# Binary Spring Search Algorithm for Solving Various Optimization Problems
## 1 Introduction  
The optimization of a process or system is a concept that has critical applications in many fields of science. Many optimization algorithms have been introduced [1, 2, 3], which has led to greater availability of heuristic optimization techniques in recent years and their application in various fields, such as energy [4, 5], protection [6], electrical engineering [7, 8, 9, 10, 11], filter design [12], and energy carriers [13, 14], to achieve the optimal solution (under specific criteria). Lately, these methods have been modified, achieving better yields [15, 16, 17]. An optimization algorithm is intelligent when its approach is to find an adequate solution to an optimization problem in the shortest possible time with the least detailed information [18]. The word \"heuristics\" in ancient Greek means \"to know,\" \"to discover,\"\"to find,\" or \"a clue for an investigation\" [19]. The heuristic approach ignores some of the information to make faster decisions with the maximum saving of time and utmost precision compared to complex approaches [20]. Processes in nature inspire many heuristic algorithms (biological processes, animals or groups of animals, and physics theories). Optimization algorithms can be classified in different ways, using a widely accepted structure of four categories, based on the main design. These categories are physics-based, swarm, game-based, and evolution-based optimization algorithms. Physics-based optimization algorithms are designed according to the simulation of various phenomena and laws of physics. Momentum Search Algorithm (_MSA_) is one of the algorithms belonging to this group. _MSA_ is based on the simulation of momentum and motion laws. Members of the _MSA_ population are balls with different weights that move in the direction of a ball with a suitable position based on the impulse [1]. Simulated Annealing (_SA_) algorithm is one of the oldest algorithms in physics. _SA_ is inspired by the process of smelting and cooling materials in metallurgy. Under controlled temperature conditions, the materials are subjected to a heat treatment that causes the molecular structures to go through different phases to change their mechanical properties. The previous phenomenon increases the strength and durability of the material. Heating the material increases its atoms' energy. It allows them to move freely, and the slow cooling process allows a new, lower-energy, higher-strength configuration to be discovered and exploited [21]. This algorithm's efficiency is due to an essential connection between statistical mechanics and optimization processes (multivariate or combinatorial in nature). The analogous behavior of these processes lays the foundations for defining values that optimize the properties of extensive and/or complex systems, which is where the use of this algorithm is mainly justified. Some other popular physics-based optimization algorithms include Galaxy-based Search Algorithm (_GbSA_) [22], Charged System Search (_CSS_) [23], Curved Space Optimization (_CSO_) [24], Artificial Chemical Reaction Optimization Algorithm (_ACROA_) [25], Ray Optimization (_RO_) algorithm [26], Small World Optimization Algorithm (_SWOA_) [27], Black Hole (_BH_) [28], Central Force Optimization (_CFO_) [29], and Big-Bang Big-Crunch (_BBBC_) [30]. Swarm-based optimization algorithms have been developed based on the simulation of natural processes, movements, and behavior of animals and other living things. _Particle Swarm Optimization_ (_PSO_) is the most famous optimization algorithm and is often used by researchers. Particle swarm optimization is a heuristic global optimization method that was proposed in 1995 [31]. It is based on the intelligence of swarms and emulates the behavior patterns of birds/fish when looking for food. One of the birds smells food and communicates it to the rest; this coordination reproduces successful behavior due to the cooperation of each bird.