This paper presents a genetic algorithm (GA) for solving the traveling salesman problem (TSP). To construct a powerful GA, we use edge assembly crossover (EAX) and make substantial enhancements to it: (i) localization of EAX together with its efficient implementation and (ii) the use of a local search procedure in EAX to determine good combinations of building blocks of parent solutions for generating even better offspring solutions from very high-quality parent solutions. In addition, we develop (iii) an innovative selection model for maintaining population diversity at a negligible computational cost. Experimental results on well-studied TSP benchmarks demonstrate that the proposed GA outperforms state-of-the-art heuristic algorithms in finding very high-quality solutions on instances with up to 200,000 cities. In contrast to the state-of-the-art TSP heuristics, which are all based on the Lin–Kernighan (LK) algorithm, our GA achieves top performance without using an LK-based algorithm.
The biological processing of Ca produces significant stable isotope fractionation. The level of isotopic fractionation can provide key information about the variation in dietary consumption or Ca metabolism. To investigate this, we measured the 43 Ca/ 42 Ca and 44 Ca/ 42 Ca ratios for bone and blood plasma samples collected from mice of various ages using multiple collector-ICP-mass spectrometry (MC-ICP-MS). The 44 Ca/ 42 Ca ratio in bones was significantly (0.44 -0.84‰) lower than the corresponding ratios in the diet, suggesting that Ca was isotopically fractionated during Ca metabolism for bone formation. The resulting 44 Ca/ 42 Ca ratios for blood plasma showed almost identical, or slightly higher, values (0.03 -0.2‰) than found in a corresponding diet. This indicates that a significant amount of Ca in the blood plasma was from dietary sources. Unlike that discovered for Fe, there were no significant differences in the measured 44 Ca/ 42 Ca ratios between female and male specimens (for either bone or blood plasma samples). Similarity, the 44 Ca/ 42 Ca ratios suggests that there were no significant differences in Ca dietary consumption or Ca metabolism between female and male specimens. In contrast, the 44 Ca/
42Ca ratios of blood plasma from mother mice during the lactation period were significantly higher than those for all other adult specimens. This suggests that Ca supplied to infants through lactation was isotopically lighter, and the preferential supply of isotopically lighter Ca resulted in isotopically heavier Ca in blood plasma of mother mice during the lactation period. The data obtained here clearly demonstrate that the Ca isotopic ratio has a potential to become a new tool for evaluating changes in dietary consumption, or Ca metabolism of animals. both of these two isotope tracer approaches are based on the assumption that the spiked isotope replaces the native element, and behaves in an identical manner.
1This indicates that mimicing of the isotopes to the native nutrients must be considered in order to obtain reliable data for elemental metabolism. Faced with this problem, we have developed a new isotope tracer technique based on changes in the isotopic composition of Ca due to a mass-dependent isotopic effect. Hence, no spiking with additional elements, such as radio isotopes or enriched isotopes, was required, and therefore, no mimicing to the native nutrients is required. Moreover, it should be noted that the present stable isotope approach allows regular monitoring of the nutritional status of Ca of the donor without any spiking or addition of isotopes. The measurement of stable isotopes of nitrogen ( 15 N/ 14 N) and carbon ( 13 C/ 12 C) is a useful tool to trace trophic relationships and food webs. 3,12,13 This method assumes that, during the assimilation process, there is an enrichment in heavy isotopes (i.e., 13 C or 15 N) compared to the dietary intake, which is compensated by the preferential excretion of lighter isotopes. 14,15 The isotopic composition of an animals' tissue reflec...
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