Large-scale Nonlinear Programming Research Articles

Real-time implementation of nonlinear model predictive control for high angle of attack Maneuvers in fighter aircrafts using deep learning

ABSTRACT Nonlinear model predictive control (NMPC) provides a nice framework for accounting for multivariable nonlinear dynamics subject to constraints; however, the cost of implementing NMPC is high due to the need to solve a large-scale nonlinear program to optimality in real-time. This research is focussed on the design of real-time solution to NMPC (low computations) for fast dynamic systems. In this work, a comprehensive and innovative solution based on a deep learning-based approximate NMPC scheme has been proposed to overcome these computational challenges. The main idea is to learn a deep neural network followed by the symbolic simplification of the NMPC law, whose evaluation cost and memory footprint can be optimized offline. Since not all the states of the system are measured, we also combine the deep learning based NMPC approach with an unscented Kalman filter (UKF) as well as show how this scheme can be easily modified to be offset-free (i.e. remove steady-state error due to persistent disturbances and modelling error). The proposed approach is implemented on a highly fast dynamic system (i.e. F-16 fighter aircraft to perform a high angle of attack maneuver) to check the controller efficiency. Fighter aircraft need to be able to make fast and complex maneuvers (that exploit strongly nonlinear dynamics) to be able to maintain air superiority. However, such aggressive maneuvers require strong coordination between the actions to avoid destabilizing the system. A quantitative analysis from comparison with the standard MPC approach shows the practical utility of the proposed approach.

A Mutual Catastrophe Insurance Framework for Horizontal Collaboration in Prepositioning Strategic Reserves

Improving Disaster Preparedness Through Mutual Catastrophe Insurance In “A Mutual Catastrophe Insurance Framework for Horizontal Collaboration in Prepositioning Strategic Reserves,” H. Zbib, B. Balcik, M.-È. Rancourt, and G. Laporte present an innovative approach to collaborative disaster preparedness. The novel framework considers a risk-averse mutual insurer offering multiyear insurance contracts with coverage deductibles and limits to a portfolio of risk-averse policyholders. It is designed to foster horizontal collaboration among policyholders for joint disaster preparedness by effectively integrating operational and financial functions. The problem is modeled as a large-scale nonlinear multistage stochastic program and solved by using an effective Benders decomposition algorithm. The framework is validated with real data from 18 Caribbean countries focusing on hurricane preparedness. Given the predicted impacts of climate change, the proposed multiyear mutual catastrophe insurance framework promises to reshape global disaster preparedness and make a profound societal impact by providing a transparent disaster financing plan to protect vulnerable regions. The study’s findings stress the importance of long-term cooperation, prenegotiation of indemnification policies, and strategic setting of deductibles and limits by taking into account the correlation between policyholders.

Multi-level optimization strategies for large-scale nonlinear process systems

With growing needs to develop and improve climate-friendly processes, optimization strategies are essential at all levels of decision-making in chemical and energy processes, including process development, process synthesis and design, as well as process operations, control, scheduling, and planning. Challenges include the formulation of well-posed and well-conditioned process models, and development and application of efficient, reliable optimization algorithms. Here we describe a synthesis of optimization concepts and algorithms that enable large-scale nonlinear programming, nonintrusive decomposition strategies and the inclusion of a wide class of surrogate models. All of these are crucial to address challenging nonconvex, multi-scale problems in Computer Aided Process Engineering (CAPE). These elements are demonstrated through dynamic optimization strategies for novel energy generation, demand-based optimization for specialty chemicals, and optimization with integrated heterogeneous models for carbon capture processes.

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.

