A real coded genetic algorithm for solving integer and mixed integer optimization problems

Applied Mathematics and Computation

Volumn 212, Issue 2, 2009, Pages 505-518

  Deep, Kusum ^a   Singh, Krishna Pratap ^a   Kansal, M L ^a   Mohan, C ^b  

^a INDIAN INSTITUTE OF TECHNOLOGY ROORKEE   (India)

^b AMBALA COLLEGE OF ENGINEERING AND APPLIED RESEARCH   (India)

Author keywords

Constrained optimization; Integer and mixed integer optimization problems; Random search based techniques; Real coded genetic algorithms

Indexed keywords

APPLIED MATHEMATICS; CONSTRAINED OPTIMIZATION PROBLEMS; CROSSOVER OPERATORS; DECISION VARIABLES; EXTENDED VERSIONS; HANDLING CONSTRAINTS; INTEGER AND MIXED INTEGER OPTIMIZATION PROBLEMS; MIXED INTEGERS; MUTATION OPERATORS; RANDOM SEARCH BASED TECHNIQUES; REAL CODED GENETIC ALGORITHMS; TEST PROBLEMS; TRUNCATION PROCEDURES;

GENETIC ALGORITHMS; INTEGER PROGRAMMING; MATHEMATICAL OPERATORS;

CONSTRAINED OPTIMIZATION;

EID: 67349155902     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2009.02.044     Document Type: Article

References (41)

