The fusion–fission optimization (FuFiO) algorithm

www.nature.com/scientificreports OPEN The fusion–fission optimization (FuFiO) algorithm Behnaz Nouhi1, Nima Darabi2, Pooya Sareh3*, Hadi Bayazidi4, Farhad Darabi5 & Siamak Talatahari6 Fusion–Fission Optimization (FuFiO) is proposed as a new metaheuristic algorithm that simulates the tendency of nuclei to increase their binding energy and achieve higher levels of stability. In this algorithm, nuclei are divided into two groups, namely stable and unstable. Each nucleus can interact with other nuclei using three different types of nuclear reactions, including fusion, fission, and β-decay. These reactions establish the stabilization process of unstable nuclei through which they gradually turn into stable nuclei. A set of 120 mathematical benchmark test functions are selected to evaluate the performance of the proposed algorithm. The results of the FuFiO algorithm and its related non-parametric statistical tests are compared with those of other metaheuristic algorithms to make a valid judgment. Furthermore, as some highly-complicated problems, the test functions of two recent Competitions on Evolutionary Computation, namely CEC-2017 and CEC-2019, are solved and analyzed. The obtained results show that the FuFiO algorithm is superior to the other metaheuristic algorithms in most of the examined cases. Optimization is a branch of applied mathematics that is widely used in various scientific disciplines because many problems can be expressed in the form of an optimization problem. Obviously, with the present rate of progress in all scientific fields, we face a variety of new real-world problems that have become more complex, such that conventional mathematical methods, such as exact optimizers, cannot solve them efficiently. In particular, exact optimizers do not have sufficient efficiency in dealing with many non-continuous, non-differentiable, and large-scale real-world multimodal p roblems1. Early studies in the field of nature-inspired computation demonstrated that some numerical methods developed based on the behavior of natural creatures can solve real-world problems more effectively than exact methods2. Metaheuristic methods are numerical techniques that combine the heuristic rules of natural phenomena with a randomization process. Notably, over the past few decades, many researchers have concluded that developing and enhancing metaheuristic algorithms are practically-effective and computationally-efficient approaches to tackling complex and challenging unsolved real-world optimization p roblems3–8. A key advantage of metaheuristic methods is that they are problem-independent algorithms which provide acceptable solutions to complex and highly nonlinear problems in a reasonable time. Furthermore, they generally do not need any significant contributions to the algorithm structure from implementers, but it is only needed that they formulate the problem according to the requirements of the chosen metaheuristic. The point worth mentioning is that the core operation of the metaheuristic approaches is based on non-gradient procedures, where there is no need for cumbersome computations such as calculations of derivatives and multivariable generalizations. Moreover, randomization components enable metaheuristic algorithms to perform generally better than conventional methods. In particular, their stochastic nature enables them to escape from local optima and move toward global optimum on the search space of large-scale and challenging optimization problems. Conventionally, two general criteria are used to classify metaheuristic methods: (1) the number of agents, and (2) the origin of inspiration. Based on the first criterion, metaheuristic algorithms can be divided into two groups: (1) single-solution-based algorithms, and (2) population-based algorithms. Also, according to inspiration, metaheuristic algorithms are divided into two main categories, namely Evolutionary Algorithms (EAs) and Swarm Intelligence (SI) algorithms. Single-solution-based methods try to modify one solution (agent) during the search process like what goes in the Simulated Annealing (SA) a lgorithm9; on the other hand, in population-based 1 Department of Mathematical Sciences, University of Tabriz, Tabriz, Iran. 2Department of Civil, Constructional and Environmental Engineering, Sapienza University of Rome, Via Eudossiana, 18, 00184 Rome, Italy. 3Creative Design Engineering Laboratory (Cdel), Department of Mechanical, Materials, and Aerospace Engineering, School of Engineering, University of Liverpool, Liverpool L69 3GH, UK. 4Department of Civil Engineering, University of Tabriz, Tabriz, Iran. 5Department of Physics, Azarbaijan Shahid Madani University, Tabriz 53714‑161, Iran. 6Faculty of Engineering and Information Technology, University of Technology Sydney, Ultimo, NSW 2007, Australia. *email: Scientific Reports | (2022) 12:12396 | https://doi.org/10.1038/s41598-022-16498-4 1 Vol.:(0123456789) www.nature.com/scientificreports/ algorithms, a population of solutions is used to find the optimal answer similar to the simulation process in the Particle Swarm Optimization (PSO) a lgorithm10. In EAs, the genetic evolution process is the main origin. Evolutionary Programming (EP)2, Evolutionary Strategy (ES)11, Genetic Algorithm (GA)12, and Differential Evolution (DE) are among the most famous methods in this domain. Besides, Simon13 proposed the Biogeography-Based Optimization (BBO) algorithm, which is used for global recombination and uniform crossover. Also, SI algorithms are based on the simulation of the collective behavior of creatures. SI algorithms are classified into three categories as follows. The first category is associated with the behavioral models of animals such as PSO10, Ant Colony Optimization (ACO)14, Artificial Bee Colony (ABC)15, Firefly Algorithm (FA)16, Cuckoo Search (CS)17, Bat Algorithm (BA)18, Eagle Strategy (ES)19, Krill Herd (KH)20, Flower Pollination Algorithm (FPA)21, Grey Wolf Optimizer (GWO)22, Ant Lion Optimizer (ALO)23, Grasshopper Optimization Algorithm (GOA)24, Symbiotic Organisms Search (SOS)25,26, Moth Flame Optimizer (MFO)27, Dragonfly Algorithm (DA)28, Salp Swarm Algorithm (SSA)29, Crow Search Algorithm (CSA)30, Whale Optimization Algorithm (WOA)31,32, Developed Swarm Optimizer (DSO)33, Spotted hyena optimizer (SHO)34, Farmland fertility algorithm (FFA)35,36, African Vultures Optimization (AVO)37, Bald Eagle Search Algorithm (BES)38,39 Tree Seed Algorithm (TSA)40,41, and Artificial Gorilla Troops (GTO) o ptimizer42. The second category concerns algorithms based on the physical and mathematical laws, such as Simulated Annealing (SA)9, Big Bang–Big Crunch optimization (BB–BC)43, Charged System Search (CSS)44,45, Chaos Game Optimization (CGO)46,47, Gravitational Search Algorithm (GSA)48, Sine Cosine Algorithm (SCA)49, Multi-Verse Optimizer (MVO)50, Atom Search Optimization (ASO)51, Crystal Structure Algorithm (CryStAl)52–55, and Electromagnetic field optimizatio (...truncated)