Real-time Optimization Problem Research Articles

Distributed Swarm Trajectory Planning for Autonomous Surface Vehicles in Complex Sea Environments

In this paper, a swarm trajectory-planning method is proposed for multiple autonomous surface vehicles (ASVs) in an unknown and obstacle-rich environment. Specifically, based on the point cloud information of the surrounding environment obtained from local sensors, a kinodynamic path-searching method is used to generate a series of waypoints in the discretized control space at first. Next, after fitting B-spline curves to the obtained waypoints, a nonlinear optimization problem is formulated to optimize the B-spline curves based on gradient-based local planning. Finally, a numerical optimization method is used to solve the optimization problems in real time to obtain collision-free, smooth and dynamically feasible trajectories relying on a shared network. The simulation results demonstrate the effectiveness and efficiency of the proposed swarm trajectory-planning method for a network of ASVs.

Workshop Facility Layout Optimization Based on Deep Reinforcement Learning

With the rapid development of intelligent manufacturing, the application of virtual reality technology to the optimization of workshop facility layout has become one of the development trends in the manufacturing industry. Virtual reality technology has put forward engineering requirements for real-time solutions to the Workshop Facility Layout Optimization Problem (WFLOP). However, few scholars have researched such solutions. Deep reinforcement learning (DRL) is effective in solving combinatorial optimization problems in real time. The WFLOP is also a combinatorial optimization problem, making it possible for DRL to solve the WFLOP in real time. Therefore, this paper proposes the application of DRL to solve the dual-objective WFLOP. First, this paper constructs a dual-objective WFLOP mathematical model and proposes a novel dual-objective DRL framework. Then, the DRL framework decomposes the WFLOP dual-objective problem into multiple sub-problems and then models each sub-problem. In order to reduce computational workload, a neighborhood parameter transfer strategy is adopted. A chain rule is constructed for the appealed sub-problem, and an improved pointer network is used to solve the bi-objective WFLOP of the sub-problem. Finally, the effectiveness of this method is verified by using the facility layout of a chip production workshop as a case study.

Real-Time Optimization of Heliostat Field Aiming Strategy via an Improved Swarm Intelligence Algorithm

Optimizing the heliostat field aiming strategy is crucial for maximizing thermal power production in solar power tower (SPT) plants while adhering to operational constraints. Although existing approaches can yield highly optimal solutions, their considerable computational cost makes them unsuitable for real-time optimization in large-scale scenes. This study introduces an efficient, intelligent, real-time optimization method based on a meta-heuristic algorithm to effectively and reliably manage SPT plant operations under varying solar conditions, such as cloud shadowing variations. To minimize redundant calculations, the real-time optimization problem is framed in a way that captures the operational continuity of the heliostat, which can be utilized to streamline the solution process. The proposed method is tested in a simulation environment that includes a heliostat field, cylindrical receiver, and cloud movement model. The results demonstrate that the algorithm presented in this paper offers higher intercept efficiency, improved robustness, and reduced optimization time in more complex scenes.

Kriging-based Model Predictive Control for Lower-limb Rehabilitation Robots

Model predictive control (MPC) has emerged as a predominant method in the realm of control systems; yet, it faces distinct challenges. First, MPC often hinges on the availability of a precise and accurate system model, where even minor deviations can drastically affect the control performance. Second, it entails a high computational load due to the need to solve complex optimization problems in real time. This study introduces an innovative method that harnesses the probabilistic nature of Gaussian processes (GPs), offering a solution that is robust, adaptive, and computationally efficient for optimal control. Our methodology commences with the collection of data to learn optimal control policies. We then proceed with offline training of GPs on these data, which enables these processes to accurately grasp system dynamics, establish input–output relationships, and, crucially, identify uncertainties, thereby informing the MPC framework. Utilizing the mean and uncertainty estimates derived from GPs, we have crafted a controller that is capable of adapting to system deviations and maintaining consistent performance, even in the face of unforeseen disturbances or model inaccuracies. The convergence of the closed-loop system is assured through the application of the Lyapunov stability theorem. In our numerical experiments, the exemplary performance of our approach is demonstrated, notably in its capacity to adeptly handle the complexities of dynamic systems, even with limited training data, underlining a significant leap forward in MPC strategies.

