A separable approximation dynamic programming algorithm for economic dispatch with transmission losses

Copyright @ 2002 University of Belgrade - This article can be accessed from the link below.The standard way to solve the static economic dispatch problem with transmission losses is the penalty factor method. The problem is solved iteratively by a Lagrange multiplier method or by dynamic programming, using values obtained at one iteration to compute penalty factors for the next until stability is attained. A new iterative method is proposed for the case where transmission losses are represented by a quadratic formula (i.e., by the traditional B-coefficients). A separable approximation is made at each iteration, which is much closer to the initial problem than the penalty factor approximation. Consequently, lower cost solutions may be obtained in some cases, and convergence is faster

Primal-dual variable neighborhood search for the simple plant-location problem

Copyright @ 2007 INFORMSThe variable neighborhood search metaheuristic is applied to the primal simple plant-location problem and to a reduced dual obtained by exploiting the complementary slackness conditions. This leads to (i) heuristic resolution of (metric) instances with uniform fixed costs, up to n = 15,000 users, and m = n potential locations for facilities with an error not exceeding 0.04%; (ii) exact solution of such instances with up to m = n = 7,000; and (iii) exact solutions of instances with variable fixed costs and up to m = n = 15, 000.This work is supported by NSERC Grant 105574-02; NSERC Grant OGP205041; and partly by the Serbian Ministry of Science, Project 1583

Improvements and comparison of heuristics for solving the uncapacitated multisource Weber problem

Copyright @ 2000 INFORMSThe multisource Weber problem is to locate simultaneously m facilities in the Euclidean plane to minimize the total transportation cost for satisfying the demand of n fixed users, each supplied from its closest facility. Many heuristics have been proposed for this problem, as well as a few exact algorithms. Heuristics are needed to solve quickly large problems and to provide good initial solutions for exact algorithms. We compare various heuristics, i.e., alternative location-allocation (Cooper 1964), projection (Bongartz et al. 1994), Tabu search (Brimberg and Mladenovic 1996a), p-Median plus Weber (Hansen ct al. 1996), Genetic search and several versions of Variable Neighbourhood search. Based on empirical tests that are reported, it is found that most traditional and some recent heuristics give poor results when the number of facilities to locate is large and that Variable Neighbourhood search gives consistently best results, on average, in moderate computing time.This study was supported by the Department of National Defence (Canada) Academic Research; Office of Naval Research Grant N00014-92-J-1194, Natural Sciences and Engineering Research Council of Canada Grant GPO 105574 and Fonds pour la Formation des Chercheurs et l’Aide a la Recherche Grant 32EQ 1048; and by an International Postdoctoral Fellowship of the Natural Sciences and Engineering Research Council of Canada, Grant OGPOO 39682

An interior point algorithm for minimum sum-of-squares clustering

Copyright @ 2000 SIAM PublicationsAn exact algorithm is proposed for minimum sum-of-squares nonhierarchical clustering, i.e., for partitioning a given set of points from a Euclidean m-space into a given number of clusters in order to minimize the sum of squared distances from all points to the centroid of the cluster to which they belong. This problem is expressed as a constrained hyperbolic program in 0-1 variables. The resolution method combines an interior point algorithm, i.e., a weighted analytic center column generation method, with branch-and-bound. The auxiliary problem of determining the entering column (i.e., the oracle) is an unconstrained hyperbolic program in 0-1 variables with a quadratic numerator and linear denominator. It is solved through a sequence of unconstrained quadratic programs in 0-1 variables. To accelerate resolution, variable neighborhood search heuristics are used both to get a good initial solution and to solve quickly the auxiliary problem as long as global optimality is not reached. Estimated bounds for the dual variables are deduced from the heuristic solution and used in the resolution process as a trust region. Proved minimum sum-of-squares partitions are determined for the rst time for several fairly large data sets from the literature, including Fisher's 150 iris.This research was supported by the Fonds National de la Recherche Scientifique Suisse, NSERC-Canada, and FCAR-Quebec

