N-queens Research Articles

Parallel genetic algorithm for N‐Queens problem based on message passing interface‐compute unified device architecture

AbstractN‐Queens problem derives three variants: obtaining a specific solution, obtaining a set of solutions and obtaining all solutions. The purpose of the variant I is to find a constructive solution, which has been solved. Variant III is aiming to find all solutions and the largest number of queens currently being resolved is 26. Variant II whose purpose is to obtain a set of solutions for larger‐scale problems relies on various intelligent algorithms. In this paper, we use a master‐slave model genetic algorithm that combines the idea of the evolutionary algorithm and simulated annealing algorithm to solve Variant III, and use a parallel fitness function based on compute unified device architecture. Experimental results show that our scheme achieved a maximum 60‐fold speedup over the single‐CPU counterpart. On this basis, a two‐level parallel genetic algorithm based on the island model and master‐slave model is implemented on the GPU cluster by using message passing interface technology. Using two‐node and three‐node GPU cluster, speedup of 1.46 and 2.01 are obtained on average over single‐node, respectively. Compared with the sequential genetic algorithm, the two‐level parallel genetic algorithm makes full use of the parallel computing power of GPU cluster in solving N‐Queen variant II and improves the performance by 99.19 times in the best case.

New Constructions for the n-Queens Problem

Let D be a digraph, possibly with loops. A queen labeling of D is a bijective function $$l:V(G)\longrightarrow \{1,2,\ldots ,|V(G)|\}$$ such that, for every pair of arcs in E(D), namely (u, v) and $$(u',v')$$ we have (i) $$l(u)+l(v)\ne l(u')+l(v')$$ and (ii) $$l(v)-l(u)\ne l(v')-l(u')$$. Similarly, if the two conditions are satisfied modulo $$n=|V(G)|$$, we define a modular queen labeling. There is a bijection between (modular) queen labelings of 1-regular digraphs and the solutions of the (modular) n-queens problem. The $$\otimes _h$$-product was introduced in 2008 as a generalization of the Kronecker product and since then, many relations among labelings have been established using the $$\otimes _h$$-product and some particular families of graphs. In this paper, we study some families of 1-regular digraphs that admit (modular) queen labelings and present a new construction concerning to the (modular) n-queens problem in terms of the $$\otimes _h$$-product, which in some sense complements a previous result due to Polya.

A Linear Time Solution for N-Queens Problem Using Generalized Networks of Evolutionary Polarized Processors

In this paper we consider a new variant of Networks of Polarized Evolutionary Processors (NPEP) named Generalized Networks of Evolutionary Polarized Processors (GNPEP) and propose them as solvers of combinatorial optimization problems. Unlike the NPEP model, GNPEP uses its numerical evaluation over the processed data from a quantitative perspective, hence this model might be more suitable to solve specific hard problems in a more efficient and economic way. In particular, we propose a GNPEP network to solve a well-known NP-hard problem, namely the [Formula: see text]-queens. We prove that this GNPEP algorithm requires a linear time in the size of a given instance. This result suggests that the GNPEP model is more suitable to address problems related to combinatorial optimization in which integer restrictions have a relevant role.

Results of Standardized Beekeeper Survey of Honey Bee Colony Losses in Ukraine for Winter 2018-2019

