<p>This paper proposes a novel metaheuristic algorithm for solving engineering optimization problems, called the Adams-Bashforth-Moulton Optimizer (ABMO). The algorithm is inspired by the Adams-Bashforth-Moulton method, a numerical technique used for solving differential equations, which combines the advantages of explicit (Adams-Bashforth) and implicit (Adams-Moulton) methods to improve accuracy and stability through a two-step process of prediction and correction. Despite the success of existing metaheuristic algorithms, many suffer from limitations such as premature convergence, poor exploration-exploitation balance, and high computational cost, particularly in large-scale and complex optimization problems. To address these challenges, ABMO introduces a unique prediction-correction mechanism that dynamically balances exploration and exploitation, ensuring faster convergence and higher solution accuracy while maintaining computational efficiency. We establish a mathematical model of ABMO based on the Adams-Bashforth-Moulton four-step prediction-correction method. To demonstrate the performance of ABMO, we first conduct a qualitative analysis through convergence behavior experiments. Then, ABMO is compared with 11 state-of-the-art algorithms using the CEC2017 and CEC2022 benchmark suites. The results show that ABMO outperforms other comparative algorithms by 91%, 92%, 96%, 67%, and 80% on CEC2017 (30/50/100 dimensions) and CEC2022 (10/20 dimensions), respectively, ranking first in terms of solution quality and convergence speed. Statistical tests, including the Wilcoxon rank sum test and the Friedman test, further confirm the superiority of ABMO. Finally, we apply ABMO to solve nine multi-constraint engineering design problems and to extract core parameters for photovoltaic systems. The results demonstrate that ABMO can find better solutions faster than existing optimizers, demonstrating its great potential in solving real optimization problems.</p>