Dynamic Optimization Framework Research Articles

Two-stage dynamic real-time optimization framework using parameter-dependent differential dynamic programming

The purpose of chemical process control includes proactive adjustment of the operation to make the most profit out of it. Within this context, real-time optimization (RTO) is proposed and extended to dynamic RTO (DRTO) in the hierarchical control structure, usually having model predictive control (MPC) below. However, online tractability confined the model complexity of RTO and MPC, which results in model inconsistency and, even, incompatible solutions. Here we use parameter-dependent differential dynamic programming (PDDP) to incorporate the closed-loop behavior of the controller in an RTO layer to reduce problem complexity and online computation time. The adaptive control performance of PDDP and the efficacy of closed-loop DRTO formulation with PDDP is demonstrated with the reaction–storage–separation network system control. Consequently, PDDP provides a useful parameterization method to express closed-loop system dynamics, which enables fast feedback control and integrated plant optimization.

A System Predictive Maintenance Framework for Advanced Reactors Using a Data-Driven Digital Twin

Advanced reactor designers are looking to maximize the system capacity factor to make advanced reactors more economically competitive and meet the projected energy demand. To achieve this goal, we propose a Dynamic Operation and Maintenance Optimization (DyOMO) framework to perform system-level predictive maintenance (PdM) using a dynamic Bayesian network and component-specific PdM using deep neural networks. At the system level, DyOMO detects the presence of anomalous phenomena, determines the most influential degradation mode, and estimates the remaining useful life (RUL) distribution for the system. At the component level, DyOMO summarizes the health state of key system components, determines the presence of an anomaly using a feedforward neural network, and predicts component RUL using a Bayesian neural network. To evaluate the overall performance of DyOMO, normal operations of a Pebble-Bed High-Temperature Gas-cooled Reactor (PB-HTGR) were simulated with realistic component degradation for the steam turbine and steam generator. Across the 20 independent reactor life simulations, it was found that maintenance was always performed before any safety limits were violated and before a component failed. Specifically, the system-level PdM suggested maintenance on the steam generator once the steam pressure approached its safety limit, and the component-specific PdM suggested maintenance on the steam turbine once the turbine blade hardness degraded. The results indicate that through the continuous monitoring of the system and individual components, the DyOMO framework improves safety and increases the availability of the reactor when compared to traditional maintenance philosophies.

Integrating Risk-Averse and Constrained Reinforcement Learning for Robust Decision-Making in High-Stakes Scenarios

This paper considers a risk-averse Markov decision process (MDP) with non-risk constraints as a dynamic optimization framework to ensure robustness against unfavorable outcomes in high-stakes sequential decision-making situations such as disaster response. In this regard, strong duality is proved while making no assumptions on the problem’s convexity. This is necessary for some real-world issues, e.g., in the case of deprivation costs in the context of disaster relief, where convexity cannot be ensured. Our theoretical results imply that the problem can be exactly solved in a dual domain where it becomes convex. Based on our duality results, an augmented Lagrangian-based constraint handling mechanism is also developed for risk-averse reinforcement learning algorithms. The mechanism is proved to be theoretically convergent. Finally, we have also empirically established the convergence of the mechanism using a multi-stage disaster response relief allocation problem while using a fixed negative reward scheme as a benchmark.

Efficient proton arc optimization and delivery through energy layer pre-selection and post-filtering.

Proton arc therapy (PAT) has emerged as a promising approach for improving dose distribution, but also enabling simpler and faster treatment delivery in comparison to conventional proton treatments. However, the delivery speed achievable in proton arc relies on dedicated algorithms, which currently do not generate plans with a clear speed-up and sometimes even result in increased delivery time. This study aims to address the challenge of minimizing delivery time through a hybrid method combining a fast geometry-based energy layer (EL) pre-selection with a dose-based EL filtering, and comparing its performance to a baseline approach withoutfiltering. Three methods of EL filtering were developed: unrestricted, switch-up (SU), and switch-up gap (SU gap) filtering. The unrestricted method filters the lowest weighted EL while the SU gap filtering removes the EL around a new SU to minimize the gantry rotation braking. The SU filtering removes the lowest weighted group of EL that includes a SU. These filters were combined with the RayStation dynamic proton arc optimization framework energy layer selection and spot assignment (ELSA). Four bilateral oropharyngeal and four lung cancer patients' data were used for evaluation. Objective function values, target coverage robustness, organ-at-risk doses and normal tissue complication probability evaluations, as well as comparisons to intensity-modulated proton therapy (IMPT) plans, were used to assess plan quality. The SU gap filtering algorithm performed best in five out of the eight cases, maintaining plan quality within tolerance while reducing beam delivery time, in particular for the oropharyngeal cohort. It achieved up to approximately 22% and 15% reduction in delivery time for oropharyngeal and lung treatment sites, respectively. The unrestricted filtering algorithm followed closely. In contrast, the SU filtering showed limited improvement, suppressing one or two SU without substantial delivery time shortening. Robust target coverage was kept within 1% of variation compared to the PAT baseline plan while organs-at-risk doses slightly decreased or kept about the same for all patients. This study provides insights to accelerate PAT delivery without compromising plan quality. These advancements could enhance treatment efficiency and patientthroughput.

