Coordination specification in distributed optimal design of multilevel systems using the χ language

Abstract

Coordination plays a key role in solving decomposed optimal design problems. Several coordination strategies have been proposed in the multidisciplinary optimization (MDO) literature. They are usually presented as a sequence of statements. However, a precise description of the concurrency in the coordination is needed for large multilevel or non-hierarchic coordination architectures. This article proposes the use of communicating sequential processes (CSP) concepts from concurrency theory for specifying and implementing coordination strategies in distributed multilevel optimization rigorously. CSP enables the description of the coordination as a number of parallel processes that operate independently and communicate synchronously. For this purpose, we introduce elements of the language χ, a CSP-based language that contains advanced data modeling constructs. The associated software toolkit allows execution of the specified coordination. Coordination specification using χ is demonstrated for analytical target cascading (ATC), a methodology for design optimization of hierarchically decomposed multilevel systems. It is shown that the ATC coordination can be compactly specified for various coordination schemes. This illustrates the advantage of using a high-level concurrent language, such as χ, for specifying the coordination of distributed optimal design problems. Moreover, the χ software toolkit is useful in implementing alternative schemes rapidly, thus enabling the comparison of different MDO methods.