Optimal placement and sizing of capacitor using Limaçon inspired spider monkey optimization algorithm

The power system is a complex interconnected network which can be subdivided into three components: generation, distribution, and transmission. Capacitors of specific sizes are placed in the distribution network so that losses in transmission and distribution is minimum. But the decision of size and position of capacitors in this network is a complex optimization problem. In this paper, Limaçon curve inspired local search strategy (LLS) is proposed and incorporated into spider monkey optimization (SMO) algorithm to deal optimal placement and the sizing problem of capacitors. The proposed strategy is named as Limaçon inspired SMO (LSMO) algorithm. In the proposed local search strategy, the Limaçon curve equation is modified by incorporating the persistence and social learning components of SMO algorithm. The performance of LSMO is tested over 25 benchmark functions. Further, it is applied to solve optimal capacitor placement and sizing problem in IEEE-14, 30 and 33 test bus systems with the proper allocation of 3 and 5-capacitors. The reported results are compared with a network without a capacitor (un-capacitor) and other existing methods.     

A novel method for optimal capacitor placement and sizing in distribution systems with nonlinear loads and DG using GA

A genetic algorithm (GA) is proposed for simultaneous power quality improvement, optimal placement and sizing of fixed capacitor banks in radial distribution networks with nonlinear loads and distributed generation (DG) imposing voltage–current harmonics. In distribution systems, nonlinear loads and DGs are often considered as harmonic sources. For optimizing capacitor placement and sizing in the distribution system, objective function includes the cost of power losses, energy losses and capacitor banks. At the same time, constraints include voltage limits, number/size of installed capacitors (at each bus) and the power quality limits of standard IEEE-519. In this study, new fitness function is used to solve the constrained optimization problem with discrete variables. Simulation results for two IEEE distorted networks (18-bus and 33-bus test systems) are presented and solutions of the proposed method are compared with those of previous methods described in the literature. The main contribution of this paper is computing the (near) global solution with a lower probability of getting stuck at a local optimum and weak dependency on initial conditions, while avoiding numerical problems in large systems. Results show that proposed method could be effectively used for optimal capacitor placement and sizing in distorted distribution systems.     

Matrix differential equations and scalar polynomials satisfying higher order recursions

We show that any scalar differential operator with a family of polynomials as its common eigenfunctions leads canonically to a matrix differential operator with the same property. The construction of the corresponding family of matrix valued polynomials has been studied in [A. Durán, A generalization of Favard's theorem for polynomials satisfying a recurrence relation, J. Approx. Theory 74 (1993) 83-109; A. Durán, On orthogonal polynomials with respect to a positive definite matrix of measures, Canad. J. Math. 47 (1995) 88-112; A. Durán, W. van Assche, Orthogonal matrix polynomials and higher order recurrence relations, Linear Algebra Appl. 219 (1995) 261-280] but the existence of a differential operator having them as common eigenfunctions had not been considered. This correspondence goes only one way and most matrix valued situations do not arise in this fashion. We illustrate this general construction with a few examples. In the case of some families of scalar valued polynomials introduced in [F.A. Grünbaum, L. Haine, Bispectral Darboux transformations: An extension of the Krall polynomials, Int. Math. Res. Not. 8 (1997) 359-392] we take a first look at the algebra of all matrix differential operators that share these common eigenfunctions and uncover a number of phenomena that are new to the matrix valued case.     

Diamond-free circle graphs are Helly circle

The diamond is the graph obtained from K₄ by deleting an edge. Circle graphs are the intersection graphs of chords in a circle. Such a circle model has the Helly property if every three pairwise intersecting chords intersect in a single point, and a graph is Helly circle if it has a circle model with the Helly property. We show that the Helly circle graphs are the diamond-free circle graphs, as conjectured by Durán. This characterization gives an efficient recognition algorithm for Helly circle graphs.     