Survey on the application of bus scheduling optimization algorithms

The issue of bus scheduling has always been the focus of researchers, and the optimization algorithms proposed constantly aim at balancing the interests of both passengers and bus companies. This paper summarizes the application of the existing algorithm to optimize the bus scheduling problem and analyzes it. Small differences between different algorithms are compared. The convergence speed of different algorithms is accelerated with continuous improvement. But these algorithms are optimized on the existing real data and strive to achieve the best. However, improving the algorithm is not enough; reality does not always match the model and is often more complex. Therefore, future optimization research needs to combine the actual situation to adjust the real-time data in time, in order to achieve real-time optimization problems. The scheduling problem of buses is an important problem related to citizens' travel conditions and social benefits. Optimizing the bus scheduling scheme can effectively improve the traffic environment and passenger satisfaction. At the same time, the bus company can also gradually maximize the benefits.

A globally convergent composite‐step trust‐region framework for real‐time optimization

AbstractInaccurate models limit the performance of model‐based real‐time optimization (RTO) and even cause system instability. Therefore, a RTO framework that guarantees global convergence in the presence of plant‐model mismatch is desired. In this regard, the trust‐region framework is intuitive and simple to implement for unconstrained problems. Constrained RTO problems are converted to unconstrained ones by the penalty function, and global convergence is guaranteed if the penalty coefficient is large enough. However, a sufficiently large penalty coefficient is hard to determine and may lead to numerical difficulties. This paper addresses this issue and proposes a novel composite‐step trust‐region framework for constrained RTO problems that handles inequality constraints directly. The trial step is decomposed into a normal step that improves feasibility and a tangential step that reduces the cost function. A rigorous proof of its global convergence property is given.

A Data-Driven Method for Online Constructing Linear Power Flow Model

To adapt the data-driven linear power flow (DD-LPF) model for online dispatch in power systems, especially when the size of historical samples or system scale are relatively large, this paper proposes an online LPF model construction method. First, the raw measurements are filtered to suppress the adverse impact of measurement noise and outliers. Then, an adaptive moment estimation-based distributed stochastic gradient descent (Adam-DSGD) method is utilized to improve solution efficiency of DD-LPF parameters. Considering the features of online dispatch in power systems, a recursive forgetting factor (RFF) method is further introduced to adapt the LPF model for the present operating condition. Subsequently, the proposed method is applied to an online dispatch-command-tracking problem to demonstrate its practicability. Case studies confirm that the proposed method can achieve 2- to 100-fold less computing time and maintain satisfactory linearization accuracy simultaneously. Moreover, the tracking rate for the optimization objective is also enhanced with applying the proposed method to the real-time optimization problem.

Multi-Objective Adaptive Optimization Model Predictive Control: Decreasing Carbon Emissions from a Zinc Oxide Rotary Kiln

The zinc oxide rotary kiln, as an essential piece of equipment in the zinc smelting industrial process, is presenting new challenges in process control. China’s strategy of achieving a carbon peak and carbon neutrality is putting new demands on the industry, including green production and the use of fewer resources; thus, traditional stability control is no longer suitable for multi-objective control tasks. Although researchers have revealed the principle of the rotary kiln and set up computational fluid dynamics (CFD) simulation models to study its dynamics, these models cannot be directly applied to process control due to their high computational complexity. To address these issues, this paper proposes a multi-objective adaptive optimization model predictive control (MAO-MPC) method based on sparse identification. More specifically, with a large amount of data collected from a CFD model, a sparse regression problem is first formulated and solved to obtain a reduction model. Then, a two-layered control framework including real-time optimization (RTO) and model predictive control (MPC) is designed. In the RTO layer, an optimization problem with the goal of achieving optimal operation performance and the lowest possible resource consumption is set up. By solving the optimization problem in real time, a suitable setting value is sent to the MPC layer to ensure that the zinc oxide rotary kiln always functions in an optimal state. Our experiments show the strength and reliability of the proposed method, which reduces the usage of coal while maintaining high profits.

