A gradient—regression search procedure for simulation experimentation

ABSTRACT

This paper examines a gradient search procedure for simulation experimentation with constrained systems. This procedure combines gradient search with curvilinear regression in moving toward a constrained optimal solution for a system involving n controllable variables. In a direction-determining block, at least n+1 simulation trials are performed around a current base point to establish an improving direction. Then in a step determining block, t simulation trials are performed along the improving direction to establish the most favorable step in moving to the next base point. This sequential block process, in which each block is executed in one input to the computer, is repeated until an approximate solution is found which satisfies all system constraints.

REFERENCES

• 1: William E. Biles, Constrained sequential-block search in simulation experimentation, Proceedings of the 6th conference on Winter simulation, p.227-241, January 17-19, 1973, San Francisco, CA [doi>10.1145/800293.811578]
• 2: Box, G.E.P., "Multi-factor Designs of First Order", Biometrika, Vol. 39, No. 1, 1952.
• 3: Box, G.E.P. and K.P. Wilson, "On the Experimental Attainment of Optimum Conditions", Journal of the Royal Statistical Society, Series B, Vol. 13, No. 1, 1951.
• 4: Brooks, S.H., and M.R. Mickey, "Optimum Estimation of Gradient Direction in Steepest Ascent Experiments", Biometrics, Vol. 17, No. 1, 1961.
• 5: Griffith, R.E., and R.A. Stewart, "A Non-linear Programming Technique for the Optimization of Continuous Processing Systems", Management Science, Vol. 7, 1961.
• 6: Himmelblau, D.M., Applied Nonlinear Programming, McGraw-Hill Book Company, New York, 1972.
• 7: Robert Hooke , T. A. Jeeves, `` Direct Search'' Solution of Numerical and Statistical Problems, Journal of the ACM (JACM), v.8 n.2, p.212-229, April 1961 [doi>10.1145/321062.321069]
• 8: G. Arthur Mihram, An efficient procedure for locating the optimal simular response, Proceedings of the fourth annual conference on Applications of simulation, p.154-161, December 09-11, 1970, New York, New York, United States
• 9: Mihram, G.A., Simulation: Statistical Foundations and Methodology, Academic Press, New York, 1972.
• 10: Myers, R.L., Response Surface Methodology, Allyn and Bacon, Boston, Massachusetts, 1971.
• 11: Nelder, J.A., and R. Mead, "A Simplex Method for Function Minimization", Computer Journal, Vol. 7, 1965.
• 12: Rosen, J.B., "The Gradient Projection Method for Nonlinear Programming, Part I - Linear Constraints", Journal of the Society of Industrial and Applied Mathematics, Vol. 8, 1961.
• 13: Rosen, J.B., "The Gradient Projection Method for Nonlinear Programming, Part II -Nonlinear Constraints", Journal of the Society of Industrial and Applied Mathematics, Vol. 9, 1961.
• 14: Schmidt, J.W., and R.E. Taylor, Simulation and Analysis of Industrial Systems, Richard D. Irwin, Homewood, Illinois, 1970.
• 15: Smith, D.E., "Requirements of an 'Optimizer' for Computer Simulations", Naval Research Logistics Quarterly, Vol. 20, No. 1, March, 1973.
• 16: Spendley, W., G.R. Hext, and R.F. Himsworth, "Sequential Application of Simplex Designs in Optimization and Evolutionary Operation", Technometrics, Vol. 4, November 1962.
• 17: Zoutendijk, G., Methods of Feasible Directions, Elsevier Press, Amsterdam, 1960.

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.6 Optimization
          Subjects: Gradient methods

Additional Classification:
  G. Mathematics of Computing
  G.3 PROBABILITY AND STATISTICS
      Subjects: Correlation and regression analysis

General Terms:
Experimentation