ZEIT4700 – S1, 2016 Mathematical Modeling and Optimization

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Presentation transcript:

ZEIT4700 – S1, 2016 Mathematical Modeling and Optimization School of Engineering and Information Technology

Mathematical Modelling & Optimization - basics What is Optimization ? Systematic process of identifying design variables so as to maximimze/minimize “objectives” of a design. Why/when is it needed? When best performance resources/time/cost are limited. When design boundaries need to be pushed. (So, all the time!) How to define an optimization problem ? Objective functions (What is being optimized?) Variables (What defines/controls a design?) Constraints (What conditions must be satisfied?)

Optimization – types / classification Single-objective / multi-objective Unimodal / multi-modal Single / multi - variable Discrete / continuous / mixed variables Constrained / unconstrained Deterministic / Robust Single / multi-disciplinary

Optimization - methods Classical Gradient based Simplex Heuristic / metaheuristics Evolutionary Algorithms Simulated Annealing Ant Colony Optimization Particle Swarm Optimization .

Approximations Design of experiments Surrogate Models / Meta-models

Robust optimization Optimization under uncertainties, e.g. manufacturing tolerance Formulation Uncertainty Quantification Search algorithms

Assessment Project 1 (Individual reports) (~10%) Identify and analyze an optimized object in nature Project 2 (Individual) (~25%) Formulate and solve a design problem of your interest Viva (~15%) (Must demonstrate adequate understanding of content and projects undertaken)

Resources Course material and suggested reading can be accessed at http://www.mdolab.net/Hemant/design-2.html