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An Explosion Based Algorithm to Solve the Optimization Problem in Quadcopter Control aerospace Article An Explosion Based Algorithm to Solve the Optimization Problem in Quadcopter Control Mohamad Norherman Shauqee 1, Parvathy Rajendran 1,2,* and Nurulasikin Mohd Suhadis 1 1 School of Aerospace Engineering, Engineering Campus, Universiti Sains Malaysia, Nibong Tebal 14300, Pulau Pinang, Malaysia; [email protected] (M.N.S.); [email protected] (N.M.S.) 2 Faculty of Engineering & Computing, First City University College, Bandar Utama, Petaling Jaya 47800, Selangor, Malaysia * Correspondence: [email protected] Abstract: This paper presents an optimization algorithm named Random Explosion Algorithm (REA). The fundamental idea of this algorithm is based on a simple concept of the explosion of an object. This object is commonly known as a particle: when exploded, it will randomly disperse fragments around the particle within the explosion radius. The fragment that will be considered as a search agent will fill the local space and search that particular region for the best fitness solution. The proposed algorithm was tested on 23 benchmark test functions, and the results are validated by a comparative study with eight well-known algorithms, which are Particle Swarm Optimization (PSO), Artificial Bee Colony (ABC), Genetic Algorithm (GA), Differential Evolution (DE), Multi-Verse Optimizer (MVO), Moth Flame Optimizer (MFO), Firefly Algorithm (FA), and Sooty Tern Optimization Algorithm (STOA). After that, the algorithm was implemented and analyzed for a quadrotor control application. Similarly, a comparative study with the other algorithms stated was done. The findings reveal that Citation: Shauqee, M.N.; Rajendran, the REA can yield very competitive results. It also shows that the convergence analysis has proved P.; Suhadis, N.M. An Explosion Based that the REA can converge more quickly toward the global optimum than the other metaheuristic Algorithm to Solve the Optimization algorithms. For the control application result, the REA controller can better track the desired reference Problem in Quadcopter Control. input with shorter rise time and settling time, lower percentage overshoot, and minimal steady-state Aerospace 2021, 8, 125. https://doi. error and root mean square error (RMSE). org/10.3390/aerospace8050125 Keywords: random explosion; metaheuristic optimization; artificial intelligence; controller design; Academic Editors: David Anderson unimodal benchmark; multimodal benchmark and Gokhan Inalhan Received: 18 February 2021 Accepted: 21 April 2021 1. Introduction Published: 27 April 2021 Over the past few years, the popularity of metaheuristic optimization techniques Publisher’s Note: MDPI stays neutral to solve complex real-life problems has grown among researchers. The main reason for with regard to jurisdictional claims in using metaheuristic optimization techniques is that they are relatively simple, flexible, published maps and institutional affil- non-transferable, and can avoid local stagnation [1]. The simplicity of the metaheuristic iations. algorithms is derived from straightforward concepts that are typically inspired by physical phenomena, animal behavior, or evolutionary ideas. Flexibility refers to applying meta- heuristic algorithms to different problems without any specific structural changes in its algorithm. Metaheuristic algorithms are easily applied to a variety of issues since they usually assume problems as black boxes. Most metaheuristic algorithms have mechanisms Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. that are free of derivation. This article is an open access article In contrast to gradient-based optimization approaches, these algorithms stochastically distributed under the terms and optimize the problems. This optimization process begins with a random solution(s), and conditions of the Creative Commons there is no need to calculate the derivative of the search spaces to find the optimum value. Attribution (CC BY) license (https:// This makes metaheuristic algorithms highly suitable for real problems with expensive or creativecommons.org/licenses/by/ unknown information on derivatives. 