N-queens Research Articles

Kaleidoscopes, Chessboards, and Symmetry

This paper describes the n-queens problem on an n by n chessboard. We discuss the possible symmetries of n-queens solutions and show how solutions to this classical chess question can be used to create examples of colorful artwork.

Enhancing the Simulation of Membrane System on the GPU for the N‐Queens Problem

Previous approaches using active membrane systems to solve the N-queens problem defined manymembranes with just one rule inside them. This resultedin many communication rules utilised to communicate between membranes, which made communications betweenthe cores and the threads a very time-consuming process.The proposed approach reduces unnecessary membranesand communication rules by defining two membranes withmany objects and rules inside each membrane. With thisstructure, objects and rules can evolve concurrently in parallel, which makes the model suitable for implementationon a Graphics processing unit (GPU). The speedup usinga GPU with global memory for N=10 is 10.6 times, butusing tiling and shared memory, it is 33 times.

Solving N Queen Problem using Genetic Algorithm

paper, explain solution to find the 92 solution of n- Queen problem based on GA (Genetic Algorithm). The n- Queen problem become a Widespread platform for the AI researcher for implement their intelligence algorithms and try them. The Genetic algorithm used to solve the problem and each chromosome is be a solution for the problem and depending on the steps of the GA, The 92 solution, all possible solution for 8 Queen problem is founded. The represent of each chromosome have been by using one dimension array with size equal 8 contain only the queens which represent a one solution and the empty location are aborted to reduce the searching time.

Comparative Study of Different Algorithms to Solve N Queens Problem

Comparative Study of Different Algorithms to Solve N Queens Problem

A parallel algorithm for solving the n-queens problem based on inspired computational model

DNA computing provides a promising method to solve the computationally intractable problems. The n-queens problem is a well-known NP-hard problem, which arranges n queens on an n×n board in different rows, columns and diagonals in order to avoid queens attack each other. In this paper, we present a novel parallel DNA algorithm for solving the n-queens problem using DNA molecular operations based on a biologically inspired computational model. For the n-queens problem, we reasonably design flexible length DNA strands representing elements of the allocation matrix, take appropriate biologic manipulations and get the solutions of the n-queens problem in proper length and O(n2) time complexity. We extend the application of DNA molecular operations, simultaneity simplify the complexity of the computation and simulate to verify the feasibility of the DNA algorithm.

Performance Analysis of N-Queen Problem using Backtracking and Genetic Algorithm Techniques

In this paper the research work has done comparative analysis of one of the famous NP hard problem: NQueen using traditional Backtraking and Genetic Algorithm(GA). The research work has implemented the solution of the NQueen problem using backtracking and using GA. Both the methods of solving NQueen problem are entirely different. The first one is general method and takes time in days , months and years as N increases. In this paper the time taken by the two methods for a given value of N are compared. The work has restricted values of N upto 50 only as beyond this it is extremely difficult to get the solution of the problem using backtracking method. Both the implementation have been carried out in MATLAB using Pentium Core 2 Duo T6600 Core 2.2 GHz processor on Windows 8 with 4GB RAM. Because of the random nature of GA instead of time taken in obtaining all possible solutions for a given value of N, the time taken in obtaining say count number of solutions was first determined using GA, then time taken in same number of solutions that is count using backtracking was noted. Results are then presented in tabular manner. General Terms Backtracking, collisions, NP, problem

A $$q$$ q -Queens Problem. II. The square board

We apply to the $n\times n$ chessboard the counting theory from Part I for nonattacking placements of chess pieces with unbounded straight-line moves, such as the queen. Part I showed that the number of ways to place $q$ identical nonattacking pieces is given by a quasipolynomial function of $n$ of degree $2q$, whose coefficients are (essentially) polynomials in $q$ that depend cyclically on $n$. Here we study the periods of the quasipolynomial and its coefficients, which are bounded by functions, not well understood, of the piece's move directions, and we develop exact formulas for the very highest coefficients. The coefficients of the three highest powers of $n$ do not vary with $n$. On the other hand, we present simple pieces for which the fourth coefficient varies periodically. We develop detailed properties of counting quasipolynomials that will be applied in sequels to partial queens, whose moves are subsets of those of the queen, and the nightrider, whose moves are extended knight's moves. We conclude with the first, though strange, formula for the classical $n$-Queens Problem and with several conjectures and open problems.

