Squid Game Optimizer (SGO): a novel metaheuristic algorithm

www.nature.com/scientificreports OPEN Squid Game Optimizer (SGO): a novel metaheuristic algorithm Mahdi Azizi 1,3,4*, Milad Baghalzadeh Shishehgarkhaneh 2,4, Mahla Basiri 1,3 & Robert C. Moehler 2 In this paper, Squid Game Optimizer (SGO) is proposed as a novel metaheuristic algorithm inspired by the primary rules of a traditional Korean game. Squid game is a multiplayer game with two primary objectives: attackers aim to complete their goal while teams try to eliminate each other, and it is usually played on large, open fields with no set guidelines for size and dimensions. The playfield for this game is often shaped like a squid and, according to historical context, appears to be around half the size of a standard basketball court. The mathematical model of this algorithm is developed based on a population of solution candidates with a random initialization process in the first stage. The solution candidates are divided into two groups of offensive and defensive players while the offensive player goes among the defensive players to start a fight which is modeled through a random movement toward the defensive players. By considering the winning states of the players of both sides which is calculated based on the objective function, the position updating process is conducted and the new position vectors are produced. To evaluate the effectiveness of the proposed SGO algorithm, 25 unconstrained mathematical test functions with 100 dimensions are used, alongside six other commonly used metaheuristics for comparison. 100 independent optimization runs are conducted for both SGO and the other algorithms with a pre-determined stopping condition to ensure statistical significance of the results. Statistical metrics such as mean, standard deviation, and mean of required objective function evaluations are calculated. To provide a more comprehensive analysis, four prominent statistical tests including the Kolmogorov–Smirnov, Mann–Whitney, and Kruskal– Wallis tests are used. Meanwhile, the ability of the suggested SGOA is assessed through the cuttingedge real-world problems on the newest CEC like CEC 2020, while the SGO demonstrate outstanding performance in dealing with these complex optimization problems. The overall assessment of the SGO indicates that the proposed algorithm can provide competitive and remarkable outcomes in both benchmark and real-world problems. Real-world optimization problems are considered quite challenging tasks and intricate problems in almost every field, classifying them in miscellaneous categories, including constrained or unconstrained, single or multiobjective, continuous or discrete, and static or dynamic. In some of engineering and industrial applications, which can be formulated as optimization problems, researchers are attempting to optimize specific variables, whether to reduce costs and energy consumption or increase profit, production, efficiency, and performance. Consequently, it is imperative to have an efficient optimizer to guarantee that the best solutions are found. The central component of an optimizer is a search or optimization algorithm that is properly designed and executed to conduct the necessary exploration. For a long time, traditional search approaches have been used to solve optimization issues. Even though these strategies provide promising results in different real-world problems, they may face failure in more complicated optimization problems. Hence, to solve these complex problems, metaheuristic algorithms have been developed. Generally, metaheuristic algorithms can be categorized into four primary groups. The first one is the evolutionary based metaheuristic algorithms, which simultaneously perform the search procedure using several initial points. Holland1 introduced the Genetic Algorithm (GA), which is a popular population-based metaheuristic algorithm inspired by Darwinian evolution theory. Differential Evolution (DE) algorithm is another wellknown stochastic population-based algorithm for global o ptimization2,3. Furthermore, with the popularity of the Imperialist Competitive Algorithm4, there have been various more frequently used population-based algorithms, including Charged System S earch5–7, Intelligent Water D rops8, Stochastic Paint O ptimizer9,10, Political 1 Department of Civil Engineering, University of Tabriz, Tabriz, Iran. 2Department of Civil Engineering, Monash University, Clayton, VIC 3800, Australia. 3Department of Civil Engineering, Near East University, Nicosia, Cyprus. 4These authors contributed equally: Mahdi Azizi and Milad Baghalzadeh Shishehgarkhaneh. *email: Scientific Reports | (2023) 13:5373 | https://doi.org/10.1038/s41598-023-32465-z 1 Vol.:(0123456789) www.nature.com/scientificreports/ Optimizer11, Dynamic Virtual Bats A lgorithm12, Ali Baba and the forty t hieves13, Tiki-taka algorithm14, and Coronavirus Optimization A lgorithm15. The second category is swarm-based metaheuristic algorithms, which are based on the social behaviour of diverse species in natural groups like ants, bees, birds, fishes, and termites. Particle Swarm Optimization (PSO)16 and Ant Colony Optimization (ACO)17,18 are prominent swarm-based algorithms While these algorithms imitate bird and ant colonies’ aggregation and foraging behaviors, r espectively19. Artificial Bee Colony (ABC)20,21, Al-Biruni Earth R adius22, Border Collie O ptimization23, Stochastic Diffusion 24 25 26 Search , Glowworm Swarm Optimization , Mountain Gazelle O ptimizer , Cuckoo Search27, Flower Pollination Algorithm28, and Black Widow Optimization A lgorithm29 are other examples of this sort. Furthermore, physicsbased metaheuristic algorithms are the third classification inspired by physics laws, such as heat transformation, gravitational force, particle motions, and wave propagation. Undoubtedly, the SA algorithm, inspired by annealing in solids’ analogy to the statistical mechanics, has gained much popularity in this category30. Big-Bang Big-Crunch algorithm, which is inspired by the theories of the evolution of the universe, is another example of a physics-based optimization a lgorithm31. Additionally, it is noteworthy to state that there are still various metaheuristic methods that take inspiration from the laws of physics that have been documented in literature. Some of the most common algorithms include Atomic Orbital Search32–34, Material Generation Algorithm35–37, Cyber-physical Systems38, Chaos Game O ptimization39,40, Archimedes Optimization A lgorithm41, Lichtenberg 42 43 44–46 Algorithm , Energy Valley Optimizer , Crystal Structure Algorithm , Thermal Exchange Optimization Algorithm47, Equilibrium O ptimizer48, Weighted Vertices O ptimizer49, and Lévy Flight Distribution50. Finally, the last group is human behavior-based metaheuristic algorithms. The development of certain human-based algorithms has been inspired by simulating various human behaviors, including Teaching–Learning-Based Optimization (TLBO)51, Cul (...truncated)