Showing papers on "Nonlinear programming published in 2021"

New Noise-Tolerant Neural Algorithms for Future Dynamic Nonlinear Optimization With Estimation on Hessian Matrix Inversion

Abstract: Nonlinear optimization problems with dynamical parameters are widely arising in many practical scientific and engineering applications, and various computational models are presented for solving them under the hypothesis of short-time invariance. To eliminate the large lagging error in the solution of the inherently dynamic nonlinear optimization problem, the only way is to estimate the future unknown information by using the present and previous data during the solving process, which is termed the future dynamic nonlinear optimization (FDNO) problem. In this paper, to suppress noises and improve the accuracy in solving FDNO problems, a novel noise-tolerant neural (NTN) algorithm based on zeroing neural dynamics is proposed and investigated. In addition, for reducing algorithm complexity, the quasi-Newton Broyden–Fletcher–Goldfarb–Shanno (BFGS) method is employed to eliminate the intensively computational burden for matrix inversion, termed NTN-BFGS algorithm. Moreover, theoretical analyses are conducted, which show that the proposed algorithms are able to globally converge to a tiny error bound with or without the pollution of noises. Finally, numerical experiments are conducted to validate the superiority of the proposed NTN and NTN-BFGS algorithms for the online solution of FDNO problems.

Separable Multi-innovation Newton Iterative Modeling Algorithm for Multi-frequency Signals Based on the Sliding Measurement Window

Abstract: Signal modeling is an important technique in many engineering applications. This paper is concerned about signal modeling problem for the sine multi-frequency signals or periodic signals. In terms of different characteristics between the signal output and the signal parameters, a separable modeling scheme is presented for estimating the signal parameters. In order to seize the real-time information of the signals to be modeled, a sliding measurement window is designed for using the observations dynamically and implementing accurate parameter estimates. Because the amplitude parameters are linear with respect to the signal output and the angular frequency parameters are nonlinear with respect to the signal output, the signal parameters are separated into a linear parameter set and a nonlinear parameter set. Based on these separable parameter sets, a nonlinear optimization problem is converted into a combination of the optimization quadric and the nonlinear optimization. Then, a separable multi-innovation Newton iterative signal modeling method is derived and implemented to estimate sine multi-frequency signals and periodic signals. The simulation results are found to be effective of modeling dynamic signals. For the reason that the proposed method is based on dynamic sliding measurement window, it can be used for online estimation applications.

Geometric picture fuzzy numbers and three-dimensional copulas with the non-linear programming approach

Abstract: This study presents a possible relationship between two main objects, which are three-dimensional copulas (3D-Cs) and geometric picture fuzzy numbers (GPFNs). This opens up a potential field for future studies for these two objects that three-dimensional copulas can become useful tools for handling uncertainty information in the form of a picture fuzzy set (PFS). Specifically, we define a GPFN as a base element of the PFS and a defined domain of three-dimensional copulas that contains a set of GPFNs, then we show some examples of three-dimensional copulas identified on this domain. In this framework, we present the theorems related to these two objects. At the same time, we provide some examples for three-dimensional semi-copulas, three-dimensional quasi-copulas, and three-dimensional empirical copulas defined on D, which is a defined domain of a three-dimensional copula and contains a set of GPFNs D g * . In addition, we also introduce a new approach to non-linear programming problems.

Distributed Probabilistic Offloading in Edge Computing for 6G-Enabled Massive Internet of Things

Abstract: Mobile-edge computing (MEC) is expected to provide reliable and low-latency computation offloading for massive Internet of Things (IoT) with the next generation networks, such as the sixth-generation (6G) network. However, the successful implementation of 6G depends on network densification, which brings new offloading challenges for edge computing, one of which is how to make offloading decisions facing densified servers considering both channel interference and queuing, which is an NP-hard problem. This article proposes a distributed-two-stage offloading (DTSO) strategy to give tradeoff solutions. In the first stage, by introducing the queuing theory and considering channel interference, a combinatorial optimization problem is formulated to calculate the offloading probability of each station. In the second stage, the original problem is converted to a nonlinear optimization problem, which is solved by a designed sequential quadratic programming (SQP) algorithm. To make an adjustable tradeoff between the latency and energy requirement among heterogeneous applications, an elasticity parameter is specially designed in DTSO. Simulation results show that compared to the latest works, DTSO can effectively reduce latency and energy consumption and achieve a balance between them based on application preferences.

