For this paper, we explored the implementation of the cuckoo search algorithm applied to the capacitated vehicle routing problem. The cuckoo search algorithm was implemented with Lévy flights with the 2-opt and double-bridge operations, and with 500 iterations for each run. The algorithm was tested on the problem instances from the Augerat benchmark dataset. The algorithm did not perform well o...

it is well known that in operations research‎, ‎degeneracy can cause a cycle in a network‎ ‎simplex algorithm which can be prevented by maintaining strong‎ ‎feasible bases in each pivot‎. ‎also‎, ‎in a network consists of n arcs‎ ‎and m nodes‎, ‎not considering any new conditions on the entering‎ ‎variable‎, ‎the upper bound of consecutive degenerate pivots is equal‎ $left( ‎begin{array}{c}‎ ‎n...

In this article we present an algorithm for converting a network problem with several sources and several sinks including several transfer nodes and condition of supplying the demand of any sink from a particular source to the transportation problem.  Towards this end, and considering the very special structure of transportation algorithm, after implementing the shortest path algorithm or ...

The Schoof-Elkies-Atkin algorithm counts the number of rational points on elliptic curves over finite fields. This paper presents a number of optimizations specific for the characteristic two case. We give a detailed description of the computation of modular polynomials over F2n and the search for an eigenvalue in the Elkies algorithm. With our implementation, we were able to count the number o...

(These notes are a slightly modified version of notes from previous offerings of the class scribed by Sanjeev.) Today’s topic is simple but gorgeous: Karger’s min cut algorithm and its extension. It is a simple randomized algorithm for finding the minimum cut in a graph: a subset of vertices S in which the set of edges leaving S, denoted E(S, S) has minimum size among all subsets. You may have ...

An attack on the A5/2 stream cipher algorithm is described, that determines the linear relations among the output sequence bits. The vast majority of the unknown output bits can be reconstructed. The time complexity of the attack is proportional to 2. Introduction: A5 is the stream cipher algorithm used to encrypt the link from the telephone to the base station in the GSM system. According to [...

In this paper, a modified fuzzy system modelling algorithm that incorporates Type 2 fuzzy sets, which is based on intervalvalued membership degrees rather than singleton membership degrees, is proposed. The proposed algorithm is evaluated in terms of predictive performance and determination of the significance degrees and compared with other algorithms in the literature, namely Stepwise Multipl...