Methodology Based on Multiagent for Solving Multidisciplinary Optimization Problem Under Uncertainty

T HERE are a large number ofmethodologies available inmultidisciplinary design optimization (MDO) for deterministic environments [1–3]. However, to design systems that are both robust and reliable, uncertainties regarding models and parameters have to be catered for to ensure success of the project in terms of timeliness, cost, and performance. This is crucial, especially during the preliminary design phasewhere there are still many uncertainties and decisions have to be compatible with the more detailed analysis of future development phases. To cope with this problem, reliability-based and robust design methods [4] have been developed to assist designers in the decision-making process. A number of relatively time-consuming techniques to solve optimization problems under uncertainty have been devised [5–8]. The main drawback with these methods is the computational burden associated with evaluation of robustness and reliability during design. A powerful methodology stemming from artificial intelligence, the autoadaptive multiagent system (AMAS), has recently been developed to solve complexmultidisciplinary optimization problems, especially in the aeronautical field [9–11]. Due to both its local and parallel approach, the AMAS method allows complex deterministic optimization problems to be solved rapidly, even in multidisciplinary contexts such as aircraft design where thermal engineering, structural, and fluid mechanics issues all interact. However, the said AMASmethodwas developed to respond to a deterministic environment only. The aim of the present Note is to extend theAMASmethodwith its multiagent framework to copewithMDO under conditions of uncertainty, providing a new methodology so it can be effectively used in an uncertain environment. To do so, a strategy to integrate and propagate uncertainties in themultiagent framework is first developed. Then, to optimize computing time,multiagent propagation is combined with a sequential optimization process coupled with the use of AMAS. This Note is organized as follows. Section II gives the approach used to solve a deterministic multidisciplinary optimization problem with a multiagent system. For didactic purposes, this approach is presented through an extremely simple mathematical application. Section III then goes on to describe the proposedmethodology to solveMDOproblems in an uncertain environment. This section is broken down into two subsections. The first describes the integration and propagation of uncertainties in the multiagent framework, whereas the second looks at the interactions between uncertainty propagation, the sequential optimization process, and the AMAS method. More precisely, at each step of the sequential optimization process, the AMAS method is effectively used to solve a deterministic optimization problem. From the given AMAS deterministic optimum, a reliability analysis is than conducted. Violated constraints are shiftedwith the introduction of adaptive safety coefficients as computed from multiagent uncertainty propagation. These coefficients are applied to define a new deterministic optimization problem to be solved by the AMAS over the following cycle. Iterations stop once the safety coefficients have been brought down to a low enough level. Finally, in Sec. IV, this newmethodology is applied to a preliminary aircraft design test case. Results show substantial improvements in terms of robustness and efficiency comparedwith the standard double-loop optimization process used to solve classicalMDOproblems. Conclusions and perspectives are presented in Sec. V.