Metaheuristics for Business Analytics by Abraham Duarte Manuel Laguna & Rafael Marti

Author:Abraham Duarte, Manuel Laguna & Rafael Marti
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

For such a small example, we can enumerate all possible solutions (selections of elements) and compute the value of the Max-Sum DP and the value of the Max-Min DP for each one. The correlation between both objective functions is 0.61, which can be considered relatively low. Therefore, we should not expect a method for one of these problems to obtain good solutions for the other one. We extend now this analysis by including the Max-MinSum, Min-Diff, Max-Sum and Max-Min models (the Max-Mean model is not included because it does not set a priori the number of elements to select, as it is the case with the others), and we see in Table 3.2 that most of them are very low correlated. This table shows the correlations on 30 instances, with randomly generated with a uniform distribution in the range [0, 20], , and .

We can implement any of the formulations in Table 3.1 in an Excel spreadsheet and apply one of its solvers to obtain a solution for a given instance. In particular, we consider the Max-Sum formulation (the first one in the table), and the data in the accompanying Excel file MDP1.xlsx corresponding to the distances of the 100 students in Example 3.1, from which we want to select five of them. In this file, the distance matrix, , is in the range A1:CV100, and the array x with the 100 binary variables, , is in the range CX1:CX100.Table 3.2Correlations between different models

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