N-queens Research Articles

On the N Non-Attacking Queens Problem

In this paper, a new version of the proof of the n-queens problem was presented. A new condition for the diagonal conflicts between the queens was added for the proof of the theorem.

The N queens problem - new variants of the Wirth algorithm

The paper presents new ways of n-queens problem solving . Briefly,this is a problem on a nxn chessboard of a set n-queens, so that any two of themare not in check. At the beginning, currently used algorithm to find solutions isdiscussed. Then sequentially 4 new algorithms, along with the interpretation ofchanges are given. The research results, including comparison, of calculation timesof all algorithms together with their interpretation are discussed. Finally, conclusionsare given. The results were obtained thanks to the pre-created application.Chapters except for By filtering ver. 2 were based on the previous studies carriedout during the Bachelor course [1].

A Hybrid Algorithm from Cuckoo Search Method with N-Queens Problem

A Hybrid Algorithm from Cuckoo Search Method with N-Queens Problem

Secure Data Hiding Using Eight Queens Solutions

The 8-queens problem of placing 8 non-attacking queens on an 8x8 chessboard is used to hide message in an image. The method helps in randomizing the bit selection in a cover image for hiding purpose. Cover image is divided into blocks of 8x1 bytes and then masked with solutions of the 8-queens problem. Bits from the block are collected corresponding to the 8-queen solution to make a 7 bit string. LSB of the block is not considered. It gives a number in the range of 0 to 127. If a bit string, corresponding to the 8-queens solutions, matches with ASCII code of the first character from message, the corresponding solution number of the 8-queens problem is encrypted using RC4, and the cipher is stored in first block of the cover. This encrypted value works as key. The solution number corresponding to next character is XORED with the key and the resultant value is embedded in the LSB of next block. The algorithm has been tested with cover of different image file formats like BMP, PNG and TIFF. The algorithm provides very good capacity, imperceptibility and robustness.

A New Solution for N-Queens Problem using Blind Approaches: DFS and BFS Algorithms

The N×N queen’s puzzle is the problem of placing N chess queen on an N×N chess board so that no two queens attack each other. This approach is a classical problem in the artificial intelligence area. A solution requires that no two queens share the same row, column or diagonal. These problems for computer scientists present practical solution to many useful applications and have become an important issue. In this paper we proposed new resolution for solving nQueens used combination of depth firs search (DFS) and breathe first search (BFS) techniques. The proposed algorithm act based on placing queens on chess board directly. This is possible by regular pattern on the basis of the work law of minister. The results show that performance and run time in this approach better then back tracking methods and hill climbing modes.

An Orbit-Based Search Algorithm to Solve N-Queens Problem

To analyze N-Queens problem in permutation space, this paper defines isomorphic operations of permutation to dihedral group D4. With these operations to find elements within an orbit, two operations on orbits are also defined to generate new orbit from existing ones. Orbit signature is proposed to uniquely identify different orbits on orbit space. A search algorithm based on orbit signature is presented, and finally the effectiveness of the algorithm is illustrated by an example.

An Unique Solution for N queen Problem

N-queens problem is a popular classic puzzle where numbers of queen were to be placed on an n x n matrix such that no queen can attack any other queen. The Branching Factor grows in a roughly linear way, which is an important consideration for the researchers. However, many researchers have cited the issues with help of artificial intelligence search patterns say DFS, BFS and backtracking algorithms. We have conducted an extensive study on this problem and realized that no algorithms so far designed with simple formula based. This paper includes a new paradigm which able to compute one unique solutions to the N-queens problem. Again our experimental study brings out a significant outcome.

Superconducting Neural Network for Solving a Combinatorial Optimization Problem

We propose a neural network using coupled-SQUIDs to solve the N-Queens problem, a combinatorial optimization problem. The N-Queen problem consists of placing N queens on an N × N chess board such that none of the queens are able to capture any other using standard chess moves for a queen. We run a numerical simulation to show that a network consisting of a combination of coupled-SQUIDs can arrive at the solution. However, conditions of the network may be trapped in incorrect answers due to the existence of local minima on the energy function of the network. The Josephson voltage oscillation effect is effective for escaping from such conditions due to the existence of local minima. We investigate network dynamics and discuss the performance of the network on the basis of the parameters of the Nb integration circuit.