A Comparative Study of Open Source Operating Systems for Virtualization with Executing Applications

Virtualization is becoming increasingly popular, both for desktop as well as server systems. It has great demand in Information Technology industry because of inherent benefits like physical resource sharing that result in better utilization and ease in managing the system. Several studies have been done to find out the impact that virtualization has on system performance. The experimentation on Virtualization is in use by educational institutions for research and teaching and this is being done at large level. This paper stresses on the comparison of execution time of two classical problem “NQueens problem (N=13)” and “Towers of Hanoi (N= 20 disks)” on various Linux distributions that are installed on VMWare Workstation 10.0. In this context, we keep the various parameters like disk size and sector size and memory size same for all the virtual guests.

Accelerated execution of P systems with active membranes to solve the N-queens problem

The N-queens problem has attracted increasing attention because of its potential applications in different areas, such as parallel memory storage approaches, image processing, and physical and chemical studies. Local search is a powerful method for solving real problems, such as the N-queens problem. Recently, models of P systems with active membranes have been used for local search to solve the N-queens problem. However, there have been insufficient studies of the parallelism of the P-system models with active membranes. In addition, the active membrane systems defined for N queens have several individual membranes that contain one object and no internal rules in each membrane, as well as several communication rules among membranes, which reduce the execution speed. In this study, a new P system model with active membranes is defined for solving the N-queens problem, and multi-core simulation of the proposed membrane system allows the execution of alternative computations in parallel, thus reducing the average time for finding a successful computation. The speed of the proposed model was compared with previous models that used P systems with active membranes for local search. The model contains two membranes, but the inclusion of several objects and rules within each membrane increases the parallelism and performance. This model reduces the number of communication rules required among membranes, and increases the execution speed. This model also increases the parallelism of previous P systems with active membranes when several rules evolve concurrently and more than one queen is exchanged during each step to reach a solution. Multi-core processing has been used to decrease the probability of restarting the P systems and to decrease processing time by distributing the processing of the active membrane on the multi-core. The speed of the proposed model when solving N=200 queens was almost 1000 times faster than previous methods.

An improved superconducting neural circuit and its application for a neural network solving a combinatorial optimization problem

We have proposed a superconducting Hopfield-type neural network for solving the N-Queens problem which is one of combinatorial optimization problems. The sigmoid-shape function of a neuron output is represented by the output of coupled SQUIDs gate consisting of a single-junction and a double-junction SQUIDs. One of the important factors for an improvement of the network performance is an improvement of a threshold characteristic of a neuron circuit. In this paper, we report an improved design of coupled SQUID gates for a superconducting neural network. A step-like function with a steep threshold at a rising edge is desirable for a neuron circuit to solve a combinatorial optimization problem. A neuron circuit is composed of two coupled SQUIDs gates with a cascade connection in order to obtain such characteristics. The designed neuron circuit is fabricated by a 2.5 kA/cm2 Nb/AlOx/Nb process. The operation of a fabricated neuron circuit is experimentally demonstrated. Moreover, we discuss about the performance of the neural network using the improved neuron circuits and delayed negative self-connections.

A linear solution to the n-Queens problem using vector spaces

This paper presents an approach to solving the n-Queens Problem using vector spaces. Although the situations in which this approach can be used are limited, it shows promise for wider generalizatio...

An Energy and Performance Efficient DVFS Scheme for Irregular Parallel Divide-and-Conquer Algorithms on the Intel SCC

The divide-and-conquer paradigm can be used to express many computationally significant problems, but an important subset of these applications is inherently load-imbalanced. Load balancing is a challenge for irregular parallel divide-and-conquer algorithms and efficiently solving these applications will be a key requirement for future many-core systems. To address the load imbalance issue, instead of attempting to dynamically balancing the workloads, this paper proposes an energy and performance efficient Dynamic Voltage and Frequency Scaling (DVFS) scheduling scheme, which takes into account the load imbalance behavior exhibited by these applications. More specifically, we examine the core of the divide-and-conquer paradigm and determine that the base-case-reached point where recursion stops is a suitable place in a divide-and-conquer paradigm to apply the proposed DVFS scheme. To evaluate the proposed scheme, we implement four representative irregular parallel divide-and-conquer algorithms, tree traversal, quicksort, finding primes, and n-queens puzzle, on the Intel Single-chip Cloud Computer (SCC) many-core machine. We demonstrate that, on average, the proposed scheme can improve performance by 41% while reducing energy consumption by 36% compared to the baseline running the whole computation with the default frequency configuration (400MHz).

