###### Abstract  
The harmonic motion of pendulum swinging centered at a pivot point is mimicked in this work. The harmonic motion's amplitude at both side of the pivot are equal, damped, and decreased with time. This behavior is mimicked by the agents of the pendulum search algorithm (PSA) to move and look for an optimization solution within a search area. The high amplitude at the beginning encourages exploration and expands the search area while the small amplitude towards the end encourages fine-tuning and exploitation. PSA is applied for a vaccine distribution problem. The extended SEIR model of Hong Kong's 2009 H1N1 influenza epidemic is adopted here. The results show that PSA is able to generate a good solution that is able to minimize the total infection better than several other methods. PSA is also tested using 13 multimodal functions from the CEC2014 benchmark function. To optimize multimodal functions, an algorithm must be able to avoid premature convergence and escape from local optima traps. Hence, the functions are chosen to validate the algorithm as a robust metaheuristic optimizer. PSA is found to be able to provide low error values. PSA is then benchmarked with the state-of-the-art particle swarm optimization (PSO) and sine cosine algorithm (SCA). PSA is better than PSO and SCA in a greater number of test functions; these positive results show the potential of PSA.  
harmonic motion; pendulum; optimization; search Article  
15 May 20  
Although many metaheuristic algorithms have been proposed in recent years-for example the sine cosine algorithm (SCA) [4], gravitational search algorithm (GSA) [5], but algorithm (BA) [6], artificial bee colony (ABC) [7], grey wolf optimization (GWO) [8], and many others-the no free lunch theorem (NFL) motivates researchers to keep introducing new algorithms or improving those existing. NFL states that no supreme algorithm that can provide the best solution for all optimization problems exists. An algorithm might be able to give the best solution for a set of problems but not for another set.  
In this work, a new metaheuristic named the Pendulum Search Algorithm (PSA) is proposed. PSA is a population-based algorithm where the solution of an optimization problem is searched for by a group of agents. The agents in PSA move around the search space looking for the optimal solution according to pendulum harmonic motion. A pendulum centered at a pivot point swings in a harmonic motion, with the amplitude of the swing decreasing with time. The proposed algorithm is validated using 13 multimodal test functions and benchmarked with PSO and SCA. The findings show that PSA is a good optimization algorithm, outperforming PSO in 8 out of 13 functions and 12 out of 13 for SCA. PSA is then applied for the optimization of vaccine distribution using the case of Hong Kong's 2009 H1N1 influenza endemic. The distribution percentage found by PSA is better in lowering the number of infections when compared with three traditional strategies usually used in health science.  
This paper is divided into five sections. The following section investigates existing algorithms with similar framework. The PSA is introduced in Section 3. Section 4 presents the experiment conducted including details of the H1N1\({}^{\prime}\)s extended SEIR and the findings obtained. Finally, the work is concluded in Section 5.