A Hybrid Approach of Bundle and Benders Applied Large Mixed Linear Integer Problem

A Hybrid Approach of Bundle and Benders Applied Large Mixed Linear Integer Problem

Consider a large mixed integer linear problem where structure of the constraint matrix is sparse, with independent blocks, and coupling constraints and variables. There is one of the groups of constraints to make difficult the application of Benders scheme decomposition. In this work, we propose the following algorithm; a Lagrangian relaxation is made on the mentioned set of constraints; we pre...

Combinatorial Benders' Cuts for Mixed-Integer Linear Programming

Mixed-Integer Programs (MIP’s) involving logical implications modelled through big-M coefficients, are notoriously among the hardest to solve. In this paper we propose and analyze computationally an automatic problem reformulation of quite general applicability, aimed at removing the model dependency on the big-M coefficients. Our solution scheme defines a master Integer Linear Problem (ILP) wi...

A Principled Approach to Mixed Integer/Linear Problem Formulation

We view mixed integer/linear problem formulation as a process of identifying disjunctive and knapsack constraints in a problem and converting them to mixed integer form. We show through a series of examples that following this process can yield mixed integer models that automatically incorporate some of the modeling devices that have been discovered over the years for making the formulation tig...

Benders Decomposition Approach to Robust Mixed Integer Programming

Generation of a reduced first - level mixed integer programmimg problem

We introduce a new way of generating cutting planes of a mixed integer programme by way of taking binary variables. Four binary variables are introduced to form quartic inequalities, which results in a reduced first-level mixed integer programme. A new way of weakening the inequalities is presented. An algorithm to carryout the separation of the inequalities, which are exponential in number, is...