A Method to Balance Dynamic Current of Paralleled SiC MOSFETs With Kelvin Connection Based on Response Surface Model and Nonlinear Optimization

Abstract: Multichip SiC power modules with Kelvin-source connection are popular in applications with large capacity and high switching frequency. However, dynamic current imbalance among paralleled dies due to asymmetric layout limits the available capacity. Thus, this article proposes a method to mitigate the mismatched dynamic current by adjusting the connection points of bonding wires and copper traces. The response surface models and nonlinear constrained optimization algorithms are introduced for the first time to help determine the optimized positions for the connection points. By this method, the dynamic current imbalance can be well suppressed under various working conditions. Besides, the method is cost-efficient and well compatible with the conventional manufacturing technologies because there need no additional efforts but some modifications on bonding wires. At first, the optimization guidelines are obtained after analyzing the mechanism of dynamic current imbalance among paralleled SiC MOSFETs with Kelvin-source connection. Based on the optimization guidelines and response surface models of parasitic inductance, the dynamic current sharing problem can be transformed into a nonlinear constrained optimization issue in mathematics. According to the solution of the mathematic problem, the optimized positions for connection points of bonding wires and copper traces can be determined. Finally, some simulations and experiments are conducted to verify the effectiveness of the proposed method.

Nonlinear Model Predictive Stabilization of DC–DC Boost Converters With Constant Power Loads

Abstract: This article addresses the problem of stabilization of dc–dc converters feeding constant power loads (CPLs). An explicit model predictive control is developed based on an average model of a boost converter. The optimal control law is obtained offline by solving a multiparametric nonlinear programming problem over a simplex partition of the state space. The performance is validated through simulation and experimental studies. A delay compensation scheme is included for online implementation. The control is able to drive the output voltage to the desired level and stabilize it despite the instability effects produced by the presence of CPLs. It also features robustness against abrupt changes on the input voltage and the load.

Machine Learning-Based Offloading Strategy for Lightweight User Mobile Edge Computing Tasks

Abstract: This paper presents an in-depth study and analysis of offloading strategies for lightweight user mobile edge computing tasks using a machine learning approach. Firstly, a scheme for multiuser frequency division multiplexing approach in mobile edge computing offloading is proposed, and a mixed-integer nonlinear optimization model for energy consumption minimization is developed. Then, based on the analysis of the concave-convex properties of this optimization model, this paper uses variable relaxation and nonconvex optimization theory to transform the problem into a convex optimization problem. Subsequently, two optimization algorithms are designed: for the relaxation optimization problem, an iterative optimization algorithm based on the Lagrange dual method is designed; based on the branch-and-bound integer programming method, the iterative optimization algorithm is used as the basic algorithm for each step of the operation, and a global optimization algorithm is designed for transmitting power allocation, computational offloading strategy, dynamic adjustment of local computing power, and receiving energy channel selection strategy. Finally, the simulation results verify that the scheduling strategy of the frequency division technique proposed in this paper has good energy consumption minimization performance in mobile edge computation offloading. Our model is highly efficient and has a high degree of accuracy. The anomaly detection method based on a decision tree combined with deep learning proposed in this paper, unlike traditional IoT attack detection methods, overcomes the drawbacks of rule-based security detection methods and enables them to adapt to both established and unknown hostile environments. Experimental results show that the attack detection system based on the model achieves good detection results in the detection of multiple attacks.

User-Centric Computation Offloading for Edge Computing

Abstract: The number of smart devices newly connected to the Internet has grown exponentially in recent years These smart devices are interwoven into huge Internet of Things There is a contradiction between mass data transmission and communication bandwidth, the distance between supercomputing power and processing object, and the demand of frequent interaction and real-time response As a new computing paradigm, edge computing processes tasks on computing resources close to data sources Considering the limited energy of the mobile terminal and the user’s demand for low delay, making decisions about tasks executed locally and offloaded to edge computing servers In the edge environment, resources are dynamically allocated to users on demand, and users need to pay for the resources they actually consume By considering energy consumption, delay, and price, a user-centered joint optimization loading scheme is proposed to minimize the weighted cost of time delay, energy consumption, and price under the constraint of satisfying the advanced personalized needs of users The optimization problem is modeled as a mixed-integer nonlinear programming problem, and a branch-and-bound algorithm based on linear relaxation improvement is proposed to solve the problem Considering the complexity of the algorithm, a particle swarm optimization algorithm based on 0–1 and weight improvement is proposed to solve the problem Simulation results show that the method proposed in this article can achieve higher performance in terms of delay, energy consumption, and price and provide personalized service for users