Bi-objective design-for-control for improving the pressure management and resilience of water distribution networks

This paper investigates control and design-for-control strategies to improve the resilience of sectorized water distribution networks (WDN), while minimizing pressure induced pipe stress and leakage. Both evolutionary algorithms (EA) and gradient-based mathematical optimization approaches are investigated for the solution of the resulting large-scale non-linear (NLP) and bi-objective mixed-integer non-linear programs (BOMINLP). While EAs have been successfully applied to solve discrete network design problems for large-scale WDNs, gradient-based mathematical optimization methods are more computationally efficient when dealing with large search spaces associated with continuous variables in optimal network control problems. Considering the advantages of each method, we propose a sequential hybrid method for the optimal design-for-control of large-scale WDNs, where a refinement stage relying on gradient-based mathematical optimization is used to solve continuous optimal control problems corresponding to design solutions returned by an initial EA search. The proposed method is applied to compute the Pareto front of a bi-objective design-for-control problem for the operational network BWPnet, where we consider reopening closed connections between isolated supply areas. The results show that the considered design-for-control strategy increases the resilience of BWPnet while minimizing pressure induced leakage. Moreover, the refinement stage of the proposed hybrid method efficiently improves the coarse approximation computed by the initial EA search, returning a continuous and even Pareto front approximation.

Stochastic Optimal Device Sizing Model for Zero Energy Buildings: A Parallel Computing Solution

Byconsuming35% of the final global energy, buildings are among major contributors to greenhouse gas emissions and global warming. If the economic justification challenge is addressed, zero energy buildings (ZEB), which are defined as buildings that generate as much renewable-based energy as they consume annually, can be a promising solution for energy efficiency improvement in the building sector. In this article, we propose a stochastic ZEB device sizing model considering uncertain parameters (i.e., building's electrical and thermal demands, solar irradiation, and outdoor temperature) and their correlation. The proposed model finds the optimal size of the thermal and electrical devices considering their nonlinear behaviors and temperature-dependent dynamics. Furthermore, two parallel computing-based solution algorithms (i.e., parallelism in the algebraic level using Schur complement decomposition and parallelism in the problem (scenario) level by progressive hedging) are proposed to solve the stochastic model. Using the real historical data, numerical studies on the Woodward library building, located on the University of British Columbia campus, illustrate the efficacy of the solution algorithms to handle large-scale nonlinear programming models with more than 32.8 million variables, which is the largest one reported in the literature so far.

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.

Isotope-assisted metabolic flux analysis as an equality-constrained nonlinear program for improved scalability and robustness.

Stable isotope-assisted metabolic flux analysis (MFA) is a powerful method to estimate carbon flow and partitioning in metabolic networks. At its core, MFA is a parameter estimation problem wherein the fluxes and metabolite pool sizes are model parameters that are estimated, via optimization, to account for measurements of steady-state or isotopically-nonstationary isotope labeling patterns. As MFA problems advance in scale, they require efficient computational methods for fast and robust convergence. The structure of the MFA problem enables it to be cast as an equality-constrained nonlinear program (NLP), where the equality constraints are constructed from the MFA model equations, and the objective function is defined as the sum of squared residuals (SSR) between the model predictions and a set of labeling measurements. This NLP can be solved by using an algebraic modeling language (AML) that offers state-of-the-art optimization solvers for robust parameter estimation and superior scalability to large networks. When implemented in this manner, the optimization is performed with no distinction between state variables and model parameters. During each iteration of such an optimization, the system state is updated instead of being calculated explicitly from scratch, and this occurs concurrently with improvement in the model parameter estimates. This optimization approach starkly contrasts with traditional “shooting” methods where the state variables and model parameters are kept distinct and the system state is computed afresh during each iteration of a stepwise optimization. Our NLP formulation uses the MFA modeling framework of Wiechert et al. [1], which is amenable to incorporation of the model equations into an NLP. The NLP constraints consist of balances on either elementary metabolite units (EMUs) or cumomers. In this formulation, both the steady-state and isotopically-nonstationary MFA (inst-MFA) problems may be solved as an NLP. For the inst-MFA case, the ordinary differential equation (ODE) system describing the labeling dynamics is transcribed into a system of algebraic constraints for the NLP using collocation. This large-scale NLP may be solved efficiently using an NLP solver implemented on an AML. In our implementation, we used the reduced gradient solver CONOPT, implemented in the General Algebraic Modeling System (GAMS). The NLP framework is particularly advantageous for inst-MFA, scaling well to large networks with many free parameters, and having more robust convergence properties compared to the shooting methods that compute the system state and sensitivities at each iteration. Additionally, this NLP approach supports the use of tandem-MS data for both steady-state and inst-MFA when the cumomer framework is used. We assembled a software, eiFlux, written in Python and GAMS that uses the NLP approach and supports both steady-state and inst-MFA. We demonstrate the effectiveness of the NLP formulation on several examples, including a genome-scale inst-MFA model, to highlight the scalability and robustness of this approach. In addition to typical inst-MFA applications, we expect that this framework and our associated software, eiFlux, will be particularly useful for applying inst-MFA to complex MFA models, such as those developed for eukaryotes (e.g. algae) and co-cultures with multiple cell types.