Variable neighbourhood search for the minimum labelling Steiner tree problem

We present a study on heuristic solution approaches to the minimum labelling Steiner tree problem, an NP-hard graph problem related to the minimum labelling spanning tree problem. Given an undirected labelled connected graph, the aim is to find a spanning tree covering a given subset of nodes of the graph, whose edges have the smallest number of distinct labels. Such a model may be used to represent many real world problems in telecommunications and multimodal transportation networks. Several metaheuristics are proposed and evaluated. The approaches are compared to the widely adopted Pilot Method and it is shown that the Variable Neighbourhood Search that we propose is the most effective metaheuristic for the problem, obtaining high quality solutions in short computational running time

Constructive Heuristics for the Minimum Labelling Spanning Tree Problem: a preliminary comparison

This report studies constructive heuristics for the minimum labelling spanning tree (MLST) problem. The purpose is to find a spanning tree that uses edges that are as similar as possible. Given an undirected labeled connected graph (i.e., with a label or color for each edge), the minimum labeling spanning tree problem seeks a spanning tree whose edges have the smallest possible number of distinct labels. The model can represent many real-world problems in telecommunication networks, electric networks, and multimodal transportation networks, among others, and the problem has been shown to be NP-complete even for complete graphs. A primary heuristic, named the maximum vertex covering algorithm has been proposed. Several versions of this constructive heuristic have been proposed to improve its efficiency. Here we describe the problem, review the literature and compare some variants of this algorithm

Heuristics based on greedy randomized adaptive search and variable neighbourhood search for the minimum labelling spanning tree problem

This paper studies heuristics for the minimum labelling spanning tree (MLST) problem. The purpose is to find a spanning tree using edges that are as similar as possible. Given an undirected labelled connected graph, the minimum labelling spanning tree problem seeks a spanning tree whose edges have the smallest number of distinct labels. This problem has been shown to be NP-complete. A Greedy Randomized Adaptive Search Procedure (GRASP) and different versions of Variable Neighbourhood Search (VNS) are proposed. They are compared with other algorithms recommended in the literature: the Modified Genetic Algorithm and the Pilot Method. Nonparametric statistical tests show that the heuristics based on GRASP and VNS outperform the other algorithms tested. Furthermore, a comparison with the results provided by an exact approach shows that we may quickly obtain optimal or near-optimal solutions with the proposed heuristics

Solving the minimum labelling spanning tree problem using hybrid local search

Given a connected, undirected graph whose edges are labelled (or coloured), the minimum labelling spanning tree (MLST) problem seeks a spanning tree whose edges have the smallest number of distinct labels (or colours). In recent work, the MLST problem has been shown to be NP-hard and some effective heuristics (Modified Genetic Algorithm (MGA) and Pilot Method (PILOT)) have been proposed and analyzed. A hybrid local search method, that we call Group-Swap Variable Neighbourhood Search (GS-VNS), is proposed in this paper. It is obtained by combining two classic metaheuristics: Variable Neighbourhood Search (VNS) and Simulated Annealing (SA). Computational experiments show that GS-VNS outperforms MGA and PILOT. Furthermore, a comparison with the results provided by an exact approach shows that we may quickly obtain optimal or near-optimal solutions with the proposed heuristic

An oil pipeline design problem

Copyright @ 2003 INFORMSWe consider a given set of offshore platforms and onshore wells producing known (or estimated) amounts of oil to be connected to a port. Connections may take place directly between platforms, well sites, and the port, or may go through connection points at given locations. The configuration of the network and sizes of pipes used must be chosen to minimize construction costs. This problem is expressed as a mixed-integer program, and solved both heuristically by Tabu Search and Variable Neighborhood Search methods and exactly by a branch-and-bound method. Two new types of valid inequalities are introduced. Tests are made with data from the South Gabon oil field and randomly generated problems.The work of the first author was supported by NSERC grant #OGP205041. The work of the second author was supported by FCAR (Fonds pour la Formation des Chercheurs et l’Aide à la Recherche) grant #95-ER-1048, and NSERC grant #GP0105574

