Dynamic Optimization Framework Research Articles

A dynamic nonlinear optimization framework for learning data-driven reduced-order microkinetic models

The use of kinetic models is key for analyzing, designing, controlling, and optimizing the manufacturing of high value chemicals. In particular, microkinetic modeling relies on large-scale networks of elementary reaction steps that map the conversion of feed materials to final products by considering a large number of pathways and intermediate species for a given reactor configuration. Intuitively, several of the (often automatically generated) reaction steps might be redundant or insignificant, and thus determining the true governing reaction network is critical to understanding and modeling the underlying chemistry. This work introduces a nonlinear dynamic optimization framework for discovering governing reaction networks from data, whereby both the model structure (the elementary reaction steps) and the model parameters (reaction rate constants, pre-exponential factors, and activation energies) are simultaneously learned from composition time series data. The proposed framework can also achieve dimensionality reduction to produce accurate reduced-order microkinetic models that are computationally parsimonious and thus better suited for applications involving simulation and optimization. Two numerical examples of different dimensions are presented to illustrate the key properties of our approach.

Model predictive control policy design, solutions, and stability analysis for longitudinal vehicle control considering shockwave damping

Longitudinal vehicle control models, such as Adaptive Cruise Control (ACC) and Cooperative Adaptive Cruise Control (CACC), have been the core component of many Automated Driving Systems (ADS) or Advanced Driver Assistance System (ADAS). ACC and CACC systems make vehicles drive with faster reaction time and smaller following distance than manual vehicles, alleviating the congestions and attenuating traffic disturbances. Many existing ACC and CACC control models focus on three strategies that can indirectly mitigate congestions and damp traffic shockwaves: time headway suppression, stability improvement, and adaptive mode-switching control based on traffic conditions. Although congestion mitigation and shockwave damping are achievable with those control strategies, the improvement is often limited to the by-product effect of their main control objectives of headway suppression and system stability. Many adaptive models also need to calibrate many parameters for different road conditions.This paper proposes a new ACC and CACC framework that directly integrates the congestion shockwave damping and traffic congestion mitigation into the objective function of a dynamic control framework. A Model Predictive Control (MPC) based dynamic optimization framework is proposed to balance the trade-offs among multiple objectives, including safety, efficiency, shockwave, elasticity, and driver’s comfort. The proposed framework is applied in both ACC and CACC platoons mixed with manual vehicles, and five different control models are explored. The stability conditions of the proposed models are derived analytically and analyzed numerically. Three experimental studies, including platoon, ring-road, and traffic simulation studies, indicate promising results of proposed models in reducing shockwave propagation speed and mitigating traffic congestion under different environments compared with existing ACC and CACC models.

Special issue on “Optimal design and operation of energy systems”

Special issue on “Optimal design and operation of energy systems”

Joint Application Placement and Request Routing Optimization for Dynamic Edge Computing Service Management

As mobile edge computing (MEC) hosting applications at the network edge with limited capacities, service providers are facing the new challenge of how to make full use of the scarce edge resources to maximize the system performance. Accommodating this challenge requires careful application placement and request routing to coordinate diverse MEC nodes. However, frequent application re-placement would greatly increase the system reconfiguration cost, indicating a performance-cost trade-off. In response, in this paper, we study the problem of joint optimization on application placement and request routing to maximize the system performance, under a long-term budget of the application reconfiguration cost. Solving this problem is non-trivial since the long-term budget is coupled with the future system states (e.g., user request arrivals) that are typically unpredictable. To address this challenge, we first advocate an approximated dynamic optimization framework to decompose the long-term optimization problem into a series of one-shot problems which do not require the future system states. Moreover, since the decomposed problem is a mixed integer linear program (MILP) which is proven to be NP-hard, we then devise an efficient dependent rounding based approximation algorithm, which can achieve the near-optimal performance in a fast manner. Both rigorous theoretical analysis and extensive trace-driven evaluations demonstrate the proposed framework can achieve superior performance gain over existing schemes.

