Speeding up IP-based Algorithms for Constrained Quadratic 0-1 Optimization

In many practical applications, the task is to optimize a non-linear objective function over the vertices of a well-studied polytope as, e.g., the matching polytope or the travelling salesman polytope (TSP).Prominent examples are the quadratic assignment problem and the quadratic knapsack problem; further applications occur in various areas such as production planning or automatic graph drawing. In order to apply branch-and-cut methods for the exact solution of such problems, the objective function has to be linearized. However, the standard linearization usually leads to very weak relaxations. On the other hand, problem-specific polyhedral studies are often time-consuming.Our goal is the design of general separation routines that can replace detailed polyhedral studies of the resulting polytope and that can be used as a black box. As unconstrained binary quadratic optimization is equivalent to the maximum cut problem, knowledge about cut polytopes can be used in our setting. Other separation routines are inspired by the local cuts that have been developed by Applegate, Bixby, Chvatal and Cook for faster solution of large-scale traveling salesman instances. Finally, we apply quadratic reformulations of the linear constraints as proposed by Helmberg, Rendl and Weismantel for the quadratic knapsack problem. By extensive experiments, we show that a suitable combination of these methods leads to a drastical speedup in the solution of constrained quadratic 0-1 problems. We also discuss possible generalizations of these methods to arbitrary non-linear objective functions

Speeding up IP-based Algorithms for Constrained Quadratic 0-1 Optimization

In many practical applications, the task is to optimize a non-linear objective function over the vertices of a well-studied polytope as, e.g., the matching polytope or the travelling salesman polytope (TSP).Prominent examples are the quadratic assignment problem and the quadratic knapsack problem; further applications occur in various areas such as production planning or automatic graph drawing. In order to apply branch-and-cut methods for the exact solution of such problems, the objective function has to be linearized. However, the standard linearization usually leads to very weak relaxations. On the other hand, problem-specific polyhedral studies are often time-consuming.Our goal is the design of general separation routines that can replace detailed polyhedral studies of the resulting polytope and that can be used as a black box. As unconstrained binary quadratic optimization is equivalent to the maximum cut problem, knowledge about cut polytopes can be used in our setting. Other separation routines are inspired by the local cuts that have been developed by Applegate, Bixby, Chvatal and Cook for faster solution of large-scale traveling salesman instances. Finally, we apply quadratic reformulations of the linear constraints as proposed by Helmberg, Rendl and Weismantel for the quadratic knapsack problem. By extensive experiments, we show that a suitable combination of these methods leads to a drastical speedup in the solution of constrained quadratic 0-1 problems. We also discuss possible generalizations of these methods to arbitrary non-linear objective functions

Weighted Consecutive Ones Problems

A 0/1-matrix has the consecutive ones property (for rows) if its columns can be permuted in such a way that in every row all ones appear consecutively. The consecutive ones property for columns is defined analogously. Furthermore a 0/1-matrix has the simultaneous consecutive ones property if it has both the consecutive ones property for rows and for columns. Whereas deciding whether a given matrix has the (simultaneous) consecutive ones property can be done in linear time by the PQ-tree algorithm, it is NP-hard to optimize a linear objective function over all 0/1-matrices with (simultaneous) consecutive ones property. The latter problem is called Weighted (Simultaneous) Consecutive Ones Problem WC1P (WSC1P). In this thesis we study both the WC1P and the WSC1P from a polyhedral point of view and derive integer programming formulations consisting only of facets of the corresponding polytopes. Additionally polynomial separation procedures are given for all these classes of inequalities. Therefore this IP formulation serves as a good basis for a branch-and-cut algorithm which is used to solve the WC1P and the WSC1P to optimality. New ideas for separating and for primal heuristics are given which improve the algorithm substantially. The thesis continues with an overview of several applications of the WC1P and the WSC1P, for example the Physical Mapping Problem occurring in computational biology or the problem of finding clusters of inorganic crystal structure types. Finally computational results are presented which show that the branch-and-cut code provides a useful tool for tackling WC1P and WSC1P problems occurring in practice