Purpose. Analysis of honey bee (Apis mellifera Linnaeus, 1758) colony losses in Ukraine for winter 2018–2019 in comparison with the previous year in different physiographic zones of Ukraine and at the operations of different sizes. Methods. Survey of Ukrainian beekeepers for winter 2018–2019 using the standardised COLOSS questionnaire (International honey bee research association COLOSS). A total of 677 valid questionnaires from five physiographic zones of Ukraine were processed. Results. The total loss rate of honey bee colonies for winter 2018–2019 in Ukraine was 11.18 %, the mortality rate was 5.95 %; the losses due to unsolvable queen problems – 3.37 %, and due to natural disasters – 1.86 %. The total losses in the forest-steppe and the mixed forest zones were 16.2 % and 15.1 %, respectively, whereas in the Ukrainian Carpathians – 7.2 %. The most common sign of dead colonies in Ukraine was the presence of a large number of dead bees in or in front of the hive (25.3 %). The loss rate in the small operations was almost 18 %, in medium – 8.38 % and in large ones – 7.6 %. 77.8 % of respondents treated their bee colonies against Varroa destructor in the period from April 2018 to April 2019. 16.4 % respondents treated their colonies without prior monitoring of mite rate. The most commonly used acaricides were the veterinary medicinal products containing flumetrin (15.1 %), amitraz in strips (11.67 %) and fumigation (9.9 %), as well as oxalic acid – spraying and sublimation (9.5 % and 8.4 %, respectively). Conclusions. The total losses of honey bee colonies for winter of 2018–2019 (11.18 %) remained stable compared to the previous year (for winter of 2017–2018: 11.30 %), the losses due to colonies death (5.95 %) and losses due to natural disasters (1.86 %) decreased slightly (for winter of 2017–2018: 6.7 % and 2.4 %, respectively), whereas losses due to unsolvable queen problems increased form 2.1 % to 3.37 %). The highest losses were observed in the forest-steppe zone and the zone of mixed forests, whereas the lowest in the Ukrainian Carpathians. The smaller beekeeping operations with at most 50 colonies suffer significantly higher losses than larger operations.

The Douglas–Rachford algorithm for convex and nonconvex feasibility problems

The Douglas–Rachford algorithm is an optimization method that can be used for solving feasibility problems. To apply the method, it is necessary that the problem at hand is prescribed in terms of constraint sets having efficiently computable nearest points. Although the convergence of the algorithm is guaranteed in the convex setting, the scheme has demonstrated to be a successful heuristic for solving combinatorial problems of different type. In this self-contained tutorial, we develop the convergence theory of projection algorithms within the framework of fixed point iterations, explain how to devise useful feasibility problem formulations, and demonstrate the application of the Douglas–Rachford method to said formulations. The paradigm is then illustrated on two concrete problems: a generalization of the “eight queens puzzle” known as the “(m, n)-queens problem”, and the problem of constructing a probability distribution with prescribed moments.

Networks of polarized splicing processors as problem solvers

In this paper we show how Networks of Polarized Splicing Processors (NPSPs) can be used as problem solvers. We give a detailed uniform solution for the 3-coloring problem using O(m*n) time and we briefly discuss a solution for the 3-SAT problem in O(n*m) time. We also give the complete algorithm that can solve the n-queens completion problem in O(n*(n−m)) time, hence the n-queens problem in O(n2) time. All of the solutions use NPSPs with 2 nodes.

ADOMC-NPR Automatic Decision-Making Offloading Framework for Mobile Computation Using Nonlinear Polynomial Regression Model

Nowadays, mobile computation applications attract major interest of researchers. Limited processing power and short battery lifetime is an obstacle in executing computationally-intensive applications. This article presents a mobile computation automatic decision-making offloading framework. The proposed framework consists of two phases: adaptive learning, and modeling and runtime computation offloading. In the adaptive phase, curve-fitting (CF) technique based on non-linear polynomial regression (NPR) methodology is used to build an approximate time-predicting model that can estimate the execution time for spending the processing of the detected-intensive applications. The runtime computation phase uses the time predicting model for computing the predicted execution time to decide whether to run the application remotely and perform the offloading process or to run the application locally. Eventually, the RESTful web service is applied to carry out the offloading task in the case of a positive offloading decision. The proposed framework experimentally outperforms a competitive state-of-the-art technique by 73% concerning the time factor. The proposed time-predicting model records minimal deviation of the originally obtained values as it is applied 0.4997, 8.9636, 0.0020, and 0.6797 on the mean squared error metric for matrix-determinant, image-sharpening, matrix-multiplication, and n-queens problems, respectively.

