A new effective dynamic program for an investment optimization problem

Evgeny A Gafarov (1, 2, 3) , Alexandre Dolgui (1, 4) , Alexander A Lazarev (2) , Frank Werner (5)

1 LIMOS - Laboratoire d'Informatique, de Modélisation et d'optimisation des Systèmes
2 ICS RAS - Trapeznikov Institute of Control Sciences
3 DEMO-ENSMSE - Département Décision en Entreprise : Modélisation, Optimisation
4 Mines Nantes - Mines Nantes
5 Fakultät für Mathematik

After a series of publications of T.E. O'Neil et al. (e.g. in 2010), dynamic programming seems to be the most promising way to solve knapsack problems. Some techniques are known to make dynamic programming algorithms (DPA) faster. One of them is the graphical method that deals with piecewise linear Bellman functions. For some problems, it was previously shown that the graph-ical algorithm has a smaller running time in comparison with the classical DPA and also some other advantages. In this paper, an exact graphical algorithm (GrA) and a fully polynomial-time approximation scheme based on it are presented for an investment optimization problem having the best known running time. The algorithms are based on new Bellman functional equations and a new way of implementing the GrA.

Mots clés: Investment problem; Dynamic; programming; FPTAS; Multi-choice knapsack problem

Domaines: Mathématique discrète [cs.DM]; Recherche opérationnelle [math.OC]

Evgeny A Gafarov, Alexandre Dolgui, Alexander A Lazarev, Frank Werner. A new effective dynamic program for an investment optimization problem. Automation and Remote Control / Avtomatika i Telemekhanika, 2016, 77 (9), pp.1633-1648. ⟨10.1134/S0005117916090101⟩. ⟨hal-01435294⟩