Marathon runner algorithm: theory and application in mathematical, mechanical and structural optimization problems

Abstract

This study proposes a novel human-inspired metaheuristic search algorithm called marathon runner algorithm. This method mimics competitive behaviors observed in real marathon runners through mathematical modeling. Unlike classical elitist algorithms that prioritize position of the best agent, the marathon runner algorithm introduces a novel concept called vision point. This point considers the quality of the entire population, not just the leader. By guiding the population towards vision point, the risk of getting trapped in local optima is reduced. A two-part evaluation was conducted to thoroughly assess the search capabilities of the marathon runner algorithm. First, it is tested against a set of unconstrained benchmark mathematical functions and the algorithm’s quantitative attributes, such as complexity, accuracy, stability, diversity, sensitivity, and convergence rate are analyzed. Subsequently, the algorithm was applied to mechanical and structural optimization problems with both continuous and discrete variables. This application demonstrated the effectiveness of the algorithm in solving practical engineering challenges with constraints. The outcomes are compared with those obtained by six other well-established techniques. The obtained results indicate that the marathon runner algorithm yields promising and competitive solutions for both mathematical, mechanical, and structural problems.