System Optimization Problems Research Articles

Distributed Optimization of High-Order Nonlinear Systems: Saving Computation and Communication via Prefiltering

This brief investigates a distributed optimization problem for high-order strict-feedback nonlinear multiagent systems. A virtual system is built for each agent using a distributed proportional-integral (PI) optimization algorithm to estimate the global optimal solution online. The estimate is then input into a prefilter to generate an alternative estimate and its high-order derivatives. Based on these signals, a backstepping controller is used to make the actual system track the alternative estimate asymptotically, which thereby realizes exact global consensus optimization. Compared to the existing result, the proposed algorithm is fully distributed under undirected topologies with much weaker assumptions on local and global objective functions, lower computation and communication cost. Exact global optimal consensus can also be reached in the cases with directed topologies and intermittent communications. The effectiveness of the method is verified by simulations.

Preference based multi-objective reinforcement learning for multi-microgrid system optimization problem in smart grid

Grid-connected microgrids comprising renewable energy, energy storage systems and local load, play a vital role in decreasing the energy consumption of fossil diesel and greenhouse gas emissions. A distribution power network connecting several microgrids can promote more potent and reliable operations to enhance the security and privacy of the power system. However, the operation control for a multi-microgrid system is a big challenge. To design a multi-microgrid power system, an intelligent multi-microgrids energy management method is proposed based on the preference-based multi-objective reinforcement learning (PMORL) techniques. The power system model can be divided into three layers: the consumer layer, the independent system operator layer, and the power grid layer. Each layer intends to maximize its benefit. The PMORL is proposed to lead to a Pareto optimal set for each object to achieve these objectives. A non-dominated solution is decided to execute a balanced plan not to favor any particular participant. The preference-based results show that the proposed method can effectively learn different preferences. The simulation outcomes confirm the performance of the PMORL and verify the viability of the proposed method.

A Study of Text Vectorization Method Combining Topic Model and Transfer Learning

With the development of Internet cloud technology, the scale of data is expanding. Traditional processing methods find it difficult to deal with the problem of information extraction of big data. Therefore, it is necessary to use machine-learning-assisted intelligent processing to extract information from data in order to solve the optimization problem in complex systems. There are many forms of data storage. Among them, text data is an important data type that directly reflects semantic information. Text vectorization is an important concept in natural language processing tasks. Because text data can not be directly used for model parameter training, it is necessary to vectorize the original text data and make it numerical, and then the feature extraction operation can be carried out. The traditional text digitization method is often realized by constructing a bag of words, but the vector generated by this method can not reflect the semantic relationship between words, and it also easily causes the problems of data sparsity and dimension explosion. Therefore, this paper proposes a text vectorization method combining a topic model and transfer learning. Firstly, the topic model is selected to model the text data and extract its keywords, to grasp the main information of the text data. Then, with the help of the bidirectional encoder representations from transformers (BERT) model, which belongs to the pretrained model, model transfer learning is carried out to generate vectors, which are applied to the calculation of similarity between texts. By setting up a comparative experiment, this method is compared with the traditional vectorization method. The experimental results show that the vector generated by the topic-modeling- and transfer-learning-based text vectorization (TTTV) proposed in this paper can obtain better results when calculating the similarity between texts with the same topic, which means that it can more accurately judge whether the contents of the given two texts belong to the same topic.

Robust design optimization by spline dimensional decomposition

This article highlights new spline-empowered computational methods for solving robust design optimization (RDO) problems in complex mechanical systems. The methods are predicated on a spline dimensional decomposition (SDD) of a high-dimensional, discontinuous, or nonsmooth stochastic response for statistical moment analysis, a novel fusion of SDD and score functions for calculating the second-moment sensitivities with respect to the design variables, and standard gradient-based optimization algorithms. New closed-form formulae are derived for the design sensitivities that are concurrently determined along with the moments. The methods depend on how the statistical moment and sensitivity analyses are engaged with an optimization algorithm, engendering direct and multi-point single-step design processes. Numerical results reveal that the proposed methods deliver accurate and computationally efficient optimal solutions to RDO problems, including an industrial-scale shape design of a robotic gripper jaw.

