Ordinal optimisation approach for locating and sizing of distributed generation

This study presents an ordinal optimisation (OO) method for specifying the locations and capacities of distributed generation (DG) such that a trade-off between loss minimisation and DG capacity maximisation is achieved. The OO approach consists of three main phases. First, the large search space of potential combinations of DG locations is represented by sampling a relatively small number of alternatives. Second, the objective function value for each of the sampled alternatives is evaluated using a crude but computationally efficient linear programming model. Third, the top-s alternatives from the crude model evaluation are simulated via an exact non-linear programming optimal power flow (OPF) programme to find the best DG locations and capacities. OO theory allows computing the size s of the selected subset such that it contains at least k designs from among the true top-g samples with a pre-specified alignment probability AP. This study discusses problem-specific approaches for sampling, crude model implementation and subset size selection. The approach is validated by comparing with recently published results of a hybrid genetic algorithm OPF applied to a 69-node distribution network operating under Ofgem (UK) financial incentives for distribution network operators.     

A Primal-Dual Interior-Point Method to Solve the Optimal Power Flow Dispatching Problem

This paper presents a primal-dual path-following interior-point method for the solution of the optimal power flow dispatching (OPFD) problem. The underlying idea of most path-following algorithms is relatively similar: starting from the Fiacco-McCormick barrier function, define the central path and loosely follow it to the optimum solution. Several primal-dual methods for OPF have been suggested, all of which are essentially direct extensions of primal-dual methods for linear programming. Nevertheless, there are substantial variations in some crucial details which include the formulation of the non-linear problem, the associated linear system, the linear algebraic procedure to solve this system, the line search, strategies for adjusting the centring parameter, estimating higher order correction terms for the homotopy path, and the treatment of indefiniteness. This paper discusses some of the approaches that were undertaken in implementing a specific primal-dual method for OPFD. A comparison is carried out with previous research on interior-point methods for OPF. Numerical tests on standard IEEE systems and on a realistic network are very encouraging and show that the new algorithm converges where other algorithms fail.     

基于Benders分解的租赁车队规划

以汽车租赁业的日常车辆调配为背景,研究租赁车队的战术规划问题。将车辆调配情况抽象到时空网络结构中,并根据车辆需求的供应策略和时空节点的流量平衡得到约束条件,以企业运营成本最小为目标建立优化模型。针对模型特点采用Benders分解算法将原问题分解为两类子问题,给出对应的算法步骤。以一周为战术规划期设计算例,对模型和算法的有效性进行检验,结果表明能够为优化车队调配提供较好的辅助决策支持。     

Transient stability constrained optimal power flow using particle swarm optimisation

A novel approach based on the particle swarm optimisation (PSO) technique is proposed for the transient-stability constrained optimal power flow (TSCOPF) problem. Optimal power flow (OPF) with transient-stability constraints considered is formulated as an extended OPF with additional rotor angle inequality constraints. For this nonlinear optimisation problem, the objective function is defined as minimising the total fuel cost of the system. The proposed PSO-based approach is demonstrated and compared with conventional OPF as well as a genetic algorithm based counterpart on the IEEE 30-bus system. Furthermore, the effectiveness of the PSO-based TSCOPF in handling multiple contingencies is illustrated using the New England 39-bus system. Test results show that the proposed approach is capable of obtaining higher quality solutions efficiently in the TSCOPF problem     

Balancing transfer lines using Benders decomposition and ant colony optimisation techniques

In this paper, we investigate a transfer line balancing problem in order to find the line configuration that minimises the non-productive time. The problem is defined at an auto manufacturing company where the cylinder head is manufactured. Technological restrictions among design features and manufacturing operations are taken into consideration. The problem is represented by an integer programming model that assigns design features and cutting tools to machining stations, and specifies the number of machines and production sequence in each station. Three algorithms are developed to efficiently solve the problem under study. The first algorithm uses Benders decomposition approach that decomposes the proposed model into an assignment problem and a sequencing problem. The second algorithm is a hybrid algorithm that mixes Benders decomposition approach with the ant colony optimisation technique. The third algorithm solves the problem using two nested ant colonies. Using 15 different problem dimensions, we compare results of the three algorithms in a computational study. The first algorithm finds optimal solutions of small problem instances only. Second and third algorithms demonstrate optimality gaps less than 4.04 and 3.8%, respectively, when compared to the optimal results given by the first algorithm. Moreover, the second and third algorithms are very promising in solving medium and large-scale problem instances.     

