Optimization algorithms handle noisy or imprecise objective function evaluations through various techniques and approaches. Here are a few common methods used in practice:

  1. Stochastic search algorithms: These algorithms use randomization to navigate the search space and cope with the noise or imprecision in the objective function evaluations. Examples include evolutionary algorithms, simulated annealing, and genetic algorithms. By employing randomness, these algorithms can explore different regions of the search space and find optimal or near-optimal solutions despite the noise.

  2. Surrogate modeling: In this approach, a surrogate model or a surrogate function is constructed based on the available noisy or imprecise objective function evaluations. The surrogate model acts as a proxy for the true objective function and can be evaluated quickly. Optimization is then performed on this surrogate model, which reduces the computational burden associated with noisy evaluations. Common surrogate modeling techniques include Gaussian process models, radial basis functions, or neural networks.

  3. Adaptive sampling: This technique involves adaptively choosing the next point for evaluation based on the available information. Algorithms like Bayesian optimization use past evaluations to build a probabilistic model of the objective function. This model is then used to determine the most promising point to evaluate next. By focusing the evaluations on regions of the search space that are likely to be optimal, adaptive sampling algorithms can efficiently handle noisy or imprecise evaluations.

  4. Robust optimization: Instead of directly optimizing the objective function, robust optimization algorithms aim to find solutions that are robust against uncertainties or noise in the evaluations. These algorithms incorporate techniques like worst-case analysis or chance-constrained programming to explicitly account for the uncertain nature of the objective function evaluations. By considering a range of possible outcomes, robust optimization algorithms can find solutions that perform well on average, even in the presence of noise.

  It's important to note that the choice of the specific optimization algorithm depends on the nature and characteristics of the noise or imprecision in the objective function evaluations. Noisy evaluations can arise from measurement errors, limited precision, or inherent variability in the system being optimized. Different algorithms may be more effective in different scenarios, and it is often recommended to experiment with different approaches to find the best fit for a particular problem.