Advances in process synthesis: New robust formulations

We present new modifications to superstructure optimization paradigms to i) enable their robust solution and ii) extend their applicability. Superstructure optimization of chemical process flowsheets on the basis of rigorous and detailed models of the various unit operations, such as in the state operator network (SON) paradigm, is prone to non-convergence. A key challenge in this optimization-based approach is that when process units are deselected from a superstructure flowsheet, the constraints that represent the deselected process unit can be numerically singular (e.g., divide by zero, logarithm of zero and rank-deficient Jacobian). In this paper, we build upon the recently-proposed modified state operator network (MSON) that systematically eliminates singularities due to unit deselection and is equally applicable to the context of both simulation-based and equation-oriented optimization. A key drawback of the MSON is that it is only applicable to the design of isobaric flowsheets at a pressure fixed a priori. In this paper, as a first step towards the synthesis of general flowsheets with variable pressures, we extend the MSON to the synthesis of a gas-liquid absorption column at variable pressure (i.e., the pressure is a degree of freedom that may be optimized). We illustrate the use of the extended MSON on a carbon-capture process. The extended MSON is robust and enables the design of the column on the basis of detailed thermodynamic models and simulation-based optimization

On the composition of convex envelopes for quadrilinear terms

International audienceWithin the framework of the spatial Branch-and-Bound algorithm for solving Mixed-Integer Nonlinear Programs, different convex relaxations can be obtained for multilinear terms by applying associativity in different ways. The two groupings ((x1x2)x3)x4 and (x1x2x3)x4 of a quadrilinear term, for example, give rise to two different convex relaxations. In [6] we prove that having fewer groupings of longer terms yields tighter convex relaxations. In this paper we give an alternative proof of the same fact and perform a computational study to assess the impact of the tightened convex relaxation in a spatial Branch-and-Bound setting

Branch-and-lift algorithm for deterministic global optimization in nonlinear optimal control

This paper presents a branch-and-lift algorithm for solving optimal control problems with smooth nonlinear dynamics and potentially nonconvex objective and constraint functionals to guaranteed global optimality. This algorithm features a direct sequential method and builds upon a generic, spatial branch-and-bound algorithm. A new operation, called lifting, is introduced, which refines the control parameterization via a Gram-Schmidt orthogonalization process, while simultaneously eliminating control subregions that are either infeasible or that provably cannot contain any global optima. Conditions are given under which the image of the control parameterization error in the state space contracts exponentially as the parameterization order is increased, thereby making the lifting operation efficient. A computational technique based on ellipsoidal calculus is also developed that satisfies these conditions. The practical applicability of branch-and-lift is illustrated in a numerical example. © 2013 Springer Science+Business Media New York

A global optimization algorithm for optimal control and parameter estimation problems

Μη διαθέσιμη περίληψηNot available summarizationΠαρουσιάστηκε στο: SIAM Conference on Optimizatio

A global optimization algorithm for systems described by ODEs

Μη διαθέσιμη περίληψηNot available summarizationΠαρουσιάστηκε στο: AIChE Annual Meetin

A new convex relaxation for systems described by ordinary differential equations

Μη διαθέσιμη περίληψηNot available summarizationΠαρουσιάστηκε στο: AIChE Annual Meetin

Global optimization of dynamic systems

Summarization: Many chemical engineering systems are described by differential equations. Their optimization is often complicated by the presence of nonconvexities. A deterministic spatial branch and bound global optimization algorithm is presented for problems with a set of first-order differential equations in the constraints. The global minimum is approached from above and below by generating converging sequences of upper and lower bounds. Local solutions, obtained using the sequential approach for the solution of the dynamic optimization problem, provide upper bounds. Lower bounds are produced from the solution of a convex relaxation of the original problem. Algebraic functions are relaxed using well-known convex underestimation techniques. The convex relaxation of the dynamic information is achieved using a new convex relaxation procedure. Parameter independent as well as parameter dependent bounds on the dynamic system are utilized. The global optimization algorithm is illustrated by applying it to case studies relevant to chemical engineering, where affine functions of the optimization variables are used as a relaxation of the dynamic system.Presented on: Computers and Chemical Engineerin