2362: Dynamic collimator rotation optimization framework for O-ring treatment systems

2362: Dynamic collimator rotation optimization framework for O-ring treatment systems

A Condition Knowledge Representation and Feedback Learning Framework for Dynamic Optimization of Integrated Energy Systems.

An optimal energy scheduling strategy for integrated energy systems (IESs) can effectively improve the energy utilization efficiency and reduce carbon emissions. Due to the large-scale state space of IES caused by uncertain factors, it would be beneficial for the model training process to formulate a reasonable state-space representation. Thus, a condition knowledge representation and feedback learning framework based on contrastive reinforcement learning is designed in this study. Considering that different state conditions would bring inconsistent daily economic costs, a dynamic optimization model based on deterministic deep policy gradient is established, so that the condition samples can be partitioned according to the preoptimized daily costs. In order to represent the overall conditions on a daily basis and constrain the uncertain states in the IES environment, the state-space representation is constructed by a contrastive network considering the time dependence of variables. A Monte-Carlo policy gradient-based learning architecture is further proposed to optimize the condition partition and improve the policy learning performance. To verify the effectiveness of the proposed method, typical load operation scenarios of an IES are used in our simulations. The human experience strategies and state-of-the-art approaches are selected for comparisons. The results validate the advantages of the proposed approach in terms of cost effectiveness and ability to adapt in uncertain environments.

Efficient dynamic topology optimization of 2D metamaterials based on a complementary energy formulation

The advent of additive manufacturing has revolutionized the design and development of hierarchical structures, with potential applications in compliant, auxetic, and band-gap structures. This paper presents an innovative approach to developing a dynamic Topology Optimization (TO) framework for designing printable lattice structures that exhibit specific dynamic properties. Utilizing parametrically defined filament-based unit cell structures for topology optimization, we achieve desired natural frequency bandgaps in the structures composed of these unit cells. To enhance computational efficiency, we employ a complementary energy-based formulation to (semi)analytically derive the flexibility and stiffness matrices of the unit cell structure, thus, eliminating extensive finite element discretization. Consequently, a wide variety of parametrically defined filament-based meso-structures can be mathematically explored. We apply this innovative framework specifically for band-gap maximization of 2D lattice structures. By tuning the geometry within each cell using TO, we maximize the band gap. Our results show the potential of this approach to create more efficient and effective hierarchical structures with desired band-gap properties.

Derivation of Growth of Import Demand: A Time Series Analysis of Less Developed Countries

In this article, growth of import demand is estimated in a dynamic optimisation framework. Since a conventional micro-theoretic import demand function cannot capture the issue of the growth of import demand, it is derived in a macro-theoretic framework of equilibrium import demand function. Growth rate of import demand in a dynamic optimisation framework (considering utility maximisation problem) has not yet been found in the literature. The main focus of this article is to derive this. It is found that growth rate of imports is the function of the growth of domestic income or expenditure, the growth rate of relative price, which is nothing but the real exchange rate, and productivity of capital. The theoretically derived import growth equation was empirically verified for 35 less developed countries. It is observed that for most of the less developed countries, independent variables are statistically significant with expected sign. JEL Codes: F130, F14

Dynamic optimisation for graded tissue scaffolds using machine learning techniques

