Weighted superposition attraction algorithm for binary optimization problems

Weighted superposition attraction algorithm (WSA) is a new generation population-based metaheuristic algorithm, which has been recently proposed to solve various optimization problems. Inspired by the superposition of particles principle in physics, individuals of WSA generate a superposition, which leads other agents (solution vectors). Alternatively, based on the quality of the generated superposition, individuals occasionally tend to perform random walks. Although WSA is proven to be successful in both real-valued and some dynamic optimization problems, the performance of this new algorithm needs to be examined also in stationary binary optimization problems, which is the main motivation of the present study. Accordingly, WSA is first designed for stationary binary spaces. In this modification, WSA does not require any transfer functions to convert real numbers to binary, whereas such functions are commonly used in numerous approximation algorithms. Moreover, a step sizing function, which encourages population diversity at earlier iterations while intensifying the search towards the end, is adopted in the proposed WSA. Thus, premature convergence and local optima problems are attempted to be avoided. In this context, the contribution of the present study is twofold: first, WSA is modified for stationary binary optimization problems, secondarily, it is further enhanced by the proposed step sizing function. The performance of the modified WSA is examined by using three well-known binary optimization problems, including uncapacitated facility location problem, 0–1 knapsack problem and a natural extension of it, the set union knapsack problem. As demonstrated by the comprehensive experimental study, results point out the efficiency of the proposed WSA modification in binary optimization problems.