## 2 Related Works  
Metaheuristic algorithms are iterative procedure where search agents repeatedly evaluate and improve their solution in each iteration. The success of a metaheuristic algorithm depends on the ability of the search agents to explore or expand their search area and to exploit or fine-tune the search around the current search area [9]. Many research show that exploration is desired at the early stage of the iterative procedure while exploitation is important towards the end of the iteration [10]. Exploration widens the search area of an agents so that a region containing an optimal solution is identified, whereas exploitation narrows down the search within the identified region so that the location with an optimal solution is found.  
A time decreasing inertia weight is an example of a mechanism frequently adopted by researchers to control agents' behaviour to favour exploration at the start of the search before switching to exploitation [11; 12; 13]. The time decreasing inertia weight reduces the step size as the iteration increases. Among the common patterns applied by researchers are linearly decreasing and exponentially decreasing inertia weight [12].  
Metaheuristic search agents often face the challenge of premature convergence where the agents are trapped in local optima [14]. In [15], crossover operation is introduced to the cat swarm optimization algorithm to overcome the local optima trap and increase diversity. Meanwhile, in [16] a simple re-initialization method is proposed for PSO. Mutation is also a popular method to avoid premature convergence, where various mutation strategies have been adopted by researchers [17; 18]. Overall, all these strategies are introduced to create a disturbance to the agents' convergence so that the premature convergence can be avoided.  
The most relevant algorithm to this work is SCA. [PERSON] adopted the sine cosine function to guide the search for the optimal solution by fluctuating around the best solution. To ensure convergence, SCA envelopes the sine and cosine function using a linearly decreasing function mirrored by the time axis. However, despite the fluctuation and linearly decreasing envelope, both [19; 20] listed premature convergence as the drawback of SCA. Additionally, [21] highlighted that the solution update equations of SCA result in a bias towards the origin, causing SCA to work very well for optimization problems where the global solution is located at the origin. The performance declines with shifted problems. Three random numbers are needed in SCA.  
In this work, a physical phenomenon-namely the harmonic motion of a pendulum- is mimicked to move the search agents so that an optimal solution is achieved. Unlike SCA, the harmonic motion of the pendulum slows down with exponential function. Exponential function had been observed to provide good exploration-exploitation balance in metaheuristics [22; 23]. The PSA agents do not randomly select between sine and cosine functions; rather, they follow the harmonic motion function. The harmonic motion function determines the maximum limit for the random numbers that controls the PSA agents' stochastic search, with respect to current solution and best solution.