Результати щорічного моніторингу втрат бджолиних колоній в Україні: зимівля 2017-2018 рр

Decline of honey bee colonies remains a global problem. It may affect catastrophically both ecosystems and the global economy. Here we present the results of the fourth year of a research project on bee colony losses in Ukraine over winter 2017-2018, conducted in the framework of international monitoring coordinated by the non-profit honey bee research association COLOSS. Overall winter loss rate and the mortality rate over winter 2017-2018 were significantly lower compared to the previous year: overall winter loss rate – 11.3% (95 % СІ 10.0-12.6); mortality rate – 6.7% (95 % СІ 5.8-7.7); rate of colony loss due to unsolvable queen problems – 2.1% (95 % СІ 1.6-2.7) and due to natural disasters – 2.4% (95 % СІ 2.0-3.0). Likewise previous years, the highest losses were observed in small operations (with 50 or fewer colonies). The highest overall loss rate was observed in the Steppe zone, with the highest both mortality rate and losses due to natural disasters compared to the other physiographic zones of Ukraine. Minimum mortality was recorded from deciduous forests 5.6 % (95 % CI 4.4-7.2) and the Ukrainian Carpathians 5.5 % (95 % CI 4.2-7.2). Winter losses related to queen problems varied greatly with a minimum in the Forest-Steppe zone 0.71 % (95 % CI 0.3-1.5). 83.3% of beekeepers treated their colonies against Varroa. The r-rank correlation analysis identified two potential risk factors (no or only a few dead bees in or in front of the empty hive; dead workers in cells and no food present) which revealed a weak positive correlation with both mortality rate and the rate of losses due to unsolvable queen problems.

A Quantum N-Queens Solver

The N-queens problem is to find the position of N queens on an N by N chess board such that no queens attack each other. The excluded diagonals N-queens problem is a variation where queens cannot be placed on some predefined fields along diagonals. This variation is proven NP-complete and the parameter regime to generate hard instances that are intractable with current classical algorithms is known. We propose a special purpose quantum simulator that implements the excluded diagonals N-queens completion problem using atoms in an optical lattice and cavity-mediated long-range interactions. Our implementation has no overhead from the embedding allowing to directly probe for a possible quantum advantage in near term devices for optimization problems.

Numerical and Symbolic Studies of the Peaceable Queens Problem

We discuss, and make partial progress on, the peaceable queens problem, the protagonist of OEIS sequence A250000. Symbolically, we prove that Jubin’s construction of two pentagons is at least a local optimum. Numerically, we find the exact numerical optimums for some specific configurations. Our method can be easily applied to more complicated configurations with more parameters.

Loss rates of honey bee colonies during winter 2017/18 in 36 countries participating in the COLOSS survey, including effects of forage sources

This short article presents loss rates of honey bee colonies over winter 2017/18 from 36 countries, including 33 in Europe, from data collected using the standardized COLOSS questionnaire. The 25,363 beekeepers supplying data passing consistency checks in total wintered 544,879 colonies, and reported 26,379 (4.8%, 95% CI 4.7–5.0%) colonies with unsolvable queen problems, 54,525 (10.0%, 95% CI 9.8–10.2%) dead colonies after winter and another 8,220 colonies (1.5%, 95% CI 1.4–1.6%) lost through natural disaster. This gave an overall loss rate of 16.4% (95% CI 16.1–16.6%) of honey bee colonies during winter 2017/18, but this varied greatly from 2.0 to 32.8% between countries. The included map shows relative risks of winter loss at regional level. The analysis using the total data-set confirmed findings from earlier surveys that smaller beekeeping operations with at most 50 colonies suffer significantly higher losses than larger operations (p < .001). Beekeepers migrating their colonies had significantly lower losses than those not migrating (p < .001), a different finding from previous research. Evaluation of six different forage sources as potential risk factors for colony loss indicated that intensive foraging on any of five of these plant sources (Orchards, Oilseed Rape, Maize, Heather and Autumn Forage Crops) was associated with significantly higher winter losses. This finding requires further study and explanation. A table is included giving detailed results of loss rates and the impact of the tested forage sources for each country and overall.

