Erratum: Corrigendum to: A heuristic and evolutionary algorithm to optimize the coefficients of curve parametrizations (Journal of Computational and Applied Mathematics (2016) 305 (18–35) (S0377042716301406) (10.1016/j.cam.2016.03.020))

In this note we correct a mistake in the paper “A Heuristic and Evolutionary Algorithm to Optimize the Coefficients of Curve Parametrizations, Journal of Computational and Applied Mathematics 305 (2016) 18–35”. The erratum is in the part where we describe how to generate a complete solution from two partial solutions. More precisely, if o1=(o1,1,o1,2),o2=(o2,1,o2,2)∈Ωe are two partial solutions, then the associated complete solution is (o1,1,o2,1,o1,2,o2,2) instead of (o1,1,o1,2,o2,1,o2,2) as it is said in the mentioned paper. Therefore, the Möbius transformation generated by o1,o2 is (formula missing) • Section 32, second paragraph, page 25, it should be The composition of complete solution candidates from partial solution candidates is defined as follows: Let (o1,o2)∈Ωe×Ωe with o1=(o1,1,o1,2), and o2=(o2,1,o2,2). Then, the associated complete solution candidate is So1,o2≔(o1,1,o2,1,o1,2,o2,2). Conversely, every complete solution candidate (a,b,c,d)∈Space(Ωe) can be seen as a combination of elements in Ωe, namely (a,c),(b,d)∈Ωe.• The paragraph after (1), in page 19, should say We visualize the space of solution candidates in 3D in so-called fitness landscapes [29]. In the x-axis we set the pair (a,c), in the y-axis we set the pair (b,d), and the color represents the height of the resulting parametrization; red is small height (i.e. good result) and blue is big height (i.e. bad result). Such a direct description of the search space is not suited for the evolutionary algorithm since it is not smooth (see Fig. 5 (left)) and small variations (for instance, due to mutations) will produce big changes of quality in the answer. Instead, in Section 3, we prove that one can associate to each pair a quantity that partially indicates the quality of the final answer (see Eq. (27)). Thus, before generating the x-axis and the y-axis of the fitness landscape, we order the pairs (a,c) as well as the pairs (b,d) according to this partial quality. This produces fitness landscapes (see Fig. 5 (right)) which are well suited for our purposes. In this situation, in each region of the search space we look for improvement by optionally using strict offspring selection.