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
(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.
A Doctoral Thesis. Submitted in partial fulfillment of the requirements for the award of Doctor of Philosophy of Loughborough University.