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Operations in areas of importance to society are frequently modeled as mixed-integer linear programming (MILP) problems. While MILP problems suffer from combinatorial complexity, Lagrangian Relaxation has been a beacon of hope to resolve the associated difficulties through decomposition. Due to the non-smooth nature of Lagrangian dual functions, the coordination aspect of the method has posed serious challenges. This paper presents several significant historical milestones (beginning with Polyak's pioneering work in 1967) toward improving Lagrangian Relaxation coordination through improved optimization of non-smooth functionals. Finally, this paper presents the most recent developments in Lagrangian Relaxation for fast resolution of MILP problems. The paper also briefly discusses the opportunities that Lagrangian Relaxation can provide at this point in time. [ABSTRACT FROM AUTHOR]

The Double Row Layout Problem (DRLP) asks for an arrangement of machines on both sides of a straight line corridor so as to minimize the total cost for transferring materials among machines. The DRLP is NP-Hard and has practical relevance, specially in manufacturing systems design. In this paper, we drastically reduce the time required to solve the problem by constructing a new and effective mixed-integer linear programming (MILP) model of the DRLP. The new model was obtained by reformulating an existing MILP model. This includes tightening some constraints, introducing new variables, implementing constraints to link the new and original variables; and adding valid inequalities and a valid system of equations. To reduce the size of the reformulated model, we eliminate several of the new introduced variables by a substitution using the system of equations. The computational results demonstrate that the proposed model requires considerably smaller computational times compared to the ones in the literature. As a consequence, optimal solutions can now be efficiently found for larger instances of the problem. Previous studies have been able to optimally solve, within reasonable time, instances with size up to 16 machines, while with the new model four instances with 20 machines could be optimally solved. [ABSTRACT FROM AUTHOR]

Linear assignment problems hold a pivotal role in combinatorial optimization, offering a broad spectrum of applications within the field of data sciences. They consist of assigning "agents" to "tasks" in a way that leads to a minimum total cost associated with the assignment. The assignment is balanced when the number of agents equals the number of tasks, with a one-to-one correspondence between agents and tasks, and it is and unbalanced otherwise. Additional options and constraints may be imposed, such as allowing agents to perform multiple tasks or allowing tasks to be performed by multiple agents. In this paper, we propose a novel framework that can solve all these assignment problems employing methodologies derived from the field of statistical physics. We describe this formalism in detail and validate all its assertions. A major part of this framework is the definition of a concave effective free energy function that encapsulates the constraints of the assignment problem within a finite temperature context. We demonstrate that this free energy monotonically decreases as a function of a parameter β representing the inverse of temperature. As β increases, the free energy converges to the optimal assignment cost. Furthermore, we demonstrate that when β values are sufficiently large, the exact solution to the assignment problem can be derived by rounding off the elements of the computed assignment matrix to the nearest integer. We describe a computer implementation of our framework and illustrate its application to multi-task assignment problems for which the Hungarian algorithm is not applicable. [ABSTRACT FROM AUTHOR]

This paper proposes a method for simultaneous evaluation of the assembly process complexity together with the performance of the future product. It allows for product design optimization, considering different aspects of the future design at the early stage of the development process. The proposed method, embodied in a fully automated framework, substitutes the traditional sequential development process with a more efficient and rapid combined procedure, which addresses multiple design aspects simultaneously. Design for assembly (DFA) rules, used as quantitative metrics of the ease-of-assembly of the whole product and individual assembly operations, are automatically evaluated together with performance metrics, estimated based on finite element (FE) simulations. The direct solution to this optimization problem might be inefficient or impossible since it requires the recurrent evaluation of computationally expensive discrete and continuous functions with unknown behavior that represent the optimization objectives and constraints. For that reason, the proposed framework employs regression models based on the Gaussian process and artificial neural networks, thus achieving the optimal design of a product as a result of metamodel-based design optimization (MBDO). The suggested approach is demonstrated in the optimization of a gearbox assembly, considering its mechanical performance and assembly process. Comparing the results of the metamodel-based and direct design optimization shows that MBDO allows finding a better solution using a three times smaller computational budget. In addition, analysis of the results obtained using stationary sampling data sets of different sizes highlighted the limitations of the employed sampling procedure. [ABSTRACT FROM AUTHOR]

