fundamental-engineering-optimization-methods.pdf

# Formulation the traveling salesman problem is

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Formulation: The traveling salesman problem is formulated as shortest path problem in an undirected weighted graph where the stores represent the vertices of the graph. The problem is then similar to Problem 10.

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Download free eBooks at bookboon.com Click on the ad to read more Fundamental Engineering Optimization Methods 16 Engineering esign Optimization Problem 15: Transportation problem Goods are to be shipped from m supply points with capacities: ݏ ǡ ݏ ǡ ǥ ǡ ݏ ³ to distribution points with demands: ݀ ǡ ݀ ǡ ǥ ǡ ݀ ² Given the transportation cost ܿ ௜௝ for each of the network routes, find the optimum quantities, ݔ ௜௝ ǡ to be shipped along those routes to minimize total shipment cost. Formulation: let ݔ ௜௝ ǡ denote the quantity to be shipped node i to node j ; then, the optimization problem is formulated as: ೔ೕ ݂ ൌ ෍ ܿ ௜௝ ݔ ௜௝ ௜ǡ௝ ± ǣ ෍ ݔ ௜௝ ൌ ݏ ǡ ݅ ൌ ͳǡ ǥ ǡ ݉Ǣ ෍ ݔ ௜௝ ൌ ݀ ǡ ݅ ൌ ͳǡ ǥ ǡ ݊Ǣ ݔ ௜௝ ൒ Ͳ (1.13) Problem 16: Power grid estimation problem Given the measurements of active and reactive power flows ൫݌ ௜௝ ǡ ݍ ௜௝ between nodes i , j and the measurements ݒ of the node voltages in an electric grid, obtain the best estimate of the state of the grid, i.e., solve for complex node voltages: ൌ ݒ סߜ ǡ where ߜ represents the phase angle. “The perfect start of a successful, international career.” CLICK HERE to discover why both socially and academically the University of Groningen is one of the best places for a student to be Excellent Economics and Business programmes at:
Download free eBooks at bookboon.com Fundamental Engineering Optimization Methods 17 Engineering esign Optimization Formulation: let ݒ ҧ ǡ ݌ ҧ ௜௝ ǡ ݍ ௜௝ represent the measured variables, and ݇ ǡ ݇ ௜௝ ǡ ݇ ௜௝ ǡ let respectively, represent the confidence in measurements of the node voltages and the power flows; further let ௜௝ ൌ ݖ ௜௝ סߠ ௜௝ represent the complex impedance between nodes ݅ǡ ݆Ǣ then, power grid state estimation problem is formulated as (Pedregal, p. 11): ǡఋ ݂ ൌ ෍ ݇ ሺݒ െ ݒ ҧ ൅ ෍ ݇ ௜௝ ൫݌ ௜௝ െ ݌ ҧ ௜௝ ௜ǡ௝ ൅ ෍ ݇ ௜௝ ൫ݍ ௜௝ െ ݍ ௜௝ ௜ǡ௝ 6XEMHFW WR± ݌ ௜௝ ೔ೕ ߠ ௜௝ ೔ೕ ൫ߠ ௜௝ ൅ ߜ െ ߜ ݍ ௜௝ ೔ೕ ߠ ௜௝ ೔ೕ ሺߠ ௜௝ ൅ ߜ െ ߜ (1.14) Problem 17 Classification problem Given a set of data points: א Թ ǡ ݅ ൌ ͳǡ ǥ ǡ ݊ǡ with two classification labels: ݕ א ሼͳǡ െͳሽ ³ find the equation of a hyperplane separating data into classes with maximum inter-class distance .

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