Optimization Cultures

Computational-optimization methods can broadly be classified into two groups: classical methods, which require and exploit specific functional forms of objective function and constraints, and heuristics. Those latter methods impose few, if any, restrictions on models, at the price of being more computationally demanding. But because of the growth of computing capacity over the last decades, those methods are now perfectly-practical tools for everyday use. Yet, instead of realizing the advantages of heuristics, users still cling to classical methods. We discuss the reasons for this non-acceptance of heuristics, and argue that the choice of numerical-optimization techniques is as much driven by the culture of the user -- field of work and educational background -- as by the quality of the method. In particular, we argue that many of the alleged shortcomings of heuristics could be overcome if researchers stopped treating optimization as a mathematical, exact discipline; instead, they should consider it a practical/computational tool