System Optimization Problems Research Articles

Code and Data Repository for Decomposable Formulation of Transmission Constraints for Decentralized Power Systems Optimization

One of the most complicating factors in decentralized solution methods for a broad range of power system optimization problems is the modeling of power flow equations. Existing formulations for direct current (DC) power flows either have limited scalability or are very dense and unstructured, making them unsuitable for large-scale decentralized studies. In this work, we present a novel sparsified variant of the injection shift factors formulation, which has a decomposable block-diagonal structure and scales well for large systems. We also propose a decentralized solution method, based on alternating direction multiplier method (ADMM), that efficiently handle transmission line outages in N-1 security requirements. Benchmarks on Multi-Zonal Security-Constrained Unit Commitment problems show that the proposed formulation and algorithm can reliably and efficiently solve interconnection-level test systems, with up to 6,515 buses, with no convergence or numerical issues.

Optimization of Radio Energy Transmission System Efficiency Based on Genetic Algorithm

In order to better understand the efficiency optimization problem of radio energy transmission systems, the author proposes a genetic algorithm based research on efficiency optimization of radio energy transmission systems. The author first addresses the issue of improving the efficiency of magnetic coupled radio energy transmission. On the basis of ensuring a certain transmission distance and voltage gain, the system is mathematically modeled using coupling circuit theory, and mathematical expressions such as transmission efficiency, transmission distance, and voltage gain are obtained as the objective functions of the algorithm. Secondly, the impact of metal obstacles on the transmission system was analyzed. Design a radio energy transmission compensation circuit, and through simulation, obtain three transmission system parameter schemes that meet the objective function and constraint conditions. Finally, the multi-objective genetic algorithm is used to optimize the system parameter design and obtain the optimal combination of transmission system parameters, with coupling coefficient k=0.1818 and mutual inductance coefficient M=23.165 × 10^(-5) H. Using multi-objective genetic algorithm, the algorithm has a fast convergence function in terms of the number of iterations, a non dominated function solution, and Pareto graphs have verified that the numerical value (3) in the text is the optimal combination design for the transmission system.

Integrated System Design for Post-Disaster Management: Multi-Facility, Multi-Period, and Bi-Objective Optimization Approach

Disaster management requires efficient allocation of essential facilities with consideration of various objectives. During the response and recovery phase of disaster management (RRDM), various types of missions occur in multiple periods, and each of them needs different support from facilities. In this study, a bi-objective mathematical model was derived to support multi-period RRDM by optimal allocation of required facilities such as drone stations, shelters, emergency medical facilities, and warehouses according to the mission life cycle. Connectivity between facilities was considered to ensure inter-facility complementarity. For efficient derivation of Pareto solutions, a modified epsilon-constraint algorithm for bi-objective optimization was developed. The algorithm was tested with a realistic disaster simulation scenario using HAZUS 4.0 as a demonstration of the benefits of the proposed approach. With the simulation experiments, the proposed approach was expected to provide efficient operational plans and guidelines to decision makers for the bi-objective optimization problem in RRDM systems. In addition, the consideration of inter-facility connectivity can play an important role in the RRDM, especially for robustness and readiness.

Enhancement of distribution system performance with reconfiguration, distributed generation and capacitor bank deployment

This paper presents a comparative study of optimal reconfiguration, distributed generation, and shunt capacitor bank deployment for power loss minimization and voltage profile improvement in distribution systems. A metaheuristic approach based on the grey wolf optimizer (GWO) algorithm has been proposed for solving this high-dimensional, nonlinear, constrained, combinatorial optimization problem. Two standard IEEE 33- and 69-bus radial distribution systems (RDSs), and a practical 83-bus RDS of Taiwan Power Company have been considered for this study. The solutions obtained are compared with one another and those in the recent literature which includes classical and non-classical, metaheuristic-based methods. Going further, the little-studied problem of simultaneous reconfiguration, distributed generation, and capacitor bank deployment has been solved. The results suggest that the GWO has excellent potential for solving complicated optimization problems in distribution systems and elsewhere.