1. Deep K., and Thakur M. A new crossover operator for real coded genetic algorithms. Applied Mathematics and Computation 188 (2007) 895-912
2. Deep K., and Thakur M. A new mutation operator for real coded genetic algorithms. Applied Mathematics and Computation 193 (2007) 211-230
3. Cooper M.W. Survey of methods for nonlinear integer programming. Management Science 27 (1981) 353-361
4. Salkin H.M. Integer Programming (1975), Eddison Wesley Publishing Com., Amsterdam
5. Floudas C.A. Nonlinear Mixed-integer Optimization. Fundamentals and Applications (1995), Oxford University Press, New York, USA
6. Grossmann I.E. Review of non-linear mixed integer and disjunctive programming techniques. Optimization and Engineering 3 (2002) 227-252
7. Marchand H., Martin A., and Weismantel R. Cutting planes in integer and mixed integer programming. Discrete Applied Mathematics 123 (2002) 397-446
8. Kirkpatrick S., Gelatt C.D., and Vecchi M. Optimization by simulated annealing. Science 220 (1983) 671-680
9. Sonilah A. Simulated anneling for manufacturing systems layout design. European Journal of Operational Research 82 (1995) 592-614
10. Cardoso M.F., Salcedo R.L., Azevedo S.F., and Barbosa D. A simulated annealing approach to the solution of minlp problems. Computers and Chemical Engineering 21 (1997) 1349-1364
11. B.V. Babu, R. Angira, A differential evolution approach for global optimization of minlp problems, in: Proceedings of Fourth Asia Pacific Conference on Simulated Evolution and Learning, Singapore, 2002, pp. 880-884.
12. Yan L., Shen K., and Hu S. Solving mixed integer nonlinear programming problems with line-up competition algorithm. Computers and Chemical Engineering 28 (2004) 2647-2657
13. Yiqing L., Xigang Y., and Yongjian L. An improved pso algorithm for solving non-convex nlp/minlp problems with equality constraints. Computers and Chemical Engineering 31 (2007) 153-162
14. Price W.L. Global optimization by controlled random search. Journal of Optimization: Theory and Applications 40 (1983) 333-348
15. Price W.L. Global optimization algorithms for cad workstation. Journal of Optimization: Theory and Application 55 (1987) 133-146
16. Mohan C., and Shanker K. A controlled random search technique for global optimization using quadratic approximation. Asia-Pacific Journal of Operation Research 11 (1994) 93-101
17. Mohan C., and Nguyen H.T. A controlled random search technique incorporating the simulating annealing concept for solving integer and mixed integer global optimization problems. Computational Optimization and Applications 14 (1999) 103-132
18. Salcedo R.L. Solving nonconvex nonlinear programming and mixed-integer non-linear programming problems with adaptive random search. Industrial & Engineering Chemistry Research 31 (1992) 262-273
19. Holland J.H. Adaptation in Natural and Artificial systems (1975), University of Michigan Press, Ann Arbor
20. K.A. De-Jong, An Analysis of the Behavior of a Class of Genetic Adaptive Systems, Ph.D. Thesis, University of Michigan, 1975.
21. Goldberg D.E. Genetic Algorithms in Search, Optimization and Machine Learning (1989), Addison-Wesley, New York, USA
22. Deb K. Multi-Objective Optimization using Evolutionary Algorithms (2001), John Wiley and Sons
23. Cheung B.K.S., Langevin A., and Delmaire H. Coupling genetic algorithm with a grid search method to solve mixed integer nonlinear programming problems. Computers and Mathematics with Applications 32 (1997) 13-23
24. Luo Y.C., Guignard M., and Chen C.H. A hybrid approach for integer programming combining genetic algorithms, linear programming and ordinal optimization. Journal of Intelligent Manufacturing 12 (2001) 509-519
25. Costa L., and Oliveria P. Evolutionary algorithms approach to the solution jof mixed integer non-linear programming problems. Computers and Chemical Engineering 21 (2001) 257-266
26. Hua Z., and Huang F. An efficient genetic algorithm approach to large scale mixed integer programming problems. Applied Mathematics and Computation 174 (2006) 897-907
27. Y.-X. Li, M. Gen, Nonlinear mixed integer programming problems using genetic algorithm and penalty function, in: Proceeding of the IEEE International Conference on Systems, Man and Cybernatics, vol. 4, 1996, pp. 2677-2682.
28. Yokota T., Gen M., and Li Y.X. Genetic algorithm for nonlinear mixed integer programming problems and its applications. Computers and Industrial Engineering 30 (1996) 905-917
29. Maiti A.K., Bhunia A.K., and Maiti M. An application of real coded genetic algorithm (rcga) for mixed integer non-linear programming in two storage multi-item inventory model with discount policy. Applied Mathematics and Computation 183 (2006) 903-915
30. Ponsich A., Pantel C.A., Domenech S., and Pibouleau L. Mixed integer nonlinear programming optimization strategies for batch plant design problems. Industrial & Engineering Chemistry Research 46 (2007) 854-863
31. D.E. Goldberg, K. Deb, A comparison of selection schemes used in genetic algorithms, in: Foundations of Genetic Algorithms 1, FOGA-1, vol. 1, 1991, pp. 69-93.
32. Deb K. An efficient constraint handling method for genetic algorithms. Computer Methods in Applied Mechanics and Engineering 186 (2000) 311-338
33. Bharti, Controlled Random Search Techniques and Their Applications, Ph.D. Thesis, Department of Mathematics, University of Roorkee, India, 1994.
34. Kocis G.R., and Grossmann I.E. Global optimazation of nonconvex mixed-integer nonlinear programming (minlp) problems in process synthesis. Industrial & Engineering Chemistry Research 27 (1988) 1407-1421
35. H.T. Nguyen, Some Global Optimization Techniques and Their Use in Solving Optimization Problems in Crisp and Fuzzy Environments, Ph.D. Thesis, Department of Mathematics, University of Roorkee, Roorkee, India, 1996.
36. Yuan X., Zhang S., Pibouleau L., and Domenech S. une methode d'optimization nonlineaire en variables mixtes pour la conception de proceds. RAIRO Operations Research 22 (1988) 131-146
37. Berman O., and Ashrafi N. Optimization models for reliability of modular software systems. IEEE Transactions on Software Engineering 19 (1993) 11-19
38. Bazaraa M.S., Sherah H.D., and Shetty C.M. Nonlinear Programming: Theory and Algorithms. second ed. (2004), John Wiley and Sons, Asia
39. Himmelblau D.M. Applied Nonlinear Programing (1972), McGraw Hill, New York, USA
40. Conley W. Computer Optimization Techniques (1984), Petrocelli Books, Newjersy, USA
41. Dhingra A.K. Optimal apportionment of reliability and redundancy in series systems under multiple objectives. IEEE Transactions on Reliability 41 (1992) 576-582