New results on the Windy Postman Problem

[EN] In this paper, we study the Windy Postman Problem (WPP). This is a well-known Arc Routing Problem that contains the Mixed Chinese Postman Problem (MCPP) as a special case. We extend to arbitrary dimension some new inequalities that complete the description of the polyhedron associated with the Windy Postman Problem over graphs with up to four vertices and ten edges. We introduce two new families of facet-inducing inequalities and prove that these inequalities, along with the already known odd zigzag inequalities, are Chvátal-Gomory inequalities of rank at most 2. Moreover, a branch-and-cut algorithm that incorporates two new separation algorithms for all the previously mentioned inequalities and a new heuristic procedure to obtain upper bounds are presented. Finally, the performance of a branch-and-cut algorithm over several sets of large WPP and MCPP instances, with up to 3,000 nodes and 9,000 edges (and arcs in the MCPP case), shows that, to our knowledge, this is the best algorithm to date for the exact resolution of the WPP and the MCPP. © 2010 Springer and Mathematical Optimization Society.The authors want to thank the three referees for their careful reading of the manuscript and for their many comments and suggestions that have contributed to improve the paper content and readability. In particular, several remarks regarding the discussion of C-G and mod-k inequalities were pointed out by one of the referees. A. Corberan, I. Plana and J.M. Sanchis wish to thank the Ministerio de Educacion y Ciencia of Spain (projects MTM2006-14961-C05-02 and MTM2009-14039-C06-02) for its support.Corberán, A.; Oswald, M.; Plana, I.; Reinelt, G.; Sanchís Llopis, JM. (2012). New results on the Windy Postman Problem. Mathematical Programming. 132(1-2):309-332. https://doi.org/10.1007/s10107-010-0399-xS3093321321-2Benavent E., Carrotta A., Corberán A., Sanchis J.M., Vigo D.: Lower bounds and heuristics for the windy rural postman problem. Eur. J. Oper. Res. 176, 855–869 (2007)Brucker P. The Chinese postman problem for mixed graphs. In Proceedings of international workshop. Lecture Notes in Computer Science 100, 354–366 (1981)Caprara A., Fischetti M.: $${\{0,\frac{1}{2}\}}$$ -Chvátal-Gomory cuts. Math. Program. 74, 221–235 (1996)Caprara A., Fischetti M., Letchford A.N.: On the separation of maximally violated mod-k cuts. Math. Program. 87, 37–56 (2000)Christof, T., Loebel, A.: PORTA—a polyhedron representation algorithm www.informatik.uni-heidelberg.de/groups/comopt/software/PORTA/ (1998)Christofides, N., Benavent, E., Campos, V., Corberán, A., Mota, E.: An optimal method for the mixed postman problem. In Thoft-Christensen, P. (ed.) System Modelling and Optimization. Lecture Notes in Control and Information Sciences 59, Springer (1984)Corberán A., Plana I., Sanchis J.M.: Zigzag inequalities: a new class of facet-inducing inequalities for arc routing problems. Math. Program. 108, 79–96 (2006)Corberán A., Plana I., Sanchis J.M.: A branch & cut algorithm for the windy general routing problem and special cases. Networks 49, 245–257 (2007)Corberán, A., Plana I., Sanchis, J.M.: Arc routing problems: data instances. www.uv.es/corberan/instancias.htm (2007)Corberán A., Plana I., Sanchis J.M.: The windy general routing polyhedron: a global view of many known arc routing polyhedra. SIAM J. Discrete Math. 22, 606–628 (2008)Grötschel, M., Win, Z.: On the windy postman polyhedron. Report No. 75, Schwerpunktprogram der Deutschen Forschungsgemeinschaft, Universität Augsburg, Germany (1988)Grötschel M., Win Z.: A cutting plane algorithm for the Windy Postman Problem. Math. Program. 55, 339–358 (1992)Guan M.: On the Windy Postman Problem. Discrete Appl. Math. 9, 41–46 (1984)Minieka E.: The Chinese postman problem for mixed networks. Manage. Sci. 25, 643–648 (1979)Naddef D., Rinaldi G.: The symmetric traveling salesman polytope and its graphical relaxation: composition of valid inequalities. Math. Program. 51, 359–400 (1991)Oswald M., Reinelt G., Seitz H.: Applying mod-k cuts for solving linear ordering problems. TOP 17, 158–170 (2009)Papadimitriou C.H.: On the complexity of edge traversing. J. Assoc. Comput. Mach. 23, 544–554 (1976)Ralphs T.K.: On the mixed Chinese postman problem. Oper. Res. Lett. 14, 123–127 (1993)Wenger, K.: Generic Cut Generation Methods for Routing Problems. PhD Dissertation, University of Heidelberg, Germany (2004)Win, Z.: Contributions to Routing Problems. PhD Dissertation, University of Augsburg, Germany (1987)Win Z.: On the Windy Postman Problem on eulerian graphs. Math. Program. 44, 97–112 (1989)Zaragoza Martínez F.J.: Series-parallel graphs are windy postman perfect. Discrete Math. 308, 1366–1374 (2008