The optimum design of fluid distribution networks with particular reference to low pressure gas distribution networks

This paper is concerned with the development of a computational algorithm to find the optimal solution to the fluid network distribution design problem. The problem is formulated as a non-linear mathematical optimization problem and is solved using a sequential unconstrained minimization technique. Illustrative examples are included and the design solutions obtained compared with the solutions obtained using a parametric method.     

Combining stochastic programming and optimal control to decompose multistage stochastic optimization problems

The paper suggests a possible cooperation between stochastic programming and optimal control for the solution of multistage stochastic optimization problems. We propose a decomposition approach for a class of multistage stochastic programming problems in arborescent form (i.e. formulated with implicit non-anticipativity constraints on a scenario tree). The objective function of the problem can be either linear or nonlinear, while we require that the constraints are linear and involve only variables from two adjacent periods (current and lag 1). The approach is built on the following steps. First, reformulate the stochastic programming problem into an optimal control one. Second, apply a discrete version of Pontryagin maximum principle to obtain optimality conditions. Third, discuss and rearrange these conditions to obtain a decomposition that acts both at a time stage level and at a nodal level. To obtain the solution of the original problem we aggregate the solutions of subproblems through an enhanced mean valued fixed point iterative scheme.     

A Genetic Algorithm to Solve Capacity Assignment Problem in a Flow Network

Computer networks and power transmission networks are treated as capacitated flow networks. A capacitated flow network may partially fail due to maintenance. Therefore, the capacity of each edge should be optimally assigned to face critical situations—i.e., to keep the network functioning normally in the case of failure at one or more edges. The robust design problem (RDP) in a capacitated flow network is to search for the minimum capacity assignment of each edge such that the network still survived even under the edge’s failure. The RDP is known as NP-hard. Thus, capacity assignment problem subject to system reliability and total capacity constraints is studied in this paper. The problem is formulated mathematically, and a genetic algorithm is proposed to determine the optimal solution. The optimal solution found by the proposed algorithm is characterized by maximum reliability and minimum total capacity. Some numerical examples are presented to illustrate the efficiency of the proposed approach.     

Multicommodity Network Expansion under Elastic Demands

We analyze some issues of network design and bandwidth allocation in telecommunication systems with congestible resources. The work is closely related to network monitoring and traffic measurement functions that must be carried out on line, in order to overcome congestion caused by an unfavorable traffic pattern or by a failure. In addition to the traditional use of routing controls, our approach achieves network efficiency with capacity assignment and also imposing variable prices for the consumers. A generalized Benders decomposition method is applied to a mixed integer nonlinear programming formulation of the integrated problem of network design and operation. The method exploits the nature of the continuous subproblem, that is a large-scale convex network flow problem with demands sensitive to commodity prices. Some numerical experience suggests that the method is usefull to address both questions of global optimality and competitive pricing in such systems.     

Optimal configuration of remanufacturing supply network with return quality decision

This research studies the configuration problem of a remanufacturing production network together with the decision for return quality thresholds, in which, the manufacturer has multiple remanufacturing facilities to satisfy different market demands. Quality of returns is stochastic, while demand for remanufactured products is either stochastic or deterministic. The problem we considered is to determine facilities to operate, minimum quality to accept into each operating facility, return quantity and demand allocation simultaneously so that the system’s profit is maximised. The problem is formulated as a mixed integer non-linear programming model. Through the use of a numerical example, the impact of quantity of returns, total spending, quality uncertainty, demand uncertainty and transportation cost on the remanufacturing system is analysed.     