Analysis of the expected discounted penalty function for a general jump-diffusion risk model and applications in finance

In this paper, we extend the Cramér-Lundberg risk model perturbed by diffusion to incorporate the jumps of surplus investment return. Under the assumption that the jump of surplus investment return follows a compound Poisson process with Laplace distributed jump sizes, we obtain the explicit closed-form expression of the resulting Gerber-Shiu expected discounted penalty (EDP) function through the Wiener-Hopf factorization technique instead of the integro-differential equation approach. Especially, when the claim distribution is of Phase-type, the expression of the EDP function is simplified even further as a compact matrix-type form. Finally, the financial applications include pricing barrier option and perpetual American put option and determining the optimal capital structure of a firm with endogenous default.     

Generating hierarchial scale-free graphs from fractals

Motivated by the hierarchial network model of E. Ravasz, A.-L. Barabási, and T. Vicsek, we introduce deterministic scale-free networks derived from a graph directed self-similar fractal Λ. With rigorous mathematical results we verify that our model captures some of the most important features of many real networks: the scale-free and the high clustering properties. We also prove that the diameter is the logarithm of the size of the system. We point out a connection between the power law exponent of the degree distribution and some intrinsic geometric measure theoretical properties of the underlying fractal. Using our (deterministic) fractal Λ we generate random graph sequence sharing similar properties.     

Path Capacity Dimensioning in a Multiprotocol Label Switched Network: Analysis of Optimal and Suboptimal Solutions

In recent years, the problem of capacity allocation for a label switched patch (LSP) in a multiprotocol label switched (MPLS) network has received great attention due to its relevance in the context of traffic control. In this paper, the problem of capacity allocation is formulated as an optimal control problem and its solution is obtained by assuming the knowledge of the bandwidth requests on the entire control interval. A suboptimal solution is also given which has the advantage of requiring limited information about future bandwidth requests. The analysis of the suboptimal solution is explored both analytically and numerically by using simulated and real data. This study demonstrates that the suboptimal solution, also with limited knowledge of the future, yields a good approximation of the optimal one and requires little additional cost.     

New modifications of Potra-Pták’s method with optimal fourth and eighth orders of convergence

In this paper, we present two new iterative methods for solving nonlinear equations by using suitable Taylor and divided difference approximations. Both methods are obtained by modifying Potra-Pták’s method trying to get optimal order. We prove that the new methods reach orders of convergence four and eight with three and four functional evaluations, respectively. So, Kung and Traub’s conjecture Kung and Traub (1974) [2], that establishes for an iterative method based on n evaluations an optimal order p=2ⁿ⁻¹ is fulfilled, getting the highest efficiency indices for orders p=4 and p=8, which are 1.587 and 1.682.We also perform different numerical tests that confirm the theoretical results and allow us to compare these methods with Potra-Pták’s method from which they have been derived, and with other recently published eighth-order methods.     

真实利率波动对长期资产配置的影响(英)

对于单期的投资者而言,无违约风险的固定收益证券被视为无风险资产.这是因为固定收益证券的收益率在投资的初期就能确定.然而在考虑长期的投资时,投资者可以调整资产配置,固定收益证券也将面临再投资的利率波动风险,因此不能再被视为无风险资产.本文在一类特殊的``习惯形成"效用函数的框架下讨论长期资产配置.在一系列为简化问题而作的假设之下,本文推导出了真实利率波动对风险资产配置权重的影响,并且为计算实际长期资产配置的最优比例提供了理论依据和算法.     

Distributional solution theory for linear DAEs

A solution theory for switched linear differential–algebraic equations (DAEs) is developed. To allow for non–smooth coordinate transformation, the coefficients matrices may have distributional entries. Since also distributional solutions are considered it is necessary to define a suitable multiplication for distribution. This is achieved by restricting the space of distributions to the smaller space of piecewise–smooth distributions. Solution formulae for two special DAEs, distributional ordinary differential equations (ODEs) and pure distributional DAEs, are given. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Managing an integrated production inventory system with information on the production and demand status and multiple non-unitary demand classes

