Advanced Optimization for Process Systems Engineering

This chapter addressed the solution of mixed-integer linear (MILP) problems for which first simple methods are introduced, namely exhaustive enumeration of all 0-1 combinations, and solution through relaxation and rounding. The branch and bound method is then formally introduced, identifying major properties such as lower bounding in order to use these tofathom nodes, or to obtain feasibleinteger solutions which yield upper bounds. The concept of cutting planes is also introduced with Gomory's cutting plane. Finally, the combination of branch and bound and cutting planes is discussed. Finally, a brief discussion on software such as CPLEX, GUROBI, and XPRESS is presented.