An analytical review of the grasshopper optimization method for multi-objective decision-making

Multi-objective optimization problems (MOPs) are common in real-world applications, including scheduling, vehicle routing, and engineering design. A key challenge in solving MOPs is balancing convergence and diversity, as these problems often involve conflicting objectives and complex constraints. To address this, researchers have developed numerous multi-objective optimization algorithms, among them the Multi-Objective Grasshopper Optimization Algorithm (MOGOA). MOGOA utilizes an external archive to store Pareto-optimal solutions and employs a roulette wheel selection mechanism to guide global optimization, effectively directing the evolution of the grasshopper population toward diverse and high-quality solutions. Since its introduction by Mirjalili et al. in 2018, MOGOA has attracted significant attention from researchers and has been widely applied to address various MOPs across diverse domains. This review paper examines key research publications utilizing MOGOA. First, an overview of MOGOA is provided, detailing its bio-inspired foundation and optimization framework. The core operations of MOGOA are explained step-by-step, and its theoretical basis is outlined. Reviewed studies are categorized into three groups based on their adaptation approach: standard, modified, and hybridized implementations. The primary applications of MOGOA are comprehensively explored. Next, a critical evaluation of MOGOA's performance is presented, comparing its effectiveness against recent multi-objective algorithms using the CEC2009 benchmark test suite. Additionally, an in-depth analysis of MOGOA's strengths, weaknesses, and key research gaps is provided. Finally, the paper concludes with insights and potential future research directions for MOGOA. This review offers a comprehensive analysis of MOGOA's performance and applications, contributing to the broader field of MOPs.