Optimization, Modeling, and Simulation Training
Optimization, Modeling, and Simulation Training Course Description
This Optimization, Modeling, and Simulation Training is an introduction to two closely related areas: (1) stochastic search methods for system optimization and (2) the analysis and construction of Monte Carlo simulations. A few of the many areas where stochastic optimization and simulation-based approaches have emerged as indispensable include decision aiding, prototype development for large-scale control systems, performance analysis of communication networks, control and scheduling of complex manufacturing processes, and computer-based personnel training. The course focuses on core issues in algorithm design and mathematical modeling, together with implications for practical implementation. The course does not dwell on theoretical details related to the methods; attendees are directed to the appropriate literature for such details. Attendees should have a solid working knowledge of probability and statistics at the beginning graduate level and knowledge of multivariate calculus, basic matrix analysis, and linear algebra. To aid understanding, the course will include a brief review of the prerequisite mathematical material. Attendees will receive a copy of the textbook Introduction to Stochastic Search and Optimization by J. C. Spall (Wiley, 2003), a comprehensive set of notes, and a CD with Matlab code of the core algorithms. Although not required, attendees are encouraged to bring a laptop with MATLAB installed. The course will include class demonstrations and opportunities to experiment with the algorithms.
• Popular methods for stochastic optimization.
• To recognize when stochastic optimization techniques are necessary or beneficial.
• Advantages and disadvantages of popular methods for system optimization.
• Essential theoretical principles and assumptions underlying optimization and Monte Carlo simulation and the implications for practical implementation.
• Basics of mathematical modeling and the link to Monte Carlo simulation.
• State-of-the-art methods for using Monte Carlo simulations to improve real system performance.
With onsite Training, courses can be scheduled on a date that is convenient for you, and because they can be scheduled at your location, you don’t incur travel costs and students won’t be away from home. Onsite classes can also be tailored to meet your needs. You might shorten a 5-day class into a 3-day class, or combine portions of several related courses into a single course, or have the instructor vary the emphasis of topics depending on your staff’s and site’s requirements.
Brief Mathematical Review. Relevant multivariate analysis, matrix algebra, probability, and statistics.
Background on Search and Optimization. Basic issues and definitions. Stochastic vs. deterministic methods. No free lunch theorems for optimization. Summary of classical methods of optimization and their limitations.
Direct Search Techniques. Introduction to direct random search. Monte Carlo methods. Nonlinear simplex (Nelder-Mead) algorithms.
Least-Squares-Type Methods. Recursive methods for linear systems. Recursive least squares (RLS). Least mean squares (LMS). Connection to Kalman filtering.
Stochastic Approximation for Linear and Nonlinear Systems. Root-finding and gradient-based stochastic approximation (Robbins-Monro). Gradient-free stochastic approximation: finite-difference (FDSA) and simultaneous perturbation (SPSA) methods.
Search Methods Motivated by Physical Processes. Simulated annealing and related methods. Evolutionary computation and genetic algorithms.
Discrete stochastic optimization. Statistical methods (e.g., ranking and selection, multiple comparisons), general random search methods, and discrete simultaneous perturbation SA (DSPSA).
Model Building. Issues particular to Monte Carlo simulation models. Bias-variance tradeoff. Selecting “best” model via cross-validation. Fisher information matrix as summary measure.
Simulation-Based Optimization. Use of Monte Carlo simulations to improve performance of real-world system performance. Gradient-based methods (infinitesimal perturbation analysis and likelihood ratio) and non-gradient-based methods (FDSA, SPSA, etc.). Common random numbers.
Markov Chain Monte Carlo. Monte Carlo methods for difficult calculations; Metropolis-Hastings and Gibbs sampling. Applications to numerical integrat ion and statistical estimation.
Input Selection and Experimental Design. Classical vs. optimal design. A practical criterion for optimal design (D-optimality). Input selection in linear and nonlinear models.
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