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Stochastic Programming
Mathematical framework for optimization under uncertainty using probability distributions to model uncertain parameters. It allows for making optimal decisions by considering multiple possible future scenarios.
Monte Carlo Method
Computational technique based on random sampling to evaluate and optimize complex systems under uncertainty. It allows approximating solutions when analytical analysis is mathematically intractable.
Scenario Analysis
Structured approach to evaluating optimization solutions through a set of possible future scenarios. It allows testing the robustness of solutions against different realizations of uncertain parameters.
Robust Constraints
Formulation of optimization constraints that must be satisfied for all possible realizations of uncertain parameters within a given uncertainty set. They guarantee the feasibility of solutions even under the most unfavorable conditions.
Min-Max Approach
Robust optimization strategy that minimizes the maximum possible loss or maximizes the minimum guaranteed gain. It is particularly used in adversarial or highly uncertain environments.
Stochastic Simulation
Process of modeling and numerically experimenting with systems containing random elements to evaluate their behavior under different conditions. It allows estimating the performance distributions of optimization solutions.
Distributionally Robust Optimization
Extension of robust optimization that considers uncertainty about the probability distribution itself rather than just the parameters. It guarantees optimal performance against a set of possible distributions.
Stochastic Metaheuristics
Optimization algorithms inspired by nature or physical processes that incorporate random components to explore the search space. They are particularly effective for complex combinatorial optimization problems.
Multi-Armed Bandits
Sequential optimization problem exploring the trade-off between exploitation and exploration in an uncertain environment. It models situations where decisions must be made with partial information about future rewards.
Stochastic Approximation
Iterative method for finding roots or optima of functions when only a noisy measurement of the function is available. It is fundamental in machine learning and online optimization.
Stochastic Multi-objective Optimization
Extension of multi-objective optimization that considers uncertainty in objectives or constraints. It seeks to identify efficient solutions for multiple conflicting objectives in an uncertain environment.
Uncertainty Set
Mathematical representation of all possible realizations of uncertain parameters in a robust optimization problem. Its precise definition determines the level of conservatism of the obtained robust solution.
Scenario Programming
Stochastic programming approach that discretizes uncertainty into a finite number of scenarios with their associated probabilities. It transforms a stochastic problem into an equivalent large-scale deterministic problem.
Probabilistic Robustness
Performance measure quantifying the probability that a solution remains feasible or satisfies certain performance criteria in the face of uncertainty. It offers a compromise between absolute robustness and average performance.