In this thesis, we present a new theory of discrete constrained optimization using Lagrange multipliers and an associated first-order search procedure (DLM) to solve general constrained optimization problems in discrete, continuous and mixed-integer space. The constrained problems are general in the sense that they do not assume the differentiability or convexity of functions. Our proposed theory and methods are targeted at discrete problems and can be extended to continuous and mixed-integer problems by coding continuous variables using a floating-point representation (discretization). We have characterized the errors incurred due to such discretization and have proved that there exists upper bounds on the errors. Hence, continuous and mixed-integer constrained problems, as well as discrete ones, can be handled by DLM in a unified way with bounded errors.

The research presented in this paper is concerned with the design automation of analog integrated circuits, simply called analog synthesis. A new algorithm, namely a simulated annealing algorithm with multi-molecule (SAMM), is proposed to solve analog synthesis problems. Besides inheriting the global convergence of the traditional simulated annealing algorithm (SA), SAMM can avoid the excessively time-consuming final iterations of SA, which makes it more efficient and suitable for analog synthesis. Several analog synthesis examples are also given in this paper to demonstrate the efficiency and validity of SAMM.

This paper deals with the simple genetic algorithm (SGA) [3] and the effect of elitism on convergence of the model parameter identification. Genetic algorithms have successfully been applied to a wide variety of optimisation and identification problems. Their main advantage is the fact that they avoid getting caught in local minima. The main handicap of genetic algorithms is their slow convergence. One way to improve this is to add elitism to the genetic algorithm