On regularization of the classical optimality conditions in the convex optimization problems for Volterra-type systems with operator constraints

On regularization of the classical optimality conditions in the convex optimization problems for Volterra-type systems with operator constraints

Distributed ADMM power optimal control for standalone hybrid generation systems

With the rapid development and increased demand for renewable energy sources, standalone hybrid generation systems have become an essential energy solution. Power optimization control is thus critical to achieving the efficient operation and stability of this system. The distributed ADMM (alternating direction method of multipliers)-based approach has the full potential to deal with the power optimization problem of standalone hybrid generation systems. This study uses an optimization algorithm with a Gaussian penalty function, ADMM-ρ, to alternately optimize the power reference values of wind, light, and battery-containing power generation subsystems. The local controller regulates the output power of the converter according to this reference value. This ensures that the wind and photovoltaic power generation subsystem work in load-tracking or maximum power-tracking modes so that the optimal operation of hybrid power generation meets the balance of supply and demand while prolonging the service life of the batteries. Simulation experiments show that the distributed ADMM algorithm can reliably address the power optimization challenge of hybrid power generation systems.

Application of Mass Service Theory to Economic Systems Optimization Problems—A Review

An interdisciplinary approach to management allows for the integration of knowledge and tools of different fields of science into a unified methodology in order to improve the efficiency of resource management of different kinds of systems. In the conditions of global transformations, it is economic systems that have been significantly affected by external destabilizing factors. This determines the focus of attention on the need to develop tools for the modeling and optimization of economic systems, both in terms of organizational structure and in the context of resource management. The purpose of this review study is to identify the current gaps (shortcomings) in the scientific literature devoted to the issues of the modeling and optimization of economic systems using the tools of mass service theory. This article presents a critical analysis of approaches for the formulation of provisions on mass service systems in the context of resource management. On the one hand, modern works are characterized by the inclusion of an extensive number of random factors that determine the performance and efficiency of economic systems: the probability of delays and interruptions in mobile networks; the integration of order, inventory, and production management processes; the cost estimation of multi-server system operation; and randomness factors, customer activity, and resource constraints, among others. On the other hand, controversial points are identified. The analytical study carried out allows us to state that the prevailing majority of mass service models applied in relation to economic systems and resource supply optimization are devoted to Markov chain modeling. In terms of the chronology of the problems studied, there is a marked transition from modeling simple systems to complex mass service networks. In addition, we conclude that the complex architecture of modern economic systems opens up a wide research field for finding a methodology for assessing the dependence of the enterprise performance on the effect of optimization provided by using the provisions of mass service theory. This statement can be the basis for future research.

Differentially private distributed online optimization via push-sum one-point bandit dual averaging

This paper focuses on the distributed online optimization problem in multi-agent systems considering privacy preservation. Each agent exchanges local information with neighboring agents on the strongly connected time-varying directed graphs. Since the process of information transmission is prone to information leakage, a distributed push-sum dual averaging algorithm based on the differential privacy mechanism is proposed to protect the privacy of the data. In addition, to handle situations where the gradient information of the node cost function is unknown, the one-point gradient estimation is designed to calculate the true gradient information and guide the update of the decision variables. With the appropriate choice of the stepsizes and the exploration parameters, the algorithm can effectively protect the privacy of agents while achieving sublinear regret with the convergence rate O(T34). Furthermore, this paper also explores the effect of one-point estimation parameters on the regret in the online setting and investigates the relation between the convergence effect of individual regret and differential privacy levels. Finally, several federated learning experiments were conducted to verify the efficacy of the algorithm.

