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Bounding Fronts in Multi-Objective Combinatorial Optimization with Application to Aesthetic Drawing of Business Process Diagrams

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Models, Algorithms and Technologies for Network Analysis

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 104))

Abstract

The main concept of branch and bound is to detect subsets of feasible solutions which cannot contain optimal solutions. In multi-objective optimization a bounding front is used—a set of bounding vectors in the objective space dominating all possible objective vectors corresponding to the subset of feasible solutions. The subset cannot contain Pareto optimal (efficient) solutions if each bounding vector in the bounding front corresponding to this subset is dominated by at least one already known decision vector. The simplest bounding front corresponds to a single ideal vector composed of lower bounds for each objective function. However, the bounding fronts with multiple bounding vectors may be tighter and therefore their use may discard more subsets of feasible solutions. In this chapter we investigate the use of bounding vectors and bounding fronts in multi-objective optimization aided to aesthetic drawing of special graphs—business process diagrams. An experimental investigation shows that the use of the bounding front considerably reduces the number of function evaluations and computational time.

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Acknowledgements

The support by Agency for Science, Innovation and Technology (MITA) trough the grant Nr.31V-145 is acknowledged.

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Authors and Affiliations

  1. Recognition Processes Department, Institute of Mathematics and Informatics, Vilnius University, Akademijos 4, LT-08663, Vilnius, Lithuania

    Julius Žilinskas & Antanas Žilinskas

  2. Department of Applied Informatics, Institute of Mathematics and Informatics, Vilnius University, Akademijos 4, LT-08663, Vilnius, Lithuania

    Antanas Žilinskas

Authors
  1. Julius Žilinskas
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  2. Antanas Žilinskas
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Corresponding author

Correspondence to Julius Žilinskas .

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Editors and Affiliations

  1. Laboratory of Algorithms and Technologies for Networks Analysis, Department of Applied Mathematics and Informatics, National Research University Higher School of Economics, Nizhny Novgorod, Russia

    Mikhail V. Batsyn

  2. Laboratory of Algorithms and Technologies for Networks Analysis, Department of Applied Mathematics and Informatics, National Research University Higher School of Economics, Nizhny Novgorod, Russia

    Valery A. Kalyagin

  3. Laboratory of Algorithms and Technologies for Networks Analysis, Department of Industrial and Systems Engineering, Center for Applied Optimization, National Research University Higher School of Economics, Nizhny Novgorod, Russia, University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

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Žilinskas, J., Žilinskas, A. (2014). Bounding Fronts in Multi-Objective Combinatorial Optimization with Application to Aesthetic Drawing of Business Process Diagrams. In: Batsyn, M., Kalyagin, V., Pardalos, P. (eds) Models, Algorithms and Technologies for Network Analysis. Springer Proceedings in Mathematics & Statistics, vol 104. Springer, Cham. https://doi.org/10.1007/978-3-319-09758-9_11

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