Large-scale Nonlinear Programming Problem Research Articles

A Tractable Linearization-Based Approximated Solution Methodology to Stochastic Multi-Period AC Security-Constrained Optimal Power Flow

The growing presence of renewable energy sources (RES), energy storage systems (ESSs) and flexible loads (FLs) in power systems necessitates a new approach to N-1 security in day-ahead operation planning considering stochasticity and time coupling. To this end, a comprehensive approach based on stochastic multi-period AC security-constrained optimal power flow (S-MP-AC-SCOPF) was proposed recently in a form of a large-scale non-linear programming problem, which is not scalable. This paper proposes the first-time new tractable solution methodology for the most complete AC-SCOPF problem to date: S-MP-AC-SCOPF. As other main novelty, the proposed methodology achieves tractability by solving sequentially a limited number of different linear approximations of the full S-MP-AC-SCOPF problem. These linear approximations differ in terms of: state dependency regarding losses approximation, carefully reduced sets of constraints or tightening of critical constraints. The performance of the methodology is demonstrated in power system models of Sweden and Portugal. Extensive numerical experiments have shown that the methodology is able to reduce progressively until complete removal the number of violated thermal or voltage constraints. It leads to reasonably accurate solution with small optimality gap within few iterations and is at least 85% faster than the competitor IPOPT solver.

Dynamic Optimization of Variable Load Process for Combined Heat and Power Unit Based on Sequential Quadratic Programming and Interior Point Method Alternating Solution Method

Aiming at the problem that the modeling and solving method of combined heat and power (CHP) unit variable load control process is challenging to meet the demand for efficient analysis of complex systems, this paper proposes a method based on sequential quadratic programming and interior point method (SQP-IPM) alternating solution for dynamic optimization of the CHP unit variable load process. Firstly, by constructing the CHP unit mechanism model, multi-variable coordination control constraints, and output variable process constraints, the dynamic optimization proposition of the CHP unit variable load control process is formed. Then, the large-scale nonlinear programming (NLP) problem formed by using the orthogonal configuration method to discrete the state and control variables is optimally solved using the IPM-SQP alternating solution method. Further, from the perspective of balancing the accuracy of the solution and computational efficiency, the flexible convergence depth control (CDC) strategy is introduced into the alternative solution method to improve the real-time performance of the algorithm. Finally, the variable load control process of 300MW extraction CHP unit is simulated to verify that the proposed method reduces the calculation time for 12 consecutive variable load scenarios by about 70%, effectively improving the real-time performance of scenario applications.

Privacy-Preserving and Secure Cloud Computing: A Case of Large-Scale Nonlinear Programming

The volume of data is increasing rapidly currently, which poses a great challenge for resource-constrained clients to process and analyze. A promising approach for solving computation-intensive tasks is to outsource them to the cloud to take advantage of the clouds powerful computing ability. However, it also brings privacy and security issues since the data uploaded to the cloud may contain sensitive and private information which should be protected. In this paper, we address this problem and focus on the privacy-preserving and secure outsourcing of large-scale nonlinear programming problems (NLPs) subject to both linear constraints and nonlinear constraints. Large-scale NLPs play an important role in the eld of data analytics but have not received enough attention. In our outsourcing protocol, we rst apply a secure and efcient transformation scheme at the client side to encrypt its private information. Then, we use the reduced gradient method and generalized gradient method at the server side to solve the transformed large-scale NLPs under linear constraints and nonlinear constraints, respectively. We provide security analysis of the proposed protocol, and evaluate its performance. The experimental results show that we can efciently solve the large-scale NLPs and save huge amount of time for the clients.

Distributed deep learning for cooperative computation offloading in low earth orbit satellite networks

Low earth orbit (LEO) satellite network is an important development trend for future mobile communication systems, which can truly realize the "ubiquitous connection" of the whole world. In this paper, we present a cooperative computation offloading in the LEO satellite network with a three-tier computation architecture by leveraging the vertical cooperation among ground users, LEO satellites, and the cloud server, and the horizontal cooperation between LEO satellites. To improve the quality of service for ground users, we optimize the computation offloading decisions to minimize the total execution delay for ground users subject to the limited battery capacity of ground users and the computation capability of each LEO satellite. However, the formulated problem is a large-scale nonlinear integer programming problem as the number of ground users and LEO satellites increases, which is difficult to solve with general optimization algorithms. To address this challenging problem, we propose a distributed deep learning-based cooperative computation offloading (DDLCCO) algorithm, where multiple parallel deep neural networks (DNNs) are adopted to learn the computation offloading strategy dynamically. Simulation results show that the proposed algorithm can achieve near-optimal performance with low computational complexity compared with other computation offloading strategies.

