INTEGRATED CONTROLLED RANDOM SEARCH: APPLICATION TO A WASTEWATER TREATMENT PLANT MODEL

An integrated procedure, ICRS, has been developed for the solution of constrained optimization problems. The method combines an equation-sequencing and design variables specification algorithm with a random search technique, CRS, which itself contains a Newton-Raphson algorithm to cope with cases where a full sequence of equality constraints is not attainable. The application of ICRS to a fairly complex model demonstrates the capabilities of the proposed procedure.

[1]  C. Dorea,et al.  Expected number of steps of a random optimization method , 1983 .

[2]  Luc Devroye,et al.  Progressive global random search of continuous functions , 1978, Math. Program..

[3]  D. Himmelblau,et al.  A new method for nonlinearly constrained optimization , 1975 .

[4]  G. Bekey,et al.  Random search techniques for optimization of nonlinear systems with many parameters , 1983 .

[5]  Samuel H. Brooks.  A Discussion of Random Methods for Seeking Maxima , 1958 .

[6]  E. J. Beltrami,et al.  An Adaptive Random Search Algorithm for Constrained Minimization , 1972, IEEE Transactions on Computers.

[7]  N. Baba.  Convergence of a random optimization method for constrained optimization problems , 1981 .

[8]  T. H. I. Jaakola,et al.  Optimization by direct search and systematic reduction of the size of search region , 1973 .

[9]  L. T. Fan,et al.  Biological wastewater treatment system design Part I. Optimal synthesis , 1973 .

[10]  J. L. Gaddy,et al.  An examination of the adaptive random search technique , 1976 .

[11]  Neil L. Book,et al.  The selection of design variables in systems of algebraic equations , 1976 .

[12]  D. Himmelblau.  OPTIMAL DESIGN VIA STRUCTURAL PARAMETERS AND NONLINEAR PROGRAMMING , 1976 .

[13]  C. Dorea,et al.  Limiting distribution for random optimization methods , 1986 .

[14]  Rein Luus,et al.  Reliability of optimization procedures for obtaining global optimum , 1978 .

[15]  Kenneth Steiglitz,et al.  Randomized Pattern Search , 1972, IEEE Transactions on Computers.

[16]  Eric Walter,et al.  A general-purpose global optimizer: implementation and applications , 1984 .

[17]  Joel A. Richardson,et al.  Algorithm 454: the complex method for constrained optimization [E4] , 1973 .

[18]  Rein Luus,et al.  Optimization of non‐unimodal systems , 1977 .

[19]  M. J. Box.  A New Method of Constrained Optimization and a Comparison With Other Methods , 1965, Comput. J..

[20]  L. T. Fan,et al.  Optimization of the activated sludge process—optimum volume ratio of aeration and sedimentation vessels , 1969 .

[21]  J.E. Dennis,et al.  A user's guide to nonlinear optimization algorithms , 1984, Proceedings of the IEEE.

[22]  W. Fred Ramirez,et al.  Algorithms for structuring design calculations , 1972 .

[23]  Michael A. Saunders,et al.  Trends in nonlinear programming software , 1984 .

[24]  Dean C. Karnopp,et al.  Random search techniques for optimization problems , 1963, Autom..

[25]  M. J. D. Powell,et al.  Variable Metric Methods for Constrained Optimization , 1982, ISMP.

[26]  R. Goulcher,et al.  The solution of steady-state chemical engineering optimisation problems using a random-search algorithm , 1978 .

[27]  Leon S. Lasdon,et al.  The Status of Nonlinear Programming Software , 1979, Oper. Res..

[28]  Roger J.-B. Wets,et al.  Minimization by Random Search Techniques , 1981, Math. Oper. Res..