The Features of Solving of the set Partitioning Problems with Moving Boundaries Between Subsets

Tetyana Shevchenko (), Elena Kiseleva () and Larysa Koriashkina ()
Additional contact information
Tetyana Shevchenko: Dnipropetrovsk National University, Department of Calculating Mathematics and Mathematical Cybernetics
Elena Kiseleva: Dnipropetrovsk National University, Department of Calculating Mathematics and Mathematical Cybernetics
Larysa Koriashkina: Dnipropetrovsk National University, Department of Calculating Mathematics and Mathematical Cybernetics

Chapter 86 in Operations Research Proceedings 2008, 2009, pp 533-538 from Springer

Abstract: Summary Problems and methods presented in this paper synthesize foundations of theory of continuous set partitioning problems (SPP) and optimal control of systems described by ordinary differential equations. In order to mathematically formulate SPP quite often one should take into account the temporal and spatial changes of object or process state. Some of such models concerned with problems of preservation of the environment were learning by our scientists. Mathematical models of problems mentioned above are new from the viewpoint of problem statement and interesting to further generalization and developing of theoretical results which could be used in practice widely. A common SPP could be formulated as follows: it is necessary to partition a given area (set) into a finite number of disjoint subsets that satisfies certain restrictions so that the objective function reaches an extreme value. We propose a new problem statement, which differs from known ones in the following way: the desired set partition is dynamic in consequence of 1) a function which describes the certain object or process state varies with time; 2) a function, choice of which has an inuence on state of this object or process, is defined by partition of considered set each moment of time. This problem amounts to optimal control one for which one should write out the necessary conditions of optimality in the form of Pontrjagin‘s maximum principle. The constructed algorithm for solving such problems bases on combining both the methods of solving continuous SPP and methods of optimal control theory. With a view to investigate the properties of solutions of new set partitioning problem we realized the series of computational experiments and made qualitative analysis of obtained results.

Keywords: Disjoint Subset; Optimal Control Theory; Optimal Control Method; Partitioning Prob; Admissible Partition (search for similar items in EconPapers)
Date: 2009
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-00142-0_86

Ordering information: This item can be ordered from
http://www.springer.com/9783642001420

DOI: 10.1007/978-3-642-00142-0_86

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().