Real-time Optimization Problem Research Articles

Optimal control of photovoltaic arrays

A high value of the energy conversion efficiency is not the only feature a photovoltaic power processing system must have. An optimal control of the photovoltaic generator must be also designed in order to maximize the electrical power it produces, even in presence of a time varying irradiation level or when a part of the photovoltaic source is shaded. An overview of the main issues related to this real time optimization problem is given in this paper and some solutions, both presented in the literature and nowadays provided by leading companies, are overviewed.

MODEL PREDICTIVE CONTROL (MPC) AND ITS CURRENT ISSUES IN CHEMICAL ENGINEERING

Model predictive control (MPC) is one of the main process control techniques explored in the recent past; it is the amalgamation of different technologies used to predict future control action and future control trajectories knowing the current input and output variables and the future control signals. It can be said that the MPC scheme is based on the explicit use of a process model and process measurements to generate values for process input as a solution of an on-line (real-time) optimization problem to predict future process behavior. There have been a number of contributions in the field of nonlinear model–based predictive control dealing with issues like stability, efficient computation, optimization, constraints, and others. New developments in nonlinear MPC (NMPC) approaches come from resolving various issues, from faster optimization methods to different process models. This article specifically deals with chemical engineering systems ranging from reactors to distillation columns where MPC plays a role in the enhancement of the systems’ performance.

A robust optimization approach for real-time multiple source drinking water blending problem

Although many optimization methods can be applied to real-time multiple source drinking water blending problems, the field still lacks an approach to rapidly produce a robust optimal solution by simultaneously optimizing multiple objectives. This paper develops a fuzzy multiple response surface methodology (FMRSM) to achieve this objective. In the FMRSM, experimental data are fitted to mean response surface models while the residuals (the error between the predicted response of the mean model and the measured data of the real system) are fitted to standard deviation models. Fuzzy linear programming using the min-operator approach is applied to optimize the multiple objectives. Six scenarios are designed based on data from a real-time multiple source drinking water blending operation. The results show the FMRSM is a robust, computationally efficient optimization approach. The FMRSM could be extended to other real-time multi-objective non-linear optimization problems.

Optimization of petroleum production networks – Through proxy models and structural constraints

This paper proposes and explores the properties of a solution algorithm designed to solve network simulation problems to optimality. Emphasis is put on the system being divisible into components, as this underlying assumption motivates the algorithm in its entirety in that rather simple relations between the system components are modeled as explicit structural constraints, while the significantly more complex relations within each component are approximated based on the underlying simulator data. The Real-Time petroleum Production Optimization (RTPO) problem is used as an example of such a network simulation problem that can benefit from using the solution approach outlined. The paper also includes the mathematical formulation of the RTPO, followed by a description of the algorithm and a comprehensive study of the algorithm's properties on a real RTPO application. Finally, the results are compared to a reference case and conclusions are reached about the method.

A Novel Predictive Control Strategy for Supply Chain Management under Networked Manufacturing

A novel predictive control strategy is applied to dynamic supply chain management under networked manufacturing. The optimisation-based control scheme aims at a complete management framework for production-inventory systems that is based on model predictive control (MPC) and on a neural network time series forecasting model. The model proves to be very useful in production-inventory systems that is enough to keep production and inventory balance. A move suppression term that penalises the rate of change in the transported quantities through the network increases the system’s robustness. The results show that the proposed scheme can improve significantly the performance of the production-inventory system, due to the fact that more accurate predictions are provided to the formulation of the MPC optimization problem in real time.

