On using a hierarchy of twofold resource allocation automata to solve stochastic nonlinear resource allocation problems

Abstract

Recent trends in AI attempt to solve difficult NP-hard problems using intelligent techniques so as to obtain approximately-optimal solutions. In this paper, we consider a family of such problems which fall under the general umbrella of "knapsack-like" problems, and demonstrate how we can solve all of them fast and accurately using a hierarchy of Learning Automata (LA). In a multitude of real-world situations, resources must be allocated based on incomplete and noisy information, which often renders traditional resource allocation techniques ineffective. This paper addresses one such class of problems, namely, Stochastic Non-linear Fractional Knapsack Problems. We first present a completely new on-line LA system - the Hierarchy of Twofold Resource Allocation Automata (H-TRAA). The primitive component of the H-TRAA is a Twofold Resource Allocation Automaton (TRAA), which in itself possesses novelty in the field of LA. For both the TRAA and H-TRAA, we then provide formal convergence results. Finally, we demonstrate empirically that the H-TRAA provides orders of magnitude faster convergence compared to state-of-the-art. Indeed, in contrast to state-of-the-art, the H-TRAA scales sub-linearly. As a result, we believe that the H-TRAA opens avenues for handling demanding real-world applications, such as the allocation of resources in large-scale web monitoring. © Springer-Verlag Berlin Heidelberg 2007.