A COMPREHENSIVE BENCHMARK STUDY ON FIVE NOVEL METAHEURISTICS: FLOOD, FOOTBALL TRAINING, GOAT, HUMAN EVOLUTIONARY, AND TORNADO-BASED OPTIMIZATION APPROACHES

Abstract

We present a unified benchmark of five recently introduced population-based metaheuristics—Flood Algorithm (FA), Football Team Training Algorithm (FTTA), Goat Optimization Algorithm (GOA), Human Evolutionary Optimization Algorithm (HEOA), and Tornado Optimization with Coriolis Force (TOC)—under strictly comparable conditions on five canonical engineering design problems (spring, welded beam, gear train, speed reducer, and pressure vessel). Each method was independently run 100 times with a population of 30 individuals and a 150-iteration budget, and performance was assessed by solution quality (best/mean), variability (std), and convergence behavior. To establish statistical robustness, we complemented pairwise t-tests with Wilcoxon signed-rank post-hoc tests under Holm correction and reported effect sizes. Results show that FTTA and FA consistently combine fast, lowvariance convergence on continuous constrained designs, TOC excels in precisionsensitive/discrete settings (notably Gear Train), GOA remains competitive yet problemdependent, and HEOA generally underperforms. Overall, superiority is problem-dependent rather than universal, aligning with the No Free Lunch perspective. Beyond aggregate rankings, the study offers practical guidance by mapping problem characteristics to algorithm strengths and provides the first head-to-head evidence base for these five methods, supporting future work on broader domains, adaptive budgets/parameters, multi-objective and noisy/dynamic settings, and runtime–quality trade-offs.