In this paper, we study a system consisting of a manufacturer or supplier serving several retailers or clients. The manufacturer produces a standard product in a make-to-stock fashion in anticipation of orders emanating from n retailers with different contractual agreements hence ranked/prioritized according to their importance. Orders from the retailers are non-unitary and have sizes that follow a discrete distribution. The total production time is assumed to follow a k₀-Erlang distribution. Order inter-arrival time for class l demand is assumed to follow a k_l-Erlang distribution. Work-in-process as well as the finished product incur a, per unit per unit of time, carrying cost. Unsatisfied units from an order from a particular demand class are assumed lost and incur a class specific lost sale cost. The objective is to determine the optimal production and inventory allocation policies so as to minimize the expected total (discounted or average) cost. We formulate the problem as a Markov decision process and show that the optimal production policy is of the base-stock type with base-stock levels non-decreasing in the demand stages. We also show that the optimal inventory allocation policy is a rationing policy with rationing levels non-decreasing in the demand stages. We also study several important special cases and provide, through numerical experiments, managerial insights including the effect of the different sources of variability on the operating cost and the benefits of such contracts as Vendor Managed Inventory or Collaborative Planning, Forecasting, and Replenishment. Also, we show that a heuristic that ignores the dependence of the base-stock and rationing levels on the demands stages can perform very poorly compared to the optimal policy.     

真实利率波动对长期资产配置的影响(英文)

对于单期的投资者而言,无违约风险的固定收益证券被视为无风险资产.这是因为固定收益证券的收益率在投资的初期就能确定.然而在考虑长期的投资时,投资者可以调整资产配置,固定收益证券也将面临再投资的利率波动风险,因此不能再被视为无风险资产.本文在一类特殊的"习惯形成"效用函数的框架下讨论长期资产配置.在一系列为简化问题而作的假设之下,本文推导出了真实利率波动对风险资产配置权重的影响,并且为计算实际长期资产配置的最优比例提供了理论依据和算法.     

Solving the forward-reserve allocation problem in warehouse order picking systems

Many warehouses store at least some goods in two areas, a reserve areathat is efficient for storage and a forward area that is efficient fororder picking. The forward-reserve allocation problem determines the set ofStock-Keeping Units and their space allocations in the forward area to maximizethe forward area's benefit by trading off the relevant costs of orderpicking and internal replenishment. The mathematical model of this decisionresembles the classical knapsack problem with the additional complexity that ithas a discontinuous nonlinear cost function. A simple greedy heuristic has beenproposed in the literature to solve this problem. This paper proposes analternative branch-and-bound algorithm that can quickly solve the problem tooptimality. Heuristic and optimal solutions are numerically compared usingproblem instances based on real warehouse data. Results suggest that theheuristic solutions are very close to the optimal ones in terms of both theobjective value and the forward assignment.     

Branch and Bound Algorithm for the <Emphasis Type="Italic">p</Emphasis>-Median Transportation Problem

The p-median transportation problem is to determine an optimal solution to a transportation problem having an additional constraint restricting the number of active supply points. The model is discussed as an example of a public sector location/allocation problem. A branch and bound procedure is proposed to solve the problem. Lagrangian relaxation is used to provide lower bounds. Computational results are given.     

Optimal buffer allocation in tandems of last come first served queues

A large fixed number of buffer spaces is given. We consider the problem of allocating these spaces among the nodes of a tandem of last-come-first-served queues with general service time distributions and Poisson external arrivals so as to optimize some performance criterion associated with the time to buffer overflow, such as maximizing its mean or maximizing the probability that it exceeds some value. Consider the following rule of thumb: allocate the buffer spaces in inverse proportion to the logarithms of the effective service rates at the nodes. Here effective service rate denotes the ratio of the service rate to the stationary arrival rate. We prove that this rule of thumb achieves a nearly optimal buffer allocation under the assumption that the service time distributions satisfy an exponential tail condition. This problem has been studied earlier in the context of Jackson networks, where it was shown that the same rule of thumb achieves an allocation that is close to optimal. The technique of proof here is similar, but there are important differences. Both Jackson networks and the LCFS tandems considered here are product form networks (with infinite buffers). Optimism should lead us to expect that the near optimality of this rule of thumb holds much more generally for product-form networks, but this remains a conjecture at present.Research supported by NSF under NCR 8857731, by AT&T, and by Bellcore Inc.Research supported by IBM under a graduate fellowship.     