Nonlinear Model Predictive Control of Post-combustion CO2 Capture Process for Flexible Operation

A large amount of energy requirement for solvent regeneration is a major barrier to the widespread adoption of amine-based post-combustion CO2 capture (PCC). Flexible operation is one of the ways to lower the energy penalty by responding to changes in economic factors like the energy price. However, for effective implementation of flexible operation strategies, it is necessary to identify the most economic operating condition under various potential scenarios and to establish an appropriate control strategy to operate the process. As flexible operation will inherently involve a large operating envelope, we investigate the use of nonlinear model predictive control (NMPC) technology. To circumvent the problem of solving a large-scale nonlinear programming problem online, a simpler NARX model is identified and used. With the NARX model, an offset-free NMPC is designed and simulated under various dynamic scenarios. The developed NARX-based NMPC shows satisfactory control performance, stabilizing the CO2 capture rate faster than LMPC by 60-100 min.

Optimal Capacity Allocation of Energy Storage in Distribution Networks Considering Active/Reactive Coordination

Energy storage system (ESS) has been advocated as one of the key elements for the future energy system by the fast power regulation and energy transfer capabilities. In particular, for distribution networks with high penetration of renewables, ESS plays an important role in bridging the gap between the supply and demand, maximizing the benefits of renewables and providing various types of ancillary services to cope the intermittences and fluctuations, consequently improving the resilience, reliability and flexibility. To solve the voltage fluctuations caused by the high permeability of renewables in distribution networks, an optimal capacity allocation strategy of ESS is proposed in this paper. Taking the life cycle cost, arbitrage income and the benefit of reducing network losses into consideration, a bilevel optimization model of ESS capacity allocation is established, the coordination between active/reactive power of associate power conversion system is considered, and the large scale nonlinear programming problem is solved using genetic algorithm, simulated annealing and mixed integer second-order cone programming method. The feasibility and effectiveness of the proposed algorithm have been verified.

Aging-Aware Optimal Energy Management Control for a Parallel Hybrid Vehicle Based on Electrochemical-Degradation Dynamics

Hybrid electric vehicles offer the best alternative to gasoline-only powered vehicles as they combine a conventional propulsion system with an electric propulsion system. A supervisory controller is needed to optimally manage the energy on-board. Published works on this topic have mainly focused on strategies aimed at minimizing the fuel consumption. In this article, we address the problem of designing a supervisory controller that achieves minimum fuel consumption while optimally preserving battery life. Electrochemical degradation dynamics are used in the multi-objective problem formulation to accurately capture, and control battery performance, and aging during the control design phase. The electrochemical degradation model accounts for the electrolyte dynamics to capture high C-rate operation of the battery which are properl in charge sustaining hybrid powertrains. We resort to the optimal control formalism, and nonlinear optimization techniques along with the full discretization approach (in the state, and in the control) to cast the energy management problem into a large scale non-linear programming problem, that is able to deal with multi-scale dynamics, namely from the stiff electrolyte battery dynamics to map-based slow dynamics of the actuators. Numerical simulations conducted over four different standard driving cycles (with, and without road grades) show that our aging-aware energy management approach is able to significantly reduce the deterioration of the battery, while retaining very good fuel reduction performance.

Estimating variances and kinetic parameters from spectra across multiple datasets using KIPET

