Multi-Objective Optimization Results and Discussion

The SOO problem (Problem A) can be formulated as a two-objective problem by adding another objective. We consider two such problems  

Case A - Maximize Profit, P and Maximize Octane Number, x  

Case B - Maximize Profit, P and Minimize Isobutane Recycle, X2 Alkylate product with a higher octane number is better for blending with refinery products. Minimizing isobutane recycle helps to reduce fractionation and other costs associated with the recycle stream. 

In a similar way, the two-objective problem in Case B can also be solved by the -constraint method the corresponding SOO problem is the same as Problem A except that the upper bound on X2 (which is an 

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