Minimax solutions of Hamilton-Jacobi equations in dynamic optimization problems for hereditary systems

A survey of the results concerning the development of the theory of Hamilton-Jacobi equations for hereditary dynamical systems is presented. One feature of these systems is that the rate of change of their state depends not only on the current position, like in the classical case, but also on the full path travelled, that is, the history of the motion. Most of the paper is devoted to dynamical systems whose motion is described by functional differential equations of retarded type. In addition, more general systems described by functional differential equations of neutral type and closely related systems described by differential equations with fractional derivatives are considered. So-called path-dependent Hamilton-Jacobi equations are treated, which play for the above classes of systems a role similar to that of the classical Hamilton-Jacobi equations in dynamic optimization problems for ordinary differential systems. In the context of applications to control problems, the main attention is paid to the minimax approach to the concept of a generalized solution of the Hamilton-Jacobi equations under consideration and also to its relationship with the viscosity approach. Methods for designing optimal feedback control strategies with memory of motion history which are based on the constructions discussed are presented. Bibliography: 183 titles.

Optimization of Solar Panel Efficiency using Genetic Algorithms

Maximizing the efficiency of solar panels is crucial for enhancing the viability of solar energy in both residential and commercial sectors. In this study, we employ Genetic Algorithms (GAs) to optimize various parameters affecting solar panel performance, such as tilt angle, azimuth angle, and environmental conditions like temperature and solar irradiance. We develop a model that simulates the efficiency of solar panels under varying conditions and apply GAs to find the optimal configuration. The results demonstrate a significant improvement in energy output, with optimized parameters yielding up to a 15% increase in solar panel efficiency. This research shows the potential of GAs in solving complex optimization problems in renewable energy systems. Keywords: Solar panel efficiency, Genetic Algorithms, Optimization, Renewable energy, Tilt angle, Azimuth angle, Temperature, Solar irradiance

High-Dimensional Multi-Objective Bayesian Optimization With Block Coordinate Updates: Case Studies in Intelligent Transportation System

Many transportation system problems can be formulated as high-dimensional expensive multi-objective problems. They are challenging for Gaussian process-based Bayesian optimization methods to find the Pareto fronts due to the curse of dimensionality and the boundary issue in the acquisition function optimization. This paper presents a multi-objective Bayesian optimization method with block coordinate updates, Block-MOBO, to solve high-dimensional expensive multi-objective problems. Block-MOBO first partitions the decision variable space into different blocks, each of which includes a low-dimensional multi-objective problem. At each iteration, one block is considered and the decision variables not in this block are approximated by context-vector generation embedded with the Pareto prior knowledge thus promoting convergence. To tackle the boundary issue, we present <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon$</tex-math> </inline-formula> -greedy acquisition function in a Bayesian and multi-objective fashion, which recommends candidates either from the exploitation-exploration trade-off perspective or with probability <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon$</tex-math> </inline-formula> from the Pareto dominance relationship perspective. We verify the effectiveness of Block-MOBO by comparing it with other multi-objective Bayesian methods on two real-world optimization problems in transportation system and three multi-objective synthetic test suites. The experimental results show that Block-MOBO can find more evenly distributed and non-dominated solutions in the whole search space with lower complexity compared with other state-of-the-art approaches. Our analyses illustrate that block coordinate updates and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon$</tex-math> </inline-formula> -greedy acquisition function contribute to computational complexity reduction and convergence-diversity trade-offs, respectively.

Minimax solutions of Hamiltoni-Jacobi equations in dynamical optimization problems for hereditary systems

Настоящая статья содержит обзор результатов, касающихся развития теории уравнений Гамильтона-Якоби для наследственных динамических систем. Особенность этих систем состоит в том, что скорость изменения их состояния зависит не только от текущего положения, как в классическом случае, но и от всего пройденного пути - истории движения. Большая часть статьи посвящена динамическим системам, движение которых описывается при помощи функционально-дифференциальных уравнений запаздывающего типа. Кроме того, затрагиваются и более общие системы, описываемые функционально-дифференциальными уравнениями нейтрального типа, а также тесно связанные с ними системы, описываемые дифференциальными уравнениями с производными дробного порядка. Рассматриваются так называемые наследственные уравнения Гамильтона-Якоби, которые для указанных классов систем играют роль, аналогичную роли классических уравнений Гамильтона-Якоби в задачах динамической оптимизации обыкновенных дифференциальных систем. В контексте приложений к задачам управления основное внимание уделяется минимаксному подходу к понятию обобщенного решения рассматриваемых уравнений Гамильтона-Якоби, а также его связи с вязкостным подходом. Приводятся опирающиеся на обсуждаемые конструкции методы построения оптимальных стратегий управления по принципу обратной связи с памятью истории движения. Библиография: 183 названия.

