UTF: Upgrade transfer function for binary meta-heuristic algorithms

Abstract

In the real world, many optimization problems are discrete and very complex to solve. Some of them are in the class of NP-hard problems and their search spaces grow exponentially with the problem size. As a result, an exhaustive search will be impractical using exact algorithms. In the last decades, meta-heuristic algorithms as approximate algorithms have shown superior performance in solving these problems. The majority of these algorithms have been designed for continuous search spaces and are not able to solve binary optimization problems. Therefore, a transfer function is applied to convert the continuous search space to the binary one. The performance of such binary algorithms depends on their ability of exploration, exploitation and transfer function. Several transfer functions have been introduced so far but they have shown poor exploration and exploitation in solving some problems. In this study, a novel adaptive transfer function, based on two linear functions, is proposed to overcome the shortcomings of existing transfer functions. The proposed method called upgrade transfer function (UTF) adapts itself during running the algorithm to switch from exploration to exploitation. This capability also covers disadvantages of metaheuristic algorithms in terms of poor exploration and exploitation. The performance of UTF has been evaluated by three discrete optimization problems: function optimization, feature selection and the 0–1 multi-knapsack problem (MKP). The results of binary particle swarm optimization (BPSO), binary artificial bee colony (BABC) and several improved BPSO and BABC have been compared with those of UTF–BPSO and UTF–BABC using function optimization problems. Also, the efficiency of UTF–BPSO and UTF–BABC and some binary meta-heuristic algorithms such as binary salp swarm algorithm (BSSA) and binary gray wolf optimization (bGWO), binary dragon algorithm (BDA), binary multi-neighborhood artificial bee colony (BMNABC), binary hybrid topology particle swarm optimization quadratic interpolation (BHTPSO-QI), binary ant lion optimizer (bALO) and binary gravitational search algorithm (BGSA) have been evaluated by feature selection problems. Moreover, UTF and seventeen transfer functions have been applied in original PSO, ABC, SSA and GWO algorithms to solve low and high dimensions 0–1 MKP benchmark instances. The results showed that the new transfer function significantly enhances the performance of algorithms to achieve the best solution in the binary search space.