Multivariate spectroscopic data is increasingly abundant in the chemical and pharmaceutical industries. However, it is often challenging to estimate reaction kinetics directly from it. Recent advances in obtaining kinetic parameter estimates from spectroscopic data based on large-scale nonlinear programming (NLP), maximum likelihood principles, and discretization on finite elements lead to increased speed and efficiency (Chen et al., 2016). These new techniques have great potential for widespread use in parameter estimation. However they are currently limited due to their applicability to relatively small problem sizes. In this work, we extend the open-source package for estimating reaction kinetics directly from spectra or concentration data, KIPET, for use with multiple experimental datasets, or multisets (Schenk et al., 2020). Through a detailed initialization scheme and by taking advantage of large-scale nonlinear programming techniques and problem structure, we are able to solve large problems obtained from multiple experiments, simultaneously. The enhanced KIPET package can solve problems wherein multiple experiments contain different reactants and kinetic models, different dataset sizes with shared or unshared individual species’ spectra, and can obtain confidence intervals quickly based on the NLP sensitivities. In addition, we propose a new variance estimation technique based on maximum likelihood derivations for unknown covariances from two sample populations. This new variance estimation technique is compared to the previously proposed iterative-heuristics-based algorithm of Chen et al. (2016) for distinguishing between variances of the noise in model variables and in the spectral measurements. We demonstrate the new techniques on a variety of example problems, with sample code, to show the utility of the approach and its ease of use. We also include the curve-fitting problem to cases where we have concentration data given directly, and are required to estimate kinetic parameters across multiple experimental datasets.

Optimal non-anticipative scenarios for nonlinear hydro-thermal power systems

The long-term operation of hydro-thermal power generation systems is modeled by a large-scale stochastic optimization problem that includes nonlinear constraints due to the head computation in hydroelectric plants. We do a detailed development of the problem model and state it by a non-anticipative scenario analysis, leading to a large-scale nonlinear programming problem. This is solved by a filter algorithm with sequential quadratic programming iterations that minimize quadratic Lagrangian approximations using exact hessians in L∞ trust regions. The method is applied to the long-term planning of the Brazilian system, with over 100 hydroelectric and 50 thermoelectric plants, distributed in 5 interconnected subsystems. This problem with 50 synthetically generated inflow scenarios and a horizon of 60 months, amounting to about one million variables and 15000 nonlinear constraints was solved by the filter algorithm in a standard 2016 notebook computer in 10 h of CPU.

Optimal utilisation of PMU measurements in power system hybrid state estimators

A state estimator provides power system states by minimising the difference between the available measurement set and expected measurements. This minimisation problem is solved using the weighted least squares method or conventional optimisation methods. Most of the optimisation-based conventional methods used for power system state estimation are based on derivative approaches. These traditional methods suffer from problems such as the complication in handling inequality constraints, slow convergence etc. Non-linear constrained optimisation problems can be efficiently solved by the sequential quadratic programming (SQP) algorithm. SQP can be applied to small as well as large-scale non-linear programming problems having a large number of constraints. In the proposed algorithm, hybrid measurement configuration, consisting of measurements from phasor measurement units as well as conventional measurement devices, is used and applied on IEEE 14 bus, IEEE 118 bus test system and Indian northern region power grid-246 bus system.

Adaptive LEO-Phase Free-Return Orbit Design Method for Manned Lunar Mission Based on LEO Rendezvous

To design a free-return orbit for manned lunar mission based on low earth orbit (LEO) rendezvous, an adaptive LEO-phase free-return orbit design method based on high-precision dynamics model is proposed. First, the radius of perilune and the absolute value of perilune velocity are decoupled using a coordinate system rotation, which is derived from moon-centric local vertical and local horizontal instantaneous coordinate system at the time of perilune. The two Euler rotation angles and the absolute value of perilune velocity are used as independent design variables because their initial values are easy to guess. Next, a two-segment numerical integration strategy is proposed to calculate orbital elements at the moments of trans-lunar injection and free-return vacuum perigee. Subsequently, an optimization algorithm software package for solving large-scale nonlinear sequential quadratic programming problems (SQP_snopt) is employed to search the objective free-return orbit with a fixed trans-lunar injection inclination and the other two constraints on radiuses of perigee at the times of trans-lunar injection and vacuum perigee. After that, an iteration algorithm is devised to adjust trans-lunar injection window for adaptive LEO-phase. Finally, numerical results show a fast and accurate performance of the direct optimization method, which can provide valuable references to manned lunar missions based on LEO rendezvous.

Optimization-based motion planning for trawling

This work presents an optimization-based motion planning system for trawling operations. The formulation makes use of simplistic physical descriptions of the vessel and fishing gear together with catch dynamics of sweeping across moving fish schools. The objective of the optimal control problem is to maximize harvest, while ensuring both feasible maneuvers and well-behaved gear characteristics. The problem is transcribed into a large-scale nonlinear programming problem and solved in a receding horizon fashion using simultaneous collocation. A numerical simulation illustrates the system’s usefulness.

