Improving benders decomposition using maximum feasible subsystem (MFS) cut generation strategy

A new multi-generation of cuts algorithm is presented in this paper to improve the efficiency of Benders decomposition approach for the cases that optimality cuts are difficult to be achieved within the iterations of the algorithm. This strategy is referred to as maximum feasible subsystem (MFS) cut generation strategy. In this approach in each iteration of the Benders algorithm an additional cut is generated that has the property to restrict the value of the objective function of the Benders master problem. To illustrate the efficiency of the proposed strategy, it is applied to a scheduling problem of multipurpose multiproduct batch plant. Two different partitioning alternatives are tested in order to show the importance of the way that a problem is decomposed upon the efficiency of the Benders algorithm. The application of the proposed acceleration procedure results in substantial reduction of CPU solution time and the total number of iterations in both decomposition alternatives.

[1]  Antonio J. Conejo,et al.  Decomposition Techniques in Mathematical Programming: Engineering and Science Applications , 2006 .

[2]  M. Laughton,et al.  Large-scale mixed integer programming: Benders-type heuristics , 1984 .

[3]  A. M. Geoffrion,et al.  Lagrangean Relaxation Applied to Capacitated Facility Location Problems , 1978 .

[4]  Marianthi G. Ierapetritou,et al.  Accelerating Benders method using covering cut bundle generation , 2010, Int. Trans. Oper. Res..

[5]  Michel Gendreau,et al.  Accelerating Benders Decomposition by Local Branching , 2009, INFORMS J. Comput..

[6]  Edoardo Amaldi,et al.  Randomized Relaxation Methods for the Maximum Feasible Subsystem Problem , 2005, IPCO.

[7]  Olvi L. Mangasarian,et al.  Misclassification minimization , 1994, J. Glob. Optim..

[8]  G. Nemhauser,et al.  Exceptional Paper—Location of Bank Accounts to Optimize Float: An Analytic Study of Exact and Approximate Algorithms , 1977 .

[9]  Golbon Zakeri,et al.  Inexact Cuts in Benders Decomposition , 1999, SIAM J. Optim..

[10]  Thomas L. Magnanti,et al.  Accelerating Benders Decomposition: Algorithmic Enhancement and Model Selection Criteria , 1981, Oper. Res..

[11]  Christodoulos A. Floudas,et al.  Effective Continuous-Time Formulation for Short-Term Scheduling. 2. Continuous and Semicontinuous Processes , 1998 .

[12]  Jacques F. Benders,et al.  Partitioning procedures for solving mixed-variables programming problems , 2005, Comput. Manag. Sci..

[13]  George L. Nemhauser,et al.  Note--On "Location of Bank Accounts to Optimize Float: An Analytic Study of Exact and Approximate Algorithms" , 1979 .

[14]  A. M. Geoffrion,et al.  Multicommodity Distribution System Design by Benders Decomposition , 1974 .

[15]  C. Floudas,et al.  Effective Continuous-Time Formulation for Short-Term Scheduling. 1. Multipurpose Batch Processes , 1998 .

[16]  Edoardo Amaldi,et al.  A two-phase relaxation-based heuristic for the maximum feasible subsystem problem , 2008, Comput. Oper. Res..

[17]  M. D. Devine,et al.  A Modified Benders' Partitioning Algorithm for Mixed Integer Programming , 1977 .

[18]  Alexander Schrijver,et al.  Discrete mathematics and optimization , 2004 .

[19]  David K. Smith,et al.  Mathematical Programming: Theory and Algorithms , 1986 .

[20]  Christodoulos A. Floudas,et al.  Effective continuous-time formulation for short-term scheduling. 3. Multiple intermediate due dates , 1999 .

[21]  Georgios K. Saharidis.  Pilotage de production à moyen et à court terme : contribution aux problématiques d'optimisation globale vs locale et à l' ordonnancement dans les raffineries , 2006 .

[22]  John W. Chinneck.  Fast Heuristics for the Maximum Feasible Subsystem Problem , 2001, INFORMS J. Comput..