conventional optimal design method, respectively. Overall, the proposed two-stage nested optimization design was tested to improve the performance and the renewable energy consumption.

Adaptive Protection Strategy in a Microgrid Under Disparate Operating Modes

—Microgrids usually operate in grid-connected or islanded mode. Due to substantial variation in fault current, same protection coordination scheme cannot be applied in both modes. Moreover, network topology keeps on changing due to momentary events. In this paper, an adaptive protection strategy is proposed to avoid any miscoordination between numerical directional overcurrent relays under a fault instance. Through this scheme, the relay settings can be updated online as per the operating mode and prevailing topology. The proposed tactic employs a central protection center with data storage and programming capability, smart electronic devices and communication channels to acquire and transfer real-time data. The relay coordination problem is formulated as a non-linear optimization function, with coordination time interval constraints. The optimal relay settings under both operating modes are obtained through non-linear programming and hybrid genetic algorithm non-linear programming method. To handle contingencies of communication channel failure, a novel inclusive mode settings are also introduced to protect the system in both modes even with line or DG outages. The proposed adaptive approach is tested on a nine bus radial distribution system with DGs. It has been found that the proposed scheme provides reliable system protection under different operating scenario.

Implementation of the nonlinear programming algorithm when optimizing the final turning mode

For computer-aided multi-variant design of machining technologies, it is important to optimize the cutting parameters at the final pass in each technological operation. When carrying out designing procedures, there emerge problems relating to the algorithm of choosing the decision-making method, the objective function, and the regions of feasibility at final machining steps. Linear programming is time-consuming for multi-variant and multi-pass machining, if the algorithm is to be clear. It is known that when simulating the optimal metal-cutting process, the optimization criterion and the system of constraints are non-linear. Therefore, a computational algorithm can be made significantly more efficient if it is a non-linear algorithm based on Lagrange multipliers Such approach to design helps simplify automating the computational algorithm for multi-pass single-tool machining with a precision cutting tool (a reamer) This is the method discussed herein.

Which Switch to Collect Statistics in Software-Defined Networks

Many monitoring methods have been proposed, due to that network measurement is essential in Software-Defined Networking. However, periodically or adaptively collecting statistics from software switches using per-flow queries incurs significant communication cost and thus increases the loads of switches. In this letter, we propose OpenCost, an approach to decide which switch to collect statistics in Software-Defined Networks based on nonlinear integer programming (NLIP). Simulation results show that OpenCost can reduce the communication cost by 55% in average. OpenCost is an approach based on nonlinear integer programming algorithm, which can be used to reduce communication cost induced by network measurement in Software-Defined Networking. Experiments show that OpenCost can be beneficial to save operating cost for Internet service provider.

An Acoustic Vehicle Detector and Classifier Using a Reconfigurable Analog/Mixed-Signal Platform

The wireless sensor nodes used in a growing number of remote sensing applications are deployed in inaccessible locations or are subjected to severe energy constraints. Audio-based sensing offers flexibility in node placement and is popular in low-power schemes. Thus, in this paper, a node architecture with low power consumption and in-the-field reconfigurability is evaluated in the context of an acoustic vehicle detection and classification (hereafter “AVDC”) scenario. The proposed architecture utilizes an always-on field-programmable analog array (FPAA) as a low-power event detector to selectively wake a microcontroller unit (MCU) when a significant event is detected. When awoken, the MCU verifies the vehicle class asserted by the FPAA and transmits the relevant information. The AVDC system is trained by solving a classification problem using a lexicographic, nonlinear programming algorithm. On a testing dataset comprising of data from ten cars, ten trucks, and 40 s of wind noise, the AVDC system has a detection accuracy of 100%, a classification accuracy of 95%, and no false alarms. The mean power draw of the FPAA is 43 μ W and the mean power consumption of the MCU and radio during its validation and wireless transmission process is 40.9 mW. Overall, this paper demonstrates that the utilization of an FPAA-based signal preprocessor can greatly improve the flexibility and power consumption of wireless sensor nodes.