MATLAB Integer Programming Implementation with Multiple Algorithm Approaches

This MATLAB-based integer programming implementation provides three distinct algorithmic approaches for solving integer programming problems. The cutting plane method implementation iteratively adds new constraints to refine the feasible region and approach the optimal solution through linear programming relaxations. The branch and bound algorithm systematically divides the problem into smaller subproblems using bounding techniques to eliminate non-promising branches, implementing tree traversal with pruning strategies. The enumeration module offers two methods for 0-1 programming: complete enumeration that evaluates all possible combinations, and implicit enumeration that uses logical tests to skip infeasible solutions early. Each algorithm includes MATLAB optimization toolbox integration, with custom functions handling constraint management and solution validation. The program's adaptive structure allows users to select the appropriate method based on problem characteristics, size, and constraint complexity, providing robust solutions for various integer programming scenarios.