The shareholders of E&P companies evaluate the future performance of these companies in terms of multiple performance attributes. Hence, E&P decision makers have the task of allocating limited resources to available project proposals to deliver the best performance on these various attributes. Additionally, the performance of these proposals on these attributes is uncertain and the attributes of the various proposals are usually correlated. As a result of the above, the E&P portfolio optimisation decision setting is characterised by multiple attributes with uncertain future performance. Most recent contributions in the E&P portfolio optimisation arena seek to adapt modern financial portfolio theory concepts to the E&P project portfolio selection problem. These contributions generally focus on understanding the tradeoffs between risk and return for the attribute NPV while acknowledging the presence of correlation among the assets of the portfolio. The result is usually an efficient frontier where one objective is set over the expected value of the NPV and the other is set over a risk metric calculated from the same attribute where, typically, the risk metric has a closed form solution (e.g., variance, standard deviation, semi-standard deviation). However, this methodology fails to acknowledge the presence of multiple attributes in the E&P decision setting. To fill this gap, this thesis proposes a decision support model to optimise risk and return objectives extracted from the NPV attribute and from other financial and/or operational attributes simultaneously. The result of this approach is an approximate Pareto front that explicitly shows the tradeoffs among these objectives whilst honouring intra-project and inter-project correlations. Intra-project correlations are incorporated into the optimisation by integrating the single project models to the portfolio model to be optimised. Inter-project correlation is included by modelling of the oil price a global variable. Additionally, the model uses a multi-objective simulation-optimisation approach and hence it overcomes the need of using risk metrics with closed form solutions. The model is applied to a set of realistic hypothetical offshore E&P projects. The results show the presence of complex relationships among the objectives in the approximate Pareto set. The ability of the method to unveil these relationships hopes to bring more insight to the decision makers and hence promote better investment decisions in the E&P industry.