System Optimization Problems Research Articles

Independent Log-Linear Learning in Potential Games With Continuous Actions

Game theoretic learning in multiagent systems is a rapidly developing area of research. It gained popularity since the wide range of optimization problems in multiagent systems can be reformulated in terms of potential games, where the set of potential function maximizers represents the set of optimal states. The crucial point of such approach is the design of local decision rules that leads the system to a potential function maximizer. In this paper, we consider the independent log-linear learning procedure applicable to continuous action potential games. We provide the analysis of the stochastic stability of potential function maximizers in case of continuous action games. To analyze the behavior of the underlying Markov chain, we develop a new method for approximating the initial chain with continuous states by chains whose long run properties can be established. After that, we study the finite time behavior of the algorithm with a definite time-dependent parameter and obtain settings that guarantee an efficient implementation of the learning procedure under consideration.

Efficient Ranking and Selection for Stochastic Simulation Model Based on Hypothesis Test

This paper proposes an efficient ranking and selection algorithm for a stochastic simulation model. The proposed algorithm evaluates an uncertainty to assess whether the observed best design is truly optimal, based on hypothesis test. Then, it conservatively allocates additional simulation resources to reduce uncertainty with an intuitive allocation rule in each iteration of a sequential procedure. This conservative allocation provides a high robustness to noise for the algorithm. The results of several experiments demonstrated its improved performance compared to the other algorithms in the literature. The algorithm can be an efficient way to solve optimization problems in real-world systems where significant noise exists.

A switched dynamical system approach towards the optimal control of chemical processes based on a gradient-based parallel optimization algorithm

This paper considers an optimal control problem of chemical processes with a novel piecewise state-feedback controller. Firstly, the chemical process optimal control problem is formulated as a switched dynamical system optimal control problem, which can be transformed into a parameter optimization problem. Next, to achieve rapid convergence from remote starting points, we propose a novel gradient-based optimization algorithm, which is suitable to a parallel implementation because the step is improved by updating its direction as well as its length simultaneously before moving to the next iteration, and the step computation involves only the inner products of vectors. Then, the convergent properties of the parameter optimization problem to the original optimal control problem are discussed. Finally, the numerical simulation results show that the gradient-based parallel optimization algorithm is an effective alternative method for solving the chemical process optimal control problems.

Limits and potentials of Mixed Integer Linear Programming methods for optimization of polygeneration energy systems

The simultaneous production of different energy vectors from hybrid polygeneration plants is a promising way to increase energy efficiency and facilitate the development of distributed energy systems. The inherent complexity of polygeneration energy systems makes their economic, environmental and energy performance highly dependent on system synthesis, equipment selection and capacity, and operational strategy. Mixed Integer Linear Programming (MILP) is the state of the art approach to tackle the optimization problem of polygeneration systems. The guarantee of finding global optimality in linear problems and the effectiveness of available commercial solvers make MILP very attractive and widely used in optimization problems of polygeneration systems. Nevertheless, several drawbacks affect the MILP formulation, such as: the impossibility of taking into account nonlinear effects; the necessity of considering all the time periods at once; the risk of high-dimensionality of the problem. To tackle these limitations, several techniques have been developed, such as: piecewise linearization methods; rolling horizon approaches; dimensionality reduction by means of energy demands clustering algorithms. In this paper, limits and potentials of MILP methods for the optimization problem of polygeneration energy systems are reviewed and discussed.

An Improved Particle Swarm Optimization Algorithm for Integrated Scheduling Model in AGV-Served Manufacturing Systems

To address the resources optimization problem of AGV-served manufacturing systems driven by multi-varieties and small-batch production orders, a scheduling model integrating machines and automated guided vehicles (AGVs) is proposed. In this model, the makespan of jobs from raw material storage to finished parts storage through multi-stage processes has been used as the objective function, and the utilization ratios of machines and AGVs have been used as the comprehensive evaluation functions. An improved particle swarm optimization algorithm with the characteristics of main particles and nested particles is developed to solve a reasonable scheduling scheme. Compared with the basic particle swarm optimization algorithm and genetic algorithm, the numerical result suggests that the nested particle swarm optimization algorithm has more advantages in convergence and solving efficiency. It is expected that this study can provide a useful reference for the flexible adjustment of AGV-served manufacturing systems.

