# XOR Binary Gravitational Search Algorithm with Repository: Industry 4.0 Applications
## 1 Introduction  
It is highly desirable to prepare products to be served and used for customers with their own dominant needs, interests, energy and use standards. Industry 4.0, the forth generation of industry, is a response to such varied requirements which is predicted to lead to highly customized and re-configurable production. Such technology rely on big data and benefits from machine learning andartificial intelligence approaches. The use of such approaches may even make it possible to update production procedure to give appropriate response to fast changes in the design of product or make product customization possible [1]. To implement this on the factory floor, it is required to use robust intelligent techniques including advanced machine learning and artificial intelligence approaches to make the production line capable of implementing such varied production modifications. To avoid safety issues as well as wasting resources, a digital twin [2], a precise electronic replica of the factory floor, can be utilized. Such digital environments make it possible to design a robust system at lower cost and times to implement. There exist different Industry 4.0 applications, in which the decision variables are binary rather than real values. Optimal task planning [3], flow shop scheduling [4] and assembly line design problems [5; 6] are example applications of binary optimization algorithms in a digital manufacturing setup. The competition between different factories emerges mass production, while maintaining robustness and giving appropriate response to continuous design changes. In such an environment, it is required for the production elements, including robots and other automated machines, to perform task planning automatically to minimize the costs and time consumed, while maximizing production rates and profit. More specifically, rapid changes in products shortens the life-cycle time of production systems [7]. For certain product assembly lines, long-term shut down may be required to redesign the line and update recipes. Automated optimization of such processes are highly commercially beneficial to reduce these inefficiencies and improve production. Intelligent optimization algorithms may be beneficial for automatizing process design on the factory floor [2] which can consider energy, time and other processes. The requirement for optimization algorithms motivate us to develop a new algorithm, study its mathematical analysis and use it to perform an automated optimization process in Industry 4.0 applications. Although classical optimization algorithms such as linear programming approaches, calculus of variations and gradient based optimization methods have proven to be efficient optimization algorithms, there are some barriers against use of these algorithms in all applications. When the function to be optimized is not explicitly defined and/or its partial derivative with respect to its parameters is hard to obtain because of high dimension and discontinuity, classical optimization processes fail. Intelligent optimization algorithms may be good candidates for high dimensional optimization problems. Intelligent optimization algorithms benefit from multiple start point, they are derivative free and are capable of finding multiple global optimums. Moreover, since these optimization algorithms are initiated from multiple points, they are less sensitive to initial conditions. Evolutionary optimization algorithms [8], swarm intelligence [9] and physics-inspired optimization methods [10] are the main categories of intelligent optimization methods applied in these cases. Each solution in swarm intelligence approaches is defined in terms of a \(d\)-dimensional vector representing position. A velocity vector updates the positions for the next generation. Velocity vector benefits from exploration as well as exploitation terms.