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Intelligent Route Construction Algorithm for Solving Traveling Salesman Problem
Rahman, Md. Azizur,Islam, Ariful,Ali, Lasker Ershad International Journal of Computer ScienceNetwork S 2021 International journal of computer science and netw Vol.21 No.4
The traveling salesman problem (TSP) is one of the well-known and extensively studied NPC problems in combinatorial optimization. To solve it effectively and efficiently, various optimization algorithms have been developed by scientists and researchers. However, most optimization algorithms are designed based on the concept of improving route in the iterative improvement process so that the optimal solution can be finally found. In contrast, there have been relatively few algorithms to find the optimal solution using route construction mechanism. In this paper, we propose a route construction optimization algorithm to solve the symmetric TSP with the help of ratio value. The proposed algorithm starts with a set of sub-routes consisting of three cities, and then each good sub-route is enhanced step by step on both ends until feasible routes are formed. Before each subsequent expansion, a ratio value is adopted such that the good routes are retained. The experiments are conducted on a collection of benchmark symmetric TSP datasets to evaluate the algorithm. The experimental results demonstrate that the proposed algorithm produces the best-known optimal results in some cases, and performs better than some other route construction optimization algorithms in many symmetric TSP datasets.
Macaulay, E,Nichol, R C,Bacon, D,Brout, D,Davis, T M,Zhang, B,Bassett, B A,Scolnic, D,Mö,ller, A,D’Andrea, C B,Hinton, S R,Kessler, R,Kim, A G,Lasker, J,Lidman, C,Sako, M,Smith, M,Sullivan, M,Abbo Oxford University Press 2019 MONTHLY NOTICES- ROYAL ASTRONOMICAL SOCIETY Vol.486 No.2
<B>ABSTRACT</B><P>We present an improved measurement of the Hubble constant (H0) using the ‘inverse distance ladder’ method, which adds the information from 207 Type Ia supernovae (SNe Ia) from the Dark Energy Survey (DES) at redshift 0.018 < z < 0.85 to existing distance measurements of 122 low-redshift (z < 0.07) SNe Ia (Low-z) and measurements of Baryon Acoustic Oscillations (BAOs). Whereas traditional measurements of H0 with SNe Ia use a distance ladder of parallax and Cepheid variable stars, the inverse distance ladder relies on absolute distance measurements from the BAOs to calibrate the intrinsic magnitude of the SNe Ia. We find H0 = 67.8 ± 1.3 km s−1 Mpc−1 (statistical and systematic uncertainties, 68 per cent confidence). Our measurement makes minimal assumptions about the underlying cosmological model, and our analysis was blinded to reduce confirmation bias. We examine possible systematic uncertainties and all are below the statistical uncertainties. Our H0 value is consistent with estimates derived from the Cosmic Microwave Background assuming a ΛCDM universe.</P>