System Optimization Problems Research Articles

Multiple-Reservoir Scheduling Using β-Hill Climbing Algorithm

Abstract The multi-reservoir systems optimization problem requires defining a set of rules to recognize the water amount stored and released in accordance with the system constraints. Traditional methods are not suitable for complex multi-reservoir systems with high dimensionality. Recently, metaheuristic-based algorithms such as evolutionary algorithms and local search-based algorithms are successfully used to solve the multi-reservoir systems. β-hill climbing is a recent metaheuristic local search-based algorithm. In this paper, the multi-reservoir systems optimization problem is tackled using β-hill climbing. In order to validate the proposed method, four-reservoir systems used in the literature to evaluate the algorithm are utilized. A comparative evaluation is conducted to evaluate the proposed method against other methods found in the literature. The obtained results show the competitiveness of the proposed algorithm.

Efficient Discrete Rate Assignment and Power Optimization in Optical Communication Systems Following the Gaussian Noise Model

Computationally efficient heuristics for solving the discrete-rate capacity optimization problem for optical fiber communication systems are investigated. In the Gaussian noise nonlinearity model regime, this class of problem is an NP-hard mixed integer convex problem. The proposed heuristic minimizes the number of calls required to solve the computationally intensive problem of determining the feasibility of proposed discrete rate allocations. In a live system, optimization using this algorithm minimizes the number of potential discrete rate allocations tested for feasibility while additional discrete system capacity is extracted. In exemplary point-to-point links at 50 Gbaud with 50 Gb/s rate steps, the mean lost capacity per modem is reduced from 24.5 Gb/s with truncation to 7.95 Gb/s with discrete-rate optimization. With 25 Gb/s rate steps, the mean lost capacity is reduced from 12.3 Gb/s to 2.07 Gb/s. An unbiased metric is proposed to extend the capacity optimization objective from point-to-point links to mesh networks. A gain of 13% in distance-times-capacity metric is obtained from discrete-rate optimization with 50 Gb/s rate steps, and a 7.5% gain is obtained with 25 Gb/s rate steps.

Optimal Voltage Control Using an Equivalent Model of a Low-Voltage Network Accommodating Inverter-Interfaced Distributed Generators

The penetration of inverter-based distributed generators (DGs), which can control their reactive power outputs, has increased for low-voltage (LV) systems. The power outputs of DGs affect the voltage and power flow of both LV and medium-voltage (MV) systems that are connected to the LV system. Therefore, the effects of DGs should be considered in the volt/var optimization (VVO) problem of LV and MV systems. However, it is inefficient to utilize a detailed LV system model in the VVO problem because the size of the VVO problem is increased owing to the detailed LV system models. Therefore, in order to formulate and solve the VVO problem in an efficient way, in this paper, a new equivalent model for an LV system including inverter-based DGs is proposed. The proposed model is developed based on an analytical approach rather than a heuristic-fitting one, and it therefore enables the VVO problem to be solved using a deterministic algorithm (e.g., interior point method). In addition, a method to utilize the proposed model for the VVO problem is presented. In the case study, the results verify that the computational burden to solve the VVO problem is significantly reduced without loss of accuracy by the proposed model.

Peak operation of hydropower system with parallel technique and progressive optimality algorithm

With the rapid economic growth in recent years, the peak operation of hydropower system (POHS) is becoming one of the most important optimization problems in power system. However, the rapid expansion of system scale, refined management and operational constraints has greatly increased the optimization difficult of POHS. As a result, it is of great importance to develop effective methods that can ensure the computational efficiency of POHS. The progressive optimality algorithm (POA) is a commonly used technique for solving hydropower operation problem, but its execution time still grows sharply with the increasing number of hydropower plants, making it difficult to satisfy the efficiency requirement of POHS. To address this problem, a novel efficient method called parallel progressive optimality algorithm (PPOA) is presented in this paper. In PPOA, the complex problem is firstly divided into several two-stage optimization subproblems, and then the classical Fork/Join framework is used to realize parallel computation of subproblems, making a significant improvement on execution efficiency. The simulations in a real-world hydropower system demonstrate that as compared with the standard POA, PPOA can use abundant multi-core resources to reduce execution time while keeping the quality of solution, providing a new alternative to solve the complex hydropower peak operation problem.

Computationally Efficient Hybrid Method for Transmission Network Expansion Planning

Abstract Transmission network expansion planning (TNEP) is an important and computationally very demanding problem in power system. Many computational approaches have been proposed to handle TNEP in the past. The problem is mixed integer, large scale and its complexity increases exponentially with the size of the system. Metaheuristic techniques have gained a lot of importance in last few years to solve the power system optimization problems, due to their ability to handle complex optimization functions and constraints. Many of them have been successfully applied for TNEP. The biggest challenge in these techniques is the requirement of large computational efforts. This paper uses a two-stage solution process to solve the TNEP problems. The first stage uses compensation based method to generate a quick, suboptimal solution. The valuable information contained in this solution is used to generate a set of heuristics aimed at drastically reducing the number of population for fitness evaluations required in the 2nd stage with application of metaheuristic method. The resulting hybrid approach produces very good quality solutions very efficiently. Results for 24 bus and 93 bus test systems have been obtained with the proposed method to ascertain the potential of the method in comparison to earlier approaches.

