Some modified stochastic global optimization algorithms with applications
Stochastic methods for global optimization problems with continuous variables have been studied. Modifications of three different algorithms have been proposed. These are (1) Multilevel Single Linkage (MSL), (2) Simulated Annealing (SA) and (3) Controlled Random Search (CRS). We propose a new topographical Multilevel Single Linkage (TMSL) algorithm as an extension of MSL. TMSL performs much better than MSL, especially in terms of number of function evaluations. A new aspiration based simulated annealing algorithm (ASA) has been derived which enhances the performance of SA by incorporating an aspirat.ion criterion. We have also proposed two new CRS algorithms, the CRS4 and CRS5 algorithms, which improve the CRS algorithm both in terms of cpu time and the number of function evaluations. The usefulness of the Halton and the Hammersley quasi-random sequences in global optimization has been investigated. These sequences are frequently used in numerical integration in the field of Bayesian statistics. A useful property of the quasi-random sequences is that they are evenly distributed and thus explore the search region more rapidly than pseudo-random numbers. Comparison of the modified algorithms with their unmodified versions is carried out on standard test problems but in addition a substantial part of the thesis consists of numerical investigations of 5 different practical global optimization problems. These problems are as follows: (1) A nonlinear continuous stirred tank reactor problem. (2) A chemical reactor problem with a bifunctional catalyst. (3) A pig-liver likelihood function. (4) Application and derivation of semi-empirical many body interatomic potentials. (5) A optimal control problem involving a car suspension system. Critical comparisons of the modified and unmodified global optimization algorithms have been carried out on these problems. The methods applied to these problems are compared from the points of view of reliability in finding the global optimum, cpu time and number of function evaluations.