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Approximate Dynamic Programming: A New Paradigm for Process Control & Optimization
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
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
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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
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15. Key to Success of ADP Store – Search – Averaging e.g.) nearest neighbor Convergence of Off-line Learning
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