Mixed-integer programming models for line pressure optimization in shale gas gathering systems

In this work we propose a mixed-integer nonlinear programming model to address the line pressure optimization problem for shale gas gathering systems. This model is designed to determine: a) the optimal timing for turning prospective wells in-line, b) the optimal pressure profile within a gathering network, and c) the necessary compression power for delivering produced gas to long-distance transmission lines.We rely on a pressure-normalized decline curve model to quantify how line pressure variations impact the gas production of individual wells. The reservoir model itself is incorporated in a transmission optimization framework which rigorously evaluates pressure drops along pipeline segments. Moreover, we explicitly consider compression requirements to lift line pressure from gas gathering levels to setpoints dictated by transmission pipeline companies. Since the resulting optimization models are large-scale, nonlinear and nonconvex, we propose a solution procedure based on an efficient initialization strategy. Finally, we present a detailed case study, and show that the proposed optimization framework can be used effectively to manage line pressures in shale gas gathering systems by properly scheduling when, and how many, new wells are brought online.

Firefly-inspired algorithm for optimal sizing of renewable hybrid system considering reliability criteria

Abstract Renewable energy sources are usually seen as a response to actual environmental, social and economic issues. However, the random nature of these sources requires the development of sizing rules and the use of these systems for their exploitation. This article presents the results of a developed hybrid PV/wind optimization sizing method, taking into account the strong combination between the intermittent energy resource (solar and wind), the storage capacity and a given load profile. This optimization method is based on the use of metaheuristic techniques. These algorithms, often inspired by nature, are designed to solve complex optimization problems. Among the most recent metaheuristics, we used the Firefly Algorithm (FA), considering the Load Dissatisfaction Rate (LDR) criteria and the Electricity Cost (EC) indicator for power reliability and system cost. The suggested method determines the system optimum configuration, which can achieve the desired LDR with minimum EC. To achieve this aim, an objective function is formulated for the EC. It must be kept to a minimum while respecting the reliability constraints (LDRdesired). The effectiveness of the FA in solving a hybrid system optimization problem is scrutinized and its performance is compared to other renamed optimization algorithms. To highlight the propounded method performance a real case study has been conducted and the results are discussed.

Distributed optimization problem for double-integrator systems with the presence of the exogenous disturbance

The aim of this paper is to study the distributed optimization problem for continuous-time multi-agent systems with the existence and the interference of external disturbance, therein each agent is described as double-integrator dynamic. To reject the exogenous disturbance, the distributed algorithm is proposed for each agent based on the internal model principle. The proposed algorithm only utilizes the position information of each agent from its neighbors subject to the undirected graph, which can reduce communication costs and energy consumptions in applications. Moreover, the algorithm only needs the cost functions of the agent itself, which can greatly protect the privacy of other agents. The optimal solution of the problem is thus obtained with the design of Lyapunov function and the help of convex analysis, LaSallel’s Invariance Principle. Finally, two numerical simulation examples and the comparison of proposed algorithm with other previous research are presented to illustrate the persuasive effectiveness of the theoretical result.

Distributed Optimization for Linear Multiagent Systems: Edge- and Node-Based Adaptive Designs

This paper studies the distributed optimization problem for continuous-time multiagent systems with general linear dynamics. The objective is to cooperatively optimize a team performance function formed by a sum of convex local objective functions. Each agent utilizes only local interaction and the gradient of its own local objective function. To achieve the cooperative goal, a couple of fully distributed optimal algorithms are designed. First, an edge-based adaptive algorithm is developed for linear multiagent systems with a class of convex local objective functions. Then, a node-based adaptive algorithm is constructed to solve the distributed optimization problem for a class of agents satisfying the bounded-input bounded-state stable property. Sufficient conditions are given to ensure that all agents reach a consensus while minimizing the team performance function. Finally, numerical examples are provided to illustrate the theoretical results.

Cycle Time Optimization of Deterministic Timed Weighted Marked Graphs by Transformation

Timed marked graphs, a special class of Petri nets, are extensively used to model and analyze cyclic manufacturing systems. Weighted marked graphs are convenient to model automated production systems, such as robotic work cells or embedded systems, and reduce the size of the model. The main problem for designers is to find a tradeoff between minimizing the cost of the resources and maximizing the system's throughput (also called cycle time). It is possible to apply analytical techniques for the cycle time optimization problem of such systems. The problem consists in finding an initial marking to minimize the cycle time (i.e., maximize the throughput) while the weighted sum of tokens in places is less than or equal to a given value. We transform a weighted marked graph into several equivalent marked graphs and formulate a mixed integer linear programming model to solve this problem. Moreover, several techniques are proposed to reduce the complexity of the proposed method. We show that the proposed method can always find an optimal solution.