Optimization of compressor standby schemes for gas transmission pipeline systems based on gas delivery reliability

To guarantee the gas delivery reliability of a gas pipeline system, some standby compressor units or standby powers are typically installed in a compressor station. A reasonable compressor standby scheme plays a vital role in the efficient operation of compressor stations. This paper presents two standby scheme optimization models considering various normal and failure scenarios for two standby modes: unit standby and power standby, respectively. The proposed models aim to maximize the gas delivery reliability subjected to rigorous operating constraints of a gas pipeline system and budget constraints (e.g., the total amount of standby power/ units). The resultant optimization models for power standby and unit standby schemes are large-scale nonlinear programming (NLP) and mixed-integer nonlinear programming (MINLP), respectively. In order to solve the unit standby optimization scheme efficiently, we decompose the original large-scale model into two sub-problems equivalently. The first sub-problem is to maximize the gas delivery flow rate under various scenarios based on determined compressor configurations. Based on the solutions from the first sub-problem, the second one is to optimize the standby scheme. Numerical results are provided to verify the effectiveness of the proposed approaches. It is demonstrated that the results of compressor standby optimization models can provide valuable information for the design and planning of gas pipeline systems.

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.

An optimisation based algorithm for finding the nucleation temperature of cosmological phase transitions

We present the OptiBounce algorithm, a new and fast method for finding the bounce action for cosmological phase transitions. This is done by direct solution of the “reduced” minimisation problem proposed by Coleman, Glaser, and Martin. Using a new formula for the action, our method avoids the rescaling step used in other algorithms based on this formulation. The bounce path is represented using a pseudo-spectral Gauss-Legendre collocation scheme leading to a non-linear optimisation problem over the collocation coefficients. Efficient solution of this problem is enabled by recent advances in automatic differentiation, sparse matrix representation and large scale non-linear programming. The algorithm is optimised for finding nucleation temperatures by sharing model initialisation work between instances of the calculation when operating at different temperatures. We present numerical results on a range of potentials with up to 20 scalar fields, demonstrating O(1%) agreement with existing codes and highly favourable performance characteristics.

Day‐ahead electricity pricing mechanism considering the conflict between distribution network congestion and renewable produce

There is practically no published work that considers distribution network use of system (DUoS) charges as a price signal in the day ahead-market, thus failing to establish a trade-off between the DUoS charges and the energy procurement costs. This paper presents a new approach to optimal design of a day-ahead pricing mechanism for managing distribution network congestion caused by renewable generation. The proposed concept of day-ahead pricing is designed to minimize customer electricity bills taking account of line power constraints resulting from increased penetration of renewable generation. It is assumed that each user is equipped with controllable appliances and a smart meter enabling two-way communications between suppliers and their customers. Suppliers employ an hourly demand side management strategy which considers the price signal from distribution network operators (DNOs), distributed generations (DGs) and wholesale market. A weighted average DUoS charge approach is applied in this paper, allowing DNOs to send a cost reflective use of system charge to electricity users in different locations based on their hourly predicted day-ahead power consumption. An optimum day-ahead pricing mechanism has been developed for DGs to manage their renewable resources to achieve revenue reconciliation and maximize generation output. Finally, power suppliers can optimally manage the controllable appliances that installed in each end user and balance the energy consumption from the main grid and DGs to minimize the electricity price. Several case studies have been conducted with a modified IEEE-33 bus distribution network, where a large-scale nonlinear optimization programming algorithm is applied to solve the problem.

