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     1.2 OPTIMIZATION TECHNIQUES IN
    MOULDING
    In the literature, various optimization procedures have
    been used but all focused on the same objectives. Tang
    et al. [4] used an optimization process to obtain a
    uniform temperature distribution in the part which gives
    the smallest gradient and the minimal cooling time.
    Huang [5] tried to obtain uniform temperature
    distribution in the part and high production efficiency i.e
    a minimal cooling time. Lin [6] summarized the
    objectives of the mould designer in 3 facts. Cool the part
    the most uniformly, achieve a desired mould temperature
    so that the next part can be injected and minimize the
    cycle time.
    The optimal cooling system configuration is a
    compromise between uniformity and cycle time. Indeed
    the longer the distance between the mould surface cavity
    and the cooling channels is, the higher the uniformity of
    the temperature distribution will be [6]. Inversely, the
    shorter the distance is, the faster the heat is removed
    from the polymer. However non uniform temperatures at
    the mould surface can lead to defects in the part. The
    control parameters to get these objectives are then the
    location and the size of the channels, the coolant fluid
    flow rate and the fluid temperature. 
    Two kinds of methodology are employed. The first one
    consists in finding the optimal location of the channels in
    order to minimize an objective function [4][7]. The
    second approach is based on a conformal cooling line.
    Lin [6] defines a cooling line representing the envelop of
    the part where the cooling channels are located. Optimal
    conditions (location on the cooling and size of the
    channels) are searched on this cooling line. Xu et al. [8]
    go further and cut the part in cooling cells and perform
    the optimization on each cooling cell.
    1.3 COMPUTATIONAL ALGORITHMS
    To compute the solution, numerical methods are needed.
    The heat transfer analysis is performed either by
    boundary elements [7] or finite elements method [4].
    The main advantage of the first one is that the number of
    unknowns to be computed is lower than with finite
    elements. Only the boundaries of the problem are
    meshed hence the time spent to compute the solution is
    shorter than with finite elements. However this method
    only provides results on the boundaries of the problem.
    In this study a finite element method is preferred because
    temperatures history inside the part is needed to
    formulate the optimal problem.
    To compute optimal parameters which minimize the
    objective function Tang  et al. [4] use the Powell’s
    conjugate direction search method. Mathey et al. [7] use
    the Sequential Quadratic Programming which is a
    method based on gradients. It can be found not only
    deterministic methods but also evolutionary methods.
    Huang  et al. [5] use a genetic algorithm to reach the
    solution. This last kind of algorithm is very time
    consuming because it tries a lot of range of solution. In
    practice time spent for mould design must be minimized
    hence a deterministic method (conjugate gradient) which Based on a morphological analysis of the part, two
    surfaces
    1
    Γ  and
    3
    Γ  are introduced respectively as the
    erosion and the dilation (cooling line) of the part (Figure
    1). The boundary condition of the heat conduction
    problem along the cooling line
    3
    Γ  is a third kind
    condition with infinite temperatures fixed as fluid
    temperatures. The optimization consists in finding these
    fluid temperatures. Using a cooling line prevents to
    choose the number and size of cooling channels before
    optimization is carried out. This represents an important
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