An efficient global optimization method based on multi-unit extremum seeking

Industrial optimization problems, e.g., maximizing production in chemical and petrochemical facilities, typically exhibit multiple local optimal points and so choosing the global one has always attracted many researchers. Many deterministic and stochastic techniques have been explored towards this end. The stochastic techniques do not always guarantee convergence to the global solution, but fare well computationally for higher dimensions. On the other hand, the deterministic methods get to the global optimum, while the challenge therein is to employ an efficient partitioning of the space in order to reduce the number of functional evaluations.;The starting point of this research was motivated by the perturbation-based extremum seeking schemes which can be used as a tool for global optimization of scalar fourth order polynomials, with one local and one global optimum. The objective of this thesis is to extend this concept and develop a deterministic global optimization technique for a general class of multi-variable, static, nonlinear and continuous systems. In this thesis, it is first shown that in the scalar multi-unit optimization framework, if the offset is reduced to zero, the scheme converges to the global optimum. The result is also extended to scalar constrained problems, with possible non-convex feasible regions, where a switching control strategy is employed to deal with the constraints.;The next step consists of extending the algorithm to more than one variable. For two-input systems, univariate global optimization was repeated on the circumference of a circle of reducing radius. With three variables, the two-variable optimization mentioned above is repeated on the surface of a sphere of reducing radius. Time-scale separation between the various layers (univariate optimization, reducing the radius of the circle and reducing the radius of the sphere) was shown to be necessary to guarantee convergence. The theoretical concepts are illustrated on the global optimization of several benchmark examples. The comparison results with other competitive methods showed the efficiency of the new technique in terms of number of function evaluations.;This thesis proposes an original approach to numerical deterministic global optimization based on real-time local optimization techniques (in particular, model-free techniques termed the extremum-seeking schemes). For unconstrained problems, extremum-seeking schemes recast the optimization problem as the control of the gradient. The way the gradient is estimated forms the main difference between different alternatives that are proposed in the literature. In perturbation methods, a temporal excitation signal is used in order to compute the gradient. As an alternative, in the multi-unit optimization framework, the gradient is estimated as the finite difference of the outputs of two identical units driven with the inputs that differ by an offset.