Discrete Optimization - Discrete Mathematics - Lecture Slides, Slides of Discrete Mathematics

Download Discrete Optimization - Discrete Mathematics - Lecture Slides and more Slides Discrete Mathematics in PDF only on Docsity! 1 Discrete Optimization Docsity.com 2 The relationship between counting techniques/graph theory and discrete optimization Adding a goal (objective function) to a counting situation or a graph model makes it a discrete optimization problem. Docsity.com 5 Graphs and discrete optimization Adding a goal (objective function) about the amount of some entity in a network makes the network model a discrete (network) optimization problem. • Goal: Build a network satisfying certain requirements with minimal cost • Move some entity (electricity, a consumer product, people, information) from one point to another in underlying network as efficiently as possible: – Provide good service to the network users – Use the network facilities efficiently Docsity.com 6 Ingredients of some common physical networks Application Physical analog of nodes Physical analog of arcs Flow Transportation systems Cities, intersections, facilities Highways, airline routes Vehicles, passengers Communication systems Phones, computers Cables, fiber optic links Voice messages, data Hydraulic systems Pumping stations, reservoirs Pipelines Water, gas, oil Docsity.com 7 How to solve discrete optimization problems? Design algorithms! The word algorithm refers to a step-by-step method for performing some action. Some examples of algorithms in everyday life: • Food preparation recipes • Driving directions • Directions for assembling equipment • Instructions for filling out income tax forms We will study algorithms for solving discrete optimization problems Docsity.com