Classified enhancement model for big data storage reliability based on Boolean satisfiability problem

Disk reliability is a serious problem in the big data foundation environment. Although the reliability of disk drives has greatly improved over the past few years, they are still the most vulnerable core components in the server. If they fail, the result can be catastrophic: it can take some days to recover data, sometimes data lost forever. These are unacceptable for some important data. XOR parity is a typical method to generate reliability syndrome, thus improving the reliability of the data. In practice, we find that the data is still likely to be lost. In most storage systems reliability improvements are achieved through the allocation of additional disks in Redundant Arrays of Independent Disks (RAID), which will increase the hardware costs, thus it will be very difficult for cost-constrained environments. Therefore, how to improve the data integrity without raising the hardware cost has aroused much interest of big data researchers. This challenge is when creating non-traditional RAID geometries, care must be taken to respect data dependence relationships to ensure that the new RAID strategy improves reliability, which is a NP-hard problem. In this paper, we present an approach for characterizing these challenges using high-dimension variants of the n-queens problem that enables performable solutions via the SAT solver MiniSAT, and use the greedy algorithm to analyze the queen’s attack domain, as a basis for reliability syndrome generation. A large number of experiments show that the approach proposed in this paper is feasible in software-defined data centers and the performance of the algorithm can meet the current requirements of the big data environment.

Dancing links for optimal timetabling

Military Operations Research Society. All rights reserved. Algorithms for timetabling solutions typically involve sequential allocation of students to courses and resources as the algorithm unfolds. Most current solutions, to this end, commonly use some form of stochastic optimization. In this paper, we propose a novel paradigm for optimal timetabling that comprises two distinct phases. First, we enumerate all feasible course schedules, along with their costs, using a modified implementation of Knuth’s Dancing Links technique for the exact cover problem. To our knowledge, the only prior use of this implementation has been to solve games such as Sudoku and N-Queens. Once the list of all solutions that satisfy prerequisite and time-clash constraints is generated, the second phase applies a standard deterministic optimization to allocate students to these feasible schedules. This method has been applied to a real complex timetabling problem in the Royal Australian Navy helicopter aircrew training program. The results are compared, in terms of computational time, to an exhaustive best practice backtracking algorithm for generating a complete set of feasible schedules, as well as to a pure integer linear programming solution for generating schedules and allocating students to schedules.

Comparison of apiculture and winter mortality of honey bee colonies (Apis mellifera) in Austria and Czechia

Honey bees are the most important managed pollinators and provide income because of bee products. In Austria and Czechia, we monitored winter losses of honey bee colonies and also collected information on the apicultural sector, hive management, population dynamics and treatment against the mite Varroa destructor from 2013–14 to 2016–17. Numbers of beekeepers and colonies, colony density and percentage of beekeepers in human population are higher in Czechia than in Austria. Winter loss rates of honey bee colonies ranged from 8.1% to 28.4% in Austria and 6.4% to 19.4% in Czechia, with significantly higher loss rates in all 4 investigated winters in Austria. The portion of colonies lost because of living colonies with unsolvable queen problems ranged from 3.6 to 4.4% in Austria and from 2.2 to 3.0% in Czechia. Despite of colony losses during winter, colony production in summer allows for compensation or even expansion of colony populations in both countries. We identified differences between the two countries in the treatments applied by beekeepers against the parasitic varroa mite. In Austria, organic acids are most commonly used, whereas the application of synthetic acaricides is widely spread in Czechia. Our study points at the better understanding of apiculture and the importance of international comparisons to facilitate our knowledge on honey bee colony losses.

Solving N-queen Problem Using Genetic Algorithm by Advance Mutation Operator

N-queen problem represents a class of constraint problems. It belongs to set of NP-Hard problems. It is applicable in many areas of science and engineering. In this paper N-queen problem is solved using genetic algorithm. A new genetic algoerithm is proposed which uses greedy mutation operator. This new mutation operator solves the N-queen problem very quickly. The proposed algorithm is applied on some instances of N-queen problem and results outperforms the previous findings.

