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1 Introduction

`What's new?' is an interesting and broadening eternal question, but one which, if pursued exclusively, results only in an endless parade of trivia and fashion, the silt of tomorrow. I would like, instead, to be concerned with the question `What is best?', a question which cuts deeply rather than broadly, a question whose answers tend to move the silt downstream.
Robert M. Pirsig
``Zen and the Art of Motorcycle Maintenance'' (1974)

Mathematical optimization is the formal title given to the branch of computational science that seeks to answer the question `What is best?' for problems in which the quality of any answer can be expressed as a numerical value. Such problems arise in all areas of mathematics, the physical, chemical and biological sciences, engineering, architecture, economics, and management, and the range of techniques available to solve them is nearly as wide.