Comparative Assessment of Algorithms and Software for Global Optimization

The thorough evaluation of global optimization algorithms and software demands devotion, time and (hardware) resources, in addition to professional objectivity. This general remark is particularly valid with respect to global optimization (GO) software since GO literally encompasses “all” mathematical programming models. It is easy not only to fabricate very challenging test problems, but also to find realistic GO problems that pose a formidable task for any algorithm of today (and of tomorrow). A report on computational experiments should ideally cover a large number of aspects, including detailed description and practical background of the models; related earlier work; solution approach; algorithm implementation and parameterization; hardware platform(s), operating system(s), and software environment; an exact description of all performance measures; report of successes and failures; analysis of solver parameterization effects; statistical characteristics for randomized problem-classes; and a summary of results in tabular and/or graphical forms. An extensive inventory of classical GO test problems, as well as often much harder test suites have been suggested more recently. This paper will review several prominent test collections, discuss comparison issues, and present illustrative numerical results. A second paper will perform a comparative study using ideas presented here and discussions from the Stochastic Global Optimization workshop to be held in New Zealand, June 2001.