Machine learning based analyses on metabolic networks supports high-throughput knockout screens

Background: Computational identification of new drug targets is a major goal of pharmaceutical bioinformatics. Results: This paper presents a machine learning strategy to study and validate essential enzymes of a metabolic network. Each single enzyme was characterized by its local network topology, gene homologies and co-expression, and flux balance analyses. A machine learning system was trained to distinguish between essential and non-essential reactions. It was validated by a comprehensive experimental dataset, which consists of the phenotypic outcomes from single knockout mutants of Escherichia coli (KEIO collection). We yielded very reliable results with high accuracy (93%) and precision (90%). We show that topologic, genomic and transcriptomic features describing the network are sufficient for defining the essentiality of a reaction. These features do not substantially depend on specific media conditions and enabled us to apply our approach also for less specific media conditions, like the lysogeny broth rich medium. Conclusion: Our analysis is feasible to validate experimental knockout data of high throughput screens, can be used to improve flux balance analyses and supports experimental knockout screens to define drug targets

Evaluation of reverse phase protein array (RPPA)-based pathway-activation profiling in 84 non-small cell lung cancer (NSCLC) cell lines as platform for cancer proteomics and biomarker discovery

AbstractThe reverse phase protein array (RPPA) approach was employed for a quantitative analysis of 71 cancer-relevant proteins and phosphoproteins in 84 non-small cell lung cancer (NSCLC) cell lines and by monitoring the activation state of selected receptor tyrosine kinases, PI3K/AKT and MEK/ERK1/2 signaling, cell cycle control, apoptosis, and DNA damage. Additional information on NSCLC cell lines such as that of transcriptomic data, genomic aberrations, and drug sensitivity was analyzed in the context of proteomic data using supervised and non-supervised approaches for data analysis. First, the unsupervised analysis of proteomic data indicated that proteins clustering closely together reflect well-known signaling modules, e.g. PI3K/AKT- and RAS/RAF/ERK-signaling, cell cycle regulation, and apoptosis. However, mutations of EGFR, ERBB2, RAF, RAS, TP53, and PI3K were found dispersed across different signaling pathway clusters. Merely cell lines with an amplification of EGFR and/or ERBB2 clustered closely together on the proteomic, but not on the transcriptomic level. Secondly, supervised data analysis revealed that sensitivity towards anti-EGFR drugs generally correlated better with high level EGFR phosphorylation than with EGFR abundance itself. High level phosphorylation of RB and high abundance of AURKA were identified as candidates that can potentially predict sensitivity towards the aurora kinase inhibitor VX680. Examples shown demonstrate that the RPPA approach presents a useful platform for targeted proteomics with high potential for biomarker discovery. This article is part of a Special Issue entitled: Biomarkers: A Proteomic Challenge

Discovering functional gene expression patterns in the metabolic network of Escherichia coli with wavelets transforms