DC Optimal Power Flow With Joint Chance Constraints

Abstract: Managing uncertainty and variability in power injections has become a major concern for power system operators due to increasing levels of fluctuating renewable energy connected to the grid. This work addresses this uncertainty via a joint chance-constrained formulation of the DC optimal power flow (OPF) problem, which satisfies all the constraints jointly with a pre-determined probability. The few existing approaches for solving joint chance-constrained OPF problems are typically either computationally intractable for large-scale problems or give overly conservative solutions that satisfy the constraints far more often than required, resulting in excessively costly operation. This paper proposes an algorithm for solving joint chance-constrained DC OPF problems by adopting an S $\ell _1$ QP-type trust-region algorithm. This algorithm uses a sample-based approach that avoids making strong assumptions on the distribution of the uncertainties, scales favorably to large problems, and can be tuned to obtain less conservative results. We illustrate the performance of our method using several IEEE test cases. The results demonstrate the proposed algorithm's advantages in computational times and limited conservativeness of the solutions relative to other joint chance-constrained DC OPF algorithms.

Nonlinear Energy-Maximizing Optimal Control of Wave Energy Systems: A Moment-Based Approach

Abstract: Linear dynamics are virtually always assumed when designing optimal controllers for wave energy converters (WECs), motivated by both their simplicity and computational convenience. Nevertheless, unlike traditional tracking control applications, the assumptions under which the linearization of WEC models is performed are challenged by the energy-maximizing controller itself, which intrinsically enhances device motion to maximize power extraction from incoming ocean waves. In this article, we present a moment-based energy-maximizing control strategy for WECs subject to nonlinear dynamics. We develop a framework under which the objective function (and system variables) can be mapped to a finite-dimensional tractable nonlinear program, which can be efficiently solved using state-of-the-art nonlinear programming solvers. Moreover, we show that the objective function belongs to a class of generalized convex functions when mapped to the moment domain, guaranteeing the existence of a global energy-maximizing solution and giving explicit conditions for when a local solution is, effectively, a global maximizer. The performance of the strategy is demonstrated through a case study, where we consider (state and input-constrained) energy maximization for a state-of-the-art CorPower-like WEC, subject to different hydrodynamic nonlinearities.

Cross-Layer Interference Management Scheme for D2D Mobile Users Using NOMA

Abstract: Device-to-device (D2D) communication is a promising technology in which the spectrum resources are reused efficiently with cellular mobile users (CMUs) in an underlay of the fifth generation network Using it, network capacity and spectral efficiency increase but it introduces the cochannel interference Moreover, massive connectivity has not been fully exploited for efficient spectral efficiency usage in the existing solutions Therefore, to address the aforementioned challenges, we integrate power domain nonorthogonal multiple access (PD-NOMA) technique with the D2D mobile groups (DMGs) to maximize their sum rate and to maintain the signal-to-interference noise ratio provided by CMUs We formulate the problem of spectrum reuse as mixed-integer nonlinear programming and then converted it into two subproblems First, the DMGs are formed between the D2D transmitter and D2D mobile users to reduce the intrauser interference using successive interference cancellation technique Second, the resource allocation scheme for both the CMUs and DMGs is designed to mitigate the cross and cochannel interference using many-to-many mapping scheme Also, to fully exploit the potential benefits of DMGs, the group rate selection criterion based resource block reuse algorithm among DMGs is designed Finally, for power optimization, we use the difference of two convex functions programming approach based on a successive convex approximation low complexity To simulate the proposed scheme, the 3GPP urban path loss model based on release 15 and RAN1 is used Numerical results demonstrated that the proposed scheme has superior sum rate as compared to the existing NOMA and orthogonal frequency-division multiple access schemes

Trajectory Optimization for a Connected Automated Traffic Stream: Comparison Between an Exact Model and Fast Heuristics

Abstract: Numerous fast heuristic algorithms, including shooting heuristics (SH), have been developed for real-time trajectory optimization, although their optimality has not yet been quantified. This paper compares the performance between fast heuristics and exact optimization models. We investigate a core trajectory optimization problem as a building block for numerous trajectory optimization problems, i.e., guiding movements of connected automated vehicles on a one-lane highway when the arrival and departure times and velocity are given. To apply the SH algorithm to this problem, we adapt it to a fast-simplified shooting heuristic (FSSH) model to solve the trajectory smoothing problems with different arrival and departure velocities. An exact trajectory optimization (ETO) model is formulated that takes the vehicle position and velocity as the decision variables, and the fuel consumption and driving comfort as the objective function. The constraints of the model are based on the limits and safety of the vehicle dynamics between consecutive vehicles. We demonstrate the convexity of the ETO objective function, ensuring the solvability of the ETO model at the true optimum using gradient descent algorithms supplied by the MATLAB optimization toolbox. Six groups of numerical experiments using different input parameters and one experiment using real Next Generation Simulation (NGSIM) data are conducted. ETO can improve the objective values by a few to tens of percentage points. However, FSSH achieves a greater solution efficiency with an average solution time of less than 0.1 s compared to ~450 s for ETO.

