Iterative Heuristic Method Research Articles

Enhanced network inference from sparse incomplete time series through automatically adapted L1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_1$$\\end{document} regularization

Reconstructing dynamics of complex systems from sparse, incomplete time series data is a challenging problem with applications in various domains. Here, we develop an iterative heuristic method to infer the underlying network structure and parameters governed by Ising dynamics from incomplete spin configurations based on sparse and small-sized samples. Our method iterates between imputing missing spin states given current coupling strengths and re-estimating couplings from completed spin state data. Central to our approach is the novel application of adaptive l1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$l_1$$\\end{document} regularization on updating coupling strengths, which features an automatic adjustment of the regularization strength throughout the iterative inference process. By doing so, we aim at preventing over-fitting and enforcing the sparsity of couplings without access to ground truth parameters. We demonstrate that this approach accurately recovers parameters and imputes missing spins even with substantial missing data and short time series, providing improvements in the inference of Ising model parameters even for relatively small sample sizes.

Service Restoration in the Medium Voltage Grid Minimizing the SAIDI Contribution After Primary Substation Failures

One of the most widely used reliability measures for the electric grid is the System Average Interruption Duration Index (SAIDI), i.e. how many minutes the average customer is without power per year. Primary substation failures may significantly increase SAIDI, since they affect a large number of customers. This may be avoided by improving the service restoration process, which requires solving complex non-convex combinatorial problems. Hence, this paper proposes an algorithm for smart, SAIDI-optimizing service restoration in meshed MV grids after primary substation failures. We first formulate service restoration as a Mixed-Integer Linear Programming (MILP) problem by using a linearization of the power flow equations that is proper for meshed grids and by applying exact Big M relaxations for linearizing other involved non-convexities. The decisions include among others the travel routes of the field crew and account for the grid security constraints. Then, we propose a low complexity heuristic iterative method that optimally solves the MILP problem.

Inner-estimating domains of attraction for discrete-time non-polynomial systems with piecewise difference inclusions

ABSTRACT In this paper, we propose two successive heuristic iterative methods for inner-estimating domains of attraction for discrete-time non-polynomial systems. Firstly, we utilise a discrete-time fuzzy model to derive a piecewise difference inclusion for the discrete-time non-polynomial system. Then, an initial heuristic iterative method is presented to inner-estimate the domain of attraction as large as possible by first iteratively calculating common Lyapunov-like functions and then heuristically updating piecewise difference inclusions. Afterwards, the initial heuristic iterative method is further improved by piecewise Lyapunov-like functions, arriving at a refined heuristic iterative method. Especially, we introduce homotopy continuation method to decrease the computational complexity. At last, our methods are applied to three discrete-time non-polynomial examples with a brief discussion.

An efficient implementation of a VNS heuristic for the weighted fair sequences problem

AbstractIn the weighted fair sequences problem (WFSP), one aims to schedule a set of tasks or activities sthat the maximum product between the largest temporal distance between two consecutive executions of a task and its priority is minimized. The WFSP covers a large number of applications in different areas, ranging from automobile production on a mixed‐model assembly line to the sequencing of interactive applications to be aired in a digital TV environment. This paper proposes an iterative heuristic method for the WFSP centered on an efficient implementation of a variable neighborhood search heuristic. Computational experiments on benchmark instances show that the proposed metaheuristic outperforms the state‐of‐the‐art method proposed to the problem, obtaining comparable solution values in much less computational time.