4.0/). Aerospace 2021, 8, 125. https://doi.org/10.3390/aerospace8050125 https://www.mdpi.com/journal/aerospace Aerospace 2021, 8, x 28 of 31 Aerospace 2021, 8, 125 2 of 30 Compared to conventional optimization techniques, metaheuristic algorithms have a superior capability in avoiding local optima. Due to these algorithms’ stochastic nature, it is possibleCompared to prevent to conventional stagnation optimization in local optima techniques, and search metaheuristic extensively algorithms throughout have the a searchsuperior space. capability The real in avoidingproblem localarea optima.is usually Due unknown to these and algorithms’ complicated stochastic with nature,many local it is optima,possible so to preventmetaheuristic stagnation algorithms in local are optima excellent and search for optimizing extensively these throughout challenging the searchprob- lems.space. The real problem area is usually unknown and complicated with many local optima, so metaheuristicGenerally, metaheuristic algorithms are algorithms excellent forcan optimizingbe divided theseinto two challenging categories problems.: single-solu- tion andGenerally, multi-solution metaheuristic based. algorithms On a single can-solution be divided basis, into the two search categories: process single-solution begins with oneand multi-solutioncandidate solution based. improved On a single-solution throughout basis,the iterations. the search Whereas process beginsmulti- withsolution one- basedcandidate optimization solution was improved carried throughout out using an the initially iterations. random Whereas set of multi-solution-basedpopulation solutions, theseoptimization populations was carriedwill be enhanced out using during an initially the iterations. random set Multiple of population solutions solutions, (population) these populations will be enhanced during the iterations. Multiple solutions (population) based based optimization has some advantages over single-solution-based optimization [2]: optimization has some advantages over single-solution-based optimization [2]: • There are multiple possible best solutions. • There are multiple possible best solutions. • There is information sharing between the multiple solutions that can assist each other • There is information sharing between the multiple solutions that can assist each other to avoid local optima. to avoid local optima. • Exploration in the search space of multiple solutions is more significant than a single • Exploration in the search space of multiple solutions is more significant than a sin- solution. gle solution. Furthermore, these metaheuristic algorithms can be classified further into three clas- Furthermore, these metaheuristic algorithms can be classified further into three classes ses which are evolutionary-based, physical-based, and swarm-based methods [3], as which are evolutionary-based, physical-based, and swarm-based methods [3], as shown shown in Figure 1. The first class is a generic population-based algorithm based on bio- in Figure1. The first class is a generic population-based algorithm based on biological logicalevolution, evolution, such as such reproduction, as reprodu mutation,ction, mutation, recombination, recombination, and selection. and selection. This method This methodoften provides often provides close-to-optimal close-to-optimal solutions solutions to all types to all of types problems of problems as it does as it not does make not makeany assumptions any assumptions about about the basic the basic fitness fitness landscape. landscape. Some Some of the of popularthe popular metaheuristic metaheu- risticalgorithms algorithms based based on the on concept the concept of evolution of evolution (EA) in (EA) nature in are nature Genetic are AlgorithmGenetic Algorithm (GA) [4], (GA)Differential [4], Differential Evolution Evolution (DE) [5], Evolution (DE) [5], StrategyEvolution (ES) Strategy [6,7], Genetic (ES) [6 Programming,7], Genetic Program- (GP) [8], mingand Biogeography-Based (GP) [8], and Biogeography Optimizer-Based (BBO) Optimi [9]. zer (BBO) [9]. Figure 1. ClassificationClassification of metaheuristic algorithms.algorithms. The second class of metaheuristic optimization is is an algorithm based on physics. Such an optimization algorithm communicates with each search agent.agent. The search agent moves acrossacross thethe search search space space according according to theto the laws laws of physics, of physics such, assuch gravitational as gravitational forces, forces,electromagnetic electromagnetic forces, inertia,forces, inertia, etc. These etc. metaheuristic These metaheuristic algorithms algorithms are Simulated are Simulated Anneal- Annealinging (SA) [10 (SA)], Gravitational [10], Gravitational Search AlgorithmSearch Algorithm (GSA) [11 (GSA)], Black [11] Hole, Black (BH) Hole algorithm (BH) algo- [12], rithmRay Optimization [12], Ray Optimization (RO) algorithm (RO) algorithm [13], Big-Bang [13], Big Big-Crunch-Bang Big (BBBC)-Crunch [14 (BBBC)], Central [14], Force Cen- tralOptimization Force Optimization (CFO) [15 ],(CFO) Charge [15] System, Charge Search System (CSS) Search [16], (CSS) Small [16] World, Small Optimization World Opti- Al- mizationgorithm (SWOA) Algorithm [17 ],(SWOA) Artificial [17] Chemical, Artificial Reaction Chemical Optimization Reaction AlgorithmOptimization (ACROA) Algorithm [18], (ACROA)Galaxy-based [18] Search, Galaxy Algorithm-based Search (GbSA) Algorithm [19], and
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