Refined cut selection for benders decomposition: applied to network capacity expansion problems

In this paper, we present a new perspective on cut generation in the context of Benders decomposition. The approach, which is based on the relation between the alternative polyhedron and the reverse polar set, helps us to improve established cut selection procedures for Benders cuts, like the one suggested by Fischetti et al. (Math Program Ser B 124(1–2):175–182, 2010). Our modified version of that criterion produces cuts which are always supporting and, unless in rare special cases, facet-defining. We discuss our approach in relation to the state of the art in cut generation for Benders decomposition. In particular, we refer to Pareto-optimality and facet-defining cuts and observe that each of these criteria can be matched to a particular subset of parametrizations for our cut generation framework. As a consequence, our framework covers the method to generate facet-defining cuts proposed by Conforti and Wolsey (Math Program Ser A 178:1–20, 2018) as a special case. We conclude the paper with a computational evaluation of the proposed cut selection method. For this, we use different instances of a capacity expansion problem for the european power system.

Hydrogel-Based Enzyme and Cofactor Co-Immobilization for Efficient Continuous Transamination in a Microbioreactor

A microbioreactor was developed in which selected amine transaminase was immobilized together with the cofactor pyridoxal phosphate (PLP) to allow efficient continuous transamination. The enzyme and cofactor were retained in a porous copolymeric hydrogel matrix formed in a two-plate microreactor with an immobilization efficiency of over 97%. After 10 days of continuous operation, 92% of the initial productivity was retained and no leaching of PLP or enzyme from the hydrogel was observed. The microbioreactor with co-immobilized cofactor showed similar performance with and without the addition of exogenous PLP, suggesting that the addition of PLP is not required during the process. The space-time yield of the microbioreactor was 19.91 g L−1 h−1, while the highest achieved biocatalyst productivity was 5.4 mg mgenzyme−1 h−1. The immobilized enzyme also showed better stability over a wider pH and temperature range than the free enzyme. Considering the time and cost efficiency of the immobilization process and the possibility of capacity expansion, such a system is of great potential for industrial application.