Hybrid Optimal Tracking Control for Linear Continuous-Time Systems by Simultaneous Optimization Approach of System States and Mode Distributions

In this paper, we study optimal LQG tracking control problems for linear continuous-time hybrid systems. We adopt an approach to prepare some candidates of mode distributions and minimize value functions at each time for the systems and performance indices. By the approach, system states and mode distributions are simultaneously optimized so that the performance indices are minimized for available information of reference signals. We consider optimization problems for averaged systems and averaged performance indices throughout mode distributions. Finally we give numerical examples and verify that we can obtain both optimal tracking performance and optimal candidate of mode distributions by the algorithm presented in this paper.

Damage Index-Based Lower Bound Structural Design

The scope of the work is to detect the most appropriate damage index, able to provide a reliable description of the structural damage level. This damage index is used to formulate a performance-based design framework to be used as a design tool for achieving safer and more economic designs. This objective is achieved by comparing alternative structural systems that comply with the design demands in the most cost-efficient approach, i.e. those requiring less material volume for concrete and steel reinforcement. In this direction, design optimization problems for structural systems are defined for each damage index under consideration and the structural optimization problems at hand are solved by means of a popular metaheuristic search algorithm.

Gbest Artificial Bee Colony for Non-convex Optimal Economic Dispatch in Power Generation

Non-convex Optimal Economic Dispatch (OED) problem is a complex optimization problem in power system operation that must be optimized economically to meet the power demand and system constraints. The non-convex OED is due to the generator characteristic such as prohibited operation zones, valve point effects (VPE) or multiple fuel options. This paper proposes a Gbest Artificial Bee Colony (GABC) algorithm based on global best particle (gbest) guided of Particle Swarm Optimization (PSO) in Artificial bee colony (ABC) algorithm for solving non-convex OED with VPE. In order to investigate the effectiveness and performance of GABC algorithm, the IEEE 14-bus 5 unit generators and IEEE 30-bus 6 unit generators test systems are considered. The comparison of optimal solution, convergence characteristic and robustness are also highlighted to reveal the advantages of GABC. Moreover, the optimal results obtained by proposed GABC are compared with other reported results of meta-heuristic algorithms. It found that the GABC capable to obtain lowest cost as compared to others. Thus, it has great potential to be implemented in different types of power system optimization problem.

System Optimization for Dynamic Wireless Charging Electric Vehicles Operating in a Multiple-Route Environment

Dynamic wireless charging (DWC) technology, a novel way of supplying vehicles with electric energy, allows the vehicle battery to be recharged remotely while it is moving over power tracks, which are charging infrastructures installed beneath the road. DWC systems mitigate the range limitation of electric vehicles by using power tracks as additional sources of electric energy. This paper proposes a model and algorithm for optimally designing DWC electric vehicle (EV) systems, particularly those operating in multiple-route environments. Multi-route system comprises several single routes that share common road segments, and the vehicles operating on a specific route are equipped with identical batteries. We build a general model to optimally allocate power tracks and determine the vehicle battery size for each route. Then, we apply a particle swarm optimization algorithm to solve the given multi-route DWC-EV system optimization problem. A numerical example is solved to illustrate the characteristics of the multi-route model, and we show that the proposed modeling approach and algorithm are effective, compared with a mixed integer programming-based exact solution approach. We also conduct a sensitivity analysis to examine the solution behavior of the problem.

