The analytical target cascading (ATC) methodology for optimizing hierarchical systems has demonstrated convergence properties for continuous, convex formulations. However, many practical problems involve both continuous and discrete design variables, resulting in mixed integer nonlinear programming (MINLP) formulations. While current ATC methods have been used to solve such MINLP formulations i...

We present a flexible framework for general mixed-integer nonlinear programming (MINLP), called Minotaur, that enables both algorithm exploration and structure exploitation without compromising computational efficiency. This paper documents the concepts and classes in our framework and shows that our implementations of standard MINLP techniques are efficient compared with other state-of-the-art...

The paper examines the applicability of mathematical programming methods to the simultaneous optimization of the structure and the operational parameters of a combined-cycle-based cogeneration plant. The optimization problem is formulated as a non-convex mixed-integer nonlinear problem (MINLP) and solved by the MINLP solver LaGO. The algorithm generates a convex relaxation of the MINLP and appl...

This paper presents an Equality Relaxation variant to the Outer-Approximation algorithm for solving mixed-integer nonlinear programming (MINLP) problems that arise in structural optimization of process flowsheets. The proposed algorithm has the important capability of being able to explicitly handle nonlinear equations within MINLP formulations that have linear integer variables and linear/nonl...

Abstract We propose a new decomposition method to solve multistage non-convex mixed-integer (stochastic) nonlinear programming problems (MINLPs). call this algorithm nested Benders (NC-NBD). NC-NBD is based on solving dynamically improved linear outer approximations of the MINLP, obtained by piecewise relaxations functions. Those MILPs are solved global optimality using an enhancement decomposi...

This paper presents scaled quadratic cuts based on scaling the second-order Taylor expansion terms for the decomposition methods Outer Approximation (OA) and Partial Surrogate Cuts (PSC) used for solving convex Mixed Integer Nonlinear Programing (MINLP). The scaled quadratic cut is proved to be a stricter and tighter underestimation for the convex nonlinear functions than the classical supporti...

The long-term planning of the shale gas supply chain is a relevant problem that has not been addressed before in the literature. This paper presents a mixed-integer nonlinear programming (MINLP) model to optimally determine the number of wells to drill at every location, the size of gas processing plants, the section and length of pipelines for gathering raw gas and delivering processed gas and...

Decentralized energy supply systems (DESS) are highly integrated and complex systems designed to meet time-varying energy demands, e.g., heating, cooling, and electricity. The synthesis problem of DESS addresses combining various types of energy conversion units, choosing their sizing and operations to maximize an objective function, e.g., the net present value. In practice, investment costs an...

This paper focuses on the collision-free coordination of multiple robots with kinodynamic constraints along specified paths. We present an approach to generate continuous velocity profiles for multiple robots; these velocity profiles satisfy the dynamics constraints, avoid collisions, and minimize the completion time. The approach, which combines techniques from optimal control and mathematical...