scholarly journals A Hybrid IP/GA Approach to the Parallel Production Lines Scheduling Problem

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
Huizhi Ren ◽  
Shenshen Sun
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Time Window ◽  
Valid Inequalities ◽  
Mixed Integer ◽  
Scheduling Problem ◽  
Production Lines ◽  
Solution Approach ◽  
Cp Decomposition

A special parallel production lines scheduling problem is studied in this paper. Considering the time window and technical constraints, a mixed integer linear programming (MILP) model is formulated for the problem. A few valid inequalities are deduced and a hybrid mixed integer linear programming/constraint programming (MILP/CP) decomposition strategy is introduced. Based on them, a hybrid integer programming/genetic algorithm (IP/GA) approach is proposed to solve the problem. At last, the numerical experiments demonstrate that the proposed solution approach is effective and efficient.

scholarly journals Global solutions of nonconvex standard quadratic programs via mixed integer linear programming reformulations

2021 ◽  
Author(s):  
Jacek Gondzio ◽  
E. Alper Yıldırım
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Valid Inequalities ◽  
Global Minimizer ◽  
Mixed Integer ◽  
Quadratic Program ◽  
Complementarity Constraints ◽  
Binary Variables ◽  
Standard Quadratic Program

AbstractA standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) quadratic form over the unit simplex. We focus on reformulating a standard quadratic program as a mixed integer linear programming problem. We propose two alternative formulations. Our first formulation is based on casting a standard quadratic program as a linear program with complementarity constraints. We then employ binary variables to linearize the complementarity constraints. For the second formulation, we first derive an overestimating function of the objective function and establish its tightness at any global minimizer. We then linearize the overestimating function using binary variables and obtain our second formulation. For both formulations, we propose a set of valid inequalities. Our extensive computational results illustrate that the proposed mixed integer linear programming reformulations significantly outperform other global solution approaches. On larger instances, we usually observe improvements of several orders of magnitude.

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