Optimization of discrete variable stochastic systems by computer simulation
Mathematics and Computers in Simulation
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Annals of Operations Research
Stochastic discrete optimization
SIAM Journal on Control and Optimization
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WSC '94 Proceedings of the 26th conference on Winter simulation
A method for discrete stochastic optimization
Management Science
Multimodularity, Convexity, and Optimization Properties
Mathematics of Operations Research
The Sample Average Approximation Method for Stochastic Discrete Optimization
SIAM Journal on Optimization
Budget-Dependent Convergence Rate of Stochastic Approximation
SIAM Journal on Optimization
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Journal of Optimization Theory and Applications
Order-Based Cost Optimization in Assemble-to-Order Systems
Operations Research
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WSC '05 Proceedings of the 37th conference on Winter simulation
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Note on Multimodularity and L-Convexity
Mathematics of Operations Research
Discrete Optimization via Simulation Using COMPASS
Operations Research
Discrete stochastic optimization using linear interpolation
Proceedings of the 40th Conference on Winter Simulation
On the Structure of Lost-Sales Inventory Models
Operations Research
On the Optimal Policy Structure in Serial Inventory Systems with Lost Sales
Operations Research
ACM Transactions on Modeling and Computer Simulation (TOMACS)
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We propose new methods to solve simulation optimization problems over multidimensional discrete sets. The proposed methods are based on extending the objective function from a discrete domain to a continuous domain and applying stochastic approximation to the extended function. The extension of the objective function is constructed as a piecewise linear interpolation of the original objective function over a particular partition of ℝd. The advantage of the proposed approach lies in that stochastic approximation is applied to the extension, not the original function, over ℝd, so the estimated optimal solution at each iteration of the proposed methods is not restricted to be an integer point. Rather, we are free to approach the optimal solution aggressively by moving toward the direction of the steepest descent, thereby skipping over intervening points, thereby resulting in fast convergence in the early stage of the procedures. We provide a set of sufficient conditions under which the proposed methods guarantee the almost sure (a.s.) convergence to the optimal solution. One of such conditions is the multimodularity or L♮-convexity of the objective function, which arises in various inventory systems and queueing networks with controlled admission. Numerical examples illustrate the effectiveness of the proposed methods in such settings.