A clever programmer will always try to choose the faster instructions for the job. This paper presents an algorithm to display squares of 1st N natural numbers without using multiplication (* operator). Instead, the same work can be done using addition (+ operator). The results can also be ...
powers of natural numbers; sum; general algorithm; geometric interpretations; 机译:自然数幂求和一般算法几何解释; 相似文献 外文文献 中文文献 专利 1. A simple tool for engineers for generating formulae for the sum of powers of natural numbers [J] . R. Venkatachalam, Umesh Chandra Sharma ...
The whale optimization algorithm has received much attention since its introduction due to its outstanding performance. However, like other algorithms, the whale optimization algorithm still suffers from some classical problems. To address the issues of
The actual behavior of a quantum network can be represented as a sum of networks, with linear error operators at each network location. This error expansion is not unique; it gives the correct input-output behavior of the network, yet it is not capable of accurately representing the ...
Since GAs for multiobjective optimization build upon the GAs for single-objective optimization, the concepts and procedures described previously in Chapter 16 should be reviewed. Because genetic algorithms do not require gradient information, they can be effective regardless of the nature of the problem...
for any constanttour bound improves the previous bound of Kangas et al. [18] by a factor ofn, up to polylogarithmic factors. For largenand smalltthe improvement is relatively significant; for instance, fort=2the bound is reduced from{\tilde{O}}(n^6)to{\tilde{O}}(n^5). For larget...
It should be noted that the metaheuristic algorithms are some sorts of stochastic methods in which randomization procedures are the key aspect of these approaches while multiple random numbers are generated through the optimization procedure in order to reach the global optimal point. For this purpose...
The main reason for this problem is that most clustering algorithms (and tensor factorization approaches) optimize objective functions that strongly depend on the number of clusters (or factors). Hence, two solutions with two different numbers of clusters can not be compared directly. Although this ...
Hence, the optimal power flow problem (OPF) is crucial for power system planning. As a result, electricity system operators can meet electricity demands efficiently and ensure the reliability of the power systems. The classical OPF problem ignores network emissions when dealing with thermal generators...
The transit time of a specific route within a city varies through the different hours of the day. It is therefore natural to consider fuzzy numbers for the duration of the paths. Note how, in most situations, finding the optimal path is equivalent to identifying the least costly or fastest ...