AI BriefingLG AI Research 156
Key point
It covers the characteristics of combinatorial optimization problems and the complexity of integer programming, as introduced at ICML 2021.
Details
LG AI Research's Data Intelligence Lab is focusing on Combinatorial Optimization research to solve real-world challenging problems. Combinatorial optimization is represented by problems such as the traveling salesman problem, minimum spanning tree, and the knapsack problem, and is characterized by the fact that the feasible solution space is discrete.
In particular, the Knapsack Problem is a problem of maximizing value within a limited weight, and as the number of items increases, the number of possible combinations grows exponentially. Due to this characteristic, many combinatorial optimization problems are classified as difficult problems belonging to NP-Complete.
Such problems can be mathematically expressed as Integer Programming. Because the variables belong to a set of integers rather than real numbers, finding an efficient optimal solution is very difficult, unlike conventional Linear Programming.
Currently, the industry uses the following software packages to solve these problems.
- CPLEX: A representative tool that supports linear and integer programming
- GUROBI: A high-performance optimization tool provided on a paid basis
- SCIP: An optimization tool available for free
- OR-Tools: An optimization solution provided by Google
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