BACKGROUND: Microarray technology produces gene expression data on a genomic scale for an endless variety of organisms and conditions. However, this vast amount of information needs to be extracted in a reasonable way and funneled into manageable and functionally meaningful patterns. Genes may be reasonably combined using knowledge about their interaction behaviour. On a proteomic level, biochemical research has elucidated an increasingly complete image of the metabolic architecture, especially for less complex organisms like the well studied bacterium Escherichia coli. RESULTS: We sought to discover central components of the metabolic network, regulated by the expression of associated genes under changing conditions. We mapped gene expression data from E. coli under aerobic and anaerobic conditions onto the enzymatic reaction nodes of its metabolic network. An adjacency matrix of the metabolites was created from this graph. A consecutive ones clustering method was used to obtain network clusters in the matrix. The wavelet method was applied on the adjacency matrices of these clusters to collect features for the classifier. With a feature extraction method the most discriminating features were selected. We yielded network sub-graphs from these top ranking features representing formate fermentation, in good agreement with the anaerobic response of hetero-fermentative bacteria. Furthermore, we found a switch in the starting point for NAD biosynthesis, and an adaptation of the l-aspartate metabolism, in accordance with its higher abundance under anaerobic conditions. CONCLUSION: We developed and tested a novel method, based on a combination of rationally chosen machine learning methods, to analyse gene expression data on the basis of interaction data, using a metabolic network of enzymes. As a case study, we applied our method to E. coli under oxygen deprived conditions and extracted physiologically relevant patterns that represent an adaptation of the cells to changing environmental conditions. In general, our concept may be transferred to network analyses on biological interaction data, when data for two comparable states of the associated nodes are made available

Heme oxygenase-1 genotype and restenosis after balloon angioplasty: a novel vascular protective factor

AbstractObjectivesWe investigated the association of the heme oxygenase-1 (HO-1) promoter genotype with the inflammatory response and restenosis after balloon angioplasty.BackgroundHeme oxygenase-1, which is induced by balloon angioplasty, can inhibit neointima formation and vascular remodeling. A dinucleotide repeat in the HO-1 gene promoter shows a length polymorphism that modulates HO-1 gene transcription. Short (<25 guanosine thymidine [GT]) repeats are associated with a 10-fold greater up-regulation of HO-1 than are longer repeats.MethodsWe studied 381 consecutive patients who underwent femoropopliteal balloon angioplasty (n = 210) and comparison groups with femoropopliteal stenting (n = 68) and lower limb angiography (n = 103). C-reactive protein (CRP) was measured at baseline, 24, and 48 h. We evaluated patency at six months by duplex sonography and assessed the association of the length of GT repeats in the HO-1 gene promoter with postintervention CRP and restenosis.ResultsRestenosis within six months was found in 74 patients (35%) after balloon angioplasty and in 21 patients (31%) after stenting. After balloon angioplasty, carriers of the short length (<25 GT) dinucleotide repeats had a lower postintervention CRP at 24 h (p = 0.009) and 48 h (p < 0.001) and a reduced risk for restenosis (adjusted relative risk 0.43, 95% confidence interval: 0.24 to 0.71, p < 0.001) compared with patients with longer alleles. After stenting or angiography, we found no association between the HO-1 genotype with CRP or restenosis.ConclusionsThe HO-1 promoter genotype that controls the degree of HO-1 up-regulation in response to stress stimuli is associated with the postintervention inflammatory response and the restenosis risk after balloon angioplasty