Parameter extraction of photovoltaic modules using a heuristic iterative algorithm

The single diode Rsh-model is considered to be an accurate and time-efficient modeling method for photovoltaic (PV) modules. However, the implicit equation in the model increases the complexity of solution. In this paper, after analyzing the parameters on the electrical characteristics of PV modules, a pure heuristic iterative method is proposed to extract the five parameters and to solve the implicit voltage and current equation simultaneously. Only three electrical key points specified in the manufacturer’s nameplate together with the Shockley equation are useful. Meanwhile, some pure heuristic strategies are used to minimize the error of the model curve. In order to evaluate the effectiveness of the method, parameters of three different PV modules are extracted, i.e., poly-crystalline, mono-crystalline, and thin-film silicon module. The results show competitive and superior performance to the De Soto model and analytic algorithms in terms of accuracy and computation speed, especially a-Si PV cell types. In addition, 99.45% of PV modules from California Energy Commission (CEC) database are identified successfully to verify the robustness. Further, the field data also indicate that the proposed algorithm can used to predict the real-time generation power of a PV power station at various operating conditions. Therefore, the proposed method can be an effective and efficient alternative for parameter extraction of all kinds of PV modules and arrays.

A new iterative method for solving the joint dynamic storage location assignment, order batching and picker routing problem in manual picker-to-parts warehouses

Short and reliable delivery lead times are crucial for many buying decisions, making efficiently operated order picking systems a critical contributor to a company’s competitiveness. To pick orders fast and with minimal effort, three planning problems need to be solved, namely the assignment of items to storage locations, the consolidation of orders in batches and the routing of the order pickers through the warehouse. Even though the problems are strongly interdependent, they have so far largely been solved separately, leading to losses in efficiency. Recent research has shown that a joint solution can lead to significant performance improvements as compared to individual solutions. Up to now, no method is available that solves all three problems jointly. This work contributes to closing this research gap by proposing an iterative heuristic method that solves the problems jointly and that takes account of future dynamics in customer demand and their influence on the three planning problems. The performance of the method is illustrated in numerical experiments. The results of our studies indicate that the method may lead to significant savings in travel distance.

Iterative resource efficient power allocation in small cell network

The major considerations in designing wireless networks are spectral efficiency (SE) and energy efficiency (EE). Though it is desirable to enhance both SE and EE, however, a trade-off exists between the two. To deal with this trade-off, a new metric called the resource efficiency (RE) has already been proposed in the literature. With RE as a performance evaluation metric, a balance can be struck between the SE and EE. Resource allocation with RE as an objective has already been proposed in the literature for a conventional cellular network. However, RE for a small cell network (a.k.a. heterogeneous network) has not been investigated yet. Small cells increase the frequency reuse factor, thus significantly enhancing the capacity and coverage of cellular networks. While already being embraced into LTE, the small cell technology will be one of the main features of the 5G cellular networks. In this paper, we investigate the problem of power allocation for a small cell network. An optimization problem is formulated with the objective of maximizing the RE such that maximum power constraint is satisfied. Finally, we propose an iterative heuristic method called the Iterative Resource Efficient Power Allocation (IREPA) algorithm to solve the formulated problem. We compare the performance of the IREPA algorithm with the Gradient Based Optimal Power Adaptation Scheme and the Uniform Power Allocation Scheme. Numerical results demonstrate the effectiveness of the proposed power allocation technique that significantly improves the resource efficiency.

Inverse Kinematics for 6-DOF Serial Manipulators With Offset or Reduced Wrists via a Hierarchical Iterative Algorithm

It is still a challenge to accurately and efficiently solve inverse kinematics (IK) using six-degrees-of-freedom (DOF) serial manipulators with offset or reduced wrists, which is mainly due to the complex, highly nonlinear, and coupled IK equations. In order to solve this problem, an efficient IK algorithm called hierarchical iterative inverse kinematic algorithm (HIIKA) is proposed in this paper. This novel IK solution algorithm consists of two-level iterations. The first-level iteration can achieve accurate initial estimates through an extended heuristic iterative method that proposed in this paper. The second-level iteration calculates all joint angles based on the results of the first-level iteration. To evaluate the performance of the HIIKA, experiments were carried out with a six-DOF manipulator with a two-DOF reduced wrist. The results obtained demonstrate the advancement and excellence of the HIIKA in terms of its convergence, accuracy, computational efficiency, and multiple solutions. The HIIKA provides a new tool for the analysis and application of manipulators with offset or reduced wrists.