Quantum computing has opened up various opportunities for the enhancement of computational power in the coming decades. We can design algorithms inspired by the principles of quantum computing, without implementing in quantum computing infrastructure. In this paper, we present the quantum predator–prey algorithm (QPPA), which fuses the fundamentals of quantum computing and swarm optimization based on a predator–prey algorithm. Our results demonstrate the efficacy of QPPA in solving complex real-parameter optimization problems with better accuracy when compared to related algorithms in the literature. QPPA achieves highly rapid convergence for relatively low- and high-dimensional optimization problems and outperforms selected traditional and advanced algorithms. This motivates the application of QPPA to real-world application problems. [ABSTRACT FROM AUTHOR]

This paper deals with p-location problem solving processes based on a decomposition, which separates the creation of a uniformly deployed set of p-location problems from the solution of the p-location problem for that specific instance. The research presented in this paper is focused on methods of construction of uniformly deployed sets of solutions and the examination of their impact on the efficiency of subsequent optimization algorithms. The approaches to the construction are used for the constitution of predetermined families of uniformly deployed sets of p-location problem solutions, which have standard sizes. We introduce two methods of uniformly deployed set construction: the first one is based on composition, followed by an enlargement process; and the second one makes use of voltage graphs. The construction approaches are completed by an algorithm, which adjusts the set of solutions to the sizes of a solved instance. The influence of a set construction approach on solving process efficiency is studied on real-world benchmarks, which include both the p-median objective function and the generalized disutility function. The solving process is performed alternatively using the swap or path-relinking based methods. Results of the computational study obtained by all combinations of the mentioned approaches are presented and evaluated in the concluding part of the paper to make the studied characteristics visible. [ABSTRACT FROM AUTHOR]

The Minimum Vertex Weighted Coloring (MinVWC) problem is an important generalization of the classic Minimum Vertex Coloring (MinVC) problem which is NP-hard. Given a simple undirected graph G = (V , E) , the MinVC problem is to find a coloring s.t. any pair of adjacent vertices are assigned different colors and the number of colors used is minimized. The MinVWC problem associates each vertex with a positive weight and defines the weight of a color to be the weight of its heaviest vertices, then the goal is the find a coloring that minimizes the sum of weights over all colors. Among various approaches, reduction is an effective one. It tries to obtain a subgraph whose optimal solutions can conveniently be extended into optimal ones for the whole graph, without costly branching. In this paper, we propose a reduction algorithm based on maximal clique enumeration. More specifically our algorithm utilizes a certain proportion of maximal cliques and obtains lower bounds in order to perform reductions. It alternates between clique sampling and graph reductions and consists of three successive procedures: promising clique reductions, better bound reductions and post reductions. Experimental results show that our algorithm returns considerably smaller subgraphs for numerous large benchmark graphs, compared to the most recent method named RedLS. Also, we evaluate individual impacts and some practical properties of our algorithm. Furthermore, we have a theorem which indicates that the reduction effects of our algorithm are equivalent to that of a counterpart which enumerates all maximal cliques in the whole graph if the run time is sufficiently long. [ABSTRACT FROM AUTHOR]

The problem of solving the task of discrete optimization is not completely solved. Lack of publications, scientific developments, algorithms and software products do not give the ability to transfer the mathematical apparatus of solving discrete optimization problems to the class P of computational complexity. All analytical and combinatorial algorithms for solving problems of linear and non-linear optimization are NP completeness. There are developments to improve the efficiency of robotic algorithms, they are filled with requests and actual ones. In this paper, it is proposed to use deterministic and probabilistic methods for forming a priority queue of decision vector components in order to assign positive values to them. After the formation of the variant of the solution, it is possible to vectorize as if the approached solution is taken away from the record value of the goal function, which in exact algorithms is like a solution, which results in a polyp. In this paper has a method for forming a priority line for concretizing the components of the solution vector. The basis of deterministic methods is the idea of a greedy algorithm. The location in the queue is determined by the value of the corresponding component of the cost vector. The appearance of the value of non-visibility in the system of restrictions increases the priority of the component. Behind such a way, another method of determination is modified. Probability assessment probability of priorities is based on the ideas of algorithms in an ant colony and simulated annealing. The scope of probability indicates the significance of the component - a contender for a positive value. A numerical example of a small variability of the task about a knapsack has been introduced, which demonstrates the imitation of a nearby solution. [ABSTRACT FROM AUTHOR]