SOX5 is involved in balanced MITF regulation in human melanoma cells

Background: Melanoma is a cancer with rising incidence and new therapeutics are needed. For this, it is necessary to understand the molecular mechanisms of melanoma development and progression. Melanoma differs from other cancers by its ability to produce the pigment melanin via melanogenesis; this biosynthesis is essentially regulated by microphthalmia-associated transcription factor (MITF). MITF regulates various processes such as cell cycling and differentiation. MITF shows an ambivalent role, since high levels inhibit cell proliferation and low levels promote invasion. Hence, well-balanced MITF homeostasis is important for the progression and spread of melanoma. Therefore, it is difficult to use MITF itself for targeted therapy, but elucidating its complex regulation may lead to a promising melanoma-cell specific therapy. Method: We systematically analyzed the regulation of MITF with a novel established transcription factor based gene regulatory network model. Starting from comparative transcriptomics analysis using data from cells originating from nine different tumors and a melanoma cell dataset, we predicted the transcriptional regulators of MITF employing ChIP binding information from a comprehensive set of databases. The most striking regulators were experimentally validated by functional assays and an MITF-promoter reporter assay. Finally, we analyzed the impact of the expression of the identified regulators on clinically relevant parameters of melanoma, i.e. the thickness of primary tumors and patient overall survival. Results: Our model predictions identified SOX10 and SOX5 as regulators of MITF. We experimentally confirmed the role of the already well-known regulator SOX10. Additionally, we found that SOX5 knockdown led to MITF up-regulation in melanoma cells, while double knockdown with SOX10 showed a rescue effect; both effects were validated by reporter assays. Regarding clinical samples, SOX5 expression was distinctively up-regulated in metastatic compared to primary melanoma. In contrast, survival analysis of melanoma patients with predominantly metastatic disease revealed that low SOX5 levels were associated with a poor prognosis. Conclusion: MITF regulation by SOX5 has been shown only in murine cells, but not yet in human melanoma cells. SOX5 has a strong inhibitory effect on MITF expression and seems to have a decisive clinical impact on melanoma during tumor progression

Customer Management Studie 2022 : Trends, Daten und Nachhaltigkeit

Die Customer Management Studie zeigt die wichtigsten Trends im Kundenmanagement im DACH-Raum aus Unternehmenssicht auf. Die aktuellen Krisen haben teilweise als weitere Beschleuniger des Wandels gewirkt und die Notwendigkeit, die wichtigen Trends für das eigene Unternehmen zu erkennen und darauf zu reagieren, nochmals erhöht. 219 Unternehmensvertreterinnen und -vertreter aus der Schweiz, Deutschland und Österreich haben für diese Studie ihre Einschätzungen geteilt und ermöglichen den Lesenden ein Benchmarking für ihr Unternehmen. Namhafte Expertinnen und Experten der Partnerunternehmen und Verbände bereichern die Studie durch Statements und Praxiscases und ordnen die Ergebnisse ein. Unternehmen legen in diesem Jahr den Schwerpunkt im Kundenlebenszyklus mehrheitlich auf die Kundenbindung. Betreffend Digitalisierung der Kundenbeziehung befindet sich rund die Hälfte der befragten Unternehmen noch eher am Anfang, obwohl es einen wichtigen Faktor für die individuelle Kundenkommunikation darstellt und kundenorientiertes Verhalten ermöglicht. Dahingegen wird CRM-Software wie in den bisherigen Jahren von über zwei Dritteln der Unternehmen zur Sammlung von Kundendaten eingesetzt. Ein aufkommendes Thema heisst dabei Customer Data Platform (CDP). Lediglich die Hälfte der Befragten gab an von CDPs gehört zu haben. Diese Hälfte ist häufig schon an konkreten Einführungsschritten. Das überrascht nicht, denn die potenziellen Vorteile von CDPs sind für die meisten Unternehmen sehr attraktiv. Künstliche Intelligenz (KI) wird in den Kundenbeziehungen bereits in vielen Anwendungen eingesetzt und die Kommunikation verläuft Mensch zu Maschine zu Mensch. Insbesondere die digitale Kommunikation und Werbung wird häufig von Algorithmen gefiltert und gesteuert. Dies ist jedoch vielen teilnehmenden Unternehmen bisher nicht bewusst. Der nächste Level wäre der bewusste und gezielte Einsatz von KI, um die jeweiligen Vorteile von Mensch und Maschine in den Kundenbeziehungen optimal zu nutzen. Nachhaltigkeit gilt als einer der wirkmächtigsten Megatrends der Gegenwart. Das erzeugt Handlungsdruck: Unternehmen müssen Stellung beziehen, wie sie zur Nachhaltigkeit stehen. Die grosse Mehrheit wird mit Nachhaltigkeitsforderungen von Kundinnen und Kunden und sogar noch stärker von Mitarbeitenden konfrontiert. Die vorliegende Studie zeigt auf, dass der Wandel im Kundenmanagement ungebrochen ist und die Unternehmen auch hier agil sein müssen. Insbesondere muss das Gleichgewicht von Daten und Emotionen sowie Mensch und Maschine immer wieder neu austariert werden