Modeling, simulation, and optimization of multiproduct cryogenic air separation unit startup

AbstractThe startup of multiproduct cryogenic air separation plants takes several hours, during which time limited revenue is generated with high costs incurred due to the highly energy‐intensive nature of these operations. This motivates the development of high‐fidelity dynamic models to capture the complexity of the startup process to aid decision‐making. This article focuses on the development of a startup model for a multiproduct air separation unit (ASU), and its use in dynamic simulation and optimization. To accomplish this, a first‐principles based dynamic ASU model is extended by including various discontinuities using smooth approximations, adding dynamics to the primary heat exchanger, and extending the handling phase change within process streams. Dynamic simulations demonstrate plant response behavior during startup, including a failed startup resulting from an injudicious choice of input trajectory. In addition, improvement of startup operation is demonstrated through the incorporation of the model within a dynamic optimization framework.

AntiDoteX: Attention-Based Dynamic Optimization for Neural Network Runtime Efficiency

Deep neural networks (DNNs) achieved great cognitive performance at the expense of a considerable computation workload. To relieve the computational burden, many optimization works are developed to reduce the model redundancy by identifying and removing insignificant model components, such as weight sparsity and filter pruning methods. However, these works only evaluate model components’ static significance with parameter information, ignoring their dynamic interaction with external inputs. Specifically, due to the difference in per-input features, the model components’ significance can dynamically change and, thus, the static methods can only achieve suboptimal performance. Focusing on this aspect, we propose a dynamic DNN optimization framework in this work. Based on the neural network attention mechanism, we propose a comprehensive dynamic optimization framework, including 1) testing-phase dynamic feature map pruning; 2) training-phase optimization by training with targeted dropout; and 3) deployment-phase one-for-all (OFA) model adaptability enhancement. By providing a holistic dynamic testing, training, and deployment co-optimization framework, our work has the following benefits: first, it can accurately identify and aggressively remove per-input feature redundancy by considering the model-input interaction and involving the channel/column-wise pruning flexibility; meanwhile, the training-testing co-optimization favors the dynamic pruning and helps maintain the model accuracy even with a very high feature pruning ratio. Finally, the deployment enhancement provides one unified OFA model to support full-spectrum feature sparsity ratios. The unified model can be dynamically reconfigured to meet different resource budgets without any retraining cost, and thus provide significant deployment flexibility. Extensive experiments show that our method could bring 37.4%–54.5% floating-point operations reduction with negligible accuracy drop on various test benchmarks. Meanwhile, the OFA deployment optimization enables us to use one model to support at most ten different resource constraints without any retraining cost.

Optimal Control of a PHEV Based on Backward-Looking Model Extended with Powertrain Transient Effects

The paper proposes a power flow control strategy for a P2 parallel plug-in hybrid electric vehicle (PHEV) which takes into account torque and power losses related to engine-on and gear shift transients. An extended backward-looking (EXT-BWD) model is proposed to account for the transient losses, while the control strategy combines a rule-based controller with an equivalent consumption minimization strategy. To describe the transient losses, the EXT-BWD model includes additional state variables related to engine on/off flag and gear ratio in the previous time step. To establish a performance benchmark for control strategy verification, a dynamic programming-based control variable optimization framework is established based on the EXT-BWD model. The proposed control strategy is demonstrated to improve the fuel efficiency and drivability compared to the original control strategy while retaining comparable computational efficiency.

