An optimization engine includes a mixed-integer programming (MIP) solver that receives a programming model, an outcome objective, and a group of start vectors. Each of the MIP start vectors in the group specify one or more restrictions to apply to the programming model. The MIP solver uses the programming model to compute a potential solution from each of the MIP start vectors included in the group, which results in a group of potential solutions. Next, the MIP solver selects one of the potential solutions in the group as an optimal intra-group solution. The optimal intra-group solution is the potential solution in the group that best achieves the outcome objective. In turn, the optimal intra-group solution is used to complete the outcome objective.