Abstract
The study is concerned with the Baldwin effect and Lamarckian evolution in a memetic algorithm for Euclidean Steiner tree problem (ESTP). The main aim is to examine the importance of the proposed local search procedures for the ability of the algorithm to find solutions to ESTP. Two local search procedures are proposed as a part of an evolutionary algorithm for ESTP, and the effect of their use is carefully analyzed. The correction procedure modifies the given chromosome so that it satisfies the degree and angle conditions in ESTP. The improvement procedure actively adds new Steiner points to the evaluated solution. The modified solutions are accepted with varying probability, leading to a spectrum of algorithms with a Baldwin effect on one end and Lamarckian evolution on the other. The results are carefully analyzed using proper statistical procedures (Friedman test and post-hoc procedures). To further check the ability of the proposed algorithm to find the optimal or near optimal solutions, results for problems from OR-Lib are provided.
Highlights
Let p be the number of points in n-dimensional Euclidean space
The ranking of algorithms is provided by the Friedman test, and the post-hoc procedure is used to control the Family-Wise Error Rate (FWER) for pair-wise comparisons
The main purpose of this work was to investigate the importance of local search procedures in a memetic algorithm (MA) for Euclidean Steiner Tree Problem (ESTP) on a plane
Summary
Let p be the number of points in n-dimensional Euclidean space. The goal in the Euclidean Steiner tree problem (ESTP) is to minimize the sum of lengths of edges spanning these points. Unlike in the minimum spanning tree (MST) problem, additional points, called Steiner points, are allowed to be added to the original set of points, called terminals. The number and locations of these additional points are difficult to find, and the problem is known to be np-complete. Presented (b) is an example Steiner tree which includes additional points (Steiner points). It can be observed that the addition of new points made the total sum of edges’ lengths to decrease
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