Optimization of oscillation damping in systems with a non-integer number of degrees of freedom

The paper discusses issues related to the choice of the optimal damping for a system with one and a half degrees of freedom - a pendulum with an elastic-movable suspension point in the presence of viscous friction. Maximization of the degree of stability of the system is taken as an optimization criterion characterizing the efficiency of damping oscillations. Two options for installing a damping device are discussed - either in the pendulum joint, or parallel to the elastic element. The analytical solution of the optimization problem is performed in each case, and it is accompanied by a visual graphic illustration. In addition, a comparison of two cases of damping is given on the basis of analysis of the maximum degree of stability and a conclusion about the advisability of using one or another option is made. The obtained results are of interest both in theoretical and practical terms, and the described plan for finding the optimal solution can also be applied to solving other optimization problems in systems with a non-integer number of degrees of freedom.

Dynamic optimization problems for mean-field stochastic large-population systems

This paper considers dynamic optimization problems for a class of control average meanfield stochastic large-population systems. For each agent, the state system is governed by a linear mean-field stochastic differential equation with individual noise and common noise, and the weight coefficients in the corresponding cost functional can be indefinite. The decentralized optimal strategies are characterized by stochastic Hamiltonian system, which turns out to be an algebra equation and a mean-field forward-backward stochastic differential equation. Applying the decoupling method, the feedback representation of decentralized optimal strategies is further obtained through two Riccati equations. The solvability of stochastic Hamiltonian system and Riccati equations under indefinite condition is also derived. The explicit structure of the control average limit and the related mean-field Nash certainty equivalence equation systems are discussed by some separation techniques. Moreover, the decentralized optimal strategies are proved to satisfy the approximate Nash equilibrium property. The good performance of the proposed theoretical results is illustrated by a practical example from the engineering field.

Optimum Tuning of Photovoltaic System Via Hybrid Maximum Power Point Tracking Technique

A new methodology is used in this paper, for the optimal tuning of Photovoltaic (PV) by integrating the hybrid Maximum Power Point Tracking (MPPT) algorithms is proposed. The suggested hybrid MPPT algorithms can raise the performance of PV systems under partial shade conditions. It attempts to address the primary research issues in partial shading conditions in PV systems caused by clouds, trees, dirt, and dust. The proposed system computes MPPT utilizing an innovative adaptive model-based approach. In order to manage the input voltage at the Maximum PowerPoint, the MPPT algorithm changes the duty cycle of the switch in the DC-DC (Direct Current-Direct Current) converter (MPP). Temperature as well as fluctuations in output power will induce alteration in PV panel operating current and voltage. MPPT is gaining a lot of interest as a key optimization sector to solve this optimization problem in PV systems. A hybrid optimization approach is utilized to produce a combination of the Cuckoo Search-Perturb & Observe (CS-PO) and incremental conductance-particle swarm optimization (IC-PSO) algorithms. After measuring the voltage and current from the solar system, this optimization computes the output power. The IC-PSO optimization achieves Maximum PowerPoint Tracking with increased efficiency of 99.5%. The proposed optimization techniques are established in the MATLAB Simulink program to validate its efficiency.

Optimal feedback control for a class of fed-batch fermentation processes using switched dynamical system approach

