Optimization-based Analysis and Training of Human Decision Making - PowerPoint PPT Presentation

Sebastian Sager Optimization-based Analysis and Training of Human Decision Making Aussois, January 5–9, 2014 Michael Engelhart Interdisciplinary Center for Scientific Computing Ruprecht-Karls-Universität Heidelberg 1 Sager | Optimization-based Analysis and Training

MODEST: Mathematical Optimization for clinical DEcision Support and Training Sebastian Sager, Magdeburg, Germany Simulators for diseases Decision support systems C L I N I C A L P R A C T I C E Clinical decision training Personalized medicine via optimization Physician training e.g., for cardiac arrhythmia Simulation : warnings and alerts what would happen if...? Probability for Atrial Fibrillation: 85% Optimization : Relevant fit models to patient data scenarios get patient-specific treatment Probability for Atrial Flutter: 93% Simulation : what would happen if... ? get patient-specific diagnosis Optimization : what would be best? Solution Challenges Solution Challenges methodology for optimization methodology for optimization Mixed-integer nonlinear optimal control MINLP MINLP A L G O R I T H M S Uncertainties , e.g., discretization discretization model-plant mismatch Switching Time Optimization patient-specific parameters convexi fi cation OCP MI(N)OCP MI(L)OCP Integrality , e.g., discretization relaxation relaxation which combination of drugs? OCP&MILP NLP OCP Wenckebach or Mobitz block? initialization discretization discretization Global optima needed NLP NLP&MILP adaptive grid re fi nement Theoretical advances New & better algorithms Open source software

Questions Optimization in practice . . . • a key technology for 21st century, enabling progress&prosperity 3 Sager | Optimization-based Analysis and Training

Questions Optimization in practice . . . • a key technology for 21st century, enabling progress&prosperity • risks to increase the gap compared to human decision making 3 Sager | Optimization-based Analysis and Training

Questions Optimization in practice . . . • a key technology for 21st century, enabling progress&prosperity • risks to increase the gap compared to human decision making This talk: can optimization also be used to train humans? 3 Sager | Optimization-based Analysis and Training

Questions Optimization in practice . . . • a key technology for 21st century, enabling progress&prosperity • risks to increase the gap compared to human decision making This talk: can optimization also be used to train humans? Questions to you: • Who thinks to perform better (without algorithms) in finding a good solution to a random combinatorial optimization problem compared to an average citizen? 3 Sager | Optimization-based Analysis and Training

Questions Optimization in practice . . . • a key technology for 21st century, enabling progress&prosperity • risks to increase the gap compared to human decision making This talk: can optimization also be used to train humans? Questions to you: • Who thinks to perform better (without algorithms) in finding a good solution to a random combinatorial optimization problem compared to an average citizen? • Who thinks this has to do with having seen optimal solutions and sensitivities of similar optimization problems? 3 Sager | Optimization-based Analysis and Training

Complex Problem Solving • Humans are asked to solve a given complex problem • Interest of psychologists: correlation to emotion regulation etc. • Gets more attention: included in future PISA evaluations 4 Sager | Optimization-based Analysis and Training

Complex Problem Solving • Humans are asked to solve a given complex problem • Interest of psychologists: correlation to emotion regulation etc. • Gets more attention: included in future PISA evaluations • Most problems nowadays computer-based test-scenarios • Tailorshop: one of the most famous ones (fruitfly of CPS) • Developped in the 1980s (Dörner et al.) 4 Sager | Optimization-based Analysis and Training

Complex Problem Solving • Humans are asked to solve a given complex problem • Interest of psychologists: correlation to emotion regulation etc. • Gets more attention: included in future PISA evaluations • Most problems nowadays computer-based test-scenarios • Tailorshop: one of the most famous ones (fruitfly of CPS) • Developped in the 1980s (Dörner et al.) • Participant has to run shirt company • Round-based scenario • Aim: maximize overall capital of company 4 Sager | Optimization-based Analysis and Training

