Solving Linear Mixed Integer Programming Models Using Branch and Bound Algorithm
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This article introduces how to utilize the branch and bound algorithm to solve linear mixed integer programming problems. As a specialized search algorithm, it efficiently identifies optimal solutions through systematic tree traversal and pruning strategies. We demonstrate MATLAB implementation with detailed procedural explanations, including key functions like intlinprog for integer constraints handling and custom branching logic. Readers will learn problem formulation techniques, algorithm workflow (node selection, bounding, and pruning), and practical adaptation for real-world scenarios. The discussion covers typical applications in logistics and resource allocation, along with performance analysis. Accompanying code examples illustrate core components: constraint matrix initialization, objective function configuration, and termination criteria implementation to solidify comprehension.
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