<abstract><p>This paper considers an optimal feedback control problem for a class of fed-batch fermentation processes. Our main contributions are as follows. Firstly, a dynamic optimization problem for fed-batch fermentation processes is modeled as an optimal control problem of switched dynamical systems, and a general state-feedback controller is designed for this dynamic optimization problem. Unlike the existing switched dynamical system optimal control problem, the state-dependent switching method is applied to design the switching rule, and the structure of this state-feedback controller is not restricted to a particular form. Then, this problem is transformed into a mixed-integer optimal control problem by introducing a discrete-valued function. Furthermore, each of these discrete variables is represented by using a set of 0-1 variables. By using a quadratic constraint, these 0-1 variables are relaxed such that they are continuous on the closed interval $ [0, 1] $. Accordingly, the original mixed-integer optimal control problem is transformed intoa nonlinear parameter optimization problem. Unlike the existing works, the constraint introduced for these 0-1 variables are at most quadratic. Thus, it does not increase the number of locally optimal solutions of the original problem. Next, an improved gradient-based algorithm is developed based on a novel search approach, and a large number of numerical experiments show that this novel search approach can effectively improve the convergence speed of this algorithm, when an iteration is trapped to a curved narrow valley bottom of the objective function. Finally, numerical results illustrate the effectiveness of this method developed by this paper.</p></abstract>

SOLVING SYSTEMS OF SECOND-ORDER MATRIX EQUATIONS

Matrix equations and systems of matrix equations are widely used in control system optimization problems. However, there are developed only methods for solving the most popular matrix equations, like Riccati and Lyapunov equations .There is no universal approach to solving all problems of this class. The previously considered method of solving systems of algebraic equations over a field of real numbers [1] is summarized in this paper and a scheme for systems of polynomial matrix equations of the second degree with many unknowns is proposed. Also, the recurrent formula for developing a solution into a chain matrix fraction is given. The convergence of the proposed method is investigated. The results of numerical experiments that confirm the validity of theoretical calculations and the effectiveness of the proposed scheme are presented.

Optimal Intelligence Planning of Wind Power Plants and Power System Storage Devices in Power Station Unit Commitment Based

Renewable energy sources (RES) such as wind turbines (WT) and solar cells have attracted the attention of power system operators and users alike, thanks to their lack of environmental pollution, independence of fossil fuels, and meager marginal costs. With the introduction of RES, challenges have faced the unit commitment (UC) problem as a traditional power system optimization problem aiming to minimize total costs by optimally determining units’ inputs and outputs, and specifying the optimal generation of each unit. The output power of RES such as WT and solar cells depends on natural factors such as wind speed and solar irradiation that are riddled with uncertainty. As a result, the UC problem in the presence of RES faces uncertainties. The grid consumed load is not always equal to and is randomly different from the predicted values, which also contributes to uncertainty in solving the aforementioned problem. The current study proposes a novel two-stage optimization model with load and wind farm power generation uncertainties for the security-constrained UC to overcome this problem. The new model is adopted to solve the wind-generated power uncertainty, and energy storage systems (ESSs) are included in the problem for further management. The problem is written as an uncertain optimization model which are the stochastic nature with security-constrains which included undispatchable power resources and storage units. To solve the UC programming model, a hybrid honey bee mating and bacterial foraging algorithm is employed to reduce problem complexity and achieve optimal results.

Society-based Grey Wolf Optimizer for large scale Combined Heat and Power Economic Dispatch problem considering power losses

Combined Heat and Power Economic Dispatch (CHPED) reflects a momentous optimization and operation problem in the power systems for optimally allocating the produced heat and power to the committed Power-only (PO), Heat-only (HO), and CHP units. In this work, a new society-based optimization algorithm using social hierarchy of grey wolves, namely Society-based Grey Wolf Optimizer (SGWO) is proposed for the CHPED problem. This scheme divides the group of wolves to some societies so that each society has its own leader. These leaders follow the dominant wolf and also guide their societies in which the classification of wolves is based on the social hierarchy. Moreover a novel attacking and hunting the prey is suggested to change the effects of dominant, ordinate, and subordinate wolves in their new roles in societies. In order to verify the capabilities of the SGWO, simulations are conducted through two large-scale CHPED problems with the related challenges like Valve-Point Loading Effect (VPLE) and Prohibited Zones (PZ) of PO units, mutual dependency of produced heat and power of CHP units, and especially transmission power losses. Moreover, it is evaluated on twenty-three standard functions to verify its stability on different low- and high-dimensional functions. Comparisons based on the obtained solutions by different methods demonstrate the robustness and superior performance of the presented technique to fast provide better optimum point (more economical benefits) and solution quality meeting all equality and inequality constraints. In addition, the results of CHPED indicate that ≈0.5% reduction in the production cost results in up to $2.6−$34×106 increase in Annual Cost Saving (ACS). Also, the transmission losses and PZs of POs can increase the production cost by about 1.4% which leads to over $1.3×107 reduction in ACS in comparison with ignoring them. Moreover, this condition increases the computational time by about 35% while the proposed method can still be up to 13−26 times faster than the other analysed algorithms.

