Mathematical optimization or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.
In computer science, formal methods are mathematically rigorous techniques for the specification, development, analysis, and verification of software and hardware systems. The use of formal methods for software and hardware design is motivated by the expectation that, as in other engineering disciplines, performing appropriate mathematical analysis can contribute to the reliability and robustness of a design.
Constraint satisfaction problems (CSPs) are mathematical questions defined as a set of objects whose state must satisfy a number of constraints or limitations. CSPs represent the entities in a problem as a homogeneous collection of finite constraints over variables, which is solved by constraint satisfaction methods. CSPs are the subject of research in both artificial intelligence and operations research, since the regularity in their formulation provides a common basis to analyze and solve problems of many seemingly unrelated families. CSPs often exhibit high complexity, requiring a combination of heuristics and combinatorial search methods to be solved in a reasonable time. Constraint programming (CP) is the field of research that specifically focuses on tackling these kinds of problems. Additionally, the Boolean satisfiability problem (SAT), satisfiability modulo theories (SMT), mixed integer programming (MIP) and answer set programming (ASP) are all fields of research focusing on the resolution of particular forms of the constraint satisfaction problem.
Richard Manning Karp is an American computer scientist and computational theorist at the University of California, Berkeley. He is most notable for his research in the theory of algorithms, for which he received a Turing Award in 1985, The Benjamin Franklin Medal in Computer and Cognitive Science in 2004, and the Kyoto Prize in 2008.
David A. Bader is a Distinguished Professor and Director of the Institute for Data Science at the New Jersey Institute of Technology. Previously, he served as the Chair of the Georgia Institute of Technology School of Computational Science & Engineering, where he was also a founding professor, and the executive director of High-Performance Computing at the Georgia Tech College of Computing. In 2007, he was named the first director of the Sony Toshiba IBM Center of Competence for the Cell Processor at Georgia Tech.
James Alexander Hendler is an artificial intelligence researcher at Rensselaer Polytechnic Institute, United States, and one of the originators of the Semantic Web. He is a Fellow of the National Academy of Public Administration.
In mathematical optimization, constrained optimization is the process of optimizing an objective function with respect to some variables in the presence of constraints on those variables. The objective function is either a cost function or energy function, which is to be minimized, or a reward function or utility function, which is to be maximized. Constraints can be either hard constraints, which set conditions for the variables that are required to be satisfied, or soft constraints, which have some variable values that are penalized in the objective function if, and based on the extent that, the conditions on the variables are not satisfied.
Kalyanmoy Deb is an Indian computer scientist. Deb is the Herman E. & Ruth J. Koenig Endowed Chair Professor in the Department of Electrical and Computing Engineering at Michigan State University. Deb is also a professor in the Department of Computer Science and Engineering and the Department of Mechanical Engineering at Michigan State University.
In computer science and formal methods, a SAT solver is a computer program which aims to solve the Boolean satisfiability problem. On input a formula over Boolean variables, such as "(x or y) and (x or not y)", a SAT solver outputs whether the formula is satisfiable, meaning that there are possible values of x and y which make the formula true, or unsatisfiable, meaning that there are no such values of x and y. In this case, the formula is satisfiable when x is true, so the solver should return "satisfiable". Since the introduction of algorithms for SAT in the 1960s, modern SAT solvers have grown into complex software artifacts involving a large number of heuristics and program optimizations to work efficiently.
Holger H. Hoos is a German-Canadian computer scientist and a Alexander von Humboldt-professor of artificial intelligence at RWTH Aachen University. He also holds a part-time appointment as a professor of machine learning at Leiden University, and he is an adjunct professor at the Computer Science Department of the University of British Columbia, where he held a full-time professorial appointment from 2000 until 2016. His research interests are focused on artificial intelligence, at the intersection of machine learning, automated reasoning and optimization, with applications in empirical algorithmics, bioinformatics and operations research. In particular, he works on automated algorithm design and on stochastic local search algorithms. Since 2015, he is a Fellow of the Association for the Advancement of Artificial Intelligence (AAAI), and since 2020 a Fellow of the European Association for Artificial Intelligence (EurAI) as well as a Fellow of the Association for Computing Machinery (ACM).
Eric Poe Xing is an American computer scientist whose research spans machine learning, computational biology, and statistical methodology. Xing is founding President of the world’s first artificial intelligence university, Mohamed bin Zayed University of Artificial Intelligence (MBZUAI).
Algorithm selection is a meta-algorithmic technique to choose an algorithm from a portfolio on an instance-by-instance basis. It is motivated by the observation that on many practical problems, different algorithms have different performance characteristics. That is, while one algorithm performs well in some scenarios, it performs poorly in others and vice versa for another algorithm. If we can identify when to use which algorithm, we can optimize for each scenario and improve overall performance. This is what algorithm selection aims to do. The only prerequisite for applying algorithm selection techniques is that there exists a set of complementary algorithms.
Thomas Lengauer is a German computer scientist and computational biologist.
Carla Pedro Gomes is a Portuguese-American computer scientist and professor at Cornell University. She is the founding Director of the Institute for Computational Sustainability and is noted for her pioneering work in developing computational methods to address challenges in sustainability. She has conducted research in a variety of areas of artificial intelligence and computer science, including constraint reasoning, mathematical optimization, and randomization techniques for exact search methods, algorithm selection, multi-agent systems, and game theory. Her work in computational sustainability includes ecological conservation, rural resource mapping, and pattern recognition for material science.
Qiskit is an open-source software development kit (SDK) for working with quantum computers at the level of circuits, pulses, and algorithms. It provides tools for creating and manipulating quantum programs and running them on prototype quantum devices on IBM Quantum Platform or on simulators on a local computer. It follows the circuit model for universal quantum computation, and can be used for any quantum hardware that follows this model.
Grigory Yaroslavtsev is a Russian-American computer scientist. He is an assistant professor of computer science at George Mason University. Previously he was an assistant professor of computer science at Indiana University and the founding director of the Center for Algorithms and Machine Learning (CAML) at Indiana University.
Marius Lindauer is a German computer scientist and professor of machine learning at the institute of artificial intelligence of the Leibniz University Hannover. He is known for his research on Automated Machine Learning and other meta-algorithmic approaches.
Ofer Strichman is a professor of computational logic and computer science at the Davidson Industrial Engineering and Management, Technion – Israel Institute of Technology. He holds the Joseph Gruenblat chair in production engineering.
Shmuel Onn is a mathematician, Professor of Operations Research and Dresner Chair at the Technion - Israel Institute of Technology. He is known for his contributions to integer programming and nonlinear combinatorial optimization.
Thomas L. Dean is an American computer scientist known for his work in robot planning, probabilistic graphical models, and computational neuroscience. He was one of the first to introduce ideas from operations research and control theory to artificial intelligence. In particular, he introduced the idea of the anytime algorithm and was the first to apply the factored Markov decision process to robotics. He has authored several influential textbooks on artificial intelligence.