Self-stabilizing economic model predictive control without pre-calculated steady-state optima: Stability and robustness

We propose a new economic nonlinear model predictive control (eNMPC) formulation that tracks the optimality conditions of the real-time optimization problem rather than any specific steady states. The proposed formulation maintains its nature of optimizing economic performance and assured stability properties with the Lyapunov inequality constraint for the closed-loop control. Under general assumptions, we prove that the proposed controller is asymptotically stable without process disturbances and is input-to-state stable when there is a process disturbance. The proposed eNMPC is demonstrated on two case studies and compared against setpoint-tracking NMPC with setpoints determined by the steady-state real-time optimizer to show improved dynamic performance. We also highlight the capability of self-stabilization of the new eNMPC with parameter updates in the process model.

Event-Triggered Model Predictive Control for Autonomous Vehicle Path Tracking: Validation Using CARLA Simulator

Model predictive control (MPC) has been widely researched for automotive control. However, the real-world application of MPC for autonomous vehicles (AV) is still limited due to the high computational requirement of solving the real-time optimization problem. To address this issue, this paper presents an event-triggered MPC framework and illustrates its application in AV path tracking control using the CARLA simulation environment. Unlike traditional time-triggered MPC, event-triggered MPC solves the optimization problem only when an event is triggered. Otherwise, the previously optimized control sequence is used to determine control action. Therefore, when following the same path, event-triggered MPC solves fewer optimization problems than time-triggered MPC, thereby reducing the computation requirements. To demonstrate the effectiveness of the proposed approach, both time-triggered MPC and event-triggered MPC are simulated and compared using CARLA. Results validate that the proposed event-triggered MPC method reduces significant computation with acceptable performance degradation.

Differential evolution-driven traffic light scheduling for vehicle-pedestrian mixed-flow networks

This study addresses the bi-objective traffic light scheduling problem (TLSP), which aims to minimize the network-wise delay time of all vehicles and pedestrians within a predefined finite-time window. In this study, to solve this real-time optimization problem, an efficient discrete differential evolution-driven approach named DDE is proposed. The DDE includes discrete versions of mutation and crossover schemes together with a usual selection operation. Furthermore, an additional operator called greedy local search operation is combined with the search procedure of the DDE to increase the convergence speed. Finally, numerical experiments are conducted on 32 different traffic case studies generated based on the infrastructure of traffic network in Jurong area of Singapore. The optimization results produced by the DDE are compared with the optimal results achieved by the commercial GUROBI solver. The performance of the DDE is also compared with other metaheuristics namely ABC, GA, HS, Jaya, DSCA and DSCA-LS, which are designed in the literature to solve the TLSP. The performance comparison is analyzed using diverse metrics such as statistical values of optimization results, statistical analysis using the Wilcoxon signed-rank test, average relative error percentage, and convergence analysis. The comparison illustrates the significantly better and promising search ability of the DDE as compared to the other metaheuristics.

Energy Management System for Microgrid System using Improved Grey Wolf Optimization Algorithm

An Energy Management System (EMS) is indispensable to monitor the power flow and load matching inside a microgrid during grid-connected mode (GCM) and islanded modes (IM) of operation. Many conventional optimization algorithms show poor reliability for real time optimization problem solving where an objective function is non-linear. An optimization technique is necessary to reduce the cost of energy obtained from the grid, generated inside the grid, and consumed by the load. This article presents, an optimization scheme based on the improved Grey wolf optimization (GWO) algorithm that considers replacement of wounded/injured wolves of one pack by strong wolves of other pack for an EMS in micro-grid. The GWO optimization algorithm's effectiveness is demonstrated forGCM and IM operation. The proposed GWO shows fast, lost cost and precise optimization of the real time EMS for the grid connected and islanded micro-grid system.

Robust closed-loop dynamic real-time optimization

Real-time optimization (RTO) is a valuable tool for economic optimization of chemical process systems. Incorporating plant dynamics and model predictive control (MPC) behavior into the RTO problem can improve its performance by accounting for plant transitions under the action of its control system, resulting in a closed-loop dynamic RTO (CL-DRTO) formulation. This paper extends the formulation for direct inclusion of uncertainty handling. A robust multi-scenario CL-DRTO scheme which models the dynamic behavior of the plant and its MPC system under uncertainty is introduced. The method is applied and its performance evaluated in two nonlinear case studies, where an input clipping approximation scheme is used to reduce the computation time. The effects of number of scenarios and multiple sources of uncertainty are also investigated.