A mixed-integer convex model for the optimal placement and sizing of distributed generators in power distribution networks

Abstract: The optimal placement and sizing of distributed generators is a classical problem in power distribution networks that is usually solved using heuristic algorithms due to its high complexity. This paper proposes a different approach based on a mixed-integer second-order cone programming (MI-SOCP) model that ensures the global optimum of the relaxed optimization model. Second-order cone programming (SOCP) has demonstrated to be an efficient alternative to cope with the non-convexity of the power flow equations in power distribution networks. Of relatively new interest to the power systems community is the extension to MI-SOCP models. The proposed model is an approximation. However, numerical validations in the IEEE 33-bus and IEEE 69-bus test systems for unity and variable power factor confirm that the proposed MI-SOCP finds the best solutions reported in the literature. Being an exact technique, the proposed model allows minimum processing times and zero standard deviation, i.e., the same optimum is guaranteed at each time that the MI-SOCP model is solved (a significant advantage in comparison to metaheuristics). Additionally, load and photovoltaic generation curves for the IEEE 69-node test system are included to demonstrate the applicability of the proposed MI-SOCP to solve the problem of the optimal location and sizing of renewable generators using the multi-period optimal power flow formulation. Therefore, the proposed MI-SOCP also guarantees the global optimum finding, in contrast to local solutions achieved with mixed-integer nonlinear programming solvers available in the GAMS optimization software. All the simulations were carried out via MATLAB software with the CVX package and Gurobi solver.

A Noise-Enduring and Finite-Time Zeroing Neural Network for Equality-Constrained Time-Varying Nonlinear Optimization

Abstract: This article focuses on the research of a general time-varying nonlinear optimization (TVNO) problem solving especially in a noise-disturbance environment. For addressing this problem more efficiently, a new noise-enduring and finite-time convergent design formula is suggested to establish a novel zeroing neural network (NZNN). In contrast to the initial zeroing neural network or the noising-enduring zeroing neural network, which either only achieves finite-time convergence or only suppresses external disturbances, the merit of the proposed NZNN model is able to find an error-free optimal solution in a finite time under various different types of external noises. In addition, the detailed mathematical analyses about finite-time convergence and noise endurance are given to prove the excellent characteristics of the NZNN model. Numerical comparative results are provided to demonstrate the accuracy, efficiency, and advantages of the NZNN model for TVNO under various types of external disturbances. Robotic tracking example further validates the applicability of the NZNN model especially in a noise-disturbance environment.

A Novel Solution Methodology Based on a Modified Gradient-Based Optimizer for Parameter Estimation of Photovoltaic Models

Abstract: In this paper, a modified version of a recent optimization algorithm called gradient-based optimizer (GBO) is proposed with the aim of improving its performance. Both the original gradient-based optimizer and the modified version, MGBO, are utilized for estimating the parameters of Photovoltaic models. The MGBO has the advantages of accelerated convergence rate as well as avoiding the local optima. These features make it compatible for investigating its performance in one of the nonlinear optimization problems like Photovoltaic model parameters estimation. The MGBO is used for the identification of parameters of different Photovoltaic models; single-diode, double-diode, and PV module. To obtain a generic Photovoltaic model, it is required to fit the experimentally obtained data. During the optimization process, the unknown parameters of the PV model are used as a decision variable whereas the root means squared error between the measured and estimated data is used as a cost function. The results verified the fast conversion rate and precision of the MGBO over other recently reported algorithms in solving the studied optimization problem.

