Genetic Algorithms for the Extended GCD Problem
نویسندگان
چکیده
The extended greatest common divisor GCD problem is given a vector a a an of positive integers compute g the greatest common divisor of these inte gers and nd a vector x x xn of integer coe cients such that
منابع مشابه
On the Complexity of the Extended Euclidean Algorithm (extended abstract)
Euclid’s algorithm for computing the greatest common divisor of 2 numbers is considered to be the oldest proper algorithm known ([10]). This algorithm can be amplified naturally in various ways. The GCD problem for more than two numbers is interesting in its own right. Thus, we can use Euclid’s algorithm recursively to compute the GCD of more than two numbers. Also, we can do a constructive com...
متن کاملThe Complexity of the Extended GCD Problem
We undertake a thorough complexity study of the following fundamental optimization problem, known as the `p-norm shortest extended GCD multiplier problem: given a1, . . . , an ∈ Z, find an `p-norm shortest gcd multiplier for a1, . . . , an, i.e., a vector x ∈ Z with minimum ( ∑n i=1 |xi|) satisfying ∑n i=1 xiai = gcd(a1, . . . , an). First, we prove that the shortest GCD multiplier problem (in ...
متن کاملGENETIC AND TABU SEARCH ALGORITHMS FOR THE SINGLE MACHINE SCHEDULING PROBLEM WITH SEQUENCE-DEPENDENT SET-UP TIMES AND DETERIORATING JOBS
This paper introduces the effects of job deterioration and sequence dependent set- up time in a single machine scheduling problem. The considered optimization criterion is the minimization of the makespan (Cmax). For this purpose, after formulating the mathematical model, genetic and tabu search algorithms were developed for the problem. Since population diversity is a very important issue in ...
متن کاملA New Approach to Solve N-Queen Problem with Parallel Genetic Algorithm
Over the past few decades great efforts were made to solve uncertain hybrid optimization problems. The n-Queen problem is one of such problems that many solutions have been proposed for. The traditional methods to solve this problem are exponential in terms of runtime and are not acceptable in terms of space and memory complexity. In this study, parallel genetic algorithms are proposed to solve...
متن کاملکمینهسازی حداکثر دیرکرد کارها در مسأله زمانبندی جریان کارگاهی جایگشتی دوباره وارد شونده چند ماشینه
This investigation considers a reentrant permutation flowshop scheduling problem whose performance criterion is maximum tardiness. The reentrant flowshop (RFS) is a natural extension of the classical flowshop by allowing a job to visit certain machines more than once. The RFS scheduling problem, in which the job order is the same for each machine in each layer, is called a reentrant permutati...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1998