Риск-ориентированный подход к решению задачи оперативного управления расписанием авиакомпании

The paper discusses the problem of optimal regulation of aircraft assignments for airline flights. Due to the fact that the activities of the airline are subject to changes caused by both external and internal environment, the planned schedule needs continuous management and control. In the event when the actual flight schedule deviates from the planned one, it is necessary to promptly make a decision on adjusting (restoring) the schedule and reassigning aircraft. Operational schedule management involves making adjustments to the current schedule from a depth of several hours to several days. The solution to the problem is to determine the unambiguous correspondence of flights and specific aircraft subject to maximizing the likelihood of meeting production targets and observing a number of restrictions. The task of managing airline schedules belongs to the class of scheduling optimization problems for parallel-sequential systems studied within the scheduling theory. It is NP-hard and requires the development of computationally efficient solution algorithms. However, the issue of choosing criteria for the optimization problem deserves special attention, since the correct choice plays an essential role in terms of assessing the effectiveness of decision-making. In the theory of decision-making, no general method for choosing the optimality criteria has been found. The definition of the target criterion depends on the expectations of the production. Within the framework of this paper, an original criterion is proposed for constructing an optimal solution to the discrete problem of managing aircraft assignments, the main idea of which is to find a balance between the duration of the schedule and the number of flights with a negative deviation from the planned schedule by assessing the level of punctuality violation risk. The paper gives a detailed concept of punctuality, describes an approach to assessing the level of risk, and also proposes an original formal formulation of the task of operational management of aircraft assignments based on the criterion of minimizing the risk of violation of flight punctuality.

Mathematical model of structural and topological optimization of logistics networks

The subject of research in the article is the topological structures of closed-loop logistics networks. The goal of the article is to increase the efficiency of centralized logistics networks by developing a mathematical model for a two-criteria problem of optimizing topological structures in the process of their reengineering. The article solves the following tasks: analysis of the current state of the problem of structural and topological optimization of logistics networks; formalization of the problem of optimization of logistics networks as geographically distributed objects; synthesis of objective functions of the mathematical model of a two-criterion optimization problem for centralized three-level topological structures of closed logistics networks at the reengineering stage; development of a system of constraints of the mathematical model of the problem of optimizing centralized three-level topological structures of closed logistics networks; a function for evaluating the overall utility of options based on the Kolmogorov-Gabor polynomial is offered. The following methods are used: methods of systems theory, methods of utility theory, optimization and operations research. The following results were obtained: the analysis of the current state of the problem of system optimization of logistics networks, mathematical models and methods for its solution was carried out; formalization of the problem of structural and topological optimization of logistics networks as geographically distributed objects; a mathematical model of a two-criterion task of reengineering of three-level topological structures of logistics networks in terms of costs and efficiency with integrated points of production and processing has been developed (originality). Conclusions: Based on the results of the analysis of the problem of optimizing the topological structures of logistics systems, it has been established that the problems of direct and reverse logistics are still considered as conditionally independent, which does not allow obtaining effective global solutions. In the context of expanding the network of consumers, changes in delivery volumes, the introduction of environmental restrictions, it is proposed to reengineer the networks, which provides for their radical redesign. The formulated statement and the developed mathematical model of a two-criterion (in terms of cost and efficiency) optimization problem for three-level topological structures for combined production and processing points will increase the efficiency of logistics networks with reverse flows by reducing the cost of reengineering (practical value).

