L. Hernando Rodriguez, A. Elorza Deias, J. A. Lozano Alonso
This study analyzes the rankings of solutions generated by permutation-based combinatorial optimization problems. Specifically, structural patterns are identified in the rankings of the linear ordering problem, significantly constraining the total set of possible rankings. By leveraging these properties, an upper bound for this number is established. Additionally, the research explores rankings in the Fourier domain, examining the effect of certain Fourier coefficient being null. This analysis has direct implications for the quadratic assignment problem, where an upper bound is also derived. The findings presented in this study offer valuable insights for the development of metaheuristics and pave the way for new research directions in combinatorial optimization.
Keywords: Combinatorial optimization, rankings, Fourier transform, linear ordering problem, quadratic assignment problem.
Scheduled
Heuristics and Metaheuristics III
June 10, 2025 7:00 PM
MR 1