Focusing on the golden ball metaheuristic: an extended study on a wider set of problems.

Nowadays, the development of new metaheuristics for solving optimization problems is a topic of interest in the scientific community. In the literature, a large number of techniques of this kind can be found. Anyway, there are many recently proposed techniques, such as the artificial bee colony and imperialist competitive algorithm. This paper is focused on one recently published technique, the one called Golden Ball (GB). The GB is a multiple-population metaheuristic based on soccer concepts. Although it was designed to solve combinatorial optimization problems, until now, it has only been tested with two simple routing problems: the traveling salesman problem and the capacitated vehicle routing problem. In this paper, the GB is applied to four different combinatorial optimization problems. Two of them are routing problems, which are more complex than the previously used ones: the asymmetric traveling salesman problem and the vehicle routing problem with backhauls. Additionally, one constraint satisfaction problem (the n-queen problem) and one combinatorial design problem (the one-dimensional bin packing problem) have also been used. The outcomes obtained by GB are compared with the ones got by two different genetic algorithms and two distributed genetic algorithms. Additionally, two statistical tests are conducted to compare these results.

The influence of genetic origin and its interaction with environmental effects on the survival of Apis mellifera L. colonies in Europe

SummaryThe survival and performance of 597 honey bee colonies, representing five subspecies and 16 different genotypes, were comparatively studied in 20 apiaries across Europe. Started in October 2009, 15.7% of the colonies survived without any therapeutic treatment against diseases until spring 2012. The survival duration was strongly affected by environmental factors (apiary effects) and, to a lesser degree, by the genotypes and origin of queens. Varroa was identified as a main cause of losses (38.4%), followed by queen problems (16.9%) and Nosema infection (7.3%). On average, colonies with queens from local origin survived 83 days longer compared to non-local origins (p < 0.001). This result demonstrates strong genotype by environment interactions. Consequently, the conservation of bee diversity and the support of local breeding activities must be prioritised in order to prevent colony losses, to optimize a sustainable productivity and to enable a continuous adaptation to environmental changes.

Results of international standardised beekeeper surveys of colony losses for winter 2012–2013: analysis of winter loss rates and mixed effects modelling of risk factors for winter loss

SummaryThis article presents results of an analysis of winter losses of honey bee colonies from 19 mainly European countries, most of which implemented the standardised 2013 COLOSS questionnaire. Generalised linear mixed effects models (GLMMs) were used to investigate the effects of several factors on the risk of colony loss, including different treatments for Varroa destructor, allowing for random effects of beekeeper and region. Both winter and summer treatments were considered, and the most common combinations of treatment and timing were used to define treatment factor levels. Overall and within country colony loss rates are presented. Significant factors in the model were found to be: percentage of young queens in the colonies before winter, extent of queen problems in summer, treatment of the varroa mite, and access by foraging honey bees to oilseed rape and maize. Spatial variation at the beekeeper level is shown across geographical regions using random effects from the fitted models, both before and after allowing for the effect of the significant terms in the model. This spatial variation is considerable.

A novel pseudoderivative-based mutation operator for real-coded adaptive genetic algorithms

Recent development of large databases, especially those in genetics and proteomics, is pushing the development of novel computational algorithms that implement rapid and accurate search strategies. One successful approach has been to use artificial intelligence and methods, including pattern recognition (e.g. neural networks) and optimization techniques (e.g. genetic algorithms). The focus of this paper is on optimizing the design of genetic algorithms by using an adaptive mutation rate that is derived from comparing the fitness values of successive generations. We propose a novel pseudoderivative-based mutation rate operator designed to allow a genetic algorithm to escape local optima and successfully continue to the global optimum. Once proven successful, this algorithm can be implemented to solve real problems in neurology and bioinformatics. As a first step towards this goal, we tested our algorithm on two 3-dimensional surfaces with multiple local optima, but only one global optimum, as well as on the N-queens problem, an applied problem in which the function that maps the curve is implicit. For all tests, the adaptive mutation rate allowed the genetic algorithm to find the global optimal solution, performing significantly better than other search methods, including genetic algorithms that implement fixed mutation rates.