Simultaneous layout and size optimization of nonlinear viscous dampers for frame buildings under stochastic seismic excitation

Viscous dampers, as effective energy-dissipation devices, have been widely used for seismic mitigation of building structures. Due to the intrinsic uncertainties of structural parameters and earthquake ground motions, to obtain an optimal performance of structural control, the stochastic design optimization of viscous dampers for buildings is essential. This paper establishes a new dynamic reliability-based optimization framework to address the simultaneous layout and size design of nonlinear viscous dampers in frame buildings, considering the dual randomness of both nonstationary seismic excitations and uncertain structural model parameters. Firstly, a mixed integer optimization problem for nonlinear viscous dampers, including discrete and continuous design variables, is formulated, and the design target is to minimize the cost of the dampers subjected to performance constraints on dynamic reliability of building structures. Then, sequential approximate mixed integer programming with trust region is proposed to solve the optimization problem. Moreover, direct probability integral method is suggested to assess the dynamic reliability and its sensitivity with respect to design variables. Finally, accounting for both stochastic nonstationary seismic excitations and random structural parameters, the optimized results of two numerical examples indicate that the proposed method is a competitive choice for realizing the layout and size optimization of limiting types of nonlinear viscous dampers in frame buildings. To ensure the same target performance of buildings in terms of the probability of exceeding the target value of inter-story drift, the larger peak ground acceleration of stochastic ground motions is, the more cost of dampers is required for seismic protection of buildings.

A dynamic optimization method for power distribution network operation with high ratio photovoltaics

With the high ratio distributed photovoltaics (PVs) penetration to the distribution network (DN), the bearing capacity, integration capacity, consuming capacity and controlling capacity of DN for PVs are all facing great challenges. Enhancing the flexible regulation and operation optimization capabilities of DN have become key factors to satisfy these new challenges. For the operation optimization problem of high ratio PVs penetration, a novel quasi-equal curtailment ratio (QCR) constraint of PVs is proposed in the dynamic optimization method for DN operation. Firstly, the uncertainty of high ratio PVs and their active power deviations are discussed. And a dynamic optimization framework of PVs based on optimal power flow (OPF) has been proposed. Secondly, the optimization model for high ratio PVs is formulated with multi-objective of maximum PVs output, minimum voltage deviation and minimum line loss, under the equality and inequality constraints of power flow, PVs power generation limit, QCR of PVs and so on. Then the multi-objective optimization problem (MOP) is transformed into a single-objective optimization problem (SOP) by weighting coefficients, and solved by sequential quadratic programming (SQP) with trust-region (TR) searching algorithm. Finally, the proposed method is tested, verified and compared with the primal dual interior point (PDIP) and traditional SQP algorithms in IEEE 33-bus, PG&E 69-bus, 292-bus and 1180-bus test cases. The experimental results show the rapidity and robustness of the proposed method.

From microalgae to bioenergy: Identifying optimally integrated biorefinery pathways and harvest scheduling under uncertainties in predicted climate

An emerging renewable energy source from living organisms, microalgae are recognized for its remarkable energy content and continuously receiving interest with a great potential in increasing its shares in fuel market. The main challenge for stable biorefinery operation is cultivation, given that the growth of microalgae is highly dependent on climate conditions, especially ambient temperature, and solar exposure. Herein, an advanced forecasting algorithm predicts daily climate conditions a year ahead. The forecast is then used in a dynamic metaheuristic optimization framework to determine optimal microalgae biorefinery process pathways with promising total annual margins and greenhouse gas emissions. In return, the optimal solution is reported with a total annual margin of 815,716 US$/y and greenhouse gas emission of 1.1 × 107 kg CO2-eqv/y. The most feasible microalgae species among the selection pool are identified in terms of kinetic growth, which is attributed to the climate behavior of the selected case-study region. A scheduling scheme is then identified for the optimal harvest period of cultivated microalgae. Next, uncertainty analysis for the selected process configuration is conducted using Monte Carlo simulation to investigate how variations in climate conditions will affect its overall performance. Additionally, the process is further enhanced by including renewable electricity sources which allow reducing 50% greenhouse gas emissions with the configuration of biomass energy (1.2%), solar power (0.1%), and wind energy (98.7%). In summary, this study provided a comprehensive guidelines on strategically deploying large scale microalgae biorefineries considering its long-term operational sustainability abiding the possible uncertainties within the system proposed.

