Stochastic Methods for Hard Optimization

Abstract

This chapter aims at solving difficult optimization problems arising in many engineering areas. To this end, a brief review of the main stochastic methods which can be used for solving continuous non-convex constrained optimization problems is presented i.e.: Simulated annealing (SA), Genetic algorithm (GA), and Particle swarm optimization (PSO). In addition to that, we will present a recently developed optimization method called Heuristic Kalman Algorithm (HKA) which seems to be, in some cases, an interesting alternative to the conventional approaches. The performance of these methods depends dramatically on the feasible search domain used to find out a solution as well as the initialization of the various user defined parameters. From this point of view, some practical indications concerning these issues will be given. Another objective of this chapter is to show that the stochastic methods, notably HKA, can be efficiently used to solve robust synthesis problems in the area of structured control and fault diagnosis systems. More precisely, we will deal with the following problems: the synthesis of a robust controller with a given fixed structure and the design of a robust residual generator. Some numerical experiments exemplify the resolution of this kind of problems.