Building covariance matrices with the desired structure

The problem of building a covariance matrix by fixing their diagonal values (variances) and all or a subset of its eigenvalues has been solved in different ways in the literature. In this paper we propose an iterative heuristic method to build such covariance matrix when a subset of its covariances is also chosen from the user. This provides a more flexible approach than those available in the literature for designing covariance matrices with the desired structure. As in other related approaches, the proposal can be useful for testing the performance of chemometric methods with data sets matching the theoretical conditions for their applicability or checking their robustness when the hypothesized properties fail.

Multiple biological sequence alignment in heterogeneous multicore clusters with user-selectable task allocation policies

Multiple Sequence Alignment (MSA) is an important problem in Bioinformatics that aims to align more than two sequences in order to emphasize similarity regions. This problem is known to be NP-Hard, so heuristic methods are used to solve it. DIALIGN-TX is an iterative heuristic method for MSA that generates alignments by concatenating ungapped regions with high similarity. Usually, the first phase of MSA algorithms is parallelized by distributing several independent tasks among the nodes. Even though heterogeneous multicore clusters are becoming very common nowadays, very few task allocation policies were proposed for this type of architecture. This paper proposes an MPI/OpenMP master/slave parallel strategy to run DIALIGN-TX in heterogeneous multicore clusters, with several allocation policies. We show that an appropriate choice of the master node has great impact on the overall system performance. Also, the results obtained in a heterogeneous multicore cluster composed of 4 nodes (30 cores), with real sequence sets show that the execution time can be drastically reduced when the appropriate allocation policy is used.

The impacts of capabilities and constraints of generating units on simultaneous scheduling of energy and primary reserve

Frequency control, as an ancillary service, is usually provided by generation reserves. Modern generating units have special technical capabilities; e.g., their governor operation mode can be selected to be either active or passive, their ramp rate can be selected to be either normal or fast, etc. On the other hand, generating units have some technical constraints; e.g. some generating units cannot participate in primary frequency control at their capacity limits. In this paper, operational capabilities and constraints of generating units are incorporated in a “simultaneous scheduling of energy and primary reserve” problem. Furthermore, a heuristic iterative method (based on genetic algorithm) is proposed to obtain the optimal scheduling. The impacts of capabilities and constraints on scheduling are investigated through simulation studies. Simulation results depicts that taking these capabilities and constraints of generating units into account, not only reduces the total operational cost of generating units, but also will end up with a feasible solution for the system, even in cases where the previously proposed methods fail.

Multi-source facility location–allocation and inventory problem

We consider a joint facility location–allocation and inventory problem that incorporates multiple sources of warehouses. The problem is motivated by a real situation faced by a multinational applied chemistry company. In this problem, multiple products are produced in several plants. Warehouse can be replenished by several plants together because of capabilities and capacities of plants. Each customer in this problem has stochastic demand and certain amount of safety stock must be maintained in warehouses so as to achieve certain customer service level. The problem is to determine number and locations of warehouses, allocation of customers demand and inventory levels of warehouses. The objective is to minimize the expected total cost with the satisfaction of desired demand weighted average customer lead time and desired cycle service level. The problem is formulated as a mixed integer nonlinear programming model. Utilizing approximation and transformation techniques, we develop an iterative heuristic method for the problem. An experiment study shows that the proposed procedure performs well in comparison with a lower bound.

Using an Interactive Approach to Finding Right Tutors on P2P Tutoring Grids

The e-Tutors Project supported by MoE, Taiwan, provides remote tutoring service for pupils of rural areas. The preliminary result shows that the learning performance of students has been improved. However, for this service to further assist rural students, the goal of adaptive learning has to be considered in tutor assignment process. Hence, a P2P Tutoring Grid is proposed for the sharing of voluntary tutor resources. In this work, we formulate the tutor finding problem and propose an interactive and iterative heuristic method. The proposed approach consists of two phases: construction phase and search phase. In construction phase, peer information is acquired and managed in a decentralized manner. In search phase, the intention of a query is verified interactively and iteratively to find right tutors. A prototype system has been developed and experiments have been conducted to evaluate the performance of this approach. The experimental results show that the interactive algorithm performs well in peer-to-peer networks with low trust and availability. Also, a survey of satisfaction shows that the proposed method is more user-friendly.

