An outer-approximation algorithm for a class of mixed-integer nonlinear programs
Mathematical Programming: Series A and B
Simulated annealing: theory and applications
Simulated annealing: theory and applications
On the average complexity of multivariate problems
Journal of Complexity
Parallel processors for planning under uncertainty
Annals of Operations Research
Optimization
Fractals and chaos
Stochastic decomposition: an algorithm for two-state linear programs with recourse
Mathematics of Operations Research
Fractals for the classroom. Part 1.: Introduction to fractals and chaos
Fractals for the classroom. Part 1.: Introduction to fractals and chaos
Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Challenges in stochastic programming
Mathematical Programming: Series A and B
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
Computational investigations of low-discrepancy sequences
ACM Transactions on Mathematical Software (TOMS)
Introduction to Stochastic Programming
Introduction to Stochastic Programming
A simplex-based numerical framework for simple and efficient robust design optimization
Computational Optimization and Applications
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The generalized approach to stochastic optimization involves two computationally intensive recursive loops: (1) the outer optimization loop, (2) the inner sampling loop. Furthermore, inclusion of discrete decision variables adds to the complexity. The focus of the current endeavor is to reduce the computational intensity of the two recursive loops. The study achieves the goals through an improved understanding and description of the sampling phenomena based on the concepts of fractal geometry and incorporating the knowledge of the accuracy of the sampling (fractal model) in the stochastic optimization framework thereby, automating and improving the combinatorial optimization algorithm. The efficiency of the algorithm is presented in the context of a large scale real world problem, related to the nuclear waste at Hanford, involving discrete and continuous decision variables, and uncertainties. These new developments reduced the computational intensity for solving this problem from an estimated 20 days of CPU time on a dedicated Alpha workstation to 18 hours of CPU time on the same machine.