A fuzzy-based function approximation technique for reinforcement learning1

5 Abstract. Reinforcement learning is hard to solve optimization problems in multi-agent system because of the inefficiency of function approximation. Sparse distributed memories, which is implemented using Radial Basis Functions or Kanerva Coding, can be used to improve the efficiency. But this approach still often gives poor performance when applied to large-scale multi-agent systems. In this paper, we attempt to solve four-rooms problem in the predator-prey pursuit domain and argue that the poor performance that we observe is caused by frequent prototype collisions. We show that dynamic prototype allocation and adaptation can give better results by reducing these collisions. By using our novel approach about fuzzy Kanerva-based function approximation, that uses a fine-grained fuzzy membership grade to describe a state-action pair's adjacency with respect to each prototype, we give some results that prototype collisions are completely eliminated and learning performance is greatly improved. We further show that prototype density varies widely across the state-action space and that this variation causes prototypes' receptive fields to be unevenly distributed. This distribution limits the ability of fuzzy Kanerva Coding to achieve better results. It can be observed that fuzzy Kanerva Coding allows prototypes to adaptively tune their receptive fields for a target application. We conclude that fuzzy Kanerva Coding with prototype tuning and adaptation can significantly improve a reinforcement learner's ability to solve large-scale multi-agent problems. 6 7 8 9 10 11 12 13 14 15 16 17 18

Multi-objective quantum-behaved particle swarm optimization for economic environmental hydrothermal energy system scheduling

With increasing attention paid to energy and environment in recent years, the hydrothermal scheduling considering economic and environmental objectives is becoming one of the most important optimization problems in power system. With two competing objectives and a set of operation constraints, the economic environmental hydrothermal scheduling problem is classified as a typical multi-objective nonlinear constrained optimization problem. Thus, in order to efficiently resolve this problem, the multi-objective quantum-behaved particle swarm optimization (MOQPSO) is presented in this paper. In MOQPSO, the elite archive set is adopted to conserve Pareto optimal solutions and provide multiple evolutionary directions for individuals, while the neighborhood searching and chaotic mutation strategies are used to enhance the search capability and diversity of population. Furthermore, a novel constraint handling method is designed to adjust the constraint violation of hydro and thermal plants, respectively. In order to verify its effectiveness, the MOQPSO is applied to a classical hydrothermal system with four hydropower plants and three thermal plants. The simulations show that the proposed method has competitive performance compared with several traditional methods.

A robust ant colony optimization for continuous functions

Ant colony optimization (ACO) for continuous functions has been widely applied in recent years in different areas of expert and intelligent systems, such as steganography in medical systems, modelling signal strength distribution in communication systems, and water resources management systems. For these problems that have been addressed previously, the optimal solutions were known a priori and contained in the pre-specified initial domains. However, for practical problems in expert and intelligent systems, the optimal solutions are often not known beforehand. In this paper, we propose a robust ant colony optimization for continuous functions (RACO), which is robust to domains of variables. RACO applies self-adaptive approaches in terms of domain adjustment, pheromone increment, domain division, and ant size without any major conceptual change to ACO's framework. These new characteristics make the search of ants not limited to the given initial domain, but extended to a completely different domain. In the case of initial domains without the optimal solution, RACO can still obtain the correct result no matter how the initial domains vary. In the case of initial domains with the optimal solution, we also show that RACO is a competitive algorithm. With the assistance of RACO, there is no need to estimate proper initial domains for practical continuous optimization problems in expert and intelligent systems.

Pointwise observation of the state given by complex time lag parabolic system

AbstractVarious optimization problems for linear parabolic systems with multiple constant time lags are considered. In this paper, we consider an optimal distributed control problem for a linear complex parabolic system in which different multiple constant time lags appear both in the state equation and in the Neumann boundary condition. Sufficient conditions for the existence of a unique solution of the parabolic time lag equation with the Neumann boundary condition are proved. The time horizon T is fixed. Making use of the Lions scheme [13], necessary and sufficient conditions of optimality for the Neumann problem with the quadratic performance functional with pointwise observation of the state and constrained control are derived. The example of application is also provided.

