SOL Optimization 1970s 1980s 1990s 2000s 2010s Summary 2020s Algorithms for Constrained Optimization: The Benefits of General-purpose Software Michael Saunders MS&E and ICME, Stanford University California, USA 3rd AI+IoT Business Conference Shenzhen, China, April 25, 2019 Optimization Software 3rd AI+IoT Business Conference, Shenzhen, April 25, 2019 1/39 SOL Optimization 1970s 1980s 1990s 2000s 2010s Summary 2020s SOL Systems Optimization Laboratory George Dantzig, Stanford University, 1974 Inventor of the Simplex Method Father of linear programming Large-scale optimization: Algorithms, software, applications Optimization Software 3rd AI+IoT Business Conference, Shenzhen, April 25, 2019 2/39 SOL Optimization 1970s 1980s 1990s 2000s 2010s Summary 2020s SOL history 1974 Dantzig and Cottle start SOL 1974{78 John Tomlin, LP/MIP expert 1974{2005 Alan Manne, nonlinear economic models 1975{76 MS, MINOS first version 1979{87 Philip Gill, Walter Murray, MS, Margaret Wright (Gang of 4!) 1989{ Gerd Infanger, stochastic optimization 1979{ Walter Murray, MS, many students 2002{ Yinyu Ye, optimization algorithms, especially interior methods This week! UC Berkeley opened George B. Dantzig Auditorium Optimization Software 3rd AI+IoT Business Conference, Shenzhen, April 25, 2019 3/39 SOL Optimization 1970s 1980s 1990s 2000s 2010s Summary 2020s Optimization problems Minimize an objective function subject to constraints: 0 x 1 min '(x) st ` ≤ @ Ax A ≤ u c(x) x variables 0 1 A matrix c1(x) B . C c(x) nonlinear functions @ . A c (x) `; u bounds m Optimization Software 3rd AI+IoT Business Conference, Shenzhen, April 25, 2019 4/39 SOL Optimization 1970s 1980s 1990s 2000s 2010s Summary 2020s 1970s Optimization Software 3rd AI+IoT Business Conference, Shenzhen, April 25, 2019 5/39 SOL Optimization 1970s 1980s 1990s 2000s 2010s Summary 2020s 1970s MS and Bruce Murtagh: MINOS solver (nonlinear objective) George Dantzig: PILOT economic model of US (LP) Alan Manne: ETAMACRO energy model (nonlinear objective) Optimization Software 3rd AI+IoT Business Conference, Shenzhen, April 25, 2019 6/39 SOL Optimization 1970s 1980s 1990s 2000s 2010s Summary 2020s 1980s Optimization Software 3rd AI+IoT Business Conference, Shenzhen, April 25, 2019 7/39 SOL Optimization 1970s 1980s 1990s 2000s 2010s Summary 2020s 1980s MINOS solver (sparse nonlinear constraints) NPSOL solver (dense nonlinear constraints) Optimal Power Flow @ General Electric Aerospace optimization @ NASA, McDonnell-Douglas Optimization Software 3rd AI+IoT Business Conference, Shenzhen, April 25, 2019 8/39 SOL Optimization 1970s 1980s 1990s 2000s 2010s Summary 2020s 1990s Optimization Software 3rd AI+IoT Business Conference, Shenzhen, April 25, 2019 9/39 SOL Optimization 1970s 1980s 1990s 2000s 2010s Summary 2020s 1990s Alan Manne: MERGE greenhouse-gas model (sparse nonlinear constraints) Philip Gill: Aerospace trajectory optimization @ McDonnell-Douglas F-4 Minimum time-to-climb DC-Y SSTO Minimum-fuel landing maneuver Optimization Software 3rd AI+IoT Business Conference, Shenzhen, April 25, 2019 10/39 SOL Optimization 1970s 1980s 1990s 2000s 2010s Summary 2020s Climb to 20,000m Start at sea-level Speed Mach 1 Optimization Software 3rd AI+IoT Business Conference, Shenzhen, April 25, 2019 11/39 SOL Optimization 1970s 1980s 1990s 2000s 2010s Summary 2020s DC-X single-stage-to-orbit prototype 1/3 full-size = 13m tall Optimization Software 3rd AI+IoT Business Conference, Shenzhen, April 25, 2019 12/39 SOL Optimization 1970s 1980s 1990s 2000s 2010s Summary 2020s DC-Y single-stage-to-orbit full-size Taking-off? Landing? Optimization Software 3rd AI+IoT Business Conference, Shenzhen, April 25, 2019 13/39 SOL Optimization 1970s 1980s 1990s 2000s 2010s Summary 2020s Optimization Software 3rd AI+IoT Business Conference, Shenzhen, April 25, 2019 14/39 SOL Optimization 1970s 1980s 1990s 2000s 2010s Summary 2020s Optimization Software 3rd AI+IoT Business Conference, Shenzhen, April 25, 2019 15/39 Don't exceed 3g New constraint needed: Optimum starting altitude = 450m(!) Come back Alan Shephard! SOL Optimization 1970s 1980s 1990s 2000s 2010s Summary 2020s DC-Y landing, 2nd OTIS/NPSOL optimization 1st optimization: starting altitude = 900m 2nd optimization: starting altitude = variable Optimization Software 3rd AI+IoT Business Conference, Shenzhen, April 25, 2019 16/39 Don't exceed 3g Optimum starting altitude = 450m(!) Come back Alan Shephard! SOL Optimization 1970s 1980s 1990s 2000s 2010s Summary 2020s DC-Y landing, 2nd OTIS/NPSOL optimization 1st optimization: starting altitude = 900m 2nd optimization: starting altitude = variable New constraint needed: Optimization Software 3rd AI+IoT Business Conference, Shenzhen, April 25, 2019 16/39 Optimum starting altitude = 450m(!) Come back Alan Shephard! SOL