Adopting basic ski technique of alpine skiing of the children aged 5-8 years

Istraživanje je sprovedeno na uzorku ispitanika (n=100), dece skijaša početnika, uzrasta 5-8 godina, pri čemu je uzorak podeljen na dva subuzorka, decu uzrasta 5-6 i decu 7-8 godina. Cilj je bio da se utvrdi da li postoje razlike prema uspešnosti usvajanja osnovne tehnike skijanja u odnosu na morfološke karakteristike, motoričke sposobnosti, pol, uzrast i učešće u organizovanim sportskim programima ispitanika. Procena uspešnosti izvršena je nakon šestodnevne obuke od strane tročlane ekspertske komisije na osnovu tri elementa tehnike, zaustavljanje u „plugu“, zaokret ka padini i vijuganje. Značajne razlike u uspešnosti usvajanja u odnosu na morfološke varijable kod ispitanika 5-6 godina su dobijene kod varijabli masa tela i obim desne natkolenice, dok su kod ispitanika uzrasta 7-8 uočene samo kod varijable masa tela. Motoričke sposobnosti procenjene su baterijom od 10 testova. Rezultati ukazuju da kod ispitanika 5-6 godina ne postoji značajna razlika u uspešnosti usvajanja u odnosu na motoričke sposobnosti. Kod ispitanika 7-8 godina dokazana je statistički značajna razlika između nekih grupa prema uspešnosti usvajanja tehnike skijanja. Ispitanici koji su tehniku skijanja usvojili uspešno postigli su dobre rezultate u testovima poligon natraške, koraci u stranu dokorakom, stajanje na levoj nozi poprečno na klupici za ravnotežu, skok uvis, taping nogom za 15 sec i podizanje trupa za 60 sekundi i srednje rezultate na testu trčanje na 20 m i stajanje na desnoj nozi poprečno na klupici za ravnotežu. Nije uočena značajna razlika u uspešnosti usvajanja između dečaka i devojčica., dok deca koja imaju iskustvo u organizovanim sportskim programima uspešnije usvajaju osnovnu tehniku skijanja. Značajana razlika u uspešnosti usvajanja uočena je između dece različitih uzrasnih grupa, deca uzrasta 7-8 godina su značajno uspešnije usvojili osnovnu tehniku skijanja u odnosu na decu uzrasta 5-6 godina.This research was conducted on 100 participants, children aged 5-8 years, all ski beginners. The sample was divided into two subsamples, children aged 5-6 and 7-8 years old. The goal of the research was to determine the possible differences in successfulness of adopting the basic ski technique in regard to children’s morphological characteristics, motor abilities, gender, age and participation in organized sports activities. After completing the six days training, the successfulness of performing the basic elements of the ski technique was determined through the following tasks: stopping in a snow-plough, uphill turn and turns around the posted marks by three independent judges. Significant differences in adopting basic ski technique in regard to morphological characteristics in children 5-6 years were obtained for the variables body mass, circumference of the right thigh and upper arm skinfold thickenss, while in children aged 7-8 years were observed only in body mass variable. The assessment of motor status was conducted using the battery of ten standardized motor tests. The research results show no significant differences in success of adopting basic ski technique compared to the examined motor abilities in children aged 5-6. Among the participants aged 7-8, significant differences in successful adoption of ski technique were noticed, the participants who successfully adopted the basic ski technique also achieved good results at tests: polygon backwards, side steps, balancing on left leg perpendicular on balance board, vertical jump, foot tapping and sit-ups and medium results at tests 20 m run and balancing on right leg perpendicular on balance board. There was no significant difference in the success of adopting basic ski technique between boys and girls, while children with experience in organized sports programs more successfully acquire the basic ski technique. A significant difference was observed between the children of different age groups, children aged 7-8 years were significantly more successfully adopted the basic techniques of skiing in relation to children aged 5-6 years