A combined adaptive entropy‐TOPSIS and model predictive control strategy for mixed loading and delay operations in the reheating furnace

SummaryIn this paper, a combined adaptive entropy‐TOPSIS and model predictive control strategy is proposed to deal with the mixed loading and delay operations in the reheating furnace. Firstly, the mathematical models consistent with the behaviour of the real reheating furnace are built to describe the complicated heat exchange process. Secondly, a dynamical optimization problem for the mixed loading operation and delay operation in the walking beam reheating furnace is obtained. To adjust the weighting factors of the optimization problem in real time, the adaptive entropy‐TOPSIS method is proposed. Then, the rolling horizon approach is applied to solve the proposed optimization problem. Finally, numerical experiments and simulation analysis are undertaken to verify the reliability and accuracy of the proposed strategy. The simulation results demonstrate that the proposed strategy can deal with three typical cases of delays effectively and the control accuracy is successfully improved from 74.79% to 99.17%.

JIRA: Joint Incentive Design and Resource Allocation for Edge-Based Real-Time Video Streaming Systems

Edge computing has been introduced as a promising technology for real-time video streaming systems. However, due to the lack of automatic incentives and the limitation of resources, traditional edge computing performs poorly in nowadays scenarios. To handle these two challenges, we propose a framework of Joint Incentive design and Resource Allocation (JIRA) for edge-based real-time video streaming systems. Technically, to ensure the trust and automatic distribution of incentives, we develop a novel smart contract based incentive mechanism and implement a prototype. Meanwhile, we propose an efficient online algorithm, i.e., JIRA, which dynamically adjusts compression ratio, offloading decision, and resource allocation to achieve performance optimization for video streaming under long-term latency and resource constraints. Specifically, JIRA is based on Lyapunov optimization, which decomposes the challenging long-term decision problem into a series of real-time optimization problems. Then we propose a multi-cut <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Generalized Benders Decomposition</i> based algorithm (MGA) to tackle the non-convexity of the decomposed problem. Through rigorous theoretical analysis, we prove the performance bound of JIRA. Extensive simulations demonstrate that the proposed schemes can achieve an efficient trade-off between accuracy performance and energy consumption.

The Scheduling Research of a Wind-Solar-Hydro Hybrid System Based on a Sand-Table Deduction Model at Ultra-Short-Term Scales

Establishing a wind-solar-hydro hybrid generation system is an effective way of ensuring the smooth passage of clean energy into the grid, and its related scheduling research is a complex and real-time optimization problem. Compared with the traditional scheduling method, this research investigates and improves the accuracy of the scheduling model and the flexibility of the scheduling strategy. The paper innovatively introduces a sand-table deduction model and designs a real-time adaptive scheduling algorithm to evaluate the source-load matching capability of the hybrid wind-solar-hydro system at ultra-short-term scales, and verifies it through arithmetic examples. The results show that the proposed adaptive sand-table scheduling model can reflect the actual output characteristics of the hybrid wind-solar-hydro system, track the load curve, and suppress the fluctuation of wind and solar energy, with good source-load matching capability.

Research on Real-Time Robust Optimization of Perishable Supply-Chain Systems Based on Digital Twins.

Aiming at the real-time robust optimization problem of perishable supply-chain systems in complex environments, a real-time robust optimization scheme based on supply-chain digital twins is proposed. Firstly, based on the quantitative logical relationship between production and sales of single-chain series supply-chain system products, the state space equation of the supply-chain system with logical characteristics, structural characteristics, and quantitative characteristics was constructed, and twin data were introduced to construct the digital twins of supply chains based on the state-space equation. Secondly, the perishable supply-chain system in complex environments was regarded as an uncertain closed-loop system from the perspective of the state space equation, and then a robust H∞ controller design strategy was proposed, and the supply-chain digital twins was used to update and correct the relevant parameters of the supply-chain system in real-time, to implement the real-time robust optimization based on the supply-chain digital twins. Finally, the simulation experiment was carried out with a cake supply-chain production as an example. The experimental results show that the real-time updating of relevant parameters through the digital twins can help enterprise managers to formulate reasonable management plans, effectively avoid the shortage problem of enterprises in the cake supply-chain system, and reduce the maximum inventory movement standard deviation of each link by 12.65%, 6.50%, and 14.87%, and the maximum production movement standard deviation by 70.21%, 56.84%, and 45.19%.

