Abstract
In this paper, a computational algorithm, named RST2ANU algorithm, has been developed for solving integer and mixed integer global optimization problems. This algorithm, which primarily is based on the original controlled random search approach of Price [22i], incorporates a simulated annealing type acceptance criterion in its working so that not only downhill moves but also occasional uphill moves can be accepted. In its working it employs a special truncation procedure which not only ensures that the integer restrictions imposed on the decision variables are satisfied, but also creates greater possibilities for the search leading to a global optimal solution. The reliability and efficiency of the proposed RST2ANU algorithm has been demonstrated on thirty integer and mixed integer optimization problems taken from the literature. The performance of the algorithm has been compared with the performance of the corresponding purely controlled random search based algorithm as well as the standard simulated annealing algorithm. The performance of the method on mathematical models of three realistic problems has also been demonstrated.
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References
V. Agarwal, “Geometric programming and transcendental programming problems,” Ph.D. Thesis, Department of Mathematics, University of Roorkee, Roorkee, India, 1984.
E. Balas, “Nonlinear 0–1 programming: Linearization technique,” Mathematical Programming, vol. 1, pp. 1–21, 1984.
Bharati, “Controlled random search techniques and their applications,” Ph.D. Thesis, Department of Mathematics, University of Roorkee, Roorkee, India, 1994.
W. Conley, “Computer optimization techniques,” Petrocelli Books, New Jersey, USA, 1984.
M.W. Cooper, “Survey of methods for pure nonlinear integer programming,” Management Science, vol. 27, pp. 353–361, 1981.
A.S. Deshpande and E. Triantaphyllou, “A greedy randomized adaptive search procedure (GRASP) for inferring logical clauses from examples in polynomial time and some extensions,” Mathematical and Computer Modeling (1997).
B.H. Dickman and M.J. Gilman, “Monte Carlo optimization,” Journal of Optimization: Theory and Applications, vol. 60, pp. 149–157, 1989.
T.A. Feo and M.G.C. Resende, “Greedy randomized adaptive search procedures,” Technical Report, AT&T Bell Lab., Mountain Avenue 600, Murray Hill, NJ, USA, 1994.
C.A. Floudas and P.M. Pardalos, “A collection of test problems for constrained global optimization,” Lecture Notes in Computer Science, vol. 455, 1991.
P.M. Himmelblau, “Applied nonlinear programming,” McGraw Hill, New York, USA, 1972.
R. Horst and P.M. Pardalos (Eds.), “Handbook on global optimization,” Kluwer Academic Press, Dordrecht, The Netherlands, 1995.
S. Kirkpatrick, C.D. Gelatt, and M. Vecchi, “Optimization by simulated annealing,” Science, vol. 220, pp. 671–680, 1983.
C. Konlamas, S.K. Antony, and R. Jaen, “A survey of simulated annealing applications to operations research problems,” Omega, vol. 22, pp. 41–56, 1994.
L.H. Li, “Global optimization for mixed 0–1 programming with convex and separable continuous functions,” J. Opl. Res. Soc., vol. 45, pp. 1068–1076, 1994.
C. Mohan and H.T. Nguyen, “A fuzzifying approach to stochastic programming,” Opseaech, vol. 34, pp. 73–96, 1997.
C. Mohan and K. Shanker Deep, “A controlled random search technique for global optimization using quadratic approximation,” Asia-Pacific Journal of Operational Research, vol. 11, pp. 93–101, 1994.
R. Motwani and P. Raghavan, “Randomized algorithms,” Cambridge University Press, New York, USA, 1995.
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.
G.L. Nemhauser and L.A. Wolsey, “Integer and combinatorial optimization,” Wiley-Interscience Publication, New York, USA, 1988.
M.T. Ozan, “Applied mathematical programming for production and engineering management,” Prentice Hall, Englewood Cliffs, New Jersey, USA, 1981.
A.N. Patel, R.S.H. Mah, and I.A. Karimi, “Preliminary design of multiproduct noncontinuous plants using simulated annealing,” Computers & Chemical Engineering, vol. 7, pp. 451–469, 1991.
W.L. Price, “Global optimization by controlled random search,” Journal of Optimization: Theory and Applications, vol. 40, pp. 333–348, 1983. (ii) W.L. Price, “Global optimization algorithms for CAD workstation,” Journal of Optimization: Theory and Applications, vol. 55, pp. 133–146, 1987.
M.G.C. Resende and T.A. Feo, “A greedy randomized adaptive procedure (GRASP) for satisfiability,” Technical Report, AT & T Bell Lab., Mountain Avenue 600, Murray Hill, NJ, USA, 1994.
M.G.C. Resende and T.A. Feo, “A GRASP for MAX-SAT,” TIMS/ORSA National Meeting in Boston, April 22–24, 1994, Presentation No.: TC 7.2, USA, 1994.
K. Shanker Deep and D.J. Evans, “The random search global optimization method for parallel computers,” Parallel Algorithms and Applications, vol. 5, pp. 251–268, 1995.
K. Schittkowski, “More examples for mathematical programming codes,” Lecture Notes in Economics and Mathematical Systems, vol. 282, 1987.
A. Sonilah, “Simulated annealing for manufacturing systems layout design,” European Journal of Operational Research, vol. 82, pp. 592–614, 1995.
Z.B. Zabinsky, R.L. Smith, J.F. McDonald, H.E. Romeijn, and D.E. Kaufmann, “Improved hit-and-run for optimization,” The Journal of Global Optimization, vol. 3, pp. 171–192, 1993.
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Mohan, C., Nguyen, H. A Controlled Random Search Technique Incorporating the Simulated Annealing Concept for Solving Integer and Mixed Integer Global Optimization Problems. Computational Optimization and Applications 14, 103–132 (1999). https://doi.org/10.1023/A:1008761113491
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DOI: https://doi.org/10.1023/A:1008761113491