Simultaneous topology design and optimization of PDE constrained processes based on mixed integer formulations

Abstract

Simultaneous topological design and optimization of complex processes that are described by partial differential equations is a challenging but promising research area. Widely adopted nested and sequential approaches are mostly applicable based on heuristic solutions, hindering the theoretical improvement potential due to decentralized decision-making in subsequent stages with a significant number of trial-and-error procedures. This study introduces a mixed integer formulation addressing the governing equations and case-dependent topological constraints at each discretization point, enabling solutions through rigorous solvers under process-related constraints and objectives. Nonlinear expressions in the formulations are further tailored using piecewise linear approximations, still representing the major nonlinear trends through a mixed-integer linear nature to favor global optimality and benefit from computational advancements, when needed. Heat and Stokes flow problems are used as case studies to demonstrate the applicability of the methodology.