“…Therefore, in terms of combinatorial theory, the obtained results contain the global minimum of the APF sizing and placement problem (all combinations are tested). Other methods of searching the set of obtained results are Number of simultaneously connected APFs (i ) , 9, 10, 11, 12, 13, 14, 15} 2 28 {(8,9), (8,10), (8,11), (8,12), (8,13), (8,14), y , (14,15)} 3 56 {(8,9,10), (8,9,11), (8,9,12), (8,9,13), y , (13,14,15)} 4 70 {(8,9,10,11), (8,9,10,12), (8,9,10,13), y , (12,13,14,15)} 5 56 {(8,9,10,11,12), (8,9,10,11,13), y , (11,12,13,14,15)} 6 28 {(8,9,10,11,12,13), (8,9,10,11,12,14), y, (10,11,12,13,14,15)} 7 8 {(8,9,10,11,12,13,14), y , (9,10,11,12,13,14,15)} 8 1 {(8, 9, 10, 11, 12, 13, 14, 15)} Classic and optimization approach to APFs also possible, but typically they require additional assumptions, (Wang et al, 2010) and usually lead to a local minimum (Grabowski et al, 2013). As it will be shown in the following sections, the presented classic approach, in spite of its popularity, does not have to lead to optimal results in terms of the total APF installation cost.…”