An Algebraic Method for the N-Queens Problem Based on Permutation Operation Group

An Algebraic Method for the N-Queens Problem Based on Permutation Operation Group

Local Search with P Systems

Local search is currently one of the most used methods for finding solutions in real-life problems. It is usually considered when the research is interested in the final solution of the problem instead of the how the solution is reached. In this paper, the authors present an implementation of local search with Membrane Computing techniques applied to the N-queens problem as a case study. A CLIPS program inspired in the Membrane Computing design has been implemented and several experiments have been performed. The obtained results show better average times than those obtained with other Membrane Computing implementations that solve the N-queens problem.

Photosynthetic algorithm approaches for bioinformatics

Photosynthetic algorithm (PA) is the newly biosystem-derived heuristic search algorithm that utilizes the dark reaction rules governing the transfer of carbon molecules from one substance into another in the Calvin–Benson cycle and photorespiration. There are only two works using this new algorithm in the literature, one for finite element analysis and one for N-queen problem. This paper presents PA based novel solution techniques in bioinformatics problems such as aligning multiple sequences and discovering association rules within bio-medical data. The simulation results demonstrate the applicability and potential of this algorithm.

HEURISTIC APPROACHES FOR SOLVING N-QUEENS PROBLEM

The research article examines the three distinguished heuristics approaches for solving the N-Queens problem. The problem is widely recognized as constraint satisfaction problems (CSP) in the domain of Artificial Intelligence. The N-Queens problem demands the non-attacking placements of finite number of queens over chessboard. So that, two or more queens cannot share the horizontal, vertical and diagonal positions in a straight line. In this research work, improved version of Backtracking Recursive Algorithm, modified Min-Conflicts Algorithm and classic Genetic Algorithm are applied to address the problem. The comparative results validate the efficiency of research direction.

HEURISTIC APPROACHES FOR SOLVING N-QUEENS PROBLEM

The research article examines the three distinguished heuristics approaches for solving the N-Queens problem. The problem is widely recognized as constraint satisfaction problems (CSP) in the domain of Artificial Intelligence. The N-Queens problem demands the non-attacking placements of finite number of queens over chessboard. So that, two or more queens cannot share the horizontal, vertical and diagonal positions in a straight line. In this research work, improved version of Backtracking Recursive Algorithm, modified Min-Conflicts Algorithm and classic Genetic Algorithm are applied to address the problem. The comparative results validate the efficiency of research direction.

An application of higher order connection to inverse function delayed network

The Inverse function Delayed model (ID model) is a neuron model with negative resistance dynamics. The negative resistance can destabilize local minimum states, which are undesirable network responses. The ID network can remove these states. Actually, we have demonstrated that the ID network can perfectly remove all local minima with N-Queen problems or 4-Color problems, where stationary stable states always give correct answers. However this method cannot apply to Traveling Salesman Problems (TSPs) or Quadratic Assignment Problems (QAPs). Meanwhile, it is proposed that the TSPs are able to be represented in terms of the quartic form energy function. In this representation, the global minimum states that represent correct answers and the local minimum states are separable clearly, thus if it is applied to the ID network, it ensures that only the local minimum states are destabilized by the negative resistance. In this paper, we aim to introduce higher order connections to the ID network to apply the quartic form energy function. We apply the ID network with higher order connections to the TSPs or QAPs, and show that the higher order connection ID network can destabilize only the local minimum states by the negative resistance effect, so that it obtains only correct answers found at stationary stable states. Moreover, we obtain minimum parameter region analytically to destabilize every local minimum state.

Queen Labelings

We introduce and investigate the concept of Queen labeling a digraph and its connection to the well-known n-queens problem. In the general case we obtain an upper bound on the size of a queen graph and show that it is tight. We also examine the existence of possible forbidden subgraphs for this problem and show that only two such subgraphs exist. Then we focus on specific graph families: First we show that every star is a queen graph by giving an algorithm for which we prove correctness. Then we show that the problem of queen labeling a matching is equivalent to a variation of the n-queens problem, which we call the rooks-and-queens problem and we use that fact to give a short proof that every matching is a queen graph. Finally, for unions of 3-cycles we give a general solution of the problem for graphs of n(n - 1) vertices.