An AGC Dynamic Optimization Method Based on Proximal Policy Optimization

The increasing penetration of renewable energy introduces more uncertainties and creates more fluctuations in power systems than ever before, which brings great challenges for automatic generation control (AGC). It is necessary for grid operators to develop an advanced AGC strategy to handle fluctuations and uncertainties. AGC dynamic optimization is a sequential decision problem that can be formulated as a discrete-time Markov decision process. Therefore, this article proposes a novel framework based on proximal policy optimization (PPO) reinforcement learning algorithm to optimize power regulation among each AGC generator in advance. Then, the detailed modeling process of reward functions and state and action space designing is presented. The application of the proposed PPO-based AGC dynamic optimization framework is simulated on a modified IEEE 39-bus system and compared with the classical proportional−integral (PI) control strategy and other reinforcement learning algorithms. The results of the case study show that the framework proposed in this article can make the frequency characteristic better satisfy the control performance standard (CPS) under the scenario of large fluctuations in power systems.

Investigation of Drought Risk Using a Dynamic Optimization Framework in Regional Water Allocation Procedure With Different Streamflow Scenarios

Recently, the water supply process has experienced serious challenges, because, with the intensification of drought, the imbalance between available water resources and demand for water in different sectors has led to increased system risk. Therefore, this study proposed an optimal dynamic framework under different scenarios aimed at improving the drought risk of the water supply system. In this sense, given the negative effects of drought on the water supply procedure, the degree of drought risk is analyzed and improved according to system performance parameters. After examining the developed model by initial data collected from a real case study of Hamoun wetland in Iran, the most sensitive parameters were included reliability and vulnerability, which, in this regard, the highest degree of drought risk is related to the agricultural and industrial sectors due to the acquisition of less reliability and greater vulnerability. In addition, given the final output, adaptation measures such as demand governance scheme and weight scenario analysis have been developed in order to investigate the drought risk of the system in more detail.

Estimation of Joint Moments During Turning Maneuvers in Alpine Skiing Using a Three Dimensional Musculoskeletal Skier Model and a Forward Dynamics Optimization Framework.

In alpine skiing, estimation of the joint moments acting onto the skier is essential to quantify the loading of the skier during turning maneuvers. In the present study, a novel forward dynamics optimization framework is presented to estimate the joint moments acting onto the skier incorporating a three dimensional musculoskeletal model (53 kinematic degrees of freedom, 94 muscles). Kinematic data of a professional skier performing a turning maneuver were captured and used as input data to the optimization framework. In the optimization framework, the musculoskeletal model of the skier was applied to track the experimental data of a skier and to estimate the underlying joint moments of the skier at the hip, knee and ankle joints of the outside and inside leg as well as the lumbar joint. During the turning maneuver the speed of the skier was about 14 m/s with a minimum turn radius of about 16 m. The highest joint moments were observed at the lumbar joint with a maximum of 1.88 Nm/kg for lumbar extension. At the outside leg, the highest joint moments corresponded to the hip extension moment with 1.27 Nm/kg, the knee extension moment with 1.02 Nm/kg and the ankle plantarflexion moment with 0.85 Nm/kg. Compared to the classical inverse dynamics analysis, the present framework has four major advantages. First, using a forward dynamic optimization framework the underlying kinematics of the skier as well as the corresponding ground reaction forces are dynamically consistent. Second, the present framework can cope with incomplete data (i.e., without ground reaction force data). Third, the computation of the joint moments is less sensitive to errors in the measurement data. Fourth, the computed joint moments are constrained to stay within the physiological limits defined by the musculoskeletal model.

