K-adaptability in stochastic optimization
Abstract
We consider stochastic problems in which both the objective function and the feasible set are affected by uncertainty. We address these problems using a K-adaptability approach, in which K solutions for a given problem are computed before the uncertainty dissolves and afterwards the best of them can be chosen for the realized scenario. We analyze the complexity of the resulting problem from a theoretical viewpoint, showing that, even in case the deterministic problem can be solved in polynomial time, deciding if a feasible solution exists is $$\mathcal {NP}$$ NP -hard for discrete probability distributions. Besides that, we prove that an approximation factor for the underlying problem can be carried over to our problem. Finally, we present exact approaches including a branch-and-price algorithm. An extensive computational analysis compares the performances of the proposed algorithms on a large set of randomly generated instances.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Feb 02, 2022
- Source ID
- 10.1007/s10107-021-01767-3
Entities
People
- Enrico Malaguti
- Jonas Pruente
- Michele Monaci
Organizations
- Air Force Office of Scientific Research
- German Research Foundation