The Memorization Paradigm: Branch & Memorize Algorithms for the Efficient Solution of Sequencing Problems

Lei Shang (1) , Vincent t'Kindt (1) , Federico Della Croce (2)

1 LIFAT - Laboratoire d'Informatique Fondamentale et Appliquée de Tours
2 DIGEP - Department of Management and Production Engineering [Politecnico di Torino]

Memorization as an algorithm design technique allows to speed up algorithms at the price of more space usage. Typically, in search tree algorithms, on lower branching levels, isomor-phic sub-problems may appear exponentially many times and the idea of Memorization is to avoid repetitive solutions as they correspond to identical sub-problems. The idea exists since a long time but apparently has not been systematically considered when designing branching algorithms. It is at least rare for sequencing problems, to the authors' knowledge. In this paper, we explore the power of Memorization on solving hard sequencing problems. We first describe a general framework of Memorization with some guidelines provided on the implementation. Then we apply the framework to four sequencing problems including the two-machine flowshop problem minimizing the sum of completion time and three single machine problems whose objective functions to minimize are the total tardiness, the sum of completion time with release date and the sum of weighted completion time with deadline. The global results suggest systematically considering Memorization as a solving block inside search tree based algorithms like Branch and Bound.

Mots clés: scheduling; exact algorithms; memorization; sequencing; branch and memorize; total tardiness; sum of completion times; flowshop; single machine

Domaines: Complexité [cs.CC]; Algorithme et structure de données [cs.DS]; Optimisation et contrôle [math.OC]; Recherche opérationnelle [math.OC]

Lei Shang, Vincent t'Kindt, Federico Della Croce. The Memorization Paradigm: Branch & Memorize Algorithms for the Efficient Solution of Sequencing Problems. 2018. ⟨hal-01599835v2⟩