Binary Fox Optimization Algorithm Based U-Shaped Transfer Functions for Knapsack Problems

Abstract

This paper examines a new optimization algorithm called Fox optimizer (FOX), which mimics the foraging behavior of foxes while hunting in nature. When the literature is examined, it is seen that there is no version of FOX that solves binary optimization problems. In this study, continuous search space is converted to binary search space by U-shaped transfer functions and BinFOX is proposed. There are four U-shaped transfer functions in the literature. Based on these transfer functions, four BinFOX variants are derived (BinFOX1, BinFOX2, BinFOX3, and BinFOX4). With BinFOX variants, 25 well-known 0-1knapsack problems in the literature have been solved and their success has been demonstrated. The best, worst, mean, standard deviation, time, and gap values of each variant were calculated. According to the results, the most successful BinFOX variant was determined. The success of BinFOX with U-shaped transfer functions was demonstrated for the first time in this study.