Optimization of Solar Panel Efficiency using Genetic Algorithms

Maximizing the efficiency of solar panels is crucial for enhancing the viability of solar energy in both residential and commercial sectors. In this study, we employ Genetic Algorithms (GAs) to optimize various parameters affecting solar panel performance, such as tilt angle, azimuth angle, and environmental conditions like temperature and solar irradiance. We develop a model that simulates the efficiency of solar panels under varying conditions and apply GAs to find the optimal configuration. The results demonstrate a significant improvement in energy output, with optimized parameters yielding up to a 15% increase in solar panel efficiency. This research shows the potential of GAs in solving complex optimization problems in renewable energy systems.

Fast System Level Synthesis: Robust Model Predictive Control using Riccati Recursions

System level synthesis enables improved robust MPC formulations by allowing for joint optimization of the nominal trajectory and controller. This paper introduces a tailored algorithm for solving the corresponding disturbance feedback optimization problem for linear time-varying systems. The proposed algorithm iterates between optimizing the controller and the nominal trajectory while converging q-linearly to an optimal solution. We show that the controller optimization can be solved through Riccati recursions leading to a horizon-length, state, and input scalability of <img???> for each iterate. On a numerical example, the proposed algorithm exhibits computational speedups by a factor of up to 103 compared to general-purpose commercial solvers.

Distributed dynamic event-triggered algorithm for optimization problem with time delay.

This paper focuses on studying the optimization problem of multi-agent systems (MAS) under undirected graph. To reduce the communication frequency among agents, a zero-gradient-sum (ZGS) algorithm based on dynamic event-triggered (DET) mechanism is investigated. The event-triggered condition of each agent only uses its own state information and the neighbor's state information at the previous triggering instants, without requiring continuous state information from the neighbor. In addition, the designed algorithm allows for the sampling period to be arbitrarily large. The Lyapunov method is utilized to derive the sufficient conditions that incorporate time delay and parameters. As the event is only checked at the periodic moment, zeno behavior can be directly excluded. Finally, numerical simulations demonstrate the effectiveness of the theoretical results.

On the minimal solution for max-product fuzzy relation inequalities

&lt;p&gt;Minimal solutions play a crucial role in constructing the complete solution set of the max-product fuzzy relation inequalities, as well as in solving the corresponding fuzzy relation optimization problems. In this work, we propose a sufficient and necessary condition for checking whether a given solution is minimal in the max-product system. Our proposed approach is useful for eliminating non-minimal solutions from the set of all quasi-minimal solutions. Our proposed checking approach helps reduce computational complexity when solving the max-product system or related optimization problems.&lt;/p&gt;

Design of Information Management System Based on Random Leapfrog Band Selection Algorithm

With the rapid development of information technology, the traditional information management system faces the challenge of efficiency and accuracy when dealing with complex data and decision-making problems. In order to solve these problems, this paper integrates the random leapfrog band selection algorithm into the information management system. This algorithm shows excellent performance in dealing with large-scale, nonlinear and multi-variable optimization problems, resource allocation, scheduling optimization and data mining. This paper mainly explains the design framework of information management system, the optimization of information management by random leap-band selection algorithm and the design of information management system. Finally, two groups of simulation experiment results are as follows: the accuracy of the optimized information management system is 96%, the running time is 7.1min, the algorithm performance is better than the traditional system, and the response time of the system is reduced by 195ms. This research provides an efficient, flexible and scalable solution for dealing with various complex information management system optimization problems.

