Comparison of Metaheuristic Optimization Algorithms in the Solution of Risk Optimization Problems

Risk optimization, also known as life-cycle cost and risk optimization, is a comprehensive stochastic approach that minimizes expected total costs by incorporating failure probabilities directly into the objective function. Despite its robustness, the formulation faces significant computational challenges due to the multidisciplinary nature of engineering systems and the complexities of rare-event reliability analysis. Crucially, computing these failure probabilities often relies on numerical methods, such as Monte Carlo simulation, which introduces inherent stochastic noise into the objective function and creates a highly rugged search landscape. This study benchmarks 10 metaheuristic methods—including particle swarm optimization, ant colony optimization, and genetic algorithms—across six representative problems of varying dimensionality (scaling up to a 20-variable structural benchmark) and time-dependency to identify the most effective strategies for this domain. The results reveal a distinct performance hierarchy, with ant colony optimization and the firefly algorithm emerging as the superior methods, closely followed by particle swarm optimization as a highly competitive alternative. These top-performing algorithms demonstrated exceptional convergence and high statistical stability, likely due to their mechanisms for collective reinforcement and momentum, which serve as numerical filters against the aforementioned stochastic noise. Conversely, methods such as simulated annealing, genetic algorithms, and invasive weed optimization showed limited applicability, characterized by high result variability and difficulty in navigating risk optimization search landscapes. Finally, when evaluating practical utility, methods including ant colony optimization, artificial bee colony, and teaching-learning-based optimization proved exceptionally robust. While the number of search agents must be scaled proportionally to problem size, these algorithms delivered consistent solutions using standard literature parameters without requiring time-consuming, problem-specific calibration. This inherent robustness distinguishes them from more sensitive heuristics and highlights their practical utility for complex engineering applications where extensive parameter tuning is computationally prohibitive.