Synthesis and scalarization of hierarchical vector criterion in production management problems

Abstract

Abstract The multicriteriality problem has many aspects. The paper is dedicated to one of them, namely: development of the methodology for building and using dynamically changing multi-level vector criteria for optimization of engineering and manufacturing complexes. The approach applied most frequently involves vector to scalar conversion of the optimization criterion. When multi-level criteria are used we have to deal with a system of embedded convolutions forming a hierarchical system of vectors. The current principles of making convolutions for such systems can be implemented in different ways depending on peculiarities of the controlled object and management goalsThis study discusses building of hierarchical criteria in mathematical setting up of engineering and manufacturing complex optimization problems. A method of forming and scalarization of a hierarchical vector criterion following a recurrent procedure based on an invariant representing a linear combination of Holder norms of partial criteria is suggested. An example of techniques usage in the development of software for multi-criterial optimization of refinery is given.