Approximate Dynamic Programming: A New Paradigm for Process Control & Optimization
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1. Approximate dynamic programming (ADP) is a computationally feasible approach for handling large-scale and uncertain systems like process industries more effectively than conventional tools. 2. ADP works by approximating the optimal "scores" or value functions for every system state and action offline through simulations, rather than computing them exactly. This allows for manageable online computation. 3. By handling uncertainties through simulations during offline learning, ADP can provide improved policies for decision making under uncertainty compared to approaches that ignore uncertainties.
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![Regulatory Control LC LC FC FC Feed Keep flow rates, levels, .. @ specified values Decisions: Valve opening [sec] Uncertainties: Valve dynamics, resolutions](https://image.slidesharecdn.com/approximate-dynamic-programming-a-new-paradigm-for-process-control-optimization-7511/85/Approximate-Dynamic-Programming-A-New-Paradigm-for-Process-Control-Optimization-5-320.jpg)
![Simulations X = [s 1 , s 2 , s 3 , s 4 , s 5 , z 1 , z 2 , z 3 , z 4 , z 5 , L 1 , L 2 , t] Which task is performed? Result of the most recent task Duration 230 billion points Simulations (150000) 1. High Success Probability Task First 2. Short Duration Task First 3. High Reward Project First Sampled X 3.7 x 10 5 probabilistic description](https://image.slidesharecdn.com/approximate-dynamic-programming-a-new-paradigm-for-process-control-optimization-7511/85/Approximate-Dynamic-Programming-A-New-Paradigm-for-Process-Control-Optimization-19-320.jpg)
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Dynamic Programmingparamalways Dynamic programming is a recursive optimization technique used to solve problems with interrelated decisions. It breaks the problem down into sequential steps, where each step builds on the solutions to previous steps. The optimal solution is determined by working through each step in order. Dynamic programming has advantages like computational savings over complete enumeration and providing insight into problem nature. However, it also has disadvantages like requiring more expertise, lacking general algorithms, and facing dimensionality problems for applications with multiple states.
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- 1. Approximate Dynamic Programming Jong Min Lee Chemical and Materials Engineering University of Alberta A New Paradigm for Process Control & Optimization
- 2. How does a process industry run? Feedstock Purchase Plant / Unit Operation Inventory Control Supply Chain Management
- 3. What decisions do we make in process industries? Regulatory Control Real Time Optimizer Production Planning Strategic Planning Customer Plant Scheduling Advaced Process Control $ $ $ $ sec min ~ day week ~ month month ~ year
- 4. Ethylene Plant Furnaces Primary Fractionator Quench Tower Charge Gas Compressor Chilling Demethanizer Deethanizer Ethylene Fractionator Debutanizer Propylene Fractionator Depropanizer Fuel Oil Hydrogen Methane Ethylene Ethane Propylene Propane B - B Gasoline Light H-C Naphtha Feedstock
- 5. Regulatory Control LC LC FC FC Feed Keep flow rates, levels, .. @ specified values Decisions: Valve opening [sec] Uncertainties: Valve dynamics, resolutions
- 6. Scheduling and Planning Demands Inventories Ethylene Plant Feedstock Market Blending Daily ~ Monthly Maximize CSL and Profit Decisions: Purchase / Blending / Unit Maintenance / Inventories / Distributions Uncertainties: Market Prices / Raw Mat. Properties / Unit Failures / Demands… ? ? ? ? ETY PPY ETA BBP GSL
- 7. All the decision-making problems are fundamentally SAME We are concerned with future performance Future Time Profit
- 8. Conventional Tools Observer Decision Feedforward New Information Real outcome Optimizer Model Constraints Objective Function max t = k+ 1 k+p performance Real World Future Past k k+ 1 k+p time
- 9. What are the issues of conventional tools? 1. They ignore UNCERTAINTIES. - Can yield wrong decisions 2. They put too much efforts ONLINE. - Can be late for timely decision
- 10. Analogy to Chess Me Opponent (Plant) Model Predictive Control Mixed Integer Programming h g f e d c b a 1 2 3 4 5 6 7 8 Opponent’s Move New Piece Position Exponential Explosion
- 11. Unbeatable Chess Player – Dynamic Programming Score (Value) for every feasible position Pick up the action giving the best “score” (position: mine & the opponent’s) Already calculated (offline) before we start a game h g f e d c b a 1 2 3 4 5 6 7 8 Expected Optimal Value Set of Next Piece Positions Decision u1 x1 45 u2 x2 55
- 12. How do we find the “scores”? Discretization of entire state & action space INFEASIBLE = J ( x ) min u ( x , u ) J ( x ’ ) + E x 1 x 2 x 3 u 1 u 2 u 3
- 13. Can we find the scores “approximately”? Converged Value Fcn On-line Implementation Simulations w/ initial policies Value Function Approximation Iterative Improvement Off-line
- 14. Advantages of Approximate Dynamic Programming Manageable online computation Applicable to practical systems Stochastic systems as well as deterministic system All about simulation! Improved policy
- 15. Key to Success of ADP Store – Search – Averaging e.g.) nearest neighbor Convergence of Off-line Learning
- 16. Resource-Constrained Project Scheduling J. Choi, et al. Computers and Chemical Engineering , 28 (2004)
- 17. Drug Discovery / Development Discovery Development Market Drug 1 Drug 2 Drug n Phase 1 Phase 2 a/b Phase 3 Submission & Approval 0.5 – 2 yrs 1 – 2 yrs 1.5 – 3.5 yrs 2.5 – 4 yrs 0.5 – 2 yrs $2-4 MM $1-3 MM $5-25 MM $50-250 MM $5-20 MM Pre-clinical Development R&D takes 6.5 – 13.5 years 60 – 300 million $
- 18. Problem Complexity I 1 I 2 P 1 I 3 I 4 P 2 I 5 I 6 I 7 P 3 I 8 I 9 I 10 P 4 I 11 I 12 P 5 Drug 1 Drug 2 Drug 3 Drug 4 Drug 5 Success/Failure, Duration, Cost 1.2 x 10 9 scenarios 5 3 6 6 5 3 7 4 5 4 6 3 3 8 4 3 5
- 19. Simulations X = [s 1 , s 2 , s 3 , s 4 , s 5 , z 1 , z 2 , z 3 , z 4 , z 5 , L 1 , L 2 , t] Which task is performed? Result of the most recent task Duration 230 billion points Simulations (150000) 1. High Success Probability Task First 2. Short Duration Task First 3. High Reward Project First Sampled X 3.7 x 10 5 probabilistic description
- 20. ADP improved on the starting policies 10000 realizations 0 4000 8000 12000 H1 H2 H3 ADP
- 22. If you ignore uncertainties… y(k+1) = y(k) + b u(k) + e(k+1) parameter change noise enters
- 23. ADP “actively” handles uncertainties Output & Input Parameter Estimate & Variance Active probing at t=t b ( 10 ) : t e =15 Decrease of parameter uncertainty t=10: parameter changes, t=15: exogenous noise enters
- 24. Summary ADP is a computationally feasible approach to large-scale and uncertain systems and provides an improved solution “ ”