Given numerical data about objects defined by descriptive and target attributes, we investigate the discovery of interesting conjunctions of descriptive attribute range of values that are associated to optimized target values. This can be useful across many application domains where one wants to perform Multi-Objective Optimization: the goal is to find the best compromise between the competing objectives that correspond to the different targets and one expects to learn about the optimal values of the descriptive attributes. For this purpose, we design Exceptional Model Mining instances: we look for subsets of objects-subgroups-whose models deviate significantly from the same models fitted on the whole dataset. A first method, called Exceptional Pareto Front Deviation Mining (EPFDM), characterizes the differences between the Pareto front computed on the original data and the Pareto front computed after removing a subgroup of objects. We discuss in detail the design of a generic quality measure for EPFDM and we provide comprehensive empirical results. We also develop an approach called Exceptional Pareto Front Approximation Mining (EPFAM), whose goal is the discovery of models that approximate exceptionally well the true Pareto front. Beside empirical studies that consider both the qualitative and quantitative aspects of EPFDM and EPFAM, we present a use-case on plant growth recipe optimization in controlled environments, a timely challenge for a smarter agriculture.