A novel pseudoderivative-based mutation operator for real-coded adaptive genetic algorithms

Recent development of large databases, especially those in genetics and proteomics, is pushing the development of novel computational algorithms that implement rapid and accurate search strategies. One successful approach has been to use artificial intelligence and methods, including pattern recognition (e.g. neural networks) and optimization techniques (e.g. genetic algorithms). The focus of this paper is on optimizing the design of genetic algorithms by using an adaptive mutation rate that is derived from comparing the fitness values of successive generations. We propose a novel pseudoderivative-based mutation rate operator designed to allow a genetic algorithm to escape local optima and successfully continue to the global optimum. Once proven successful, this algorithm can be implemented to solve real problems in neurology and bioinformatics. As a first step towards this goal, we tested our algorithm on two 3-dimensional surfaces with multiple local optima, but only one global optimum, as well as on the N-queens problem, an applied problem in which the function that maps the curve is implicit. For all tests, the adaptive mutation rate allowed the genetic algorithm to find the global optimal solution, performing significantly better than other search methods, including genetic algorithms that implement fixed mutation rates.

Landscape analysis and efficient metaheuristics for solving the n-queens problem

The n-queens problem is a classical combinatorial optimization problem which has been proved to be NP-hard. The goal is to place n non-attacking queens on an n×n chessboard. In this paper, two single-solution-based (Local Search (LS) and Tuned Simulated Annealing (SA)) and two population-based metaheuristics (two versions of Scatter Search (SS)) are presented for solving the problem. Since parameters of heuristic and metaheuristic algorithms have great influence on their performance, a TOPSIS-Taguchi based parameter tuning method is proposed, which not only considers the number of fitness function evaluations, but also aims to minimize the runtime of the presented metaheuristics. The performance of the suggested approaches was investigated through computational analyses, which showed that the Local Search method outperformed the other two algorithms in terms of average runtimes and average number of fitness function evaluations. The LS was also compared to the Cooperative PSO (CPSO) and SA algorithms, which are currently the best algorithms in the literature for finding the first solution to the n-queens problem, and the results showed that the average fitness function evaluation of the LS is approximately 21 and 8 times less than that of SA and CPSO, respectively. Also, a fitness analysis of landscape for the n-queens problem was conducted which indicated that the distribution of local optima is uniformly random and scattered over the search space. The landscape is rugged and there is no significant correlation between fitness and distance of solutions, and so a local search heuristic can search a rugged plain landscape effectively and find a solution quickly. As a result, it was statistically and analytically proved that single-solution-based metaheuristics outperform population-based metaheuristics in finding the first solution of the n-queens problem.

A Polynomial-Time DNA Computing Solution for the N-Queens Problem

The N-queens problem is a classic combinatorial problem that there is no polynomial time solution for it in silicon based computers. It belongs to the set of NP-Complete problems and needs a plenty of calculations. On the other hand, it has been evidenced that DNA computing is able to solve such complex problems efficiently. In this paper we propose a method based on Adleman-Lipton model, a model of DNA computing, which is able to solve the N-queens problem in a polynomial time complexity. It provides all the solutions and runs in O(N2).

Using computation to enhance diagnosis and therapy: a novel mutation operator for real-coded adaptive genetic algorithms

The fields of molecular biology and neurobiology have advanced rapidly over the last two decades. These advances have resulted in the development of large proteomic and genetic databases that need to be searched for the prediction, early detection and treatment of neuropathologies and other genetic disorders. This need, in turn, has pushed the development of novel computational algorithms that are critical for searching genetic databases. One successful approach has been to use artificial intelligence and pattern recognition algorithms, such as neural networks and optimization algorithms (e.g. genetic algorithms). The focus of this paper is on optimizing the design of genetic algorithms by using an adaptive mutation rate based on the fitness function of passing generations. We propose a novel pseudo-derivative based mutation rate operator designed to allow a genetic algorithm to escape local optima and successfully continue to the global optimum. Once proven successful, this algorithm can be implemented to solve real problems in neurology and bioinformatics. As a first step towards this goal, we tested our algorithm on two 3-dimensional surfaces with multiple local optima, but only one global optimum, as well as on the N-queens problem, an applied problem in which the function that maps the curve is implicit. For all tests, the adaptive mutation rate allowed the genetic algorithm to find the global optimal solution, performing significantly better than other search methods, including genetic algorithms that implement fixed mutation rates.