Global Optimization: My principle area of research is the development, analysis and application of methods for global optimization, especially stochastic heuristics and derivative-free methods. These methods are being incorporated into the SGOPT optimization library.

• Parallel branch-and-bound: Branch-and-bound algorithms can be used to solve a wide range of optimization problems. For example, they are a method commonly used to exactly solve mixed integer programming (MIP) problems. I am developing PICO an object-oriented parallel branch-and-bound algorithm for MIP problems that can effectively use a large number of processors.

• Evolutionary Algorithms (EAs): These heuristic global optimization methods use a population of search points that are used to search with the evolutionary mechanisms of selection and recombination.
  • Convergence Analysis: I have developed several analyses of the convergence of EAs, particularly on continuous search domains. In particular, I have developed Evolutionary Pattern Search Algorithms, which have a weak stationary-point convergence theory on smooth problems.

  • Hybrids: Hybrid EAs that use local search are among the most effective EAs used in real applications. I have evaluated the design of these hybrid EAs for continuous and mixed-continuous problem domains.

• Drug Docking: I am working with the Scripps Research Institute and UCSD on docking methods used within the AutoDock docking tool. We have developed hybrid EAs that rapidly and robustly find optimal docking configurations.

• Protein Folding: Working with members of the Tortilla Project, I have developed methods for solving protein structure prediction problems with the HP lattice model, which abstracts the dominant force of protein folding: the hydrophobic interaction. the
  • Approximate Folding Methods: A variety of methods have been proposed to predict the three-dimensional structure of proteins from their amino acid sequence. Very few of these methods provide the user with measure of confidence in the predicted structure. I have developed algorithms that generate protein structures whose energy is guaranteed to be within a fixed fraction of the energy of the optimal protein structure.
  • Exact Methods: I am working on exact methods for folding large protein sequences in the HP model using integer programming formulations.

• Logistics: I am working with collaborators at RPI, Cornell and Sandia on several logistics problems at Pantex and Sandia. This team's work with production planning for Pantex was a finalist in the 1999 Edelman Competition.

• Agent-based Learning: I am working to develop machine learning methods for software agents that are used to model human behavior in small-scale combat simulations. Our work involves developing learning methods like hybrid methods for genetic programming and global optimization methods for fitting neural networks.