Modelling testing mechanism for mitigating genetically modified wheat contamination risks

Recent discoveries of genetically modified (GM) wheat growing in farm fields across several U.S. states have renewed public worries about GM wheat contamination if GM wheat is commercialised. There would appear to be a need for research designed to identify reactive risk mitigation strategies to maintain the sustainability of grain supply chains (SCs) before any potential GM wheat contamination undermines their integrity. This research attempts to identify cost-effective testing strategies to mitigate the GM wheat contamination risks. We explicitly model the U.S. wheat supply chain in a realistic manner to embrace complexity inherent in the system. The specification of appropriate wheat handling strategies in the SC is formulated as system optimisation problems and solved using simulation. Once solved for a base scenario, sensitivity analysis is conducted on key variables that influence wheat varietal testing strategies.

Optimal overcurrent relay coordination in distribution network based on Lightning Flash Algorithm

PurposeDistribution network protection is a complicated problem and mal-operation of the protective relays due to false settings make the operation of the network unreliable. Besides, obtaining proper settings could be very complicated. This paper aims to discuss an innovative evolutionary Lightning Flash Algorithm (LFA) which is developed for solving the relay coordination problems in distribution networks. The proposed method is inspired from the movements of cloud to ground lightning strikes in a thunderstorm phenomenon. LFA is applied on three case study systems including ring, interconnected and radial distribution networks. The power flow analysis is performed in Digsilent Power Factory software; then the collected data are sent to MATLAB software for optimization process. The proposed algorithm provides optimum time multiplier setting and plug setting of all digital overcurrent relays in each system. The results are compared with other methods such as particle swarm optimization and genetic algorithm. The result comparisons demonstrate that the proposed LFA can successfully obtain proper relay settings in distribution networks with faster speed of convergence and lower total operation time of relays. Also, it shows the superiority and effectiveness of this method against other algorithms.Design/methodology/approachA novel LFA is designed based on the movements of cloud to ground lightning strikes in a thunderstorm. This method is used to optimally adjust the time multiplier setting and plug setting of the relays in distribution system to provide a proper coordination scheme.FindingsThe proposed algorithm was tested on three case study systems, and the results were compared with other methods. The results confirmed that the proposed method could optimally adjust the relay settings in the electric distribution system to provide a proper protection scheme.Practical implicationsThe practical implications can be conducted on distribution networks. The studies provided in this paper approve the practical application of the proposed method in providing proper relay protection in real power system.Originality/valueThis paper proposes a new evolutionary method derived from the movements of cloud to ground lightning strikes in thunderstorm. The proposed method can be used as an optimization toolbox to solve complex optimization problems in practical engineering systems.

Adaptive distributed convex optimization for multi-agent and its application in flocking behavior

This paper studies adaptive optimization problem of continuous-time multi-agent systems. Multi-agents with second-order dynamics are considered. Each agent is equipped with a time-varying cost function which is known only to an individual agent. The objective is to make multi-agents velocities minimize the sum of local functions by local interaction. First, a distributed adaptive algorithm is presented, in which each agent depends only on its own velocity and neighbors velocities. It is indicated that all agents can track the optimal velocity. Then we apply the distributed adaptive algorithm to flocking of multi-agents. It is proved that all agents can track the optimal trajectory. The agents will maintain connectivity and avoid the inter-agent collision. Finally, two simulations are included to illustrate the results.

Optimal control of bioprocess systems using hybrid numerical optimization algorithms

In the paper, we consider the bioprocess system optimal control problem. Generally speaking, it is very difficult to solve this problem analytically. To obtain the numerical solution, the problem is transformed into a parameter optimization problem with some variable bounds, which can be efficiently solved using any conventional optimization algorithms, e.g. the improved Broyden–Fletcher–Goldfarb–Shanno algorithm. However, in spite of the improved Broyden–Fletcher–Goldfarb–Shanno algorithm is very efficient for local search, the solution obtained is usually a local extremum for non-convex optimal control problems. In order to escape from the local extremum, we develop a novel stochastic search method. By performing a large amount of numerical experiments, we find that the novel stochastic search method is excellent in exploration, while bad in exploitation. In order to improve the exploitation, we propose a hybrid numerical optimization algorithm to solve the problem based on the novel stochastic search method and the improved Broyden–Fletcher–Goldfarb–Shanno algorithm. Convergence results indicate that any global optimal solution of the approximate problem is also a global optimal solution of the original problem. Finally, two bioprocess system optimal control problems illustrate that the hybrid numerical optimization algorithm proposed by us is low time-consuming and obtains a better cost function value than the existing approaches.

