This paper proposes a new nonlinear dimensionality-reduction model based on a bicriteria global optimization approach for the color display of hyperspectral images. The proposed fusion model is derived from two well-known and contradictory criteria of good visualization, which are useful in any multidimensional imagery color display, namely, accuracy, with the preservation of spectral distance criterion, and contrast, guaranteeing that colors are well distinguished or concretely allowing the good separability of each observed existing material in the final visualized color image. An internal parameter allows our algorithm to express the contribution or the importance of these two criteria for a specific application. In this framework, which also can be viewed as a classical Bayesian optimization strategy involving a tradeoff between fidelity to the unreduced (raw) spectral data and the expected highly contrasted resulting mapping, we will show that a hybrid optimization strategy, combining a global and deterministic optimization procedure and a local stochastic search using the Metropolis criterion, can be exploited to efficiently minimize the complex nonlinear objective cost function related to our model. The experiments reported in this paper demonstrate that the proposed model, taking into account these two criteria of good visualization, makes easier and more reliable the interpretation and quick overview of such multidimensional hyperspectral images.