Biodiversity Hotspots from a Multigroup Perspective: Mosses and Senecios in the Transmexican Volcanic Belt

Geographical information for 703 mosses and Senecios (species of the tribe Senecioneae, Asteraceae) has been analyzed to identify patterns of species richness in the Transmexican Volcanic Belt (TMVB) of Mexico. Because the TMVB holds a high proportion of these taxa (596 mosses out of 980, and 107 Senecios out of 228) in the country, it is considered a high diversity area. However, the biodiversity is not uniform, as shown by the number of species in each of seventy nine 0.5° latitude and 0.5° longitude cells covering the surface area of the mountain range. Nineteen cells were identified as hotspots and further analysis showed that 11 of such hotspots were common to both groups. The application of a heuristic iterative method and a complementarity criterion indicated that the selection of 18 cells would conserve the total diversity of mosses and Senecios found in such hotspots.

The flow of viscoplastic material between two concentric spheres

The motion of a viscoplastic medium between two concentric spheres is considered upon rotation of one sphere with constant angular velocity. This problem is solved by an heuristic iterative method. The boundary of the stagnation zones is found and its specific shape is shown. The flow characteristics versus the parameter of the medium are obtained.

Application of partitioning techniques for decomposing large-scale electric power networks

Two efficient heuristic algorithms for solving cluster problems associated with partitioning of power networks are presented in this paper. Both algorithms are divided into two stages. In the first stage, an initial partition is created based on the electrical distance among system buses. The second stage involves interchanging pairs of buses among the various clusters of the initial partition. The first algorithm solves an optimal k-decomposition problem. In the optimal k-decomposition, the partitioning of a network into k clusters of buses is performed by maximizing the number of uncut links among clusters. This type of decomposition is known to be equivalent to a 0–1 quadratic programming problem which is approximated by a linear transportation problem. By defining a link weight as the electrical distance between linking buses, the algorithm clusters strongly-connected buses together while weakly-connected buses are placed in different clusters. The second algorithm solves the placement problem of n-connected buses in a k-dimensional Euclidean space; such a problem is reduced to finding k eigenvectors of a connectivity matrix, defined as the bus admittance matrix. The node interchange is an iterative heuristic method that can be used to improve an initial partition, such as that obtained by either the k-decomposition technique or the eigenvector approach. The method moves one bus at a time, from one cluster of the initial partition to another, in an attempt to maximize the total electric distance among clusters of the final partition. Applications of the proposed algorithms to both small and medium-size power systems, and comparing the results with those obtained in another study, are illustrated in this paper.

A heuristic algorithm for power-network clustering

An efficient heuristic algorithm for solving cluster problems associated with partitioning of power networks is presented. The algorithm is divided into two stages. The first stage creates an initial partition based on the electrical distance between system buses. The second stage involves interchanging pairs of buses among the various clusters of the initial partition. The first stage solves the placement problem of n connected buses in an r-dimensional Euclidean space; such a problem is reduced to finding r eigenvectors of a connectivity matrix, defined as the bus admittance matrix. The second stage is based on a node interchange technique. The node interchange is an iterative heuristic method that can be used to improve an initial partition. The method moves one bus at a time, from one cluster of the initial partition to another, in an attempt to maximize the total electrical distance between clusters of the final partition. Applications of the proposed algorithm to both small and medium-size power systems are illustrated.

Facility Location on a Sphere

In this paper, we consider a modification of the Weber problem which consists of locating a new facility on a sphere so that the weighted sum of distances to given demand points is minimized. Two ways of measuring distance are used. One is simply the length of shortest arc on the sphere. The other norm, first suggested by Katz and Cooper, may be used to approximate squared arc distance on a hemisphere and also as a rough approximation for arc distance. Several properties of the problem are established. An iterative heuristic method for solving the problem with shortest arc distances is presented.