Using stochastic programming and statistical extrapolation to mitigate long-term extreme loads in wind turbines

We propose stochastic programming formulations to enforce mechanical load requirements in wind turbine controller design procedures. The formulations use statistical extrapolation techniques to construct a probabilistic (chance) constraint that controls the long-term probability of exceeding an extreme load threshold (as described by the IEC-61400 standard). This approach is based on the observation that extreme loads follow a generalized extreme value distribution, which enables an explicit algebraic representation of the probabilistic constraint. We illustrate how to use the formulations to find design parameters for pitch angle and torque controllers that maximize power output while constraining long-term extreme loads. We also use the formulation to explore the ability of a hypothetical model predictive controller to mitigate extreme loads. The proposed formulations can be cast as large-scale (but structured) nonlinear programming problems that contain up to 7.5 million variables and constraints. We show that these problems can be solved in less than 1.3 h on a multi-core computer with existing optimization tools.

Parallel cyclic reduction strategies for linear systems that arise in dynamic optimization problems

Dynamic optimization problems are constrained by differential and algebraic equations and are found everywhere in science and engineering. A well-established method to solve these types of problems is direct transcription, where the differential equations are replaced with discretized approximations based on finite-difference or Runge–Kutta schemes. However, for problems with thousands of state variables and discretization points, direct transcription may result in nonlinear optimization problems which are too large for general-purpose optimization solvers to handle. Also, when an interior-point solver is applied, the dominant computational cost is solving the linear systems resulting from the Newton step. For large-scale nonlinear programming problems, these linear systems may become prohibitively expensive to solve. Furthermore, the systems also become too large to formulate and store in memory of a standard computer. On the other hand, direct transcription can exploit sparsity and structure of the linear systems in order to overcome these challenges. In this paper we investigate and compare two parallel linear decomposition algorithms, Cyclic Reduction (CR) and Schur complement decomposition, which take advantage of structure and sparsity. We describe the numerical conditioning of the CR algorithm when applied to the linear systems arising from dynamic optimization problems, and then compare CR with Schur complement decomposition on a number of test problems. Finally, we propose conditions under which each should be used, and describe future research directions.

Optimal control problems with time delays: Two case studies in biomedicine.

There exists an extensive literature on delay differential models in biology and biomedicine, but only a few papers study such models in the framework of optimal control theory. In this paper, we consider optimal control problems with multiple time delays in state and control variables and present two applications in biomedicine. After discussing the necessary optimality conditions for delayed optimal control problems with control-state constraints, we propose discretization methods by which the delayed optimal control problem is transformed into a large-scale nonlinear programming problem. The first case study is concerned with the delay differential model in [21] describing the tumour-immune response to a chemo-immuno-therapy. Assuming L¹-type objectives, which are linear in control, we obtain optimal controls of bang-bang type. In the second case study, we introduce a control variable in the delay differential model of Hepatitis B virus infection developed in [7]. For L¹-type objectives we obtain extremal controls of bang-bang type.

Mine Ventilation Network Optimization Based on Airflow Asymptotic Calculation Method

The main objective of mine ventilation network optimization studies is to develop a reasonable method for ventilation system control that minimizes the total cost of mine ventilation. The fundamental principles for ventilation network optimization are discussed, and a multi-objective optimization model is established from the viewpoint of total cost. Furthermore, an optimization algorithm based on the airflow asymptotic calculation is presented by the hierarchical analysis of objective functions and analysis of the structure characteristics of a ventilation network. In the proposed approach, the regulated branches are determined by the directed path matrix; the optimal solution is obtained by airflow asymptotic calculation using the existing software for ventilation network analysis, and it does not need to solve the large-scale nonlinear programming problem. The results of example analysis validated the reliability of this approach.