The IWR Tailorshop [Engelhart, Funke, S., Journal of Computational Science, 2013] m a n a g e i a l s m r e t e m a n u a f m n a c t t u maintenance production r i n g sites + - + + employees machine quality + (shirts) - + production - resources quality shirt + + quality shirts h u m a n r e s o in stock u r + c distribution e s sites wages + - price - + success + per shirt reputation + + + - + motivation of + + employees + - + sales advertising + d + i s demand t r i b u t i maximize o n & m a r k e t i n g overall balance g o a l s Diamonds indicate influence of participant’s decisions. 5 Sager | Optimization-based Analysis and Training

IWR Tailorshop web interface • implementation with AJAX, PHP using a MySQL database • adaptive interface for mobile devices 6 Sager | Optimization-based Analysis and Training

Complex Problems: Complexity Production Resources Human Resources Marketing Distribution 7 Sager | Optimization-based Analysis and Training

Complex Problems: Interdependence Production Resources Human Resources Marketing Distribution 8 Sager | Optimization-based Analysis and Training

Complex Problems: Intransparency Production ? ? ? Resources ? Human ? ? ? Resources Marketing Distribution 9 Sager | Optimization-based Analysis and Training

Complex Problems: Dynamics Wages k k+1 k+2 10 Sager | Optimization-based Analysis and Training

Complex Problems: Dynamics Motivation of Employees Wages Product Quality k k+1 k+2 10 Sager | Optimization-based Analysis and Training

Complex Problems: mixed-integer decisions • Continuous decisions, e.g., wages • Discrete decisions, e.g., open/close a distribution site 11 Sager | Optimization-based Analysis and Training

Optimization and Complex Problem Solving • First: use optimization to define interesting microworld • Bounded solution, multiple local maxima, important / unimportant decisions, . . . 12 Sager | Optimization-based Analysis and Training

Optimization and Complex Problem Solving • First: use optimization to define interesting microworld • Bounded solution, multiple local maxima, important / unimportant decisions, . . . • Second: optimal solution as performance indicator! 12 Sager | Optimization-based Analysis and Training

Optimization and Complex Problem Solving • First: use optimization to define interesting microworld • Bounded solution, multiple local maxima, important / unimportant decisions, . . . • Second: optimal solution as performance indicator! • Simple test-scenarios (e.g. Tower of Hanoi): optimal solution known • Complex test-scenarios: optimal solution unknown • Third: can optimal solutions be used for training? 12 Sager | Optimization-based Analysis and Training

Formulate abstract optimization problem • Same mathematical model (equations) for all tasks • Dynamic model with discrete time k = 0 . . . N • Decisions u k = u ( k ) and states x k = x ( k ) • Scenario specified by initial values x 0 and parameters p 13 Sager | Optimization-based Analysis and Training

Formulate abstract optimization problem • Same mathematical model (equations) for all tasks • Dynamic model with discrete time k = 0 . . . N • Decisions u k = u ( k ) and states x k = x ( k ) • Scenario specified by initial values x 0 and parameters p • First: use optimization to define interesting microworld: → determine initial values x 0 and parameters p 13 Sager | Optimization-based Analysis and Training

Formulate abstract optimization problem • Same mathematical model (equations) for all tasks • Dynamic model with discrete time k = 0 . . . N • Decisions u k = u ( k ) and states x k = x ( k ) • Scenario specified by initial values x 0 and parameters p • First: use optimization to define interesting microworld: → determine initial values x 0 and parameters p • Second and Third: analysis and training → find decisions u k to maximize objective function → Compare participant’s performance to optimal solution → Provide feedback on better choice for learning 13 Sager | Optimization-based Analysis and Training

IWR Tailorshop states States Variable Unit x EM employees person(s) x PS production sites site(s) x DS distribution sites site(s) x SH shirts in stock shirt(s) x PR production shirt(s) x SA sales shirt(s) x DE demand shirt(s) x RE reputation — x SQ shirts quality — x MQ machine quality — x MO motivation of employees — x CA capital M.U. M.U. means monetary units. 14 Sager | Optimization-based Analysis and Training