Experiments with hybrid Bernstein global optimization algorithm for the OPF problem in power systems

This article presents an algorithm based on the Bernstein form of polynomials for solving the optimal power flow (OPF) problem in electrical power networks. The proposed algorithm combines local and global optimization methods and is therefore referred to as a ‘hybrid’ Bernstein algorithm in the context of this work. The proposed algorithm is a branch-and-bound procedure wherein a local search method is used to obtain a good upper bound on the global minimum at each branching node. Subsequently, the Bernstein form of polynomials is used to obtain a lower bound on the global minimum. The performance of the proposed algorithm is compared with the previously reported Bernstein algorithm to demonstrate its efficacy in terms of the chosen performance metrics. Furthermore, the proposed algorithm is tested on the OPF problem for several benchmark IEEE power system examples and its performance is compared with generic global optimization solvers such as BARON and COUENNE. The test results demonstrate that the hybrid Bernstein global optimization algorithm delivers satisfactory performance in terms of solution optimality.     

Optimal acquisition policy in remanufacturing under general core quality distributions

The quality of acquirable used products (cores) is highly variable, which has made production planning and control of remanufacturing systems difficult. This paper studies an acquisition problem in presence of uncertain core quality. In order to derive optimal acquisition policy, the problem is formulated as a non-linear integer programming model in the framework of order statistics. The model is a strictly discrete convex problem with a unique global minimal solution. Then, a single bisection method is developed to obtain the optimal solution under a general continuous quality distribution. Moreover, the expressions of the optimal solution in some frequently used quality distributions are derived. Furthermore, the model is extended to the case of a general remanufacturing cost function, and corresponding results are presented. Finally, numerical experiments are conducted to test the effects of quality distribution, cost relationships of acquirable cores and remanufacturing cost function.     

Optimum laminate design for strength and stiffness

A method is presented for minimum weight optimum design of symmetric fibre-composite laminates subject to multiple in-plane loading conditions which takes into account membrane stiffness requirements and strength limitations. The problem is cast as a non-linear mathematical programming problem in which the thicknesses of material placed at preassigned orientation angles are treated as the only design variables. The non-linear programming formulation is transformed into a sequence of linear programs employing an adaptation of the method of inscribed hyperspheres in which only critical and near critical constraints are considered at each stage in the procedure. Example applications illustrate that the method presented offers an efficient and practical optimum design procedure for the fundamental and recurring problem treated.     

Intermittent wind generation in optimal power flow dispatching

A stochastic model of wind generation in an optimal power flow (OPF) dispatching program is presented. The model includes the error in wind power forecasts using a probability or relative frequency histogram. Compared with the deterministic OPF, the proposed model allows the coordination of wind and thermal power while accounting for (i) the expected penalty cost for not using all available wind power and (ii) the expected cost of calling up power reserves because of wind power shortage. The stochastic model is integrated in an extended conic quadratic OPF program in which wind driven generators are represented as induction machines. Simulation results are presented for cases where the forecasting error histogram is either derived from historical data or estimated by a bimodal normal distribution. The effect of the skewness of the error distribution on the optimal dispatch policy is studied.     

An augmented Lagrange programming optimization neural network for short-term hydroelectric generation scheduling

An approach based on augmented Lagrange programming neural networks is proposed for determining the optimal hourly amounts of generated power for the hydro-units in an electric power system. This methodology is based on the Lagrange multiplier theory in optimization and searches for solutions satisfying the necessary conditions of optimality in the state space. The equilibrium point of the network satisfies the Kuhn–Tucker condition for the problem. The equilibrium point of the network corresponds to the Lagrange solution of the problem. The proposed technique has been applied to a multi-reservoir cascaded hydro-electric system with a non-linear power generation function of water discharge rate and storage volume. The water transportation delay between connected reservoirs is also taken into account. Results obtained from this approach are compared with those obtained from the two phase optimization neural network and the conventional augmented Lagrange multiplier method. It is concluded from the results that the proposed method provides better results with respect to constraint satisfaction and is very effective in yielding optimal hydro-generation schedules.     

