A novel hybrid optimization algorithm for diferential-algebraic control problems

Abstract

-Dynamic optimization problems can be numerically solved by direct, indirect and HamiltonJacobi-Bellman methods. In this paper, the differential-algebraic approach is incorporated into a hybrid method, extending the concepts of structural and differential indexes, consistent initialization analysis, index reduction and dynamic degrees of freedom to the optimal control problem. The resultant differential-algebraic optimal control problem is solved in the following steps: transformation of the original problem into a standard nonlinear programming problem that provides control and state variables, switching time estimates and costate variables profiles with the DIRCOL code; definition of the switching function and the automatically generated sequence of index-1 differential-algebraic boundary value problems from Pontryagin's minimum principle by using the developed Otima code; and finally, application of the COLDAE code with the results of the direct method as an initial guess. The proposed hybrid method is illustrated with a pressure-constrained batch reactor optimization problem associated with the slack variable method.

Hydrogen production from methane steam reforming: parametric and gradient based optimization of a Pd-based membrane reactor

“…Trying it would possible result in exhaustive enumeration of the search space, which is not feasible even for relatively small problems" (Weise 2009). Each approach has advantages and disadvantages, and it is beyond the scope of our paper discuss that point, but further information can be found elsewhere (Lobato et al 2007). So, to solve our optimization problem we have chosen to use an indirect or deterministic method by means of DIRCOL because our group has a tradition in using such methods and also because there is no need to use a probabilistic method whose results, to date, are largely case-dependent and as yet inconclusive regarding the global efficiency of the approach.…”

Estudo Do Desempenho Do Algoritmo De Evolução Diferencial Na Solução De Um Problema De Otimização Dinâmica De Fermentação Alcoólica Em Batelada

“…Os métodos híbridos combinam a precisão dos métodos indiretos com uma maior facilidade dos métodos diretos em encontrar estimativas para algumas variáveis obtidas através do método indireto. (Stryk e Bulirsch, 1992), (Lobato et al, 2007), (Pfeifer, 2007).…”