Optimization 1970s 1980s 1990s 2000s 2010s Summary 2020s DC-Y landing, 2nd OTIS/NPSOL optimization 1st optimization: starting altitude = 900m 2nd optimization: starting altitude = variable New constraint needed: Don't exceed 3g Optimization Software 3rd AI+IoT Business Conference, Shenzhen, April 25, 2019 16/39 Come back Alan Shephard! SOL Optimization 1970s 1980s 1990s 2000s 2010s Summary 2020s DC-Y landing, 2nd OTIS/NPSOL optimization 1st optimization: starting altitude = 900m 2nd optimization: starting altitude = variable New constraint needed: Don't exceed 3g Optimum starting altitude = 450m(!) Optimization Software 3rd AI+IoT Business Conference, Shenzhen, April 25, 2019 16/39 SOL Optimization 1970s 1980s 1990s 2000s 2010s Summary 2020s DC-Y landing, 2nd OTIS/NPSOL optimization 1st optimization: starting altitude = 900m 2nd optimization: starting altitude = variable New constraint needed: Don't exceed 3g Optimum starting altitude = 450m(!) Come back Alan Shephard! Optimization Software 3rd AI+IoT Business Conference, Shenzhen, April 25, 2019 16/39 SOL Optimization 1970s 1980s 1990s 2000s 2010s Summary 2020s 2000s Optimization Software 3rd AI+IoT Business Conference, Shenzhen, April 25, 2019 17/39 SOL Optimization 1970s 1980s 1990s 2000s 2010s Summary 2020s 2000s David Saunders, NASA Ames (Calif) Wˇoshu¯angb¯aot¯ai! 1970: visit Stanford for 1 month (now 49 years) Shape optimization Supersonic airliners Trajectory optimization SHARP (next Space Shuttle) Optimization Software 3rd AI+IoT Business Conference, Shenzhen, April 25, 2019 18/39 SOL Optimization 1970s 1980s 1990s 2000s 2010s Summary 2020s OAW oblique all-wing airliner Optimization Software 3rd AI+IoT Business Conference, Shenzhen, April 25, 2019 19/39 SOL Optimization 1970s 1980s 1990s 2000s 2010s Summary 2020s HSCT high speed civil transport Optimization Software 3rd AI+IoT Business Conference, Shenzhen, April 25, 2019 20/39 Trajectory optimization with SNOPT Could always abort to Kennedy, Boston, Gander, or Shannon 4000-mile cross-range capability during reentry Image credit: David Kinney, NASA Ames Research Center SOL Optimization 1970s 1980s 1990s 2000s 2010s Summary 2020s CTV crew transfer vehicle SHARP design (Slender Hypervelocity Aerothermodynamic Research Probes) Aerothermal performance constraint in (Velocity, Altitude) space, used during trajectory optimization with UHTC materials (Ultra High Temperature Ceramics) to avoid exceeding material limits Optimization Software 3rd AI+IoT Business Conference, Shenzhen, April 25, 2019 21/39 SOL Optimization 1970s 1980s 1990s 2000s 2010s Summary 2020s CTV crew transfer vehicle SHARP design (Slender Hypervelocity Aerothermodynamic Research Probes) Aerothermal performance constraint in (Velocity, Altitude) space, used during trajectory optimization with UHTC materials (Ultra High Temperature Ceramics) to avoid exceeding material limits Trajectory optimization with SNOPT Could always abort to Kennedy, Boston, Gander, or Shannon 4000-mile cross-range capability during reentry Image credit: David Kinney, NASA Ames Research Center Optimization Software 3rd AI+IoT Business Conference, Shenzhen, April 25, 2019 21/39 SOL Optimization 1970s 1980s 1990s 2000s 2010s Summary 2020s SNOPT Applications Trajectory optimization Manoeuver ISS Launch 2 satellites Space Station Torque minimization Robot at JPL Radiation therapy Daniel Clemente Control problem Paul Keall Optimization Software 3rd AI+IoT Business Conference, Shenzhen, April 25, 2019 22/39 SOL Optimization 1970s 1980s 1990s 2000s 2010s Summary 2020s 2010s Optimization Software 3rd AI+IoT Business Conference, Shenzhen, April 25, 2019 23/39 SOL Optimization 1970s 1980s 1990s 2000s 2010s Summary 2020s 2010s David Saunders, NASA Ames (Calif) Orion Apollo-type capsule to ISS and moon MSL (Mars Science Lab) Heat flux during atmospheric entry Stratolaunch Descent trajectory of space vehicle Optimization Software 3rd AI+IoT Business Conference, Shenzhen, April 25, 2019 24/39 SOL Optimization 1970s 1980s 1990s 2000s 2010s Summary 2020s Crew Exploration Vehicle (Orion) Tried shape optimization of heat shield and shoulder curvature (but the Apollo folk were pretty close already) Optimization Software 3rd AI+IoT Business Conference, Shenzhen, April 25, 2019 25/39 Landing of launched space vehicle Preliminary computation: Space vehicle will land in Mojave Desert, California OTIS trajectory optimization: Vehicle would land 2500km too soon! SOL Optimization 1970s 1980s 1990s 2000s 2010s Summary 2020s Stratolaunch carrier aircraft (first flight April 15) AIAA 2018 Optimization Software 3rd AI+IoT Business Conference, Shenzhen, April 25, 2019 26/39 Fig. 2 Stratolaunch carrier aircraft. Downloaded by Stephen Corda on September 20, 2018 | http://arc.aiaa.org DOI: 10.2514/6.2018-5257