Constrained Blackbox Optimization
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Derivative-Free and Blackbox Optimization
This book is designed as a textbook, suitable for self-learning or for teaching an upper-year university course on derivative-free and blackbox optimization. The book is split into 5 parts and is designed to be modular; any individual part depends only on the material in Part I. Part I of the book discusses what is meant by Derivative-Free and Blackbox Optimization, provides background material, and early basics while Part II focuses on heuristic methods (Genetic Algorithms and Nelder-Mead). Part III presents direct search methods (Generalized Pattern Search and Mesh Adaptive Direct Search) and Part IV focuses on model-based methods (Simplex Gradient and Trust Region). Part V discusses dealing with constraints, using surrogates, and bi-objective optimization. End of chapter exercises are included throughout as well as 15 end of chapter projects and over 40 figures. Benchmarking techniques are also presented in the appendix.
Black Box Optimization, Machine Learning, and No-Free Lunch Theorems
This edited volume illustrates the connections between machine learning techniques, black box optimization, and no-free lunch theorems. Each of the thirteen contributions focuses on the commonality and interdisciplinary concepts as well as the fundamentals needed to fully comprehend the impact of individual applications and problems. Current theoretical, algorithmic, and practical methods used are provided to stimulate a new effort towards innovative and efficient solutions. The book is intended for beginners who wish to achieve a broad overview of optimization methods and also for more experienced researchers as well as researchers in mathematics, optimization, operations research, quantitative logistics, data analysis, and statistics, who will benefit from access to a quick reference to key topics and methods. The coverage ranges from mathematically rigorous methods to heuristic and evolutionary approaches in an attempt to equip the reader with different viewpoints of the same problem.
Constrained Blackbox Optimization
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.