Vehicle Selection and Resource Optimization for Federated Learning in Vehicular Edge Computing

Abstract: As a distributed deep learning paradigm, federated learning (FL) provides a powerful tool for the accurate and efficient processing of on-board data in vehicular edge computing (VEC). However, FL involves the training and transmission of model parameters, which consumes the vehicles' precious energy resources and takes up much time. It is a departure from many applications with severe real-time requirements in VEC. And the capabilities and data quality of each vehicle are distinct that will affect the performance of training the model. Therefore, it is crucial to select the appropriate vehicles to participate in learning tasks and optimize resource allocation under learning time and energy consumption constraints. In this paper, taking the vehicle position and velocity into consideration, we formulate a min-max optimization problem to jointly optimize the on-board computation capability, transmission power, and local model accuracy to achieve the minimum cost in the worst case of FL. Specifically, we propose a greedy algorithm to select vehicles with higher image quality dynamically, and it keeps the system's overall cost to a minimum in FL. The formulated optimization problem is a nonlinear programming problem, so we decompose it into two subproblems. For the resource allocation problem, we use the Lagrangian dual problem and the subgradient projection method to approximate the optimal value iteratively. For the local model accuracy problem, we develop an adaptive harmony algorithm for heuristic search. The simulation results show that our proposed algorithms have well convergence and effectiveness and achieve a tradeoff between cost and fairness.

Vehicle dispatching in modular transit networks: A mixed-integer nonlinear programming model

Abstract: Modular vehicle (MV) technology offers the possibility of flexibly adjusting the vehicle capacity by docking/undocking modular pods into vehicles of different sizes en route to satisfy passenger demand Based on the MV technology, a modular transit network system (MTNS) concept is proposed to overcome the mismatch between fixed vehicle capacity and spatially varying travel demand in traditional public transportation systems To achieve the optimal MTNS design, a mixed-integer nonlinear programming model is developed to balance the tradeoff between the vehicle operation cost and the passenger trip time cost The nonlinear model is reformulated into a computationally tractable linear model The linear model solves the lower and upper bounds of the original nonlinear model to produce a near-optimal solution to the MTNS design This reformulated linear model can be solved with off-the-shelf commercial solvers (eg, Gurobi) Two numerical examples are used to demonstrate the applicability of the proposed model and its effectiveness in reducing system costs

Efficient Trajectory Planning for Multiple Non-Holonomic Mobile Robots via Prioritized Trajectory Optimization

Abstract: In this letter, we present a novel approach to efficiently generate collision-free optimal trajectories for multiple non-holonomic mobile robots in obstacle-rich environments. Our approach first employs a graph-based multi-agent path planner to find an initial discrete solution, and then refines this solution into smooth trajectories using nonlinear optimization. We divide the robot team into small groups and propose a prioritized trajectory optimization method to improve the scalability of the algorithm. Infeasible sub-problems may arise in some scenarios because of the decoupled optimization framework. To handle this problem, a novel grouping and priority assignment strategy is developed to increase the probability of finding feasible trajectories. Compared to the coupled trajectory optimization, the proposed approach reduces the computation time considerably with a small impact on the optimality of the plans. Simulations and hardware experiments verified the effectiveness and superiority of the proposed approach.

Minotaur: a mixed-integer nonlinear optimization toolkit

Abstract: We present a flexible framework for general mixed-integer nonlinear programming (MINLP), called Minotaur, that enables both algorithm exploration and structure exploitation without compromising computational efficiency. This paper documents the concepts and classes in our framework and shows that our implementations of standard MINLP techniques are efficient compared with other state-of-the-art solvers. We then describe structure-exploiting extensions that we implement in our framework and demonstrate their impact on solution times. Without a flexible framework that enables structure exploitation, finding global solutions to difficult nonconvex MINLP problems will remain out of reach for many applications.

Population-based Tabu search with evolutionary strategies for permutation flow shop scheduling problems under effects of position-dependent learning and linear deterioration

Abstract: This paper investigates permutation flow shop scheduling (PFSS) problems under the effects of position-dependent learning and linear deterioration. In a PFSS problem, there are n jobs and m machines in series. Jobs are separated into operations on $$ m $$ different machines in series, and jobs have to follow the same machine order with the same sequence. The PFSS problem under the effects of learning and deterioration is introduced with a mixed-integer nonlinear programming model. The time requirement for solving large-scale problems type of PFSS problem is exceedingly high. Therefore, well-known metaheuristic methods for the PFSS problem without learning and deterioration effects such as iterated greedy algorithms and discrete differential evolution algorithm are adapted for the problem with learning and deterioration effects in order to find a faster and near-optimal or optimal solution for the problem. Furthermore, this paper proposes a hybrid solution algorithm that is called population-based Tabu search algorithm (TSPOP) with evolutionary strategies such as crossover and mutation. The search algorithm is built on the basic structure of Tabu search and it searches for the best candidate from a solution population instead of improving the current best candidate at each iteration. Furthermore, the performances of these methods in view of solution quality are discussed in this paper by using test problems for 20, 50, and 100 jobs with 5, 10, 20 machines. Experimental results show that the proposed TSPOP algorithm outperforms the other existing algorithms in view of solution quality.