Stochastic methods and simulation

Abstract

This chapter develops stochastic computational methods that assume random elements within their computational task. The methods prior to this chapter have largely been deterministic, as they have not depended on random elements in their computation—previous exceptions being our studies of linear regression, simulated annealing, and genetic algorithms. These exceptions point to a dichotomy into how randomness leaks itself into the computational arena. One way is to use a random element to help decide a deterministic quantity. For example, solving a deterministic TSP problem with either simulated annealing or a genetic algorithm incorporates a stochastic search in the attempt to calculate the deterministic value that is the shortest tour. In this case the problem is deterministic, but the calculation method is stochastic.