Swarm-Intelligence Optimization Method for Dynamic Optimization Problem

In recent years, the vigorous rise in computational intelligence has opened up new research ideas for solving chemical dynamic optimization problems, making the application of swarm-intelligence optimization techniques more and more widespread. However, the potential for algorithms with different performances still needs to be further investigated in this context. On this premise, this paper puts forward a universal swarm-intelligence dynamic optimization framework, which transforms the infinite-dimensional dynamic optimization problem into the finite-dimensional nonlinear programming problem through control variable parameterization. In order to improve the efficiency and accuracy of dynamic optimization, an improved version of the multi-strategy enhanced sparrow search algorithm is proposed from the application side, including good-point set initialization, hybrid algorithm strategy, Lévy flight mechanism, and Student’s t-distribution model. The resulting augmented algorithm is theoretically tested on ten benchmark functions, and compared with the whale optimization algorithm, marine predators algorithm, harris hawks optimization, social group optimization, and the basic sparrow search algorithm, statistical results verify that the improved algorithm has advantages in most tests. Finally, the six algorithms are further applied to three typical dynamic optimization problems under a universal swarm-intelligence dynamic optimization framework. The proposed algorithm achieves optimal results and has higher accuracy than methods in other references.

Robust dynamic optimization for nonlinear chemical processes under measurable and unmeasurable uncertainties

AbstractWe formulate an integrated framework for the robust dynamic optimization of nonlinear chemical processes under measurable and unmeasurable uncertainties. An affine decision rule is proposed to approximate the causal dependence of the wait‐and‐see decision variables on the gradually revealed measurable uncertainties. To overcome the computational intractability of the proposed model, a linearization technique based on the first‐order Taylor expansion is introduced around the nominal values of uncertainties to derive the robust dynamic counterpart, which can be discretized to a large‐scale nonlinear programming (NLP) formulation. Effects of first discretizing the dynamic models or introducing the affine decision rule are investigated. The proposed framework is also compared with the state‐of‐the‐art re‐optimization and traditional robust optimization approaches. An illustrative example and an industrial semi‐batch 2‐mercaptobenzothiazole production case are involved to demonstrate the advantages and applicability of the proposed framework.

Water resource recovery facilities as potential energy generation units and their dynamic economic dispatch

The dynamic nature of wastewater treatment and the significant number of energy conversion and recovery technologies applicable to the process, require a modelling framework that can be used for optimization and planning. This paper introduces a dynamic energy dispatch optimization framework with a combination of energy recovery and reserve options for water resource recovery facilities (WRRFs). Energy potentials, including biogas, electricity, and heat, were assessed for 15 large-scale WRRFs, which serve approximately 80% of the Irish population. The framework was applied by simulation of the national electrical system on an hourly basis for 2030 using mixed-integer programming (MIP) for eight scenarios. The simulation enabled automatic operational command scheduling for the production, conversion, storage, and supply over a year at an hourly time resolution. Meanwhile, the significance of several energy resources was assessed, and the impact of dynamic energy dispatch examined. A total potential cost saving of €46.35 M was possible through implementation of dynamic economic dispatch optimization (54% from biogas cogeneration, 40 %from thermal energy recovery, and 6% from micro-hydropower electricity). In addition, reductions in carbon emissions (2%), fossil fuel consumption (3%), startup costs (18%) and outsourcing dependency (5%) were possible. Up to 0.5% of whole system power demand and 90% of considered heat demand at peak periods could be provided by the proposed framework through dynamic economic dispatch. Therefore, this study suggests that WRRFs can participate into energy system through the dynamic economic dispatch of recovered energy, and provide potential energy flexibility, as well as adding value to overall sustainability of energy system.

Predicting neuromuscular control patterns that minimize ACL forces during injury-prone jump-landing manoeuvres in downhill skiing using a musculoskeletal simulation model