Embedding evolutionary strategy in ordinal optimization for hard optimization problems

This work proposes a method for embedding evolutionary strategy (ES) in ordinal optimization (OO), abbreviated as ESOO, for solving real-time hard optimization problems with time-consuming evaluation of the objective function and a huge discrete solution space. Firstly, an approximate model that is based on a radial basis function (RBF) network is utilized to evaluate approximately the objective value of a solution. Secondly, ES associated with the approximate model is applied to generate a representative subset from a huge discrete solution space. Finally, the optimal computing budget allocation (OCBA) technique is adopted to select the best solution in the representative subset as the obtained “good enough” solution. The proposed method is applied to a hotel booking limits (HBL) problem, which is formulated as a stochastic combinatorial optimization problem with a huge discrete solution space. The good enough booking limits, obtained by the proposed method, have promising solution quality, and the computational efficiency of the method makes it suitable for real-time applications. To demonstrate the computational efficiency of the proposed method and the quality of the obtained solution, it is compared with two competing methods – the canonical ES and the genetic algorithm (GA). Test results demonstrate that the proposed approach greatly outperforms the canonical ES and GA.

Real-Time Optimization via Modifier Adaptation Integrated with Model Predictive Control

AbstractIn order to deal with plant-model mismatch, real-time optimization schemes use some adaptation strategy based on measurements. The modifier-adaptation approach is to correct the constraints and gradients in the optimization problem by adapting the values of bias modifiers expressing the difference between the constraints and gradients of the plant and the model. The approach has the ability to converge to the plant optimum but does not guarantee feasibility prior to convergence if the evaluated optimal inputs are applied directly to the plant. In this paper, an approach for integrating modifier adaptation with model predictive control is presented where both automation layers use the same decision variables. The control targets are included as equality constraints in the real-time optimization problem, and are continuously enforced by the model predictive controller. In order to apply modifier adaptation, new gradient modifiers are defined that correct the projected gradients in the tangent space of the equality constraints, rather than the full gradients. An illustrative case study shows the applicability of the approach.

Oil production optimization—A piecewise linear model, solved with two decomposition strategies

This paper presents a new method for real-time optimization of process systems with a decentralized structure where the idea is to improve computational efficiency and transparency of a solution. The contribution lies in the application and assessment of the Lagrange relaxation and the Dantzig–Wolfe methods, which allows us to efficiently decompose a real-time optimization problem. Furthermore, all nonlinearities are modeled by piecewise linear models, resulting in a mixed integer linear program, with the added benefit that error bounds on the solution can be computed. The merits of the method are studied by applying it to a semi-realistic model of the Troll west oil rim, a petroleum asset with severe production optimization challenges due to rate dependent gas-coning wells. This study indicates that both the Lagrange relaxation and in particular the Dantzig–Wolfe approach offers an interesting option for complex production systems. Moreover, the method compares favorably with the non-decomposed method.

Pseudospectral method based trajectory optimization and fairing rejection time analysis of solid launch vehicle

The problem of real-time trajectory optimization for small solid launch vehicle of operational responsive space (ORS) was studied by using pseudospectral method. According to the characteristic of the trajectory design, the dynamics model was set up in the inertia right-angled reference frame, and the equation and parameter at the orbit injection point were simplified and converted. The infinite dimension dynamic optimal control problem was converted to a finite dimension static state optimization problem and the algorithm reduced the complexity so as to become a general algorithm in trajectories optimization. With the trajectories optimization of a three-stage solid vehicle with a liquor upper stage as example, the model of the trajectory optimization was set up and simulations were carried out. The results demonstrated the advantage and validity of the pseudospectral method. The rejection time of fairing was also analyzed by the simulation results, and the optimal flight procedure and trajectory were obtained.

