The paper examines a previously proposed computational model, called the Amoeba TSP algorithm, for solving the traveling salesman problem (TSP) using an amoeba-inspired approach. It focuses on three key elements of the model and investigates how modifying these elements affects the optimization performance.
The first element is the use of uniform random numbers to introduce fluctuations in the dynamics of the amoeba branches. The authors find that replacing this with normal random numbers can improve the number of iterations required to find a solution.
The second element is the condition of volume conservation, which was believed to be essential for the amoeba's solution-search ability. Surprisingly, the authors discover that this condition can be relaxed without compromising the performance, and in fact, removing it can lead to much better solutions.
The third element is the use of sigmoid functions in the model. The authors identify specific modifications to these functions that can further enhance the optimization results.
By incorporating these three modifications, the authors propose an "Improved Amoeba TSP algorithm" that outperforms the original model. The new model exhibits a scaling of the number of iterations with the square root of the number of cities, which is a significant improvement over the linear scaling of the original algorithm. Additionally, the average normalized route length of the solutions obtained by the Improved model is comparable to or even better than the original.
The study provides valuable insights into the key factors that contribute to the amoeba's remarkable problem-solving ability and offers guidelines for enhancing the performance of amoeba-inspired combinatorial optimization machines.
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by Yusuke Miyaj... at arxiv.org 04-11-2024
https://arxiv.org/pdf/2404.06828.pdfDeeper Inquiries