ABSTRACT Competitive skiers encounter a high risk of sustaining an ACL injury during jump-landing in downhill ski racing. Facing an injury-prone landing manoeuvre, there is a lack of knowledge regarding optimum control strategies. So, the purpose of the present study was to investigate possible neuromuscular control patterns to avoid injury during injury-prone jump-landing manoeuvres. A computational approach was used to generate a series of 190 injury-prone jump-landing manoeuvres based on a 25-degree-of-freedom sagittal plane musculoskeletal skier model. Using a dynamic optimization framework, each injury-prone landing manoeuvre was resolved to identify muscle activation patterns of the lower limbs and corresponding kinematic changes that reduce peak ACL force. In the 190 injury-prone jump-landing simulations, ACL forces peaked during the first 50 ms after ground contact. Optimized muscle activation patterns, that reduced peak ACL forces, showed increased activation of the monoarticular hip flexors, ankle dorsi- and plantar flexors as well as hamstrings prior to or during the early impact phase (<50 ms). The corresponding kinematic changes were characterized by increased hip and knee flexion and less backward lean of the skier at initial ground contact and the following impact phase. Injury prevention strategies should focus on increased activation of the monoarticular hip flexors, ankle plantar flexors and rapid and increased activation of the hamstrings in combination with a flexed landing position and decreased backward lean to reduce ACL injury risk during the early impact phase (<50 ms) of jump landing. Highlights First study investigating advantageous control strategies during injury-prone jump-landing manoeuvres in downhill skiing using a musculoskeletal simulation model and dynamic optimization framework. The simulation results predicted high injury risk during the first 50 ms after initial ground contact. Optimized neuromuscular control patterns showed adapted activation patterns (timing and amplitude) of muscles crossing the knee as well as the hip and ankle joints prior to and after initial ground contact, respectively. An optimized control strategy during an injury-prone landing manoeuvre was characterized kinematically by increasing hip and knee flexion and less backward lean of the skier at initial ground contact and the following impact phase.

An uncertainty-aware dynamic shape optimization framework: Gravity dam design

Uncertainties such as material randomness, manufacturing anomalies, and external loading play an important role in the design of engineering structures. Therefore, reliability-based design optimization (RBDO) is frequently used as a tool to guarantee economic aspects without compromising safety. In this paper, an uncertainty-aware framework is proposed for seismic optimization of structures. This algorithm is founded on the stochastic dynamic stressor, and therefore, reduces the bias due to the aleatory nature of ground motion. Safety constraints are evaluated in quantiles instead of the exact solution of reliability analysis. Kriging approach approximates the actual model, while a global search algorithm solves the RBDO problem. The proposed algorithm is used for the optimal shape design of gravity dams with a series of local and global time-variant/invariant performance indices. Two sets of deterministic and probabilistic shape optimization algorithms were compared to demonstrate the impact of uncertainty quantification. Finally, the framework is extended to a class of generic dams with different heights, concrete strengths, and foundation-to-concrete flexibility. By probabilistic seismic performance evaluation, system safety is guaranteed using the proposed dynamic RBDO compared to the median response in applying a set of as-recorded ground motions. This paper provides a new paradigm for RBDO of structures with dynamic loading and a robust decision-making during dam design.

Energy optimization of the electric arc furnace for operations at a fixed electrical power level

This paper presents an optimal control problem (OCP) that finds the optimal voltage and impedance setpoints that improve the electrical efficiency of an EAF for operations at a fixed power level. In the optimization framework, an electric arc model and an EAF process model are embedded into a dynamic optimization framework that aims at minimizing the radiation losses of the process. A numerical case study shows a reduction of 5% of the electrical power consumption of the process and an increment of 2% in the energy efficiency. It is demonstrated that the electrical power consumption of the process can be reduced under a mono profile setting of the EAF.

Does Delayed Retirement Crowd Out Workforce Welfare? Evidence in China

Does delayed retirement crowd out the welfare of the workforce? To answer this question, a dynamic optimization framework is established to simulate the impact of delayed retirement on the welfare of the working population over time. Simulations are conducted based on practical and feasible parameters. Delayed retirement was found to improve the welfare of the working population rather than crowding it out. Furthermore, the results are robust against changes in parameters and modes of supporting elderly individuals. In terms of policymaking, it is suggested that such facts be shared with the public and that a delayed retirement plan be introduced as soon as possible to manage the pension and retirement wave caused by post-1960s baby boomers. However, to ensure that the delayed retirement plan does not lead to a reduction in the welfare of the working population, increases in fertility costs and the pension replacement rate should be appropriately controlled.