Real-time energy optimization and scheduling of buildings integrated with renewable microgrid

Real-time energy optimization is essential for effective load scheduling, cost reduction, maintaining demand and supply balance, and ensuring reliable power system operations. However, real-time energy optimization is challenging due to the unpredictable nature of renewable energy sources (RES) and the behavior of electric loads. On this note, a rigid model is required that can deal with this dilemma. Thus, the Lyapunov optimization technique (LOT) emerged as a solution for the real-time energy optimization problem. This work investigates a smart home equipped with inflexible loads (TV, computer, light, etc.), flexible loads (EVs, HVAC, water heaters, etc.), and RES (photovoltaic and wind energy) in a grid-connected mode that ensures energy trading (purchasing and selling of energy). The aim is to optimize total cost, thermal discomfort cost, and batteries and EVs charging/discharging using LOT by real-time energy optimization, which does not require any system parameters to be anticipated. The proposed algorithm employs LOT for four queues to solve the real-time energy optimization problem. Simulations are conducted for different scenarios and varying weather conditions to endorse the effectiveness of the developed real-time energy optimization solution in various aspects of the performance metrics.

Fast and safe heating-up control of a planar solid oxide cell stack: A three-dimensional model-in-the-loop study

A fast heating-up rate generally conflicts with the temperature homogeneity of solid oxide cell (SOC) stacks. This study designs an adaptive model predictive controller (MPC) to regulate the heating-up process of SOC stacks. The controller solves an optimization problem in real time to obtain optimal control that shortens the heating-up time by fully using the safety limit. The controller is verified with a three-dimensional (3D) hotbox–stack model calibrated with experiments. 3D model-in-the-loop (MiL) simulations show that the controller is effective under two heating modes despite of model deviations. Under the electrical heating mode, the controller achieves a 33% acceleration compared with a reference control strategy. Comparisons of electrical and gas heating reveal that the former is 63% faster but the latter consumes 41.6% less energy if the waste heat is fully recovered. The hotbox heat capacity is a major limiting factor for the heating-up process, particularly under the gas heating mode. An 80% reduction in the hotbox heat capacity, which can be achieved by reducing the thickness of the insulation layer, improves the heating-up time and the net energy consumption by 69% and 65% under the gas heating mode, respectively.

Long-Term Matching Optimization With Federated Neural Temporal Difference Learning in Mobility-on-Demand Systems

Efficient bipartite graph matching of orders and drivers is a central operational problem in industrial mobility-on-demand (MOD) systems. Traditional studies adopt pure combinatorial optimization models for order-and-driver matching, which do not consider the long-term rewards of the dynamic MOD decision making process. Toward long-term optimization, this article presents a systemic paradigm of online matching with federated neural temporal difference learning (FedTDLearning), which encompasses learning and matching phases. During the learning phase, the long-term matching process is modeled as a Markov decision process, which is typically solved by employing data-driven reinforcement learning in an offline central training scheme. Massive amounts of data would be generated on the network by industrial MOD systems. It is impossible to send all the large-scale industrial data to the cloud server for centralized model training due to network bandwidth limitations and safety concerns. Therefore, a generic and innovative FedTDLearning is proposed to achieve long-term matching in a distributed manner. During the matching phase, a real-time bipartite matching optimization problem is formulated to maximize the learned spatiotemporal value and minimize the pickup distance, which is reducible to the minimum-cost maximum weight bipartite graph matching problem. A distance-learned-value ratio algorithm is proposed to find an optimal matching in the bipartite graph based on the joint optimization of FedTDLearning and the combinatorial fractional programming approach. Furthermore, to pursue optimal computation efficiency, we solve the real-time matching problem by constructing a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> -nearest neighbor <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(k$ </tex-math></inline-formula> NN) bipartite graph where each order is connected with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> NN drivers. Using openly available real-world data, the prototype system and experimental evaluations show that our proposed algorithms have effective problem-solving capability in practice.