Difference-genetic co-evolutionary algorithm for nonlinear mixed integer programming problems

Volume 9, Issue 3, pp 1261--1284 http://dx.doi.org/10.22436/jnsa.009.03.51

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 2141 Downloads
• 2873 Views

Authors

Yuelin Gao - Institute of Information and System Science, Beifang University of Nationalities, Yinchuan, 750021, China. - School of Computer Science and Information Engineering, Hefei University of Technology, Hefei, 230009, China. Ying Sun - School of Computer Science and Information Engineering, Hefei University of Technology, Hefei, 230009, China. Jun Wu - Institute of Information and System Science, Beifang University of Nationalities, Yinchuan, 750021, China.

Abstract

In this paper, the difference genetic co-evolutionary algorithm (D-GCE) is proposed for the mixed integer programming problems. First, the mixed integer programming problem with constrains converted to unconstrained bi-objective optimization problems. Secondly, selection mechanism combines the Pareto dominance and superiority of feasible solution methods to choose the excellent individual as the next generation. Final, differential evolution algorithm and genetic algorithm handle the continuous part and discrete part, respectively. Numerical experiments on 24 test functions have shown that the new approach is efficient. The comparison results among the D-GCE and other evolutionary algorithms indicate that the proposed D-GCE algorithm is competitive with and in some cases superior to, other existing algorithms in terms of the quality, efficiency, convergence rate, and robustness of the final solution.

Share and Cite

Keywords

• Mixed integer programming
• differential evolution
• genetic algorithm
• co-evolution
• constrained optimization.

MSC

•  90C11
•  65J08
•  65K10

References

• [1] M. M. Ali, Z. Kajee-Bagdadi, A local exploration-based differential evolution algorithm for constrained global optimization, Appl. Math. Comput., 208 (2009), 31-48.


• [2] L. Costa, P. Oliveira, Evolutionary algorithms approach to the solution of mixed integer non-linear programming problems, Comput. Chem. Eng., 25 (2001), 257-266.


• [3] S. Das, Differential Evolution: A Survey of the State-of-the-Art, IEEE Trans. Evol. Comput., 15 (2011), 4-31.


• [4] K. Deb, An efficient constraint handing method for genetic algorithms, Comput. Method Appl. M, 186 (2000), 311-338.


• [5] K. Deep, K. P. Singh, M. L. Kansal, C. Mohan, A real coded genetic algorithm for solving integer and mixed integer optimization problems, Appl. Math. Comput., 212 (2009), 505-518.


• [6] A. Hedar, Filter-based genetic algorithm for mixed variable programming, Numer. Algebra Control Optim., 1 (2011), 99-116.


• [7] F. Huang, L. Wang, Q. He, An effective co-evolutionary differential evolution for constrained optimization, Appl. Math. Comput., 186 (2007), 340-356.


• [8] S. Kitayama, K. Yasuda, A method for mixed integer programming problems by particle swarm optimization, Electr. Eng. Jpn., 157 (2006), 40-49.


• [9] J. Lampinen, I. Zelinka, On stagnation of the differential evolution algorithm, 6th International Mendel Conference on Soft Computing, 2000 (2000), 76-83.


• [10] T. W. Liao, Two hybrid differential evolution algorithms for engineering design optimization, Appl. Soft Comput., 10 (2010), 1188-1199.


• [11] T. W. Liao, R. J. Kuo, J. T. L. Hu, Hybrid ant colony optimization algorithms for mixed discrete-Ccontinuous optimization problems, Appl. Math. Comput., 219 (2012), 3241-3252.


• [12] Y. C. Lin, K. S Hwang, F. S Wang, A Mixed-Coding Scheme of Evolutionary Algorithms to Solve Mixed-Integer Nonlinear Programming Problems, Comput. Math. Appl., 47 (2004), 1295-1307.


• [13] M. Mahdavi, M. Fesanghary, E. Damangir, An improved harmony search algorithm for solving optimization problems, Appl. Math. Comput., 188 (2007), 1567-1579.


• [14] A. K. Maiti, A. K. Bhunia, M. Maiti , An application of real-coded genetic algorithm for mixed integer non-linear programming in two-storage multi-item inventory model with discount policy , Appl. Math. Comput., 183 (2006), 903-915.


• [15] R. Mallipeddi, P. N. Suganthan, Ensemble of Constraint Handling Techniques, Evolutionary Comput., 14 (2010), 561-579.


• [16] K. Miettinen, M. Makela, J. Toivanen, Numerical comparison of some penalty based constraint handling techniques in genetic algorithm, J. Global Optim., 27 (2003), 427-446.


• [17] A. W. Mohamed, H. Z. Sabry, Constrained optimization based on modified differential evolution algorithm, Inf. Sci., 194 (2012), 171-208.


• [18] L. Pallottino, E. M. Feron, A. Bicchi , Conflict resolution problems for air trafic management systems solved with mixed integer programming, IEEE Trans. Intell. Transp. Syst., 3 (2002), 3-11.


• [19] M. Schluter, J. A. Egea, J. R Banga, Extended ant colony optimization for non-convex mixed integer nonlinear programming, Comput. Oper. Res., 36 (2009), 2217-2229.


• [20] T. Schouwenaars, B. De Moor, E. Feron, J. How, Mixed integer programming for multi-vehicle path planning, Eur. Control Conf., 1 (2001), 2603-2608.


• [21] M. Srinivas, G. P. Rangaiah , Differential evolution with tabu list for solving nonlinear and mixed-integer nonlinear programming problems , Ind. Eng. Chem. Res., 46 (2007), 7126-7135.


• [22] R. Storn, K. Price, Differential evolution: A simple and efficient adaptive scheme for global optimization over continuous spaces, Int. Comput. Sci. Inst., Berkeley (1995)


• [23] R. Storn, K. Price, Minimizing the real functions of the ICEC 1996 contest by Differential Evolution, IEEE Conference on Evolutionary Computation, 1996 (1996), 3 pages.


• [24] R. Storn, K. Price, Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces, J. Global Optim., 11 (1997), 341-359.


• [25] S. S. Syam, A dual ascent method for the portfolio selection problem with multiple constraints and linked proposals, Eur. J. Oper. Res., 108 (1998), 196-207.


• [26] B. Tessema, G. G. Yen, A Self Adaptive Penalty Function Based Algorithm for Constrained Optimization, Evol. Comput., 2006 (2006), 8 pages.


• [27] Y. Wang, Z. Cai, G. Guo, Y. Zhou, Multiobjective optimization and hybrid evolutionary algorithm to solve constrained optimization problems, IEEE Trans. Syst. Man Cybern. Part B Cybern., 37 (2007), 560-575.


• [28] L. Wang, L. Li , An effective differential evolution with level comparison for constrained engineering design, Struc. Multidisciplinary Optim., 41 (2010), 947-963.


• [29] L. Yan, K. Shen, S. Hu, Solving mixed integer nonlinear programming problems with line-up competition algorithm, Comput. Chem. Eng., 28 (2004), 2647-2657.


• [30] H. Yi, Q. Duan, T. W. Liao, Three improved hybrid metaheuristic algorithms for engineering design optimization, Appl. Soft Comput., 13 (2013), 2433-2444.


• [31] M. Yuceer, L. Atasoy, R. Berber, A semiheuristic MINLP algorithm for production scheduling, Comput. Aided Chem. Eng., 14 (2003), 335-340.