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<p>The speed reducer design problem is a classical benchmark in constrained mechanical optimization, characterized by a highly nonlinear objective function, mixed discrete–continuous design variables, and a narrow feasible region governed by multiple stress, deflection, and geometric constraints. Although numerous evolutionary and swarm-based metaheuristic algorithms have been applied to this problem, many existing methods exhibit premature convergence, instability in feasibility maintenance, and strong sensitivity to control parameters, particularly when operating near constraint-active regions. These limitations indicate a persistent need for more robust and adaptive optimization strategies. This paper proposes a novel application of the Scuba Diver Optimization Algorithm (SDOA) for minimizing the total weight of a speed reducer subject to eleven nonlinear inequality constraints. From an optimization perspective, SDOA is formulated as a population-based metaheuristic that employs an adaptive control variable to regulate search depth, exploration–exploitation balance, and operator selection throughout the optimization process. The algorithm integrates staged global exploration, controlled local refinement, and diversity restoration mechanisms, enabling effective navigation of highly constrained design spaces. A penalty-augmented constraint-handling scheme is incorporated to ensure reliable discrimination between feasible and infeasible solutions. Extensive numerical experiments were conducted under 30 parameter scenarios spanning three population sizes (50, 200, and 500 divers), multiple iteration budgets, and different oxygen-decay and elite-preservation settings. Each scenario was evaluated over 30 independent runs, yielding a total of 900 optimization runs. The best overall configuration attained a minimum reducer weight of 2992.859644, while the complete campaign achieved an overall feasibility rate of 899/900 runs (99.89%). Best, mean, worst, and standard deviation statistics consistently indicate stable convergence, narrow best–mean gaps, and strong repeatability across the tested settings. The results demonstrate that SDOA provides an effective and competitive optimization framework for constrained mechanical design problems. At the same time, the study acknowledges its current scope: the experimental validation is limited to the canonical speed reducer benchmark, and broader confirmation on additional constrained test suites remains a natural direction for future work.</p>

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Constrained speed reducer design optimization using a novel Scuba Diver Optimization Algorithm

  • 期刊论文

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  • 发表日期：

    2026年7月21日

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  • Saman M. Almufti,
  • Amira Bibo Sallow

摘要

The speed reducer design problem is a classical benchmark in constrained mechanical optimization, characterized by a highly nonlinear objective function, mixed discrete–continuous design variables, and a narrow feasible region governed by multiple stress, deflection, and geometric constraints. Although numerous evolutionary and swarm-based metaheuristic algorithms have been applied to this problem, many existing methods exhibit premature convergence, instability in feasibility maintenance, and strong sensitivity to control parameters, particularly when operating near constraint-active regions. These limitations indicate a persistent need for more robust and adaptive optimization strategies. This paper proposes a novel application of the Scuba Diver Optimization Algorithm (SDOA) for minimizing the total weight of a speed reducer subject to eleven nonlinear inequality constraints. From an optimization perspective, SDOA is formulated as a population-based metaheuristic that employs an adaptive control variable to regulate search depth, exploration–exploitation balance, and operator selection throughout the optimization process. The algorithm integrates staged global exploration, controlled local refinement, and diversity restoration mechanisms, enabling effective navigation of highly constrained design spaces. A penalty-augmented constraint-handling scheme is incorporated to ensure reliable discrimination between feasible and infeasible solutions. Extensive numerical experiments were conducted under 30 parameter scenarios spanning three population sizes (50, 200, and 500 divers), multiple iteration budgets, and different oxygen-decay and elite-preservation settings. Each scenario was evaluated over 30 independent runs, yielding a total of 900 optimization runs. The best overall configuration attained a minimum reducer weight of 2992.859644, while the complete campaign achieved an overall feasibility rate of 899/900 runs (99.89%). Best, mean, worst, and standard deviation statistics consistently indicate stable convergence, narrow best–mean gaps, and strong repeatability across the tested settings. The results demonstrate that SDOA provides an effective and competitive optimization framework for constrained mechanical design problems. At the same time, the study acknowledges its current scope: the experimental validation is limited to the canonical speed reducer benchmark, and broader confirmation on additional constrained test suites remains a natural direction for future work.