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Heuristic Optimization and Dynamical System Safety Verification. Todd W. Neller Knowledge Systems Laboratory Stanford University. Outline. Motivating Problem Heuristic Optimization Approach Comparative Study of Global Optimization Techniques Information-Based Optimization
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Heuristic Optimization and Dynamical System Safety Verification Todd W. Neller Knowledge Systems Laboratory Stanford University
Outline • Motivating Problem • Heuristic Optimization Approach • Comparative Study of Global Optimization Techniques • Information-Based Optimization • Recent Research Results
Focus • Global optimization techniques can be powerfully applied to a class of hybrid system verification problems. • When each function evaluation of an optimization is costly, such information should be used intelligently in the course of optimization.
Stepper Motor Safety Verification • Given: • Bounds on stepper motor system parameters • Bounds on initial conditions • Verify: • No stalls in all possible acceleration scenarios
Heuristic Search Landscape • Make use of simple knowledge of problem domain to provide landscape helpful to search
Verification through Optimization • Transform verification problem into an optimization problem with a heuristic measure of relative safety • Apply efficient global optimization
Comparative Testing • Methods: • Simulated Annealing: AMEBSA, ASA, SALO • Multi Level Single Linkage (MLSL) and variants • Random Local Optimization (RANDLO) • Test Functions: • From optimization literature and method demos • Used to gain rough idea of relative strengths
Comparative Study Results • SALO and RANDLO generally best for functions with many and few minima respectively • Local optimization “flattens” and simplifies these search spaces. • Local optimization doesn’t always lead to nearest optimum. • Minima rarely located at bounds of search space.
For test functions STEP1 and STEP2, RANDLO and LMLSL performed best for both constrained local optimization procedures. SALO: ASA did not search the locally optimized search spaces (f´) efficiently. Recent experiments indicate that information-based global optimization performs even better. Comparative Study Results (cont.)
Global Optimization Results (cont.) CONSTR YURETMIN
Information-Based Approach • Information-Based Optimization - Previous function evaluations shape probability distribution over possible functions. • Most methods waste costly information.
Information-Based Local Optimization • Choose initial point and search radius • Iterate: • Evaluate point in sphere where minimum most likely according to information gained thus far • If less than initial point, make new point center
Multi-Level Local Optimization • Each layer of local optimization simplifies search space for the layer above. • MLLO-RIQ: Perform random (Monte-Carlo) optimization of: • f´´: Information-based local optimization of: • f´: Quasi-Newton local optimization of: • f : heuristic function
MLLO-RIQ Results • For our first set of functions, MLLO-RIQ trial results are very encouraging • Local optimization procedure not suited to discontinuous CMMR • No startup cost as with MLSL or GA
Other Work in Progress • Global Information-Based Optimization • Information-Based Direction-Set Methods • Dynamic Search Tuning • Future work: • Parallel Information-Based Methods • Expert System for Global Optimization • Main challenge: Approximating optimal decision procedures
Summary • Heuristically use domain knowledge to transform an initial safety problem into a global optimization problem • Information is costly Use information well in the course of optimization with information-based approaches