Optimization-Based Dynamic Sensor Management for Distributed Multitarget Tracking

In this paper, the general problem of dynamic assignment of sensors to local fusion centers (LFCs) in a distributed tracking framework is considered. With technological advances, a large number of sensors can be deployed for multitarget tracking purposes. However, due to physical limitations such as frequency, power, bandwidth, and fusion center capacity, only a limited number of them can be used by each LFC. The transmission power of future sensors is anticipated to be software controllable within certain lower and upper limits. Thus, the frequency reusability and the sensor reachability can be improved by controlling transmission powers. Then, the problem is to select the sensor subsets that should be used by each LFC and to find their transmission frequencies and powers in order to maximize the tracking accuracies and minimize the total power consumption. The frequency channel limitation and the advantage of variable transmitting power have not been discussed in the literature. In this paper, the optimal formulation for the aforementioned sensor management problem is provided based on the posterior Cramer-Rao lower bound. Finding the optimal solution to the aforementioned NP-hard multiobjective mixed-integer optimization problem in real time is difficult in large-scale scenarios. An algorithm is presented to find a suboptimal solution in real time by decomposing the original problem into subproblems, which are easier to solve, without using simplistic clustering algorithms that are typically used. Simulation results illustrating the performance of sensor array manager are also presented.

On-line economic optimization of energy systems using weather forecast information

We establish an on-line optimization framework to exploit weather forecast information in the operation of energy systems. We argue that anticipating the weather conditions can lead to more proactive and cost-effective operations. The framework is based on the solution of a stochastic dynamic real-time optimization (D-RTO) problem incorporating forecasts generated from a state-of-the-art weather prediction model. The necessary uncertainty information is extracted from the weather model using an ensemble approach. The accuracy of the forecast trends and uncertainty bounds are validated using real meteorological data. We present a numerical simulation study in a building system to demonstrate the developments.

Dantzig-Wolfe decomposition for real-time optimization - applied to the Troll west oil rim

Abstract Abstract This paper studies different decomposition approaches for real-time optimization of process systems with a decentralized structure where the idea is to improve computational efficiency and transparency of a solution. The contribution lies in the application and assessment of the Dantzig-Wolfe method which allows us to efficiently decompose a real-time optimization problem into parts. Furthermore, the nonlinear system is modeled by piecewise linear models with the added benefit that error bounds on the solution can be computed. The merits of the method are studied by applying it to a semi-realistic model of the Troll west oil rim, a petroleum asset with severe production optimization challenges due to rate dependent gas-coning wells. This study indicates that the Dantzig-Wolfe approach offers an interesting and robust option for complex production systems. Moreover, the method compares favourable with earlier results using Lagrangian relaxation which again was favourable compared to a global approach.

Recursive estimation algorithms for power controls of wireless communication networks

Power control problems for wireless communication networks are investigated in direct-sequence code-division multiple-access (DS/CDMA) channels. It is shown that the underlying problem can be formulated as a constrained optimization problem in a stochastic framework. For effective solutions to this optimization problem in real time, recursive algorithms of stochastic approximation type are developed that can solve the problem with unknown system components. Under broad conditions, convergence of the algorithms is established by using weak convergence methods.

Real-time process optimization based on grey-box neural models

This paper investigates the feasibility of using grey-box neural models (GNM) in Real Time Optimization (RTO). These models are based on a suitable combination of fundamental conservation laws and neural networks, being used in at least two different ways: to complement available phenomenological knowledge with empirical information, or to reduce dimensionality of complex rigorous physical models. We have observed that the benefits of using these simple adaptable models are counteracted by some difficulties associated with the solution of the optimization problem. Nonlinear Programming (NLP) algorithms failed in finding the global optimum due to the fact that neural networks can introduce multimodal objective functions. One alternative considered to solve this problem was the use of some kind of evolutionary algorithms, like Genetic Algorithms (GA). Although these algorithms produced better results in terms of finding the appropriate region, they took long periods of time to reach the global optimum. It was found that a combination of genetic and nonlinear programming algorithms can be use to fast obtain the optimum solution. The proposed approach was applied to the Williams-Otto reactor, considering three different GNM models of increasing complexity. Results demonstrated that the use of GNM models and mixed GA/NLP optimization algorithms is a promissory approach for solving dynamic RTO problems.

