For capacitated multi-item lot sizing problems, we propose a predictive search method that integrates machine learning/advanced analytics, mathematical programming, and heuristic search into a single framework. Advanced analytics can predict the probability that an event will happen and has been applied to pressing industry issues, such as credit scoring, risk management, and default management. Although little research has applied such technique for lot sizing problems, we observe that advanced analytics can uncover optimal patterns of setup variables given properties associated with the problems, such as problem attributes, and solution values yielded by linear programming relaxation, column generation, and Lagrangian relaxation. We, therefore, build advanced analytics models that yield information about how likely a solution pattern is the same as the optimum, which is insightful information used to partition the solution space into incumbent, superincumbent, and nonincumbent regions where an analytics-driven heuristic search procedure is applied to build restricted subproblems. These subproblems are solved by a combined mathematical programming technique to improve solution quality iteratively. We prove that the predictive search method can converge to the global optimal solution point. The discussion is followed by computational tests, where comparisons with other methods indicate that our approach can obtain better results for the benchmark problems than other state-of-the-art methods. Summary of Contribution: In this study, we propose a predictive search method that integrates machine learning/advanced analytics, mathematical programming, and heuristic search into a single framework for capacitated multi-item lot sizing problems. The advanced analytics models are used to yield information about how likely a solution pattern is the same as the optimum, which is insightful information used to divide the solution space into incumbent, superincumbent, and nonincumbent regions where an analytics-driven heuristic search procedure is applied to build restricted subproblems. These subproblems are solved by a combined mathematical programming technique to improve solution quality iteratively. We prove that the predictive search method can converge to the global optimal solution point. Through computational tests based on benchmark problems, we observe that the proposed approach can obtain better results than other state-of-the-art methods.