Energy trading among electric vehicles based on Stackelberg approaches: A review

• We discuss the role of Stackelberg game in energy trading. •; We present novel classification of electric vehicles energy trading using Stackelberg approaches. • We also include various simulation tools in the literature to formulate optimization problems in energy trading. • Finally, we consider some potential challenges and future research directions in energy trading for electric vehicles based on Stackelberg game. Integration of renewable and other distributed generated energy resources has put enormous strains on the traditional power grid. The world is moving towards green energy and trying hard to reduce carbon footprints by promoting distribution generation at their end. By generating surplus energy, consumers want to inject extra energy to the grid or trade it with nearby consumers. Likewise, increasing number of electric vehicles (EVs) also necessitate the energy trading mechanisms to motivate other prosumers to participate in energy trading. There are various challenges associated with the current energy trading system like fluctuating energy prices, demand uncertainty, capacity and time uncertainty, congestion and charging station location, energy storage system capacity, security and privacy preservation, voltage and frequency regulation, communication overheads, charging strategies etc. Stackelberg game is a powerful strategic tool to model the interaction between various agents in the energy market including EV users, prosumers, energy retailers, grid stations, and charging stations. It is a leader following game, in which there is a leader who sets his strategy first and other players become his followers, who adjust their strategies by looking at the strategy announced by the leader. Stackelberg game plays a crucial role in an environment where people involved are rational and all want to optimize their payoffs. This paper presents a novel classification of EVs energy trading using the Stackelberg game approach to the date, and technical approaches to find corresponding optimal strategies. The paper also gives a brief overview of the simulation tools reported in the literature to formulate and solve optimization problems in the current energy trading systems. Finally, the manuscript highlights the potential challenges and prospective solutions associated with the integration of EVs into current energy trading framework that can be solved and modelled through Stackelberg game.

Distributed Optimization of Second-Order Nonlinear Multiagent Systems With Event-Triggered Communication

In this article, we study the event-triggered distributed optimization problem of second-order nonlinear multiagent systems under undirected and connected communication topologies. To reduce the cost of information exchange in an optimization problem, a distributed event-triggered communication-based algorithm is proposed. In an event-triggered mechanism, the information interaction process of the network is controlled by a set of trigger conditions. The trigger condition of each agent only requires its own state information and its neighboring agents’ state information. Each agent updates its own states only at the triggering time. In order to achieve the optimal result of the optimization problem and reduce the cost of communicatio, we propose a distributed event-triggered algorithm based on gradient descent. Moreover, we analyze the convergence of the algorithm by constructing a suitable Lyapunov function. Furthermore, we prove that the Zeno behavior can be avoid. Finally, we provide examples to validate the effectiveness of the obtained result.

Probabilistic approach in solving an optimization problem with application to in physical and technical systems

The article considers some optimization models with a nonlinear objective function and constraints in the form of equalities and inequalities. The model is considered in two forms – deterministic and stochastic, which allows it to be used to solve various optimization problems in physical and technical systems. The presented stochastic model is based on the inclusion of stochastic parameters into the well-known Cobb-Douglas function. The influence of stochastic variables on the optimal value of the objective function, depending on their distribution type, is analyzed.

A simulation-based multi-objective genetic optimization framework for efficient building design in early stages: application for Vietnam's hot and humid climates

