Proposal of grid area search with UCB for discrete optimization problem

Abstract

In this paper, a novel method for the discrete optimization problem is proposed based on the UCB algorithm. Definition of the neighborhood in the search space of the problem easily affects the performance of the existing algorithms because they do not well take into account the dilemma of exploitation and exploration. To optimize the balance of exploitation and exploration, we divide the search space into several grids to reconsider the discrete optimization problem as a Multi-Armed Bandit Problem, and therefore the UCB algorithm is directly introduced for the balancing. We proposed a UCB-grid area search and conducted numerical experiments on the 0-1 Knapsack Problem. Our method showed stable results in different environments.