Advanced Mathematical/Statistical Optimization Methods

- Deterministic and Probabilistic/Stochastic Algorithms; steady state, dynamic, and Large-scale systems

- Continuous/Discrete/Combinatorial Optimization for linear, (“highly”) nonlinear, Multi-Dimensional Systems

- Mathematical Methods;

- Statistical/Probabilistic; Advanced Sampling/Simulation (Variation Reduction Techniques); Combined Application of Methods;

• Importance sampling (IS) methods, Directional sampling, Line Sampling, Subset Sampling/ Markov Chain Monte Carlo Sampling, Latin hypercube simulation (LHS)/ Stratified Sampling, Adaptive sampling, Axis orthogonal (IS) simulation, Dimensionality Reduction (DR) Method, Cross-Entropy Method, Combination of cellular automata (CA) and Monte Carlo (MC) sampling

- Stochastic-process Models;

• Discrete Time Markov processes (Markov Chains), Markov processes (Continuous Time); Semi/ Hidden Markov/Partially Observable models, (Renewal models- Brownian motion with drift (the Gaussian or Wiener process- Diffusion model) and the gamma (levy) processes)

- Reliability Models-Methods for System/Structural Reliability:

• Probabilistic Reliability Procedures: First/second-order Reliability methods; Advanced Approaches and Combined Application with Advanced Sampling/Simulation methods

• State-Space Methods; Markov Modeling (Discrete/Continuous Time Processes- Homogeneous, Non-Homogeneous, (Hidden) Semi Markov); Petri nets (SPN), Evidential Networks, Bayesian Networks (Discrete/Continuous Time, Dynamic), etc.

• Combinatorial Methods; Reliability Allocation- Networks, Reliability Block Diagram (RBD), Event Tree Analysis (ETA), Fault Tree Analysis (FTA), Boolean Logic, Binary Decision Diagrams, Decomposition Method, Fault Tree Evaluation/ Minimal Cut Sets/ Path Sets

• Hybrid Techniques (combinatorial/state space); Dynamic Fault Trees (DFT) - Sequential Dependency, Compiling (Dynamic) Fault Trees into Petri Nets / (Dynamic) Bayesian Nets, Dynamic Reliability Block Diagrams (DRBD) or Simulation (Monte Carlo, Discrete Event);

- Uncertainty Analysis;

- Surrogate Models;

- Monte Carlo Meta Heuristics Algorithms (Population/Trajectory Based);

- Data Mining- Soft Computing/Intelligent Techniques- Methods; Pattern Recognition, Image Processing

- Multi-objective Optimization Methods; Programming, Meta Heuristics models/Surrogate Models