An effective genetic algorithm approach to large scale mixed integer programming problems

Abstract To effectively reduce the search space of GAs on large-scale MIP problems, this paper proposed a new variable grouping method based on structure properties of a problem. Taking the capacity expansion and technology selection problem as a typical example, this method groups problem’s decision variables over time period and machine line. Based on this new variable grouping method, we developed a variable-grouping based genetic algorithm according to problem’s structure properties (VGGA-S). We tested the performance of VGGA-S by applying it on the capacity expansion and technology selection problem. Numerical experiments suggested that, VGGA-S outperforms the standard GA and variable-grouping based GAs without considering problem’s structure properties, both on computation time and solution quality. Although VGGA-S is proposed based on structure properties of a specific MIP problem, it is a general optimization algorithm and theoretically applicable to other large scale MIP problems.

[1]  Mahmoud A. Abo-Sinna,et al.  An effective genetic algorithm approach to multiobjective routing problems (MORPs) , 2005, Appl. Math. Comput..

[2]  Masatoshi Sakawa,et al.  An interactive fuzzy satisficing method for general multiobjective 0-1 programming problems through genetic algorithms with double strings based on a reference solution , 2002, Fuzzy Sets Syst..

[3]  Malcolm Irving,et al.  A genetic algorithm for generator scheduling in power systems , 1996 .

[4]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[5]  Chun-Hung Chen,et al.  A Hybrid approach for integer programming combining genetic algorithms, linear programming and ordinal optimization , 2001, J. Intell. Manuf..

[6]  S. Selçuk Erengüç,et al.  Exact solution procedures for certain planning problems in flexible manufacturing systems , 1997, Comput. Oper. Res..

[7]  Malcolm Irving,et al.  Large scale unit commitment using a hybrid genetic algorithm , 1997 .

[8]  B. Freisleben,et al.  Genetic algorithms for binary quadratic programming , 1999 .

[9]  K. Katayama,et al.  The efficiency of hybrid mutation genetic algorithm for the travelling salesman problem , 2000 .

[10]  Masatoshi Sakawa,et al.  Genetic algorithms with double strings for 0-1 programming problems , 2003, Eur. J. Oper. Res..

[11]  Zhongsheng Hua,et al.  Aggregate line capacity design for PWB assembly systems , 2000 .

[12]  S. Chatterjee,et al.  Genetic algorithms and traveling salesman problems , 1996 .

[13]  Manoj Kumar Tiwari,et al.  Modelling the slab stack shuffling problem in developing steel rolling schedules and its solution using improved Parallel Genetic Algorithms , 2004 .

[14]  D. Goldberg,et al.  An investigation of messy genetic algorithms , 1990 .

[15]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[16]  Justo Puerto,et al.  A multiperiod two-echelon multicommodity capacitated plant location problem , 2000, Eur. J. Oper. Res..

[17]  Ryohei Yokoyama,et al.  A MILP decomposition approach to large scale optimization in structural design of energy supply systems , 2002 .

[18]  Mahmoud A. Abo-Sinna,et al.  A solution to the optimal power flow using genetic algorithm , 2004, Appl. Math. Comput..

[19]  Shinn-Ying Ho,et al.  A novel approach to production planning of flexible manufacturing systems using an efficient multi-objective genetic algorithm , 2005 .

[20]  Mitsuo Gen,et al.  Loop layout design problem in flexible manufacturing systems using genetic algorithms , 1998 .

[21]  Shigeyoshi Tsutsui,et al.  Search Space Division in GAs using Phenotypic Squares Estimates , 1998, Inf. Sci..