Solving Integer Programming Problems Using Branch and Bound Method

This example demonstrates how to solve integer programming problems using MATLAB's branch and bound method implementation. Integer programming refers to optimization problems where decision variables must take integer values. The branch and bound method is a fundamental algorithm for solving integer programming problems by recursively dividing the problem into smaller subproblems, branching each subproblem into two new problems, solving each subproblem, and progressively narrowing the feasible region until the optimal solution is found. The MATLAB implementation uses the intlinprog function, which automatically applies the branch and bound algorithm. Key parameters include specifying integer variables, objective function coefficients, constraint matrices, and variable bounds. The code defines an integer programming problem with: - intcon = [1,2] specifies that variables 1 and 2 must be integers - f = [2 3] represents the objective function coefficients - A = [-1 -1; 1 2; 2 1] defines the constraint coefficient matrix - b = [-2; 2; 3] specifies the right-hand side values for constraints - lb = [0 0] sets lower bounds for variables - ub = [Inf Inf] sets upper bounds (unbounded above) The intlinprog function call [x, fval] = intlinprog(f, intcon, A, b, [], [], lb, ub) solves the problem using branch and bound method, returning the optimal solution x and objective value fval. Interested users can study and adapt this code for their specific integer programming applications.