PurposeIn many countries, innovation in building design for improving energy performance, reducing CO2 emissions and minimizing life cycle cost has received much attention for sustainable development. This paper investigates the importance of optimization tools for enhancing the design performance in the early stages of Vietnam's cooling-dominated buildings in hot and humid climates using an integrated building design approach.Design/methodology/approachThe methodology of this study exploits the non-dominated sorting genetic algorithm (NSGA-II) optimization algorithm coupled with building simulation to research a trade-off between the optimization of investment cost and energy consumption. Our approach focuses on the whole optimization problem of thermal envelope, glazing and energy systems from preliminary design phases. The methodology is then tested for a case study of a non-residential building located in Hanoi.FindingsThe results show a considerable improvement in design performance by our method compared to current building design. The optimal solutions present the trade-off between energy consumption and capital cost in the form of a Pareto front. This helps architects, engineers and investors make important decisions in the early design stages with a large view of impacts of all factors on energy performance and cost.Originality/valueThis is one of the original research to study integrated building design applying the simulation-based genetic optimization algorithm for cooling-dominated buildings in Vietnam. The case study in this article is for a non-residential building in the north of Vietnam but the methodology can also be applied to residential buildings and other regions.

A general mixed-integer programming framework for efficient modeling, integration and optimization of thermodynamic cycle-based energy systems

Thermodynamic cycles are imperative systems for energy conversion, and optimization has been an important tool to improve their thermo-economic benefits. However, off-the-shelf software is often limited by long computational time, inflexibility for modeling and numerical difficulties. Here, we present an equation-based optimization framework featuring: (1) an inclusive modeling structure applicable to various thermodynamic cycles design problems; (2) versatile thermodynamic properties estimation for different working fluids; (3) capability of working fluids optimization with complex composition; (4) an efficient formulation method to model potential phase change of streams in simple/complicated heat exchangers; (5) a systematic optimization strategy to improve solution efficiency. The framework is formulated as mixed-integer nonlinear programming models, and its performance is demonstrated by two thermodynamic cycle optimization problems and one system design problem, including a supercritical CO2 Brayton cycle, cryogenic cycle (PRICO), and concentrated solar power (CSP) system. The Brayton cycle case serves as an illustrative example to show thermodynamic cycle design combining the consideration of stream properties calculation, unit operations, and flowsheet optimization. The PRICO example shows the efficacy of the proposed framework in simultaneously optimizing flowsheet and working fluids composition with complex heat exchangers and stream phase unknown a priori. The CSP case demonstrates that the framework can be extended to system optimization problems with high accuracy multi-parameter equation of state. Results prove that the framework is efficient and effective in solving thermodynamic cycle and related energy systems optimization problems.

Multi-objective constrained optimization for energy applications via tree ensembles

Energy systems optimization problems are complex due to strongly non-linear system behavior and multiple competing objectives, e.g. economic gain vs. environmental impact. Moreover, a large number of input variables and different variable types, e.g. continuous and categorical, are challenges commonly present in real-world applications. In some cases, proposed optimal solutions need to obey explicit input constraints related to physical properties or safety-critical operating conditions. This paper proposes a novel data-driven strategy using tree ensembles for constrained multi-objective optimization of black-box problems with heterogeneous variable spaces for which underlying system dynamics are either too complex to model or unknown. In an extensive case study comprised of synthetic benchmarks and relevant energy applications we demonstrate the competitive performance and sampling efficiency of the proposed algorithm compared to other state-of-the-art tools, making it a useful all-in-one solution for real-world applications with limited evaluation budgets.

Observer‐based optimal adaptive control for multimotor driving servo systems

AbstractAn adaptive control strategy based on the optimal sliding surface is designed for multimotor driving servo systems in this article. By dividing the system into load subsystem and motor subsystem and decomposing the tracking performance index, the optimal control problem of a high‐order systems is simplified into a second‐order system optimal control problem. Then based on the decomposed performance indexes, the optimal sliding surfaces are determined by solving two algebraic Riccati equations. Combined with an adaptive gain, an optimal adaptive tracking controller is designed, which can reduce the settling time and the energy consumption with a small overshoot. In addition, to obtain the unmeasurable angular velocities of motors and the load, an leaky echo state network‐based observer is applied that ensures fast and accurate estimation. Furthermore, to solve the synchronization problem of the multimotor driving servo systems, the mean relative coupling synchronization controller is designed. The simulation and experimental results have demonstrated that the presented control scheme is effective.