Constrained blackbox optimization: The SEARCH perspective

Search and optimization in the context of blackbox objective function evaluation subject to blackbox constraints satisfaction is the thesis of this work. The SEARCH (Search Envisioned As Relation and Class Hierarchizing) framework introduced by Kargupta (1995) offered an alternate perspective of blackbox optimization in terms of relations, classes, and partial ordering. The primary motivation comes from the observation that sampling in blackbox optimization is essentially an inductive process and in the absence of any relation among the members of the search space, induction is no better than enumeration. SEARCH also offers conditions for polynomial complexity search and bounds on sample complexity using its ordinal, probabilistic, and approximate framework. In this work the authors extend the SEARCH framework to tackle constrained blackbox optimization problems. The methodology aims at characterizing the search domain into feasible and infeasible relations among which the feasible relations can be explored further to optimize an objective function. Both -- objective function and constraints -- can be in the form of blackboxes. The authors derive results for bounds on sample complexity. They demonstrate their methodology on several benchmark problems.