A New Compromise Solution Model Based on Dantzig–Wolfe Decomposition for Solving Belief Multi-Objective Nonlinear Programming Problems with Block Angular Structure

This paper presents an integrated model based on a compromised solution method to solve fuzzy belief multi-objective large-scale nonlinear programming (FBMOLSNLP) problem with block angular structure. A new method is proposed to transfer each belief decision-making problem into some fuzzy problems. Furthermore, we propose a new compromise method of decision-making as one of the most efficient methods based on the particular measure of closeness to the ideal solution to aggregate multi-objective decision-making (MODM) problems into a single problem. The decomposition algorithm based on Dantzig–Wolfe is utilized to reduce the large-dimensional objective space into a two-dimensional space. Then, Zimmerman method is applied to transfer each bi-objective to a single-objective. Moreover, TOPSIS and VIKOR are utilized as two independent solution methods to aggregate each multi-objective sub-problem. Finally, a new single-objective nonlinear programming problem is solved to find the final solution. To justify the proposed model, two illustrative examples are provided, and the results of three decision methods are compromised.

Centralized and optimal motion planning for large-scale AGV systems: A generic approach

A centralized multi-AGV motion planning method is proposed. In contrast to the prevalent planners with decentralized (decoupled) formulations, a centralized planner contains no priority assignment, decoupling, or other specification strategies, thus is free from being case-dependent and deadlock-involved. Although centralized motion planning is computationally expensive, it deserves investigations in schemes that are sensitive to solution quality but insensitive to computation time. Specifically, centralized multi-AGV motion planning is formulated as an optimal control problem in this work, wherein differential algebraic equations are used to describe the AGV dynamics, mechanical restrictions, and exterior constraints. Orthogonal collocation direct transcription method is adopted to discretize the original infinite-dimensional optimal control problem into a large-scale nonlinear programming (NLP) problem, which is solved using interior point method thereafter. Exhaustive simulations are conducted on 10-AGV formation reconfiguration tasks. Simulation results show the validation, unification, and real-time implementation potential of the introduced centralized planner. Particularly, the computation time on a PC reduces to several seconds with near-optimal initial guess in the NLP solving process, making receding horizon replanning possible via this centralized planner.

An Improved Finite Element Meshing Strategy for Dynamic Optimization Problems

The finite element orthogonal collocation method is widely used in the discretization of differential algebraic equations (DAEs), while the discrete strategy significantly affects the accuracy and efficiency of the results. In this work, a finite element meshing method with error estimation on noncollocation point is proposed and several cases were studied. Firstly, the simultaneous strategy based on the finite element is used to transform the differential and algebraic optimization problems (DAOPs) into large scale nonlinear programming problems. Then, the state variables of the reaction process are obtained by simulating with fixed control variables. The noncollocation points are introduced to compute the error estimates of the state variables at noncollocation points. Finally, in order to improve the computational accuracy with less finite element, moving finite element strategy was used for dynamically adjusting the length of finite element appropriately to satisfy the set margin of error. The proposed strategy is applied to two classical control problems and a large scale reverse osmosis seawater desalination process. Computing result shows that the proposed strategy can effectively reduce the computing effort with satisfied accuracy for dynamic optimization problems.

Asteroid retrieval missions enabled by invariant manifold dynamics

Near Earth Asteroids are attractive targets for new space missions; firstly, because of their scientific importance, but also because of their impact threat and prospective resources. The asteroid retrieval mission concept has thus arisen as a synergistic approach to tackle these three facets of interest in one single mission. This paper reviews the methodology used by the authors (2013) in a previous search for objects that could be transported from accessible heliocentric orbits into the Earth's neighbourhood at affordable costs (or Easily Retrievable Objects, a.k.a. EROs). This methodology consisted of a heuristic pruning and an impulsive manoeuvre trajectory optimisation. Low thrust propulsion on the other hand clearly enables the transportation of much larger objects due to its higher specific impulse. Hence, in this paper, low thrust retrieval transfers are sought using impulsive trajectories as first guesses to solve the optimal control problem. GPOPS-II is used to transcribe the continuous-time optimal control problem to a nonlinear programming problem (NLP). The latter is solved by IPOPT, an open source software package for large-scale NLPs. Finally, a natural continuation procedure that increases the asteroid mass allows to find out the largest objects that could be retrieved from a given asteroid orbit. If this retrievable mass is larger than the actual mass of the asteroid, the asteroid retrieval mission for this particular object is said to be feasible. The paper concludes with an updated list of 17 EROs, as of April 2016, with their maximum retrievable masses by means of low thrust propulsion. This ranges from 2000tons for the easiest object to be retrieved to 300tons for the least accessible of them.