Tissue scaffolds have emerged as a promising solution for treatment of critical size bone defects, offering significant advantages over conventional strategies. One of the key functionalities of bone scaffolds is their ability to promote long-term bone ingrowth effectively. To enhance this functionality, we develop a novel dynamic optimisation framework to customise bone scaffolds for achieving maximum bone ingrowth outcomes over a certain period in this study. To improve the design efficiency, we extensively leverage machine learning (ML) techniques within our proposed dynamic optimisation framework. Specifically, two neural networks are integrated into a dynamic bone growth model, and another neural network is coupled with a genetic algorithm for dynamic optimisation process. To demonstrate the effectiveness and efficiency of the approach, we employ a sheep mandible reconstruction for treating a critical size bone defect as an illustraive example. To validate the finite element (FE) model established, we first conduct a mechanical test on the sheep mandible assembled with a tailored 3D printed scaffold made of Polyetherketone (PEK) material. Then, we compare three different optimisation schemes, namely uniform design, lateral gradient design, and vertical gradient design, with an empirical design under the same biomechanical conditions. A 18.5 % enhancement is found in the long-term bone ingrowth when the optimised scaffold is adopted in comparison with the empirical design, which is attributed to the fine-tuning of strut sizes within lattice scaffold structures for facilitating bone regeneration in the gradient regions. This study proposes a novel design framework by combining ML and time-dependent topology optimisation, which provides a new methodology for developing innovative tissue scaffolds with better clinical outcomes.

An efficient transient dynamic topology optimization framework based on successive iteration of analysis and design

Topology optimization of transient dynamics is of great importance in engineering. However, the computational cost required by the repeated dynamic response and design sensitivity analysis during design iterations is often extremely high for large-scale problems, which significantly limits its practical application. To address this issue, we propose a new method based on successive iteration of analysis and design in conjunction with a quasi-static response-enhanced mode displacement method. The conventional mode displacement method requires an inner-loop iteration in addition to the outer-loop design updating, for finding the eigenmodes of the undamped system. In order to avoid the high computational burden caused by the nested double-loop solution, we employ the concept of successive iteration of analysis and design, which integrates approximate eigenvalue analysis and design variable updating into a single iteration loop. By this means, the eigenmodes are sequentially improved through a one-step inverse iteration in each design iteration, and simultaneous convergence of the eigenmodes and the design is sought during the optimization process. These approximate eigenmodes and the quasi-static response are used as the model reduction basis for each intermediate design, and the direct time integration of the reduced-dimensional system is then performed to calculate the structural responses of interest and their derivatives with respect to the design variables. Several numerical examples are presented to demonstrate the efficiency of the proposed method. It is shown that the method can be used to solve transient dynamic topology optimization problems up to 15 million degrees of freedom on a desktop computer at affordable time cost.

Implementing the Dynamic Feedback-Driven Learning Optimization Framework: A Machine Learning Approach to Personalize Educational Pathways

This study introduces a novel approach named the Dynamic Feedback-Driven Learning Optimization Framework (DFDLOF), aimed at personalizing educational pathways through machine learning technology. Our findings reveal that this framework significantly enhances student engagement and learning effectiveness by providing real-time feedback and personalized instructional content tailored to individual learning needs. This research demonstrates the potential of leveraging advanced technology to create more effective and individualized learning environments, offering educators a new tool to support each student’s learning journey. The study thus contributes to the field by showcasing how personalized education can be optimized using modern technological advancements.

Multi-agent cooperative swarm learning for dynamic layout optimisation of reconfigurable robotic assembly cells based on digital twin

AbstractTo meet the requirement of product variety and short production cycle, reconfigurable manufacturing system is considered as an effective solution in addressing current challenges, such as increasing customisation, high flexibility and dynamic market demand. Dynamic factory layout design and optimisation are the crucial factors in response to rapid change in the mechanical structure, software and hardware integration, as well as production capability and functionality adjustment. Nevertheless, in the current research, the layout design for reconfigurable manufacturing systems is usually simplified with autonomous devices being regarded as 2D shapes. Issues such as overlapping and transportation distance are also addressed in an approximate form. In this paper, we present a novel multi-agent cooperative swarm learning framework for dynamic layout optimisation of reconfigurable robotic assembly cells. Based on its digital twin established in the proposed learning environment (constructed in Visual Components and controlled by TWINCAT), the optimisation framework uses 3D digital representation of the facility models with minimal approximation. Moreover, instead of using a traditional centralised learning manner, multi-agent system could provide an alternative way to address the layout issues combined with the proposed decentralised multi-agent cooperative swarm learning. In order to verify the application feasibility of the learning framework, two aerospace manufacturing use cases were implemented. In the first use case, the layout compactness is reduced by 3.8 times compared with the initial layout setting, the simulated production time is reduced by 2.3 times, and the rearrangement cost decreased by 33.4$$\%$$ % . In addition, all manufacturing activity within the cell can be achieved with a feasible robot path, meaning without any joint limits, reachability or singularity issue at each key assembly point. In the second use case, we demonstrated that with the proposed dynamic layout optimisation framework, it is possible to flexibly adjust learning objectives by selecting various weight parameters among layout compactness, rearrangement cost and production time.