An easy counting lemma

While investigating the N-Queens Puzzle, Thomas Preußer came to a simplification for the search; this is generalized and proven here. The main point is: if you have a suitable mapping of a big set to a small one, explore and use the symmetry of the small set, and transfer the result to the big set. With this mapping and the lemma, you no longer bother with the symmetry of a single element in the big set.The paper is written for two different groups: first for computer scientists implementing searches under symmetry, and second for mathematicians supporting them, and interested in understanding how search spaces can be diminished under symmetry.

Hybridization of Bat and Genetic Algorithm to Solve N-Queens Problem

In this paper, a hybrid of Bat-Inspired Algorithm (BA) and Genetic Algorithm (GA) is proposed to solve N-queens problem. The proposed algorithm executes the behavior of microbats with changing pulse rates of emissions and loudness to final all the possible solutions in the initialization and moving phases. This dataset applied two metaheuristic algorithms (BA and GA) and the hybrid to solve N-queens problem by finding all the possible solutions in the instance with the input sizes of area 8*8, 20*20, 50*50, 100*100 and 500*500 on a chessboard. To find the optimal solution, consistently, ten run have been set with 100 iterations for all the input sizes. The hybrid algorithm obtained substantially better results than BA and GA because both algorithms were inferior in discovering the optimal solutions than the proposed randomization method. It also has been discovered that BA outperformed GA because it requires a reduced amount of steps in determining the solutions.

Investigation of the Regularities in the Formation of Solutions n-Queens Problem

Investigation of the Regularities in the Formation of Solutions n-Queens Problem

Solving N-Queens Problem Using Subproblems based on Genetic Algorithm

&lt;span lang="EN-US"&gt;Nowadays, permutation problems with large state spaces and the path to solution is irrelevant such as N-Queens problem has the same general property for many important applications such as integrated-circuit design, factory-floor layout, job-shop scheduling, automatic programming, telecommunications network optimization, vehicle routing, and portfolio management. Therefore, methods which are able to find a solution are very important. Genetic algorithm (GA) is one the most well-known methods for solving N-Queens problem and applicable to a wide range of permutation problems. In the absence of specialized solution for a particular problem, genetic algorithm would be efficient. But holism and random choices cause problem for genetic algorithm in searching large state spaces. So, the efficiency of this algorithm would be demoted when the size of state space of the problem grows exponentially. In this paper, the subproblems used based on genetic algorithm to cover this weakness. This proposed method is trying to provide partial view for genetic algorithm by locally searching the state space. This method works to take shorter steps toward the solution. To find the first solution and other solutions in N-Queens problem using proposed method: dividing N-Queens problem into subproblems, which configuring initial population of genetic algorithm. The proposed method is evaluated and compares it with two similar methods that indicate the amount of performance improvement.&lt;/span&gt;

Multi-country loss rates of honey bee colonies during winter 2016/2017 from the COLOSS survey

In this short note we present comparable loss rates of honey bee colonies during winter 2016/2017 from 27 European countries plus Algeria, Israel and Mexico, obtained with the COLOSS questionnaire. The 14,813 beekeepers providing valid loss data collectively wintered 425,762 colonies, and reported 21,887 (5.1%, 95% confidence interval 5.0–5.3%) colonies with unsolvable queen problems and 60,227 (14.1%, 95% CI 13.8–14.4%) dead colonies after winter. Additionally we asked for colonies lost due to natural disaster, which made up another 6,903 colonies (1.6%, 95% CI 1.5–1.7%). This results in an overall loss rate of 20.9% (95% CI 20.6–21.3%) of honey bee colonies during winter 2016/2017, with marked differences among countries. The overall analysis showed that small operations suffered higher losses than larger ones (p < 0.001). Overall migratory beekeeping had no significant effect on the risk of winter loss, though there was an effect in several countries. A table is presented giving detailed results from 30 countries. A map is also included, showing relative risk of colony winter loss at regional level.