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

  • Julius ŽilinskasEmail author
  • Antanas Žilinskas
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 104)


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.



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


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Recognition Processes DepartmentInstitute of Mathematics and Informatics, Vilnius UniversityVilniusLithuania
  2. 2.Department of Applied InformaticsInstitute of Mathematics and Informatics, Vilnius UniversityVilniusLithuania

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