Discrete Filled Function Method for Discrete Global Optimization

Abstract

A discrete filled function method is developed in this paper to solve discrete global optimization problems over "strictly pathwise connected domains." Theoretical properties of the proposed discrete filled function are investigated and a solution algorithm is proposed. Numerical experiments reported in this paper on several test problems with up to 200 variables have demonstrated the applicability and efficiency of the proposed method.

Design of broadband beamformers with low complexity

“…Thus, we shall derive a discrete filled function method to search for the best local minimizer. We introduce the following function based on the one constructed in [23]. (4:17) where ║ ⋅ ║ denotes the usual Euclidean norm.…”

“…It searches for a better minimizer among local minimizers by means of a function, which is called a filled function. A discrete filled function method was later developed in [23] for solving discrete global optimization problems. In this article, a novel method is proposed for the finite precision beamformer design using a discrete filled function.…”

A critical review of discrete filled function methods in solving nonlinear discrete optimization problems

“…At this point, the algorithms in [27,28,44] will adjust the parameters of the filled function and return to Step 4 ifx ∈ X\X.…”

“…However, the filled function proposed by Zhu contains an exponential term, which consequently makes it difficult to determine a point in a lower basin [26,27]. Since then, several types of discrete filled functions with improved theoretical properties have been proposed in [16,27,28,32,33,[42][43][44] to enhance computational efficiency.…”

“…Many discrete filled function algorithms in the literature, such as those in [16,27,28,44], are also directly applicable to linearly constrained problems as long as the resulting feasible region is convex and pathwise connected.…”