Identifying Redundant Flow Limits on Parallel Lines

Many power system optimization problems constrain line flows with limits specified in terms of the magnitudes of apparent power or current flows. The set of line-flow constraints may have redundancies (i.e., the feasible space may be unchanged upon removal of a subset of the line-flow constraints), which unnecessarily complicate optimization problems. This letter describes an algorithm for identifying redundant line-flow constraints corresponding to certain parallel lines. After formulating the constraints as ellipsoids in the voltage variables, redundancies are detected from the absence of intersections between pairs of ellipsoids corresponding to parallel lines. This algorithm is demonstrated using several large test cases.

Extended ADMMs for RPO of large‐scale power systems with discrete controls

The reactive power optimization (RPO) problem of power systems is a mixed-integer nonlinear programming problem, which can be computationally expensive. This paper applies the alternating direction method of multipliers (ADMM) to solve it. By duplicating discrete control variables with one copy allowed to vary continuously, the RPO model is formulated as a modified model in which the objective function and constraints have a separable structure with respect to the continuous and discrete variables, except for the coupling constraint. We then applied the ADMM to solve this model with the separable structure, and hence the original problem is converted into two optimization sub-problems, which are nonlinear programming (NLP) and mixed-integer quadratic programming (MIQP) problems, respectively. To improve the convergence of the algorithm, we proposed an extended ADMM by adding the upper and lower limits on state variables into the MIQP sub-problem based on the sensitivities obtained in the NLP sub-problem. We also established a mechanism to filter out inactive inequality constraints in the MIQP sub-problem to improve computational speed. Moreover, numerical results tested on IEEE test systems and a real 739-bus system have shown the correctness of the proposed method and its adaptability for power systems with different sizes and configurations..

A multi-objective robust optimization approach for engineering design under interval uncertainty

PurposeEngineering system design and optimization problems are usually multi-objective and constrained and have uncertainties in the inputs. These uncertainties might significantly degrade the overall performance of engineering systems and change the feasibility of the obtained solutions. This paper aims to propose a multi-objective robust optimization approach based on Kriging metamodel (K-MORO) to obtain the robust Pareto set under the interval uncertainty.Design/methodology/approachIn K-MORO, the nested optimization structure is reduced into a single loop optimization structure to ease the computational burden. Considering the interpolation uncertainty from the Kriging metamodel may affect the robustness of the Pareto optima, an objective switching and sequential updating strategy is introduced in K-MORO to determine (1) whether the robust analysis or the Kriging metamodel should be used to evaluate the robustness of design alternatives, and (2) which design alternatives are selected to improve the prediction accuracy of the Kriging metamodel during the robust optimization process.FindingsFive numerical and engineering cases are used to demonstrate the applicability of the proposed approach. The results illustrate that K-MORO is able to obtain robust Pareto frontier, while significantly reducing computational cost.Practical implicationsThe proposed approach exhibits great capability for practical engineering design optimization problems that are multi-objective and constrained and have uncertainties.Originality/valueA K-MORO approach is proposed, which can obtain the robust Pareto set under the interval uncertainty and ease the computational burden of the robust optimization process.