A digital twin-based decision support approach for AGV scheduling

The dynamic and complex environment affects the operational efficiency of automated guided vehicles (AGVs) at automated container terminals, in which artificial intelligent approaches are applied to address optimization problems in dynamic systems. This paper proposes a digital twin-based decision support approach to improve the efficiency of AGV scheduling service. Accordingly, the factors that affect AGV scheduling performance, including conflicts, failures, and battery constraints, are discussed first. Then, the framework and main steps of the proposed approach are described. The physical operation space is mapped into the virtual space, and both spaces keep synchronized to support the verification of solutions. A mathematical programming model and Q-learning algorithm are used to generate the AGV scheduling plan considering battery charging. Numerical experiments are conducted to demonstrate the effectiveness of the proposed approach. Comparisons of the digital twin-based approach, genetic algorithm (GA), and particle swarm optimization (PSO) are also made with different scale experiments. It appears that the proposed digital twin-based approach is superior to GA and PSO when solving small- and large-scale cases. A sensitivity analysis is performed concerning the battery utilization rate, task, and AGV number. Experimental results show that an optimal configuration of AGV and task can improve the battery utilization rate and reduce the completion time.

Мathematical model of the problem of optimizing logistics networks under conditions of interval determination of input data

Problem. In the conditions of rapid changes in demand and supply in transportation markets, there is a need for corresponding changes in logistics technologies and networks, which are carried out through their reengineering. Existing mathematical models for the optimization of logistics networks are designed for conditions with point-wise, clearly defined input data, which does not allow obtaining solutions resistant to changes in the external environment. This determined the relevance of the scientific and applied task of developing mathematical models of multi-criteria optimization problems of logistics networks for the conditions of interval submission of input data. Goal. The goal is to increase the efficiency of the logistics network optimization technology at the stage of re-engineering by developing a mathematical model of the multi-criteria optimization problem for the conditions of interval submission of input data. Methodology. According to the results of the decomposition of the problem of system optimization of logistics networks as the most complex defined task of their structural and topological optimization. When developing the model, the methodology of system design of territorially distributed objects, methods of multi-criteria optimization, theories of utility and decision-making were used. The apparatus of interval mathematics was used to compare solution options with vaguely specified input data. The results. The result are the formulated and completed formalization of the task of optimizing logistics networks as territorially distributed objects. The relationship for the objective function and constraints of the optimization task of topological structures of centralized three-level logistics networks is proposed. Originality. A mathematical model of the task of reengineering topological structures of centralized three-level logistics networks according to cost and efficiency indicators for interval defined input data and values of local criteria using comparison indices based on the Hukuhara difference has been developed. Practical value. The obtained results make it possible to increase the reliability of optimization results in the processes of design, development planning and reengineering of logistics networks, to obtain variants of the construction of their topological structures that are resistant to changes in external conditions.

A variegated GWO algorithm implementation in emerging power systems optimization problems

This paper proposes a novel hybrid algorithm which is mathematically modelled by amalgamating the superior features of recently developed Grey Wolf Optimizer (GWO), Sine Cosine Algorithm (SCA), and Crow Search Algorithm (CSA). Researchers have already implemented the aforementioned three algorithms and obtained superior quality results for solving diverse optimization problems. The novel hybrid Variegated GWO Algorithm (VGWO) developed in this proposed research work is initially realized and validated for solving IEEE CEC-C06 2019 benchmark functions. Thereafter, the proposed VGWO is utilized as an optimization tool to solve three emerging and complex power system optimization problems which includes energy management of microgrid systems operated in both islanded and grid-connected mode, dynamic economic emission dispatch and reactive power planning (RPP) problem. A comparative analysis of the proposed VGWO approach with other established metaheuristics is undertaken for each optimization problem. Numerical results show that the novel hybrid VGWO algorithm outperformed an ample number of optimization techniques in providing better quality solutions. The proposed hybrid algorithm yielded a 36.93% reduction in active power loss and 36.80% reduction in operating cost with respect to base case condition for RPP problem. Likewise while solving microgrid energy management problems 9–30% savings was realized in the generation cost compared to the ones mentioned in literature. The capability of handling many complex constraints within a minimum amount of computational time to provide consistently best solutions prioritize the proposed hybrid algorithm among its kinds. Statistical analysis validates the authenticity and viability of the proposed algorithm.