An integrated reliable four-level supply chain with multi-stage products under shortage and stochastic constraints

ABSTRACT In this paper, we design and optimise an integrated four-level Supply Chain (SC), which contains a supplier, a producer, a wholesaler and multiple retailers. The levels cooperate to make an Integrated SC (ISC) so that the inventory cost is minimised and the reliability is maximised, simultaneously. The model is constrained by real stochastic constraints on total space, number of orders, procurement cost, shortage cost, setup cost and production capacity. An Lp-Metric function converts the reliability function and cost function into a single-objective function to optimise the number of stockpiles and period lengths. The designed ISC is a large-scale Nonlinear Programming (NLP) and hard to solve by generic methods. Accordingly, two algorithms, entitled ‘Sequential Quadratic Programming (SQP)’ and ‘Interior Point (IP)’ with super-linear convergence rates are applied for finding the optimum solution. The performance of proposed algorithms is compared based on optimality criteria. Findings showed that the obtained solutions by SQP algorithm have better performance than IP algorithm in terms of optimality error and solution quality. However, the number of taken iterations by IP is less than SQP algorithm. Finally, the result of sensitivity analyses confirmed the excellent performance of the presented methods for solving the large-scale NLP models.

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.

Fast and stable nonconvex constrained distributed optimization: the ELLADA algorithm

Distributed optimization using multiple computing agents in a localized and coordinated manner is a promising approach for solving large-scale optimization problems, e.g., those arising in model predictive control (MPC) of large-scale plants. However, a distributed optimization algorithm that is computationally efficient, globally convergent, amenable to nonconvex constraints remains an open problem. In this paper, we combine three important modifications to the classical alternating direction method of multipliers for distributed optimization. Specifically, (1) an extra-layer architecture is adopted to accommodate nonconvexity and handle inequality constraints, (2) equality-constrained nonlinear programming (NLP) problems are allowed to be solved approximately, and (3) a modified Anderson acceleration is employed for reducing the number of iterations. Theoretical convergence of the proposed algorithm, named ELLADA, is established and its numerical performance is demonstrated on a large-scale NLP benchmark problem. Its application to distributed nonlinear MPC is also described and illustrated through a benchmark process system.

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.

Efficient and verifiable outsourcing computation of large-scale nonlinear programming

Efficient and verifiable outsourcing computation of large-scale nonlinear programming

Dynamic Optimization of a Fed-Batch Nosiheptide Reactor

Nosiheptide is a sulfur-containing peptide antibiotic, showing exceptional activity against critical pathogens such as methicillin-resistant Staphylococcus aureus (MRSA) and vancomycin-resistant Enterococci (VRE) with livestock applications that can be synthesized via fed-batch fermentation. A simplified mechanistic fed-batch fermentation model for nosiheptide production considers temperature- and pH-dependence of biomass growth, substrate consumption, nosiheptide production and oxygen mass transfer into the broth. Herein, we perform dynamic simulation over a broad range of possible feeding policies to understand and visualize the region of attainable reactor performances. We then formulate a dynamic optimization problem for maximization of nosiheptide production for different constraints of batch duration and operability limits. A direct method for dynamic optimization (simultaneous strategy) is performed in each case to compute the optimal control trajectories. Orthogonal polynomials on finite elements are used to approximate the control and state trajectories allowing the continuous problem to be converted to a nonlinear program (NLP). The resultant large-scale NLP is solved using IPOPT. Optimal operation requires feedrate to be manipulated in such a way that the inhibitory mechanism of the substrate can be avoided, with significant nosiheptide yield improvement realized.