IMPLEMENTATION OF OPTIMAL OPERATION USING OFF-LINE COMPUTATIONS

The computational effort involved in the solution of real-time optimization problems can be very demanding. Hence, simple but effective implementation of optimal policies are attractive. The main idea is to use off-line calculations and analysis to determine the structure and properties of the optimal solution. This will be used to determine alternate representations of the optimal solution that are more suitable for implementation.

Size Matters: Logarithmic Space is Real Time

We show that all the problems solvable by a nondeterministic machine with logarithmic work space (NL) can be solved in real time by a parallel machine, no matter how tight the real-time constraints are. We also show that several other real-time problems are in effect solvable in nondeterministic logarithmic space once their real-time constraints are dropped and they become non-realtime. We thus conjecture that NL contains exactly all the problems that admit feasible real-time parallel algorithms. The issue of real-time optimization problems is also investigated. We identify the class of such problems that are solvable in real time. In the process, we determine the computational power of directed reconfigurable multiple bus machines (DRMBMs) with polynomially bounded resources and running in constant time, which is found to be the same as the power of directed reconfigurable networks with the same properties. We also show that write conflict resolution rules such as Priority or even Combining do not add computational power over the Collision rule, and that a bus of width 1 (a wire) suffices for any constant time computation on DRMBM.

Real-time optimization of an off-gas distribution system of an iron and titanium plant

In this paper, the distribution of off-gas used as fuel by many different plant units in an iron and titanium plant, is studied. An optimization algorithm is applied to find the operating strategy leading to the best use of available off-gas by the different consumers. This is realized by adjusting the flow of the material through different kilns and the stock piles. In addition, the choice of whether or not to operate a certain kiln is treated as a decision variable. The contribution of this paper lies in formulating a linear model describing the system and solving the above mentioned problem as a mixed integer optimization problem in real time. A simulation result is shown and explained.

Challenges in particulate polymerization reactor modeling and optimization: A population balance perspective

In the present article, recent developments on modeling and optimization of particulate polymerization processes are reviewed. A unified population balance approach is described to follow the time evolution of molecular and morphological polymer properties in batch and continuous polymerization reactors. The numerical methods as well as the computational issues related with the solution of the dynamic population balance equation are critically assessed. The orthogonal collocation on finite elements (OCFE) method and the fixed-pivot technique (FPT) are then applied to a free-radical batch polymerization reactor to calculate the dynamic evolution of the molecular weight distribution (MWD). Moreover, theoretical and experimental results are shown on the dynamic evolution of particle size distribution (PSD) in a suspension polymerization reactor. Recent advances in on-line monitoring of “polymer quality” are briefly discussed in the context of available hardware and software sensors. The problem of real-time optimization of polymerization processes under parametric uncertainty is also examined. Finally, new issues related with the modeling, numerical solution and control of multidimensional population balance equations are conferred.

On-line free-flight path optimization based on improved genetic algorithms

Free flight (FF) is the ideal strategy of current investigations on air traffic management systems, where an on-line flight path optimization algorithm is of top importance. This paper proposes an innovative algorithm with potential real-time properties for FF path optimization, by using an improved genetic algorithm (GA). Two kinds of mathematical models for the on-line flight path optimization problem are proposed to cover the near and far future applications. Several improvements are introduced to the GA to speed up its convergence as well as to improve performance. Simulation results show that the new algorithm is effective and has potential to solve the on-line FF path optimization problem in real time.

Challenges in Polymerization Reactor Modeling and Optimization: A Population Balance Perspective

In the present article, recent developments on modeling, monitoring, optimization and control of particulate polymerization processes are reviewed. A unified population balance approach is described to follow the time evolution of molecular and morphological polymer properties in batch and continuous polymerization reactors. Recent advances on the online monitoring of “polymer quality” are discussed in the context of available hardware and software sensors. The problem of real-time optimization of polymerization processes under parametric uncertainty is also examined along with its online implementation. Finally, new issues related with the modeling, numerical solution and control of multidimensional PBEs are conferred.