A global method for the limited K‐partitioning of hypergraphs representing optimal design problems in complex machine systems

Abstract

Purpose

The purpose of this paper is to find a global method for the limited K‐partitioning of hypergraphs representing optimal design problems in complex machine systems.

Design/methodology/approach

To represent some real design considerations, a new concept of semi‐free hypergraphs is proposed and a method to apply semi‐free hypergraphs to the decomposition of complex design problems based on optimal models is also suggested. On this basis, the limited K‐partitioning problem of semi‐free hypergraphs and its partitioning objective for the optimal design of complex machines is presented. A global method based on genetic algorithms, GALKP, for the limited K‐partitioning of semi‐free hypergraphs is also proposed. Finally, a case study is presented in detail.

Findings

Semi‐free hypergraphs are a more powerful tool to map a complex engineering design problem. The decomposition of complex design problems may be converted to a limited K‐partitioning problem of semi‐free hypergraphs. The algorithm presented in this paper for the limited K‐partitioning of semi‐free hypergraphs is fast, effective, and powerful.

Research limitations/implications

The traditional methods based on hypergraphs have some limitations while applied to the decomposition of some complex problems such as the design of large‐scale machine systems. The proposed method is helpful to solve similar engineering design problems.

Practical implications

The paper illustrates a faster and more effective method to implement the decomposition of large‐scale optimal design problems in complex machine systems.

Originality/value

This paper shows a new way to solve the complex engineering design problems based on semi‐free hypergraphs and its K‐partitioning method.

Citation

Shuiping, L. and Xiaoxue, W. (2010), "A global method for the limited K‐partitioning of hypergraphs representing optimal design problems in complex machine systems", Kybernetes, Vol. 39 No. 6, pp. 980-989. https://doi.org/10.1108/03684921011046753