The Effect of Noise on Artificial Intelligence and Metaheuristic Techniques

Artificial intelligence methods and search techniques such as simulated annealing and simultaneous perturbation can be used in simulation optimization of complex stochastic systems. Simultaneous perturbation has also been applied in the area of neural networks. Simulation optimization methods are often used when it is difficult to obtain the closed form of the objective function, but it is possible to estimate the objective function value at any point via simulation of the system. However, when the objective function is estimated via simulation, simulation-induced noise cannot be avoided. We theoretically analyze the effect of noise on the performance of simulated annealing. We also theoretically analyze simultaneous perturbation under some special conditions and then present some empirical results with this algorithm from a revenue management problem in the airline industry. Keyword 1: Optimization Keyword 2: Algorithm, Artificial Intelligence, Convergence analysis, combinatorial optimization, gradient descent algorithm, simulated annealing, stochastic control, simulation approximation, steepest descent, search heuristics, operations research, convergence time, engineering optimization, binomial distribution, local minima. INTRODUCTION Simulated annealing is a popular meta-heuristic that has been adapted for use in simulation-based optimization. We analyze what happens when the function value is contaminated with simulation-induced noise in Section 2. The method of gradient descent is a popular method in operations research, which has been used extensively in simulation-based optimization and also in neural network algorithms. We discuss a relatively new approach called simultaneous perturbation, which is due to Spall (1992), to gradient descent. We analyze the convergence of this approach under some special conditions in Section 3. Finally, in Section 4, we present some numerical results from the use of simultaneous perturbation in a problem of revenue management in airlines.