Dynamic Global Optimization Methods for Determining Guaranteed Solutions in Chemical Engineering

Engineers seek optimal solutions in designing systems but a crucial element is to ensure bounded performance. For example, chemical reactors are often very heavy energy users so it is important to find designs that minimize energy use but the solution must be within strict safety limits.Currently, the deterministic solution of dynamic systems to global optimality can only be addressed for small problems. The solution of the ordinary differential equation (ODE) systems in a verified way is only able to address low dimensional problems mainly because the integration has to be stopped early due to the overestimation generated by the verified method. Chemical engineering researchers have used a range of techniques to tackle this problem using ways of finding tight over/under-estimators. This chapter will review research work in chemical engineering for such problems and present results of work we are undertaking using interval methods.In our work a verified solver that constructs upper and lower bounds on the dynamic variables of initial value problem (IVP) for ODEs is used in a dynamic global optimization method (sequential approach). Particular attention is paid to the reduction of the overestimation by means of interval contractors. The solver is used to provide guaranteed bounds on the objective function and on the first order sensitivity equations in a branch and bound framework. Uncertainty can be introduced in the dynamic constraints of the dynamic optimization problem and therefore it is possible to account for it in a guaranteed way. The chapter shows three examples from process engineering.