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Given a directed graph G, a feedback arc set of G is a subset of its edges containing at least one edge of every cycle in G. Finding a feedback arc set of minimum cardinality is the minimum feedback arc set problem. The minimum set cover formulation of the minimum feedback arc set problem is appropriate as long as all the simple cycles in G can be(More)
Multiple steady states are typically discovered by tracing a solution path, including turning points. A new technique is presented here that does not follow this approach. The original problem is solved directly, without tracing a solution path. The proposed branch and prune algorithm is guaranteed to find all solutions automatically. Core components of the(More)
Chemical process models are highly structured. Information on how the hierarchical components are connected helps to solve the model efficiently. Our ultimate goal is to develop structure-driven optimization methods for solving nonlinear programming problems (NLP). The structural information retrieved from the JModelica environment will play an important(More)
The need of reliably solving systems of nonlinear equations often arises in the everyday practice of chemical engineering. In general, standard methods cannot provide theoretical guarantee for convergence to a solution, cannot reliably find multiple solutions, and cannot prove non-existence of solutions. Interval methods provide tools to overcome these(More)
1 Significance A method is proposed that either returns all solutions to steady-state models of distillation columns or proves infeasibility. No initial estimates are required. The computational effort grows linearly with the number of stages. Successful solution of a numerically challenging reactive distillation column with 7 steady-states show the(More)
Cheminformatics systems usually focus primarily on handling specific molecules and reactions. However, Markush structures are also indispensable in various areas, like combinatorial library design or chemical patent applications for the description of compound classes. The presentation will discuss how an existing molecule drawing tool (Marvin) and chemical(More)
A general framework is presented for finding all solutions to systems of nonlinear equations, or proving that there is no solution to the problem. Components of this framework are interval arithmetic, affine arithmetic, constraint propagation based on directed acyclic graph (DAG) representation of the problem, a pruning technique based on linear programming(More)