Mixed integer multi-objective optimization

In this paper, we extend the work of [10] by simultaneously considering minimization of the total utility consumption, maximization of operational flexibility to source-stream temperatures, and even minimum number of matches as multiple design objectives. The flexible HEN synthesis problem is thus formulated as the one of multi-objective mixed-integer linear programming (MO-MILP). This formulation also assumes that the feasible region in the space of uncertain input parameters is convex, so that the optimal solution can thus be explored on the basis of the vertices... 

Based on the given probabilities of success for each potential product, the problem is then to find the optimal product portfolio and investment decisions together with detailed production and sales plans so as to maximise the eNPV. The eNPV is simply the summation of all scenario NPVs, weighted by their associated probabilities. The derivation of the objective function is similar to the one in Papageorgiou et al. (2001). The overall problem is formulated as a two-stage, multi-scenario mixed integer linear programming (MILP) model. 

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