On complementary principles of object-oriented constraint programming

The paper is devoted to the implementation of the paradigm of the object-oriented constraint programming (OOCP), which combines complementary ideas and principles of the object-oriented programming (OOP) and constraint logical programming (CLP). Although the idea looks attractive and there have been attempts to implement it with the use of logical and functional languages, its future outline is still not clear. In the paper, a survey of the existing technologies of the constraint programming is given, and a new systematic approach to the implementation of the object-oriented constraint programming based on the use of declarative data modeling languages is discussed. The advantages of the approach related to the expressiveness and generality of the constraint problem declarations are demonstrated on the example of the classical mathematical queen problem. A general algorithmic strategy of solving the constraint problems is also discussed.

A Hybrid Approach Using Particle Swarm Optimization and Simulated Annealing for N-queen Problem

This paper presents a hybrid approach for solving nqueen problem by combination of PSO and SA. PSO is a population based heuristic method that sometimes traps in local maximum. To solve this problem we can use SA. Although SA suffer from many iterations and long time convergence for solving some problems, By good adjusting initial parameters such as temperature and the length of temperature stages SA guarantees convergence. In this article we use discrete PSO (due to nature of n-queen problem) to achieve a good local maximum. Then we use SA to escape from local maximum. The experimental results show that our hybrid method in comparison of SA method converges to result faster, especially for high dimensions n-queen problems. Keywords—PSO, SA, N-queen, CSP

제약 만족 최적화 문제의 해결을 위한 지역 탐색과 제약 프로그래밍의 결합

제약 만족 최적화 문제는 복잡한 제약 조건을 포함하는 동시에 비용을 최소화하는 최적화 문제로 정의된다. 지역 탐색과 제약 프로그래밍은 각각 이와 같은 문제의 해결을 위한 도구로서 활용되어 왔다. 본 논문에서는 탐색 성능 향상을 위해 지역 탐색과 제약 프로그래밍을 결합하는 방안을 제시하고 있다. 기본적으로 대상 문제의 해결을 위해 지역 탐색을 사용한다. 그러나 지역 탐색만을 사용할 경우 제약 조건을 모두 만족하는 실행 가능한 이웃해를 생성하는 것이 매우 힘들어진다. 따라서 본 논문에서는 이웃해 생성을 위한 도구로 제약 프로그래밍을 도입하였다. 가중치가 부여된 N-Queens 문제를 대상으로 한 실험 결과, 본 논문에서 제시한 방법을 통해 탐색 성능을 획기적으로 향상시킬 수 있음을 확인할 수 있었다. Constraint satisfaction optimization problem is a kind of optimization problem involving cost minimization as well as complex constraints. Local search and constraint programming respectively have been used for solving such problems. In this paper, I propose a method to integrate local search and constraint programming to improve search performance. Basically, local search is used to solve the given problem. However, it is very difficult to find a feasible neighbor satisfying all the constraints when we use only local search. Therefore, I introduced constraint programming as a tool for neighbor generation. Through the experimental results using weighted N-Queens problems, I confirmed that the proposed method can significantly improve search performance.

A New Differential Evolution Based Metaheuristic for Discrete Optimization

The Differential Evolution (DE) algorithm is an important and powerful evolutionary optimizer in the context of continuous numerical optimization. Recently, some authors have proposed adaptations of its differential mutation mechanism to deal with combinatorial optimization, in particular permutation-based integer combinatorial problems. In this paper, the authors propose a novel and general DE-based metaheuristic that preserves its interesting search mechanism for discrete domains by defining the difference between two candidate solutions as a list of movements in the search space. In this way, the authors produce a more meaningful and general differential mutation for the context of combinatorial optimization problems. The movements in the list can then be applied to other candidate solutions in the population as required by the differential mutation operator. This paper presents results on instances of the Travelling Salesman Problem (TSP) and the N-Queen Problem (NQP) that suggest the adequacy of the proposed approach for adapting the differential mutation to discrete optimization.

Counting solutions for theN-queens and Latin-square problems by Monte Carlo simulations

We apply Monte Carlo simulations to count the numbers of solutions of two well-known combinatorial problems: the N -queens problem and Latin-square problem. The original system is first converted to a general thermodynamic system, from which the number of solutions of the original system is obtained by using the method of computing the partition function. Collective moves are used to further accelerate sampling: swap moves are used in the N -queens problem and a cluster algorithm is developed for the Latin squares. The method can handle systems of 10;{4}degrees of freedom with more than 10;{10,000} solutions.