The University of Southampton
Courses

# FEEG6009 Design Search and Optimisation (DSO) - Principles, Methods, Parameterizations and Case Studies

## Module Overview

This module introduces students to formal design search and optimization (DSO) approaches using a mixture of lectures covering theory and practice and a series of worked case studies with student participation.

### Aims and Objectives

#### Learning Outcomes

##### Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

• the basic elements of single and multi-variable optimizers;
• the ways in which these simple elements can be combined to provide solutions to DSO problems
• the ways in which problem parameters can be used to formulate design intent in DSO problems;
• the issues confronting engineers as they seek usable DSO approaches;
• the ways in which CAD tools can be used to formulate design intent in DSO problems.
• the ways in which various tools can be brought together to tackle realistic DSO problems via the use of bespoke workflows;
• the issues confronting engineers as they seek practical DSO approaches.
##### Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

• more fully understand the components of a successful DSO approaches to design;
• make intelligent choices among the available DSO approaches;
• evaluate the utility and robustness of DSO produced designs.
##### Subject Specific Practical Skills

Having successfully completed this module you will be able to:

• set-up and solve simple DSO problems using a range of software tools including FEA codes and Excel.

### Syllabus

Design Search and Optimization (DSO) (1 lecture): • Beginnings. • A Taxonomy of Optimization. • A Brief History of Optimization Methods. • The Place of Optimization in Design – Commercial Tools. Geometry Modelling & Design Parameterization (2 lectures): • The Role of Parameterization in Design. • Discrete and Domain Element Parameterizations. • NACA Airfoils. • Spline Based Approaches. • Partial Differential Equation and Other Analytical Approaches. • Basis Function Representation. • Morphing. • Shape Grammars. • Mesh Based Evolutionary Encodings. • CAD Tools v's Dedicated Parameterization Methods. Single Variable Optimizers – Line Search (1 lecture): • Unconstrained Optimization with a Single Real Variable. • Optimization with a Single Discrete Variable. • Optimization with a Single Non-Numeric Variable. Multi-Variable Optimizers (2 lectures): • Population versus Single Point Methods. • Gradient-based Methods. - Newton's Method. - Conjugate Gradient Methods. - Quasi-Newton or Variable Metric Methods. • Noisy/Approximate Function Values. • Non-Gradient Algorithms. - Pattern or Direct Search. - Stochastic and Evolutionary Algorithms. • Termination and Convergence Aspects. Constrained Optimization (1 lecture): • Problem Transformations • Lagrangian Multipliers • Feasible Directions Method • Penalty Function Methods • Combined Lagrangian and Penalty Function Methods • Sequential Quadratic Programming • Chromosome Repair Meta-models and Response Surface Methods (1 lecture): • Global versus Local Meta-models. • Meta-modelling Tools. • Simple RSM Examples. Combined Approaches – Hybrid Searches, Meta-heuristics(1 lecture): • Glossy – a Hybrid Search Template. • Meta-heuristics – Search Workflows. • Visualization – understanding the results of DSO. Multi-objective Optimization (1 lecture): • Multi-objective Weight Assignment Techniques. • Methods for Combining Goal Functions, Fuzzy Logic & Physical Programming. • Pareto Set Algorithms. • Nash Equilibria. Robustness (1 lecture): • Robustness versus Nominal Performance. • Evolutionary Algorithms for Robust Design. • Robustness Metrics. - Noisy Phenotype One -- Tsutusi and Ghosh's Method (NP). - Noisy Phenotype Two -- Modified Tsutusi and Ghosh Method (NP2). - Design of Experiment One -- One-at-a-time Experiments(OAT). - Design of Experiments Two and Three -- Orthogonal Arrays (L64 & L81). • Comparison of Metrics. Problem Classification (1 lecture): • Run-time. • Deterministic v's Probabilistic Analyses. .• Number of Variables to be explored. • Goals and Constraints Initial Search Process Choice (1 lecture): External Speakers (2 lectures): Case studies from industry • Case study 1: The design of an encastre cantilever beam. (2 lectures): This isbased around simple Euler-Bernoulli beam theory and Excel to set up and solve a simple structures DSO problem. Each student pairing tackles a different set of boundary conditions and the whole class’s studies then allow a Pareto Front to be constructed illustrating which pairings have produced Pareto optimal designs and which have produced sub-optimal designs. This is a very simple case study just to get students used to the whole idea of DSO approaches. • Case study 2: Fast global optimisation. (4 lectures): You will be finding optimum answers to three problems. To allow you to concentrate on optimisation methods rather than software integration these problems will take the form of `black box' MATLAB functions which can be called directly from a suite of MATLAB based optimisers. Your objective is to find the minimum of the three functions in the smallest possible time. To have successfully found the minimum, you must be within one decimal place of the actual minimum (which you don't know!). It is appreciated that you may not have had much experience with MATLAB, so two demo .m files are provided which include almost all of the commands you will need to use. • Case study 3: Global versus local search methods (4 lectures): An airplane wing design problem will be used to demonstrate the differences between local and global search methods. A key element of this study concerns the fixed computational budget often faced in real engineering problems. It is not necessary to have to have an aerodynamics background to follow this design study. • Case study 4: Multi-objective design problem. (6 lectures): For this final case study, a multi-objective design problem will be described, which will have to be solved and presented during the course of the laboratory sessions. Students will be free to employ any method(s) learnt earlier in the course, or from elsewhere. • Reserve Case study – may be substituted in for case studies 2-4: Geometry optimisation: A problem from biology. Certain segments in the human arterial system produce a haemodynamic environment that is susceptible to disease. The associated narrowing of arteries from atherosclerosis can lead to serious health problems, and possibly fatality. An increasingly popular method for treating atherosclerosis involves the insertion of a scaffold (clinically called a stent) into the diseased artery to recover and maintain its shape. This case study will demonstrate how Solidworks can be used as a complete problem solving environment for the design of a relatively simple stent. This will require the use of parametric geometry definition, design tables, configuration changes, finite element analysis (FEA), and the built-in optimiser will be used for the constrained geometry optimisation. MATLAB will be used to support the analysis of results obtained in this introductory exploration of a biological design space, and it will be further used to demonstrate how to setup and use a surrogate modelling approach. • Revision (3 lectures).

### Learning and Teaching

#### Teaching and learning methods

Teaching methods include - Lectures. - Talks by invited speakers from industry. - Computer sessions. Learning activities include - Using the DSO capabilities of the Excel spreadsheet system. - Using a commercial parametric CAD system to prepare a model for FEA based DSO. - Using MATLAB based workflows and optimization toolkits.

TypeHours
Preparation for scheduled sessions18
Revision20
Seminar2
Lecture17
Follow-up work18
Practical classes and workshops17
Total study time150

### Assessment

#### Summative

MethodPercentage contribution
Continuous Assessment 50%
Final Assessment  50%

#### Repeat

MethodPercentage contribution