A Simulation Test Approach to the Evaluation of Nonlinear Optimization Algorithms

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Abstract
A simulation test methodology has been developed to evaluate unconstrained nonlinear optimization computer algorithms. The test technique simulates problems optimization algorithms encounter in practice by employing a repertoire of problems representing various topographies (descending curved valleys, saddle points, ridges, etc.), dimensions, degrees of nonlinearity (e.g. linear to exponential) and minima, addressing them from various randomly generated initial approximations to the solution and recording their performances in the form of statistical summaries. These summaries, consisting of categorized results and statistical averages, are generated for each algorithm as tested over members of the problem set. The individual tests are composed of a series of runs from random starts over a member of the problem set. Descriptions of the test technique, test problem, and test results are provided.