Simulated annealing and Boltzmann machines: a stochastic approach to combinatorial optimization and neural computing
Query size estimation by adaptive sampling
Selected papers of the 9th annual ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Algorithms in Search, Optimization and Machine Learning
Adaptive Sampling Methods for Scaling Up Knowledge Discovery Algorithms
DS '99 Proceedings of the Second International Conference on Discovery Science
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
A survey on approaches for reliability-based optimization
Structural and Multidisciplinary Optimization
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A random sampling approach is presented for worst-case design of structures. Uncertainties are considered in structural and material parameters, which are assumed to exist in intervals with prescribed upper and lower bounds. Constraints are given for the worst responses that are found by solving anti-optimization problems. Optimal cross-sections are then selected from the list of available sections. The regions of uncertainty of parameters are discretized into integer values to formulate the hybrid problem of optimization and anti-optimization as an integer programming problem. The accuracy of solution is defined based on the order of the objective value; hence, a random sampling approach is successfully applied to obtain optimal and anti-optimal solutions within the prescribed accuracy. It is shown in the numerical examples that a good approximate optimal solution is found by random sampling with small number of analyses.