ABSTRACT
There is a broad array of algorithms available for Œnding roots or extrema of functions, for multicriteria optimization, or for solving sets of equations (either linear or nonlinear). ¬ey diŠer greatly by their ease of implementation, robustness, and speed. Usually, these three characteristics do not go hand in hand, that is, a robust algorithm will be slow, while one that is fast but less robust will require additional preparation eŠort, like providing information about the derivative, or a good initial guess of the solution to be found. It is considered robust an algorithm that converges even for badly chosen initial conditions or parameter settings, while a fast algorithm will converge a®er fewer numbers of iterations or function calls-a characteristic desirable particularly if each function evaluation takes signiŒcant computational eŠort or when the algorithm is used in real-time applications. A number of such algorithms will be discussed in this chapter, including a new evolutionary algorithm for exploring the boundary of the feasible space in constrained optimization problems.
