Stochastic methods in engineering design

Frequently, problems encountered in engineering design deal with finding an optimal solution to problems that are of a stochastic nature. The fundamental problem of optimization is to arrive at the best possible decision in any given set of circumstances. The first step, therefore in a mathematical optimization problem is to choose some quantity, typically a function of several variables, to be maximized or minimized, subject possibly to one or more constraints. The most common types of constraint are equalities and inequalities which must be satisfied by the variables of the problem, but many other types of constraint are possible; for example, a solution in integers may be required. The next step is to choose a mathematical method to solve the optimization problem; such methods are usually called optimization techniques, or algorithms. The author discusses combinatorial optimization, optimization methods (calculus based methods, enumerative methods and random methods) and randomised techniques (simulated annealing and genetic algorithms)