A realistic multi-manned five-sided mixed-model assembly line balancing and scheduling problem with moving workers and limited workspace

The assembly line balancing problem can completely vary from one production line to the other. This paper deals with a realistic assembly line for the automotive industry inspired by Fiat Chrysler Automotive in North America and Parskhodro in Iran (both large-scale automotive companies). This problem includes some specific requirements that have not been studied in the literature. For example, the assembly line is five-sided, and workers can move along these sides. Due to the limited workspace, all the sides cannot work simultaneously at one station. First, a mixed integer linear programming model is proposed for the problem. Then, the model is improved to have a tighter linear relaxation. Moreover, an effective logic-based Benders’ decomposition algorithm is developed. After careful analysis of problem’s structure, three propositions are introduced. The master problem is well restricted by eight valid inequalities. Two different sub-problem types are defined to extract more information from the master problem’s solution. In this case, the algorithm adds effective cuts that reduce the solution space to the extent possible at each iteration. Thus, the number of iterations is significantly cut down. The performance of the model and algorithm, as well as improvement made on both, is evaluated.     

Optimal solution for the flow path design problem of a balanced unidirectional AGV system

An optimal flow path layout (FPL) design method is introduced as a handy tool for an automated guided vehicle (AGV) system planing stage. The problem is analysed and formulated by linear mixed-integer programming. A procedure based on the branch-and-bound depth-first search technique is proposed to solve the FPL problem. The procedure is implemented as an efficient computer program and yields an optimal solution in a small number of iterations. Using the transportation model for calculating the required and optimal flow of empty vehicles, system balance is achieved. Finally, two examples are given. A simple illustrative example is discussed to demonstrate the procedure, and a realistic FPL problem with 23 nodes, 66 arcs and nine pick-up/delivery stations is solved.     

Decomposition method for solving optimal material orientation problems

The strain energy density is considered as a measure of the stiffness/flexibility of the composite structure. A methodology for determining the stationary points of the strain energy density in anisotropic solids is developed. The methodology proposed is based on new problem formulation, derivation and analysis of optimality conditions, and decomposition method. The optimal material orientation problem is formulated in terms of strains. The optimality conditions derived cover different material symmetries, linear and also some non-linear material models. The complexity analysis of the optimality conditions has been performed. The proposed approach allows to divide the solution of the optimal material orientation problem into less complicated subtasks.     

Bilevel programming applied to power system vulnerability analysis under multiple contingencies

This study examines the use of bilevel programming to analyse the vulnerability of power systems under multiple contingencies. One of the main purposes of this study is to explain the state of the art of the subject matter. A minimum vulnerability model and a maximum vulnerability model are presented and discussed. In both models, the upper-level optimisation determines a set of simultaneous outages in the transmission network whereas the lower-level optimisation models the reaction of the system operator against the outages identified in the upper level. The system operator reacts by minimising the system load shed through an optimal operation of the power system. Two solution approaches for the resulting mixedinteger non-linear bilevel programs are analysed and compared. Both methodologies are based on the equivalent transformation of the lower-level problem into a set of constraints, so that the original bilevel programs, respectively, become a single-level optimisation problem. The first approach is based on the application of Karush--Kuhn--Tucker optimality conditions whereas the second procedure relies on duality theory. This study shows that both approaches are essentially equivalent from a rigorous mathematical viewpoint; however, the second method is more suitable for off-the-shell branch-and-cut software as corroborated by numerical simulations.     

Minimization of load reduction in pipe networks subject to interrupted supply

The paper considers the question of reduction of loads on a pipe network, which may be necessary as a result of failure in supply or interruption of a pipe. The non-linear relationship between pressure loss and flow along a pipe makes the problem of minimizing the reduction of loads also non-linear. An iterative linear approximation technique is therefore adopted. When the question is formulated as a problem in linear programming, the constraints include nodal pressures as well as loads. It is shown how the number of these constraints may be reduced.