Multi-objective optimization and sensitivity analysis of an organic Rankine cycle coupled with a one-dimensional radial-inflow turbine efficiency prediction model

The organic Rankine cycle (ORC) has been demonstrated to be a viable approach to recover low-grade waste heat and has been widely investigated in recent years. In the current research focused on the multi-objective optimization problem of ORC systems, few scholars consider the variation in turbine efficiency with the cycle parameters. This paper focused on the comparison of multi-objective optimization with variable turbine efficiency and that with constant turbine efficiency. The results obtained for the two types of turbine efficiency were compared, and the differences were analyzed. Flue gas at 523.15 K was used as the heat source, and pentane, hexane, heptane, cyclohexane, benzene and toluene were selected as working fluid candidates. The one-dimensional radial-inflow turbine efficiency prediction model was applied to replace constant turbine efficiency. The multi-objective model in conjunction with the turbine efficiency model was constructed by defining the net power output and system total cost per unit net power output as the objective functions. The non-dominated sorting genetic algorithm-II (NSGA-II) was used to optimize the evaporation temperature and condensation temperature as the decision variables. With the aid of the ideal point, the optimal solution of each working fluid was selected from the Pareto frontier. The results showed that the turbine efficiency varies with changes in evaporation temperature and condensation temperature. In the multi-optimization with constant turbine efficiency, toluene and cyclohexane are the optimal working fluids, whereas with variable turbine efficiency, benzene is the optimal working fluid. In the sensitivity analysis, the optimal exergy efficiency shows opposite trends for the multi-objective optimization with constant and variable turbine efficiency.

Distributed optimization of multi-agent systems with delayed sampled-data

Abstract In this paper, we study the distributed optimization problem of multi-agent systems with delayed sampled-data, where the interconnected topology is directed, weighted-balanced and strongly connected, and also local cost functions are strongly convex with globally Lipschitz gradients. Based on synchronous and asynchronous sampled-data, we construct two respective algorithms. Our main results, sufficient conditions for the convergence to an optimal solution, are obtained under assumption that all design parameters are chosen properly. We also present one example to validate our theoretical results.

Multiobjective economic-environmental power dispatch with stochastic wind-solar-small hydro power

Economic-environmental power dispatch is one of the most popular bi-objective non-linear optimization problems in power system. Classical economic power dispatch problem is formulated with only thermal generators often ignoring security constraints of the network. But importance of reduction in emission is paramount from environmental sustainability perspective and hence penetration of more and more renewable sources into the electrical grid is encouraged. However, most common forms of renewable sources are intermittent and uncertain. This paper proposes multiobjective economic emission power dispatch problem formulation and solution incorporating stochastic wind, solar and small-hydro (run-of-river) power. Weibull, lognormal and Gumbel probability density functions are used to calculate available wind, solar and small-hydro power respectively. Some conventional generators of the standard IEEE 30-bus system are replaced with renewable power sources for study purpose. Network security constraints such as transmission line capacities and bus voltage limits are also taken into consideration alongwith constraints on generator capabilities and prohibited operating zones for the thermal units. Decomposition based multiobjective evolutionary algorithm and summation based multiobjective differential evolution algorithm are applied to the problem under study. An advanced constraint handling technique, superiority of feasible solutions, is integrated with both the multiobjective algorithms to comply with system constraints. The simulation results of both the algorithms are summarized, analyzed and compared in this study.

Distributed optimization problem for second-order multi-agent systems with event-triggered and time-triggered communication

This paper deals with the large category of convex optimization problems on the framework of second-order multi-agent systems, where each distinct agent is assigned with a local objective function, and the overall optimization problem is defined as minimizing the sum of all the local objective functions. To solve this problem, two distributed optimization algorithms are proposed, namely, a time-triggered algorithm and an event-triggered algorithm, to make all agents converge to the optimal solution of the optimization problem cooperatively. The main advantage of our algorithms is to remove unnecessary communications, and hence reduce communication costs and energy consumptions in real-time applications. Moreover, in the proposed algorithms, each agent uses only the position information from its neighbors. With the design of the Lyapunov function, the criteria about the controller parameters are derived to ensure the algorithms converge to the optimal solution. Finally, numerical examples are given to illustrate the effectiveness of the proposed algorithms.