This paper considers algorithm unions (portfolios and teams) of optimization algorithms, their properties, and their impact on the acceleration of the optimization process. The authors have investigated the application of unions of global equilibrium search algorithms to specific discrete optimization problems and various information exchange schemes within algorithm teams. They devoted significant attention to experimental research of developed portfolios and algorithm teams in real-time mode using the multi-processor computing complex SCIT-4 at the V. M. Glushkov Institute of Cybernetics of the National Academy of Sciences of Ukraine and to their comparative analysis. The authors have obtained estimates of the efficiency of algorithm unions, indicating that the team approach has significant advantages over algorithm portfolios. [ABSTRACT FROM AUTHOR]

Robots are widely used in present day situations. Since a robot consists of number of systems with different mechanisms, it needs to be planned and programmed systematically. Discrete Mathematics helps us in designing and functioning of a robotic system. For instance Robotic arm is a type of linkage and the study of which is a part of Discrete Geometry. Scheduling tasks to be completed by a set of machines use the concept of Bin-packing problem, which is a part of Discrete Optimization. Discussing functions like these, motion and path planning of the robotic system is the main concern of any industry to adapt new and modern technologies in its functioning. Literature surveys reveal that there a worldwide attempts to develop robotic systems with minimum errors and maximum efficiency. This Paper includes the usage of the Concepts of Discrete Mathematics to have a path planning for a Robotic System to work with high efficiency. [ABSTRACT FROM AUTHOR]

The integral column generation algorithm (ICG) was recently introduced to solve set partitioning problems involving a very large number of variables. This primal algorithm generates a sequence of integer solutions with decreasing costs, leading to an optimal or near-optimal solution. ICG combines the well-known column generation algorithm and a primal algorithm called the integral simplex using decomposition algorithm (ISUD). In this paper, we develop a generalized version of ICG, denoted I2CG, that can solve efficiently large-scale set partitioning problems with side constraints. This new algorithm can handle the side constraints in the reduced problem of ISUD, in its complementary problem, or in both components. Computational experiments on instances of the airline crew pairing problem (CPP) and the multidepot vehicle routing problem with time windows show that the latter strategy is the most efficient one and I2CG significantly outperforms basic variants of two popular column generation heuristics, namely, a restricted master heuristic and a diving heuristic. For the largest tested CPP instance with 1,761 constraints, I2CG can produce in less than one hour of computational time more than 500 integer solutions leading to an optimal or near-optimal solution. Summary of Contribution: In this paper, we develop a new integral column generation algorithm that can solve efficiently large-scale set partitioning problems with side constraints. The latter alter the quasi-integrality property needed for primal integral algorithms. The paper adds a methodological contribution remedying this issue. This remedy should, in our opinion, boost the use of primal exact methods, especially in the column generation context. The paper also has a computational contribution. Effectively, computational experiments on instances of the airline crew pairing problem and the multidepot vehicle routing problem with time windows are extensively discussed. We compare the proposed algorithm to basic variants of two popular column generation heuristics. [ABSTRACT FROM AUTHOR]

Feature extraction is an important part of perceptual hashing. How to compress the robust features of images into hash codes has become a hot research topic. Converting a two-dimensional image into a one-dimensional descriptor requires a higher computational cost and is not optimal. In order to maintain the internal feature structure of the original two-dimensional image, a new Bilinear Supervised Neighborhood Discrete Discriminant Hashing (BNDDH) algorithm is proposed in this paper. Firstly, the algorithm constructs two new neighborhood graphs to maintain the geometric relationship between samples and reduces the quantization loss by directly constraining the hash codes. Secondly, two small rotation matrices are used to realize the bilinear projection of the two-dimensional descriptor. Finally, the experiment verifies the performance of the BNDDH algorithm under different feature types, such as image original pixels and a Convolutional Neural Network (CNN)-based AlexConv5 feature. The experimental results and discussion clearly show that the proposed BNDDH algorithm is better than the existing traditional hashing algorithm and can represent the image more efficiently in this paper. [ABSTRACT FROM AUTHOR]

The vertex cover problem is a famous combinatorial problem, and its complexity has been heavily studied. It is known that it is hard to approximate to within any constant factor better than 2, while a 2-approximation for it can be trivially obtained. In this paper, new properties and new techniques are introduced which lead to approximation ratios smaller than 2 on special graphs; e.g. graphs for which their maximum cut values are less than 0.999|E|. In fact, we produce a (1.9997)-approximation ratio on graph G, where the (0.878)- approximation algorithm of the Goemans-Williamson for the maximum cut problem on G produces a value smaller than 0.877122|E|. [ABSTRACT FROM AUTHOR]

The paper solves the problem of constructing an evolutionary tree and the evolution of structures along it. This problem has long been posed and extensively researched; it is formulated and discussