Permutation Problem Research Articles

A class of permutation quadrinomials

In this paper, we investigate the permutation behavior of a class of quadrinomials. Each term of these quadrinomials has a Niho-type exponent, and two sets of coefficient triples making the quadrinomials to be permutations are obtained. We use a substitution to transform the permutation problem into the root distribution problem in the unit circle of certain quadratic and cubic equations.

Solving N-Queens Problem Using Subproblems based on Genetic Algorithm

<span lang="EN-US">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.</span>

Algorithm 989

Permutation problems are combinatorial optimization problems whose solutions are naturally codified as permutations. Due to their complexity, motivated principally by the factorial cardinality of the search space of solutions, they have been a recurrent topic for the artificial intelligence and operations research community. Recently, among the vast number of metaheuristic algorithms, new advances on estimation of distribution algorithms (EDAs) have shown outstanding performance when solving some permutation problems. These novel EDAs implement distance-based exponential probability models such as the Mallows and Generalized Mallows models. In this article, we present a Matlab package, perm_mateda, of estimation of distribution algorithms on permutation problems, which has been implemented as an extension to the Mateda-2.0 toolbox of EDAs. Particularly, we provide implementations of the Mallows and Generalized Mallows EDAs under the Kendall’s-τ, Cayley, and Ulam distances. In addition, four classical permutation problems have also been implemented: Traveling Salesman Problem, Permutation Flowshop Scheduling Problem, Linear Ordering Problem, and Quadratic Assignment Problem.

Co‐frequency Interference Suppression for Aerostat Passive Bistatic Radar

Co-frequency interference is frequently encountered in the aerostat passive bistatic radar exploiting frequency modulated broadcasting signals. Independent component analysis (ICA) in frequency domain, one of the classic Blind source separation (BSS) algorithms, is utilized to recover the direct signal in the above scenarios. To solve the permutation problem of the frequency domain BSS, we use the method of correlation in time-frequency domain between the output of ICA and the coarse reference signal achieved by pattern synthesis with nulls in the direction of the interference or reference stations. In order to suppress the interferences and clutters, the separated direct signals of the reference and interference broadcasting signals are fed into a type of two dimensional adaptive filters in space and fast temporal domain. The processing scheme shows good performance in target detection, which is validated by computer simulation.

Speaker-Independent Speech Separation With Deep Attractor Network

Despite the recent success of deep learning for many speech processing tasks, single-microphone, speaker-independent speech separation remains challenging for two main reasons. The first reason is the arbitrary order of the target and masker speakers in the mixture permutation problem, and the second is the unknown number of speakers in the mixture output dimension problem. We propose a novel deep learning framework for speech separation that addresses both of these issues. We use a neural network to project the time-frequency representation of the mixture signal into a high-dimensional embedding space. A reference point attractor is created in the embedding space to represent each speaker which is defined as the centroid of the speaker in the embedding space. The time-frequency embeddings of each speaker are then forced to cluster around the corresponding attractor point which is used to determine the time-frequency assignment of the speaker. We propose three methods for finding the attractors for each source in the embedding space and compare their advantages and limitations. The objective function for the network is standard signal reconstruction error which enables end-to-end operation during both training and test phases. We evaluated our system using the Wall Street Journal dataset WSJ0 on two and three speaker mixtures and report comparable or better performance than other state-of-the-art deep learning methods for speech separation.

The Unit-capacity Constrained Permutation Problem

The Unit-capacity Constrained Permutation Problem (UCPP) is to find a sequence of moves for pieces over a set of locations. From a given location, a piece can be moved towards a location with a unit-capacity constraint, i.e. the latter location must be free of its original piece. Each piece has a specific type and at the end every location must contain a piece of a required type. A piece must be handled using a specific tool incurring a setup cost whenever a tool changeover is required. The aim of the UCPP is finding a sequence of moves with a minimum total setup cost. This problem arises in the Nuclear power plant Fuel Renewal Problem (NFRP) where locations correspond to fuel assemblies and pieces to fuel assembly inserts. We first show that the UCPP is NP-hard. We exhibit some symmetry and dominance properties and propose a dynamic programming algorithm. Using this algorithm, we prove that the UCPP is polynomial when two tools and two types are considered. Experimental results showing the efficiency of the algorithm for some instances coming from the NFRP are presented.

Bent functions from nonlinear permutations and conversely

This work extends the idea introduced by Hou and Langevin (J. Combin. Theory, Ser. A, 80:232–246, 1997) of applying nonlinear permutations to (a portion of) the input variable space of a given Boolean function so that the resulting function is bent. Applying such a permutation to a bent function that can be represented in a suitable form then gives an affine inequivalent bent function which potentially does not belong to the same class as the original one. While Hou and Langevin only provided two sporadic examples of bent functions that can be turned into affine inequivalent ones, in this article we identify two generic families of bent functions suitable for generating such affine inequivalent counterparts. The same method when applied to the Marioana-McFarland class of bent functions, depending on the subset of inputs to which a nonlinear action is applied, either lead to bent functions that are provably within the same class or to bent functions that are potentially outside this class. The problem of finding suitable permutations that act nonlinearly on more than two input variables of the initial function and ensure the bentness of the resulting function appears to be generally hard. In this direction, we only slightly extend the approach of Hou and Langevin by identifying suitable permutations that act nonlinearly on three input variabl es. Most notably, the existence of nonlinear permutations that act without strict separation of the input space in terms of linear and nonlinear action is also confirmed. Finally, we show a direct correspondence between (some classes of) bent functions and permutations by providing an efficient method to define permutations using the derivatives of a given bent function. This not only gives a relationship between two seemingly different algebraic objects, but also provides us with a new infinite family of permutations over finite fields.

Optimization on permutations: related structures, problems interrelation, heuristic compositions, applications

A heuristics based approach to practical solving theoretically intractable combinatory and network problems is discussed. Compound heuristics (heuristics compositions) are suggested to be more efficient procedures for real size problem instances. Some aspects of the heuristics compositions topic are illustrated by optimum permutation problems. We describe a uniform presentation of the chief types of the problems and their interrelations, including the relation “to be a special case of a problem”. We consider a number of algebraic structures and combinatory constructions on permutation sets and present an inclusion chain of these constructions. The chain enables us to establish and clarify many interrelations for the minimum permutation problems, with algorithmic and complexity aspects taken into account. We also concern the applications of some problems as well.

Determining optimal combination of roller compacted concrete pavement mixture containing recycled asphalt pavement and crumb rubber using hybrid artificial neural network–genetic algorithm method considering energy absorbency approach

The present study investigates the effectiveness of evolutionary algorithms such as genetic algorithm (GA) evolved neural network in estimating roller compacted concrete pavement (RCCP) characteristics including flexural and compressive strength of RCC and also energy absorbency of mixes with different compositions. A real coded GA was implemented as training algorithm of feed forward neural network to simulate the models. The genetic operators were carefully selected to optimize the neural network, avoiding premature convergence and permutation problems. To evaluate the performance of the genetic algorithm neural network model, Nash-Sutcliffe efficiency criterion was employed and also utilized as fitness function for genetic algorithm which is a different approach for fitting in this area. The results showed that the GA-based neural network model gives a superior modeling. The well-trained neural network can be used as a useful tool for modeling RCC specifications.

Fully Automated Quantum‐Chemistry‐Based Computation of Spin–Spin‐Coupled Nuclear Magnetic Resonance Spectra

We present a composite procedure for the quantum‐chemical computation of spin–spin‐coupled 1H NMR spectra for general, flexible molecules in solution that is based on four main steps, namely conformer/rotamer ensemble (CRE) generation by the fast tight‐binding method GFN‐xTB and a newly developed search algorithm, computation of the relative free energies and NMR parameters, and solving the spin Hamiltonian. In this way the NMR‐specific nuclear permutation problem is solved, and the correct spin symmetries are obtained. Energies, shielding constants, and spin–spin couplings are computed at state‐of‐the‐art DFT levels with continuum solvation. A few (in)organic and transition‐metal complexes are presented, and very good, unprecedented agreement between the theoretical and experimental spectra was achieved. The approach is routinely applicable to systems with up to 100–150 atoms and may open new avenues for the detailed (conformational) structure elucidation of, for example, natural products or drug molecules.

Multitalker Speech Separation With Utterance-Level Permutation Invariant Training of Deep Recurrent Neural Networks

In this paper, we propose the utterance-level permutation invariant training (uPIT) technique. uPIT is a practically applicable, end-to-end, deep-learning-based solution for speaker independent multitalker speech separation. Specifically, uPIT extends the recently proposed permutation invariant training (PIT) technique with an utterance-level cost function, hence eliminating the need for solving an additional permutation problem during inference, which is otherwise required by frame-level PIT. We achieve this using recurrent neural networks (RNNs) that, during training, minimize the utterance-level separation error, hence forcing separated frames belonging to the same speaker to be aligned to the same output stream. In practice, this allows RNNs, trained with uPIT, to separate multitalker mixed speech without any prior knowledge of signal duration, number of speakers, speaker identity, or gender. We evaluated uPIT on the WSJ0 and Danish two- and three-talker mixed-speech separation tasks and found that uPIT outperforms techniques based on nonnegative matrix factorization and computational auditory scene analysis, and compares favorably with deep clustering, and the deep attractor network. Furthermore, we found that models trained with uPIT generalize well to unseen speakers and languages. Finally, we found that a single model, trained with uPIT, can handle both two-speaker, and three-speaker speech mixtures.

Comparison and applicability study of blood volume pulse extraction based on facial video

Blind source separation technique based on independent component analysis (ICA) can separate blood volume pulse (BVP) from the facial video and then realize the telemetry of heart rate, blood oxygen saturation, respiratory rate and other vital signs parameters. However, the superiority of ICA in BVP extraction has not been demonstrated in the existing researches. Some researchers suggested using traditional G-channel method for BVP extraction (G-BVP) instead of ICA method (ICA-BVP). This study investigated the applicability of ICA-BVP comparatively. To solve the inherent permutation problem of ICA, a spectral kurtosis-based method was proposed for BVP identification. The experimental results based on the facial video datasets from 9 subjects shows that ICA-BVP method has apparent advantages in motion artifacts attenuation and ambient light changes elimination. The kurtosis-based method achieved a good performance in BVP identification and dynamic heart rate (HR) estimation. In practical application, the proposed ICA-BVP method could present a better stability and accuracy in vital signs parameters extraction.

Effective Iterated Greedy Algorithm for Flow-Shop Scheduling Problems with Time lags

Flow shop scheduling problem with time lags is a practical scheduling problem and attracts many studies. Permutation problem(PFSP with time lags) is concentrated but non-permutation problem(non-PFSP with time lags) seems to be neglected. With the aim to minimize the makespan and satisfy time lag constraints, efficient algorithms corresponding to PFSP and non-PFSP problems are proposed, which consist of iterated greedy algorithm for permutation(IGTLP) and iterated greedy algorithm for non-permutation (IGTLNP). The proposed algorithms are verified using well-known simple and complex instances of permutation and non-permutation problems with various time lag ranges. The permutation results indicate that the proposed IGTLP can reach near optimal solution within nearly 11% computational time of traditional GA approach. The non-permutation results indicate that the proposed IG can reach nearly same solution within less than 1% computational time compared with traditional GA approach. The proposed research combines PFSP and non-PFSP together with minimal and maximal time lag consideration, which provides an interesting viewpoint for industrial implementation.

Particle Swarm Ant Colony Optimization Algorithm for Solving Circle Permutation Problem

Particle Swarm Ant Colony Optimization Algorithm for Solving Circle Permutation Problem

A mixed integer linear programming formulation for low discrepancy consecutive k-sums permutation problem

In this paper, low discrepancy consecutive k-sums permutation problem is considered. A mixed integer linear programing (MILP) formulation with a moderate number of variables and constraints is proposed. The correctness proof shows that the proposed formulation is equivalent to the basic definition of low discrepancy consecutive k-sums permutation problem. Computational results, obtained on standard CPLEX solver, give 88 new exact values, which clearly show the usefulness of the proposed MILP formulation.

JAMES: An object‐oriented Java framework for discrete optimization using local search metaheuristics

SummaryThis paper describes the Java Metaheuristics Search framework (JAMES, v1.1): an object‐oriented Java framework for discrete optimization using local search algorithms that exploits the generality of such metaheuristics by clearly separating search implementation and application from problem specification. A wide range of generic local searches are provided, including (stochastic) hill climbing, tabu search, variable neighbourhood search and parallel tempering. These can be applied to any user‐defined problem by plugging in a custom neighbourhood for the corresponding solution type. Using an automated analysis workflow, the performance of different search algorithms can be compared in order to select an appropriate optimization strategy. Implementations of specific components are included for subset selection, such as a predefined solution type, generic problem definition and several subset neighbourhoods used to modify the set of selected items. Additional components for other types of problems (e.g. permutation problems) are provided through an extensions module which also includes the analysis workflow. In comparison with existing Java metaheuristics frameworks that mainly focus on population‐based algorithms, JAMES has a much lower memory footprint and promotes efficient application of local searches by taking full advantage of move‐based evaluation. Releases of JAMES are deployed to the Maven Central Repository so that the framework can easily be included as a dependency in other Java applications. The project is fully open source and hosted on GitHub. More information can be found at http://www.jamesframework.org. Copyright © 2016 John Wiley & Sons, Ltd.

Source separation employing beamforming and SRP-PHAT localization in three-speaker room environments

This paper presents a new blind speech separation algorithm using beamforming technique that is capable of extracting each individual speech signal from a mixture of three speech sources in a room. The speech separation algorithm utilizes the steered response power phase transform for obtaining a localization estimate for each individual speech source in the frequency domain. Based on those estimates each desired speech signal is extracted from the speech mixture using an optimal beamforming technique. To solve the permutation problem, a permutation alignment algorithm based on the mutual output correlation is employed to group the output signals into the correct sources from each frequency bin. Evaluations using real speech recordings in a room environment show that the proposed blind speech separation algorithm offers high interference suppression level whilst maintaining low distortion level for each desired signal.

Algebraic Differential Evolution Algorithm for the Permutation Flowshop Scheduling Problem With Total Flowtime Criterion

This paper introduces an original algebraic approach to differential evolution (DE) algorithms for combinatorial search spaces. An abstract algebraic differential mutation for generic combinatorial spaces is defined by exploiting the concept of a finitely generated group. This operator is specialized for the permutations space by means of an original randomized bubble sort algorithm. Then, a discrete DE algorithm is derived for permutation problems and it is applied to the permutation flowshop scheduling problem with the total flowtime criterion. Other relevant components of the proposed algorithm are: a crossover operator for permutations, a novel biased selection strategy, a heuristic-based initialization, and a memetic restart procedure. Extensive experimental tests have been performed on a widely accepted benchmark suite in order to analyze the dynamics of the proposed approach and to compare it with the state-of-the-art algorithms. The experimental results clearly show that the proposed algorithm reaches state-of-the-art performances and, most remarkably, it is able to find some new best known results. Furthermore, the experimental analysis on the impact of the algorithmic components shows that the two main contributions of this paper, i.e., the discrete differential mutation and the biased selection operator, greatly contribute to the overall performance of the algorithm.

A High Invariance Motion Representation for Skeleton-Based Action Recognition

Human action recognition is very important and significant research work in numerous fields of science, for example, human–computer interaction, computer vision and crime analysis. In recent years, relative geometry features have been widely applied to the description of relative relation of body motion. It brings many benefits to action recognition such as clear description, abundant features etc. But the obvious disadvantage is that the extracted features severely rely on the local coordinate system. It is difficult to find a bijection between relative geometry and skeleton motion. To overcome this problem, many previous methods use relative rotation and translation between all skeleton pairs to increase robustness. In this paper we present a new motion representation method. It establishes a motion model based on the relative geometry with the aid of special orthogonal group SO(3). At the same time, we proved that this motion representation method can establish a bijection between relative geometry and motion of skeleton pairs. After the motion representation method in this paper is used, the computation cost of action recognition reduces from the two-way relative motion (motion from A to B and B to A) to one-way relative motion (motion from A to B or B to A) between any skeleton pair, namely, permutation problem [Formula: see text] is simplified into combinatorics problem [Formula: see text]. Finally, the experimental results of the three motion datasets are all superior to present skeleton-based action recognition methods.

Iterated Local Search and Column Generation to solve Arc-Routing as a permutation set-covering problem

We propose a method that combines Column Generation (CG) and Iterated Local Search (ILS) to solve the Capacitated Arc-Routing Problem (CARP). One of the goals is to integrate into the ILS (some of) the duality information that underpins the CG paradigm. The CARP is expressed in a space of permutations and sub-permutations (sequences, routes) of the set of required edges. For this, the ILS uses an exact decoder that maps any permutation s to a list of sequences (routes) of minimum cost servicing all edges in the order s(1), s(2), s(3), etc. This permutation space is explored both by an ILS process and a CG process that run in parallel and that communicate by exchanging sequences. The first use of the CG paradigm in ILS is the following: all sequences discovered by CG are sent to the ILS process that can inject them into the current ILS solution. The second application of CG in ILS is a “CG improver” operator that acts on the current ILS solution, so as to (try to) improve it by running several CG iterations. The first half of the paper describes the method in a general framework based on sequences, permutations and set covering. The second part is devoted to more specialized Arc-Routing techniques. For instance, the CG convergence could be accelerated by factors of tens or even hundreds by exploiting two ideas in the Dynamic Programming (DP) pricing: (i) avoid as much as possible to traverse edges without service, and (ii) record only non-dominated DP states using a fast-access data structure mixing an array and a red-black tree. Regarding the ILS, we show that the permutation-level search can be substantially improved if the exact decoder is reinforced by a deterministic post-decoder acting on explicit routes. The general results are competitive (reducing the best-known gap of five instances) and certain ideas could be potentially useful for other set-covering or permutation problems.