Abstract—Nature-inspired metaheuristic algorithms, particularly those founded on swarm intelligence, have attracted much attention over the past decade. Firefly algorithm has appeared in approximately seven years ago, its literature has enlarged considerably with different applications. It is inspired by the behavior of fireflies. The aim of this paper is the application of firefly algorithm for solving a nonlinear algebraic system. This resolution is needed to study the Selective Harmonic Eliminated Pulse Width Modulation strategy (SHEPWM) to eliminate the low order harmonics; results have been applied on multilevel inverters. The final results from simulations indicate the elimination of the low order harmonics as desired. Finally, experimental results are presented to confirm the simulation results and validate the efficaciousness of the proposed approach. Keywords—Firefly algorithm, metaheuristic algorithm, multilelvel inverter, SHEPWM. I. INTRODUCTION ETAHEURISTICS methods inspired by nature are currently among the most powerful tools for the optimization of many non-linear hard combinatorial problems (NP-hard). These methods are based on an existing biological mechanisms natural phenomenon. Natural systems are those of the most interesting inspiration to design new techniques dedicated to solve many optimization problems. Particle Swarm Optimization (PSO), a colony of ants and bee colony algorithms are methods inspired by the observation of nature. These optimization algorithms use the behavior of the swarm intelligence. They are based on live insects or simple interactions between individual entities [1], [2]. This is the subject of this work. The firefly algorithm (FA), proposed by Xin-She Yang at the University of Cambridge, is a new metaheuristic algorithm, which is inspired by the behavior of fireflies. Their population is estimated at about two thousand species of fireflies. Most of them produce short, rhythmic flashes. Their flashing light, generated by a process of bioluminescence, can be used as part of courtship rituals or signals [1]-[3]. Multilevel inverters are controlled by PWM strategies. Among the most well known strategies, one finds SHEPWM [4]-[6] which is the subject of this work. This strategy consists in calculating the switching angles (firing angles) for the N. Ould Cherchali, A. Tlemçani and A. Morsli are with the Research Laboratory in Electrical Engineering and Automatic (LREA), University of Medea, Ain D’heb, Medea, Algeria (e-mail: nocherchali@yahoo.fr). M.S. Boucherit is with the Process Control Laboratory (LPC), National Polytechnic School ENP, Algiers, Algeria. multilevels inverter to have a shape nearest sinusoidal. But to find the switching angles, we must solve an algebraic nonlinear equations. In this paper, we will solve this system by the application of FA. II. FA In the FA, the objective function (or fitness) of a given optimization problem is based on the differences in light intensity. It helps fireflies to move towards brighter and more attractive places for optimal solutions. All fireflies are characterized by their light intensity associated with the objective function. Each firefly is changing its position iteratively. The FA has three rules [1]-[3]:  All fireflies are unisex, and they will move towards more attractive and brighter ones.  The attractiveness of a firefly is proportional to its brightness that decreases as the distance from the other firefly increases. If there is not a more attractive firefly than a particular one, it will move randomly.  The brightness of a firefly is determined by the value of the objective function. For maximization problems, the brightness is proportional to the value of the objective function. Each firefly has its attractiveness β described by monotonically decreasing function of the distance between two any fireflies:   1 , 0    m e r m r    (1) where β 0 designates the maximum attractiveness (at r = 0) and γ is the light absorption coefficient, which controls the decrease of the light intensity. The distance between two fireflies i and j at positions x i and x j can be defined as [1], [3]: 2 1 , , ) (       d k k j k i j i ij x x x x r (2) where x i,k is the k-th component of the spatial coordinate x i of i-th firefly and d represents the number of dimensions. The movement of a firefly i is described by the following form [1]: Elimination of Low Order Harmonics in Multilevel Inverter Using Nature-Inspired Metaheuristic Algorithm N. Ould Cherchali, A. Tlemçani, M. S. Boucherit, A. Morsli M World Academy of Science, Engineering and Technology International Journal of Energy and Power Engineering Vol:13, No:9, 2019 638 International Scholarly and Scientific Research & Innovation 13(9) 2019 ISNI:0000000091950263 Open Science Index, Energy and Power Engineering Vol:13, No:9, 2019 waset.org/Publication/10010750