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Optimization of product in dynamic design space and selection through the arc-elasticity concept


In the industrial design process, “trial-and-error” loops are usually used between design departments and simulation departments, to design and validate a candidate solution. Such a solution is defined by instantiated design variables, characterizing the main parameters of the product. This paper proposes to replace the trial-and-error process by an optimization method; two bottlenecks were identified: the importance of the initial design solution which has already engaged delays and costs, and the formalization of designers preferences to select high-performance solutions. To take into account the initial solution, a strategy is proposed to explore the global design space (which represents all the candidate solutions) starting from the initial one, and using a hierarchical organization of the design variables. Then, the Observation–Interpretation–Aggregation method is used first to formalize designer knowledge related to the product to design and then to rank every design solution using a single performance value. Moreover, the concept of arc-elasticity is used to qualify a solution through its neighborhood, and to characterize technological breakthroughs, compared to the initial solution. This method is discussed and illustrated through the design of an aeronautical riveted assembly.

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Vector of design variables, candidate solution

xi :

Design variable

\({\left[ \overline{{\rm x}}_{\rm i}^{-};\overline{{\rm x}}_{\rm i}^{+} \right]}\) :

Value domain of xi

\({\overline \Omega }\) :

Design space

X0 :

Initial solution

x 0i :

Design variable of the initial solution


Discrete-time-equivalent variable

Ω (t):

Relative design space

\({\left[ {{\rm x}_{\rm i}^- \left( {\rm t} \right);{\rm x}_{\rm i}^+ \left( {\rm t} \right)} \right]}\) :

Relative values domain


Exploration function associated to xi

\({{\rm t}_{\rm i}^- ; \quad {\rm t}_{\rm i}^+ }\) :

Parameters of αi (t)


Membership function associated to xi


Vector of observation variables

yi :

Observation variable


Vector of interpretation variables

zi :

Interpretation variable

ωi :

Weighting parameter of zi

DOIi :

Design objective index

νi :

Weighting parameter of DOIi


Performance of a candidate solution X


Objective function linking X to GDI



GDI0 :

Performance of the initial solution X0


Performance variation

distnED :

Nondimensional euclidian distance


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Correspondence to Arnaud Collignan.

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Collignan, A., Sebastian, P., Pailhes, J. et al. Optimization of product in dynamic design space and selection through the arc-elasticity concept. Int J Interact Des Manuf 5, 243–254 (2011).

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  • Design space
  • Optimization
  • Desirability
  • Arc-elasticity
  • Genetic algorithm