LIFO Distribution Systems

The regional distribution problem for a perishable product is examined, under the important assumption that younger units are issued first (LIFO) to satisfy the demands of the customers at the locations. Optimal and approximately optimal allocation policies for two alternative distribution systems are derived. Their properties are discussed, and comparisons are made with the equivalent policies in a FIFO environment.     

Newsvendor characterizations for one-warehouse multi-retailer inventory systems with discrete demand under the balance assumption

This paper considers a one-warehouse multi-retailer inventory system that faces discrete stochastic demand of the customers. Under the so-called balance assumption (also known as the allocation assumption), base stock policies are optimal. Our main contribution is to show that the optimal base stock levels satisfy newsvendor characterizations, which are in terms of inequalities, and to extend the newsvendor equalities known for the continuous demand model. These characterizations are appealing because they (i) are easy to explain to nonmathematical oriented people like managers and MBA students, (ii) contribute to the understanding of optimal control, (iii) help intuition development by providing direct relation between cost and optimal policy parameters.     

Network modelling and variational Bayesian inference for structure analysis of signed networks

Currently, structure analysis of signed networks with positive and negative links has received wide attention and is becoming a research focus in the area of network science. In recent years, many community detection methods for signed networks have been proposed to analyze the structure of signed networks. However, current methods can only efficiently analyze the signed networks with the single community structure and unable to analyze the signed networks with the coexisting structure of communities and peripheral nodes, bipartite, or other structures. To address this problem, in this study, we present a mathematically principled method for the structure analysis of signed networks with positive and negative links, in which a probabilistic model firstly is proposed to model the signed networks with the single community or the coexisting structure, and a variational Bayesian approach is deduced to learn the approximate distribution of model parameters. For determining the optimal model, we also deduce a model selection criterion based on the evidence theory. In addition, to efficiently analyze the large signed networks, we propose a fast learning version of our algorithm with the time complexity O(k²E) where k is the number of groups and E is the number of links. In our experiments, the proposed method is validated in the synthetic and real-world signed networks, and is compared with the state-of-the-art methods. The experimental results demonstrate that the proposed method can more efficiently and accurately analyze to the structure of signed networks than the state-of-the-art methods.     

Modeling fuzzy capacitated p-hub center problem and a genetic algorithm solution

Hub and spoke networks are used to switch and transfer commodities between terminal nodes in distribution systems at minimum cost and/or time. The p-hub center allocation problem is to minimize maximum travel time in networks by locating p hubs from a set of candidate hub locations and allocating demand and supply nodes to hubs. The capacities of the hubs are given. In previous studies, authors usually considered only quantitative parameters such as cost and time to find the optimum location. But it seems not to be sufficient and often the critical role of qualitative parameters like quality of service, zone traffic, environmental issues, capability for development in the future and etc. that are critical for decision makers (DMs), have not been incorporated into models. In many real world situations qualitative parameters are as much important as quantitative ones. We present a hybrid approach to the p-hub center problem in which the location of hub facilities is determined by both parameters simultaneously. Dealing with qualitative and uncertain data, Fuzzy systems are used to cope with these conditions and they are used as the basis of this work. We use fuzzy VIKOR to model a hybrid solution to the hub location problem. Results are used by a genetic algorithm solution to successfully solve a number of problem instances. Furthermore, this method can be used to take into account more desired quantitative variables other than cost and time, like future market and potential customers easily.     

An insurance risk model with stochastic volatility

In this paper, we extend the Cramér-Lundberg insurance risk model perturbed by diffusion to incorporate stochastic volatility and study the resulting Gerber-Shiu expected discounted penalty (EDP) function. Under the assumption that volatility is driven by an underlying Ornstein-Uhlenbeck (OU) process, we derive the integro-differential equation which the EDP function satisfies. Not surprisingly, no closed-form solution exists; however, assuming the driving OU process is fast mean-reverting, we apply the singular perturbation theory to obtain an asymptotic expansion of the solution. Two integro-differential equations for the first two terms in this expansion are obtained and explicitly solved. When the claim size distribution is of phase-type, the asymptotic results simplify even further and we succeed in estimating the error of the approximation. Hyper-exponential and mixed-Erlang distributed claims are considered in some detail.