Optimizing Dynamic Optimization of a Reconfigurable Manufacturing System under Risk and Human Factors

The adaptability of Reconfigurable Manufacturing Systems (RMSs) to ever-changing product demand and their responsiveness to unpredictable events has made them a popular solution for modern manufacturing in today’s competitive industries. The proper scheduling of RMSs is important in ensuring optimal resource utilization, achieving production objectives, and responding to dynamic changes in a realtime. This study aims to tackle job scheduling and workforce planning in RMSs by considering dynamic events, such as the risk of machine unavailability, and human factors in the manufacturing process, to minimize the makespan and delay-related cost. At first, a comprehensive framework for dynamic optimization in an RMS environment has been developed. A multi-level bi-objective mathematical modeling presented to address job scheduling and workforce planning proposed as a MILP model. Finally, numerical studies evaluated two scenarios: risk and human factors addressed or not, for small to medium-sized cases. The results demonstrate a significant gap between these scenarios.

Towards Wearable and Portable Spine Motion Analysis Through Dynamic Optimization of Smartphone Videos and IMU Data.

Monitoring spine kinematics is crucial for applications like disease evaluation and ergonomics analysis. However, the small scale of vertebrae and the number of degrees of freedom present significant challenges for noninvasive and convenient spine kinematics estimation. This study developed a dynamic optimization framework for wearable spine motion tracking at the intervertebral joint level by integrating smartphone videos and Inertia Measurement Units (IMUs) with dynamic constraints from a thoracolumbar spine model. Validation involved motion data from 10 healthy males performing static standing, dynamic upright trunk rotations, and gait. This data included rotations of ten IMUs on vertebrae and virtual landmarks from three smartphone videos preprocessed by OpenCap, an application leveraging computer vision for pose estimation. The kinematic measures derived from the optimized solution were compared against simultaneously collected infrared optical marker-based measurements and in vivo literature data. Solutions only based on IMUs or videos were also compared for accuracy evaluation. The proposed optimization approach closely matched the reference data in the intervertebral or segmental rotation range, demonstrating minimal angular differences across all motions and the highest correlation in 3D rotations (maximal Pearson and intraclass correlation coefficients of 0.92 and 0.94, respectively). Time-series changes of joint angles also aligned well with the optical-marker reference. Dynamic optimization of the spine simulation that integrates IMUs and computer vision outperforms the single-modality method. This markerless 3D spine motion capture method holds potential for spinal health assessment in large cohorts in real-world settings without dedicated laboratories.

Incentive Mechanism of Online Leaning Based on Blockchain

Incentive mechanism plays an important role in online education. In order to better play the role of the incentive mechanism, it must rely on contemporary information technology, such as blockchain technology, big data technology and so on. In this paper an incentive mechanism based on blockchain technology is proposed with which can establish a good trust relationship between multiple learning resource nodes and improve data security during the process of online education. A structure of online learning resource chain is proposed in this paper also. And a dynamic optimization framework of learning resource chain by analyzing a series of problems faced in the process of online education is formed. The private chain of learning resource is constructed on the basis of the design of incentive smart contract. The learners and the builders of learning resources can obtain the dynamic rewards by performing a smart method of contract. The experimental results show that the incentive method based on blockchain can well mobilize participants’ enthusiasm for resource construction and dynamic improvement of resource quality, and effectively solve a series of problems in the learning process.

Improving critical buildings energy resilience via shared autonomous electric vehicles — A sequential optimization framework

The interdependence between electric power systems and transportation systems is rapidly increasing due to the high adoption of Electric Vehicles (EVs) and their charging infrastructures. Electric vehicles can represent additional load for the power system, but can also bring new opportunities for contributing to the efficient and resilient operations of the power grid. This is mainly because of their ability to provide back power to the system when it is not used for transportation, essentially serving as a moving battery source for the power grid. This so-called Vehicle-to-Grid (V2G), Vehicle-to-Building (V2B), or, generally, Vehicle-to-X (V2X) capability of EVs has been extensively studied in the literature. However, the upcoming development of autonomous driving systems and their integration within sharing mobility services can significantly add to the possibilities of interaction between the transportation system and the power grid. This paradigm is studied to a much lesser extent in the existing literature. Shared Autonomous Electric Vehicles (SAEVs) could allow for more control of the actions of the fleet allowing for large-scale coordinated responses both to mobility and energy demands. This coordinated response can be particularly useful for providing emergency power services in case of power loss while maintaining a high level of transportation service. Thus, improving the overall resilience of the system. In this work, we develop a dynamic optimization framework to evaluate the potential contribution of the SAEV fleet for improving critical buildings’ energy resilience via V2B services. The model considers passengers’ pick-up and transportation, relocation of vehicles, and battery charging and discharging. Power outage scenarios for critical buildings are considered and the potential of the SAEV fleet to fully or partially respond to the emergency power outage is studied. In addition, sensitivity analysis for key parameters such as the outage parameters is introduced. The results of the case study for the Ile-de-France region in France shows that the SAEV fleet has the potential to provide V2B service for critical building at an acceptable loss of passenger total waiting time on the transportation side. Furthermore, it is shown that it is capable of satisfying the emergency power load at a lower cost compared to investing in extra backup generators unless the outage occurs at significantly high frequencies.

