'Objective function values' diaporamas de présentation

Duality Theory

Duality Theory. LI Xiaolei. Finding the dual of an LP. When taking the dual of a given LP, we refer to the given LP as the primal. If the primal is a max problem, the dual will be a min problem, and vice versa.

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More Classifiers

More Classifiers. Agenda. Key concepts for all classifiers Precision vs recall Biased sample sets Linear classifiers Intro to neural networks. Recap: Decision Boundaries.

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Linear Programming

Linear Programming. A linear programming problem has linear objective function and linear constraint and variables that are restricted to non-negative values. -X 1 +2X 2 -X 3 <=70 2X 1 -2X 3 =50 X 1 -2X 2 2 +4X3<=10 X1+X2+X3=6 2X 1 +5X 2 +X 1 X 2 <=25 3X 1/2 +2X 2 -X 3 >=15.

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Chapter 3 An Introduction to Linear Programming

Chapter 3 An Introduction to Linear Programming. Linear Programming Problem Problem Formulation A Maximization Problem A Minimization Problem Graphical Solution Procedure Extreme Points and the Optimal Solution Special Cases. Linear Programming (LP) Problem.

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Evolutionary Computational Inteliigence

Evolutionary Computational Inteliigence. Lecture 6a: Multimodality. Multimodality. Most interesting problems have more than one locally optimal solution and our goal is to detect all of them. Multi-Objective Problems (MOPs).

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Simplex method (algebraic interpretation)

Simplex method (algebraic interpretation). Add slack variables( ???? ) to each constraint to convert them to equations. (We may refer it as an augmented LP). (1). (2).

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Genetic Algorithms

Genetic Algorithms. Dr. Sadiq M. Sait & Dr. Habib Youssef (special lecture for oometer group) November 2003. Contents. Introduction Basics of GA Genetic Algorithm(s) Schema Theorem and Implicit Parallelism Genetic Algorithm In Practice Other issues A Brief Survey of Applications

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Use duality theory to check if the solution implied by the dictionary is correct.

Use duality theory to check if the solution implied by the dictionary is correct. Maximize x 1 + 3 x 2 + 6 x 3 subject to 1 x 1 + 1 x 2 - 1 x 3 ? 5 1 x 1 + 0 x 2 + 2 x 3 ? 3 0 x 1 + 1 x 2 + 6 x 3 ? 4 x 1 ,x 2 ,x 3 ? 0 X2 = 2+ 3 X3 - 1 X4 + 1 X6

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EMIS 8373: Integer Programming

EMIS 8373: Integer Programming. Refinements to LP-Based Branch-and-Bound updated 31 March 2009 . Divide and Conquer. Optimization problem: z = max{ cx : x ? S }

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VI. Evaluate Model Fit

VI. Evaluate Model Fit. Basic questions that modelers must address are: How well does the model fit the data? Do changes to a model, such as reparameterization, actually improve the model fit? What aspects of the model or data need to be changed to improve model fit?

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Elements of the Heuristic Approach

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