Steepest ascent can be exponential in bounded treewidth problems

David Cohen (1) , Martin Cooper (2, 3) , Artem Kaznatcheev (4, 5) , Mark Wallace (6)

1 RHUL - Royal Holloway [University of London]
2 IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage
3 UT3 - Université Toulouse III - Paul Sabatier
4 University of Oxford
5 Cleveland Clinic
6 Monash University [Melbourne]

We investigate the complexity of local search based on steepest ascent. We show that even when all variables have domains of size two and the underlying constraint graph of variable interactions has bounded treewidth (in our construction, treewidth 7), there are fitness landscapes for which an exponential number of steps may be required to reach a local optimum. This is an improvement on prior recursive constructions of long steepest ascents, which we prove to need constraint graphs of unbounded treewidth.

Keywords: Local search; Steepest ascent; Long path; VCSP; Bounded treewidth; Fitness landscape

Domains: Multiagent Systems [cs.MA]

David Cohen, Martin Cooper, Artem Kaznatcheev, Mark Wallace. Steepest ascent can be exponential in bounded treewidth problems. Operations Research Letters, 2020, 48 (3), pp.217-224. ⟨10.1016/j.orl.2020.02.010⟩. ⟨hal-02887815⟩