Learn how to formulate and solve linear programming problems with integer or binary variables using branch and bound and cutting planes methods.

An integer linear programming with thousand variables to compare the running time between parallels and without parallels using Gurobi First create a new environment and model using the GRBEnv and ...

Cutting plane method is a technique for solving linear programming problems that involve integer variables. It works by iteratively adding linear inequalities, called cuts, to the original problem ...

In contrast, restricting the variables to integer values requires a time increasing exponentially with n, even if the constraints and objective function are linear (known as integer linear programming ...

With the increasing design complexities, the design of pin-constrained digital microfluidic biochips (PDMFBs) is of practical importance for the emerging marketplace. However, solutions of current pin ...

This code generates an instance with two objectives, four decision variables, five constraints, 0.5 the sparsity of matrix A, 0.5 sparisty of matrix D, 25 percent of the decision variables are ...

We present integer linear models with a polynomial number of variables and constraints for combinatorial optimization problems in graphs: optimum elementary cycles, optimum elementary paths and ...

Learning Objectives Formulate a problem as a Linear Program (LP) Convert a LP into a required form, e.g., inequality form Plot the graphical representation of a linear optimization problem with two ...

Discrete differential evolution algorithm for integer linear bilevel programming problems Abstract: A discrete differential evolution algorithm combined with the branch and bound method is developed ...