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# An Analysis of All the Issues Connected to the N-Queens Problem

1 Introduction The N-Queens problem is a classical AI problem Its name is derived from the allowed moves for the queen piece in chess Queens are allowed to move horizontally vertically or diagonally backward and forward with the only restriction being that they can move in only one direction at a time A queen that can reach another piece in one move captures it The N-Queens problem is based on the notion of trying to place N queens on an N x N grid such that no queen will be able to capture any other queen The N-queens problem is typical of many combinatorial problems in that it is simple to state and relatively easy to solve for small N but becomes difficult with a large N There are few ways to solve the N-queens problem Some of them are trying all the permutations using backtracking methods using reinforcement learning methods and etc In this project genetic algorithm will be used to solve this problem by using GAlib package Genetic Algorithms are adaptive methods which may be used to solve search and optimization problems They are based on the genetic processes of biological organisms Over many generations natural populations evolve according to the principles of natural selection and survival of the fittest By mimicking this process genetic algorithms are able to evolve solutions to real world problems if they have been suitably encoded Genetic Algorithms use a direct analogy of natural behavior They work with a population of individuals each representing a possible solution to a given problem Each individual is assigned a fitness score according to how good a solution to the problem it is The highly fit individuals are given opportunities to reproduce by cross breeding with other individuals in the population This produces new individuals known as offsprings which share some features taken from each parent The least fit members of the population are less likely to get

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