Adaptive Estimation Approach for Parameter Identification of Photovoltaic Modules

This paper presents a novel identification technique for estimation of unknown parameters in photovoltaic (PV) systems. A single-diode model is considered for the PV system, which consists of five unknown parameters. Using information about standard test conditions, three unknown parameters are written as functions of the other two parameters in a reduced model. An objective function and a set of inequality constraints are defined for the reduced model, considering limitations of the physical system. It is shown that the nonconvex optimization problem of PV systems is converted to a convex optimization one. The constraints are enforced using a modified barrier function that generates an augmented convex objective function. An adaptive identification technique is utilized to find the optimal values of the augmented cost. Unlike most identification techniques, the proposed algorithm has a precise and unique solution, which is easy to implement. The effectiveness of the proposed approach is confirmed using some simulation and experiments.

Physarum solver: a bio-inspired method for sustainable supply chain network design problem

A supplier of products and services aims to minimize the capacity investment cost and the operational cost incurred by unwanted byproducts, e.g. carbon dioxide emission. In this paper, we consider a sustainable supply chain network design problem, where the capacity and the product flow along each link are design variables. We formulate it as a multi-criteria optimization problem. A bio-inspired algorithm is developed to tackle this problem. We illustrate how to design a sustainable supply chain network in three steps. First, we develop a generalized model inspired by the foraging behaviour of slime mould Physarum polycephalum to handle the network optimization with multiple sinks. Second, we propose a strategy to update the link cost iteratively, thus making the Physarum model to converge to a user equilibrium. Third, we perform an equivalent operation to transform a system optimum problem into a corresponding user equilibrium problem so that it is solvable in the Physarum model. The efficiency of the proposed algorithm is illustrated with numerical examples.

Symbolic elimination in dynamic optimization based on block-triangular ordering

We consider dynamic optimization problems for systems described by differential-algebraic equations (DAEs). Such problems are usually solved by discretizing the full DAE. We propose techniques to symbolically eliminate many of the algebraic variables in a preprocessing step before discretization. These techniques are inspired by the causalization and tearing techniques often used when solving DAE initial value problems. Since sparsity is crucial for some dynamic optimization methods, we also propose a novel approach to preserving sparsity during this procedure. The proposed methods have been implemented in the open-source JModelica.org platform. We evaluate the performance of the methods on a suite of optimal control problems solved using direct collocation. We consider both computational time and probability of solving the problem in a timely manner. We demonstrate that the proposed methods often are an order of magnitude faster than the standard way of discretizing the full DAE, and also significantly increase probability of successful convergence.

Optimal Reactive Power Dispatch with Static VAR Compensator Using Harmony Search Algorithms

One of the major optimization problems in power systems is the optimal reactive power dispatch (ORPD) problem. ORPD plays an important role for secure and reliable operation of power systems. The main purpose of ORPD is to find the settings of control variables such as voltage rating of generators, reactive power injection of VAr compensators and tap ratios of the tap setting transformers in order to minimize the total active power losses of the network while satisfying a given set of constraints. The whole ORPD problem is considered as a non-linear multi-modal optimization problem with a combination of discrete and continuous variables. Along with the conventional control variables in ORPD the optimal location and the Var settings of SVC are included in the optimization problem for additional active power loss reduction. In this paper, two versions of harmony search algorithms namely basic Harmony Search Algorithm (HSA) and Improved Harmony Search algorithm (IHSA) are applied to solve conventional ORPD, as well as ORPD with the FACTS device Static Var Compensator (SVC), to minimize the total active power loss of the power system. The harmony search algorithms for ORPD, as well as ORPD considering SVC are implemented on IEEE 14 and 57 bus systems. Comparison of simulation results reveals the effectiveness of harmony search algorithms over other well established population based optimization techniques.

A hybrid MACO and BFOA algorithm for power loss minimization and total cost reduction in distribution systems

This paper presents a multiobjective optimization methodology to optimally place a STATCOM in electric power distribution networks. The combination of multiobjective ant colony optimization (MACO) and the bacterial foraging optimization algorithm (BFOA) is proposed to minimize the power loss and total cost. The main intention of this analysis is to optimally place the STATCOM at multiple locations such as the transmission side, middle, and load side. Identifying the type and location of the STATCOM is a combinatorial optimization problem in power systems. In order to overcome this problem, the combination of hybrid MACO and BFOA algorithms is applied in this analysis to minimize the total cost and power loss. The total cost of the overall network is calculated by using system average interruption duration index and[ system average interruption frequency index metrics. Moreover, the BFOA is used in this paper to minimize the power loss during distribution, which is adequate in searching for the optimal solution. The problem of reducing power losses in distribution systems through the BFOA approach is described here for a 5-bus system. Test results of a 5-bus network show that the proposed MACO with BFOA method can efficiently ensure the power loss and total cost minimization.

Hybrid Optimal Tracking Control by Most Probable Trajectory Approach

In this paper, we study optimal tracking control problems for linear continuous-time hybrid systems. We adopt most probable trajectory approach to control system states and mode distributions simultaneously. We consider optimization problems for averaged systems and averaged performance indices throughout mode distributions.