Machine Learning Augmented Algorithms for Combinatorial Optimization Problems (Dagstuhl Seminar 24441)

Abstract

Combinatorial optimization problems are pervasive across critical domains, including business analytics, engineering, supply chain management, transportation, and bioinformatics. Many of these problems are NP-hard, posing significant challenges for even moderately sized instances. Moreover, even when polynomial-time algorithms exist, their practical implementation can be computationally expensive for real-world applications.
This has driven decades of research across diverse fields, encompassing exact and approximation algorithms, parameterized algorithms, algorithm engineering, operations research, optimization solvers (such as mixed-integer linear programming and constraint programming solvers), and nature-inspired metaheuristics.
Recently, there has been a surge in research exploring the synergistic integration of machine learning techniques with algorithmic insights and optimization solvers to enhance the scalability of solving combinatorial optimization problems. However, research efforts in this area are currently fragmented across several distinct communities, including those focused on "Learning to scale optimization solvers," "Algorithm Engineering," "Algorithms with predictions," and "Decision-focused learning."
This seminar brought together researchers from these diverse communities, fostering a dialogue on effectively combining algorithm engineering techniques, optimization solvers, and machine learning to address these challenging problems. The seminar facilitated the development of a shared vocabulary, clarifying similarities and distinctions between concepts across different research areas. Furthermore, significant progress was made in identifying key research directions for the future advancement of this field. We anticipate that these outcomes will serve as a valuable roadmap for advancing this exciting research area.