Dynamic multi-objective workflow scheduling for combined resources in cloud

Cloud resource providers offer idle resources to users as spot instances. The price of the instances changes with market supply and demand, and the dynamic price can have a significant impact on workflow scheduling. In this work, we use a combination of spot and on-demand instances as the foundation cloud resource and characterize the dynamic workflow scheduling problem as a dynamic multi-objective optimization problem (DMOP), where the dynamics originate from the dynamic price of spot instances. The scheduling solution is found by considering three objectives: maximizing the reliability of the instances while minimizing the makespan and cost. In addition, we provide an enhanced MOEAD algorithm called MOEA/D-URDI that combines diversity introduction and uniform random sampling, where the uniform random sampling paradigm is used to generate the initial weight vector. The dynamic multi-objective optimization evolutionary algorithm DMOEA/D-URDI is then created by combining the method with a dynamic optimization framework. Our technique beats existing algorithms, according to experimental data based on dynamic benchmark sets and three well-known scientific procedures in terms of metrics on dynamic benchmark sets and better ensures reliability in scheduling scientific workflows while reducing makespan and cost.

A deep reinforcement learning framework for dynamic optimization of numerical schemes for compressible flow simulations

Marginal or under-resolved simulations of compressible flow configurations that often occur in practical applications classically are enabled by administering sufficient numerical dissipation to keep the simulation stable. Such measures, however, often are physically inconsistent due to non-selectively altering of dynamics across scales. Sustaining physically consistent large scale dynamics requires the numerical solution to effectively model non-resolved small scale dynamics. In this work, we propose a general deep-reinforcement-learning framework for devising an agent to interact with high-resolution scheme in order to balance dissipation and dispersion such that physically consistent modeling of non-resolved scales is achieved. A densely distributed reward function without involving labeled data is defined. The agent is trained on low-resolution uniform grids that capture the dominant flow structures. We demonstrate that it can be applied directly to high-resolution simulations without the need for retraining or fine-tuning, thereby, demonstrating significantly improved modeling performance compared to empirically designed high-resolution schemes. The proposed methodology opens a new path for self-adaptive numerical solutions whose truncation errors act as physically consistent model for unresolved scales of widely differing flow configurations.

Potential Welfare Gains from Optimal Macro Hedging for Oil Exporters

This paper computes the welfare gains from optimal hedging with futures contracts for an oil-exporting country. Unlike previous studies, this paper derives the welfare gains under a more realistic futures hedging model. This is accomplished by considering basis risk and by relaxing the full-hedging assumption. Furthermore, this is the first paper to derive the welfare gains under optimal hedging strategies. We also incorporate the empirical relationship between spot and futures prices within our models, rather than the theoretical relationship which most studies employ. The models were developed under a dynamic stochastic optimization framework and the optimal consumption and value functions were found using the method of Endogenous Gridpoints. The results showed that the choice of the optimal hedging strategy employed led to a slight improvement in the country’s welfare gains relative to full hedging. We also found that the strategies with the highest welfare gains were the most effective at volatility reduction. Finally, this paper provides compelling evidence for the use of optimal macro futures hedging as an effective risk management tool for oil-exporting developing countries.

System reliability evaluation and dynamic optimization based on an improved reliability block diagram

Reliability block diagram (RBD) is an effective tool for modeling and evaluating system reliability. During operation, a system’s reliability may decrease significantly due to the failure of certain critical nodes and thus should be reconfigured. This paper presents a framework for system reliability evaluation and dynamic optimization based on RBD, designed from the perspective of system users. First, we improve the classic RBD model with a new encoding scheme and develop an accurate RBD computation algorithm that is easily recognized by computers and highly efficient. Second, we create an optimization algorithm based on Tabu Search to reconfigure the system after node failure, striking a balance between system reliability recovery and RBD variation amplitude. Finally, we provide some numerical examples and a computational experiment based on a practical instance from a navy fleet to demonstrate the correctness and effectiveness of our proposed methods.