Dynamic Multi-Armed Bandit Algorithm for the Cyclic Bandwidth Sum Problem

Abstract

Memetic algorithms (MAs) are a powerful resource when dealing with optimization problems, combining the diversification of the population-based approaches with the intensification of local search. However, their success depends on the combination of operators and their ability to cope with the intrinsic difficulties of a problem. Choosing the most suitable combination of operators that better suits a given problem (or a set of instances of a problem) has proved to be a defiant and time-consuming task. An approach to this task is the adaptive operator selection (AOS), based on the idea of choosing operators during execution time based on some reward system related to their performance. In this paper, we continue our previous work on studying the effectiveness of several operators of an MA to solve the cyclic bandwidth sum problem (CBSP), now extending the operator set and incorporating the dynamic multi-armed bandit (DMAB) framework to adaptively adjust the MA's operators. The resulting technique, named DMAB+MA, is compared to the independent MA versions in a full factorial experiment and with respect to two reference algorithms of the literature. It was found that the quality of the solutions achieved by DMAB+MA significantly improved the best-known results provided by the state-of-the-art algorithms while keeping the competitive execution times with respect to the independent MA versions. Moreover, DMAB+MA was able to provide optimal/best-known solutions for the 40 tested graphs (with different topologies) and to establish new better upper bounds for 12 of them. INDEX TERMS Cyclic bandwidth sum problem, dynamic multi-armed bandit, adaptive operator selection, memetic algorithms.