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I have a data set with two columns. The variable names are cost 1 and cost 2. I want to minimize both cost 1 and cost 2 using the Pareto optimization method. So, while implementing NSGA II I have two objective functions i.e. cost 1 values and cost 2 values but I don't have any variables in it since my data set already contains the cost values which are calculated by using the variable values (see the data set below). So, what I want is find the pair of cost values [cost 1,cost 2] which lie in the Pareto front. Can I perform NSGA II for this scenario?

data = np.array([[97, 23], [55, 77], [34, 76], [80, 60], [99, 4], [81, 5], [ 5, 81], [30, 79], [15, 80], [70, 65], [90, 40], [40, 30], [30, 40], [20, 60], [60, 50], [20, 20], [30, 1], [60, 40], [70, 25], [44, 62], [55, 55], [55, 10], [15, 45], [83, 22], [76, 46], [56, 32], [45, 55], [10, 70], [10, 30], [79, 50]])

vp_050
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1 Answers1

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In this case, since you do not have integer/float 'decision variables', I do not see the point of using NSGA II. Your case is much simpler. From the question, I gather that you have all the discrete 'options' as given and their attributed costs with respect to two objectives. In this case, in fact, by implementing a rather simple function you can determine whether an option is 'Pareto dominated' by another option, and then use this function to find the non-dominated ones. The non-dominated options will be the Pareto frontier or the Pareto optimal options. For gaining a better insight you can visualize these points on a 2D plot, noting that each of them represents an option, and then you will see that the ones in whose lower-left quadrant there does not exist any other point are the Pareto (cost-minimal) optimal solutions. A solution/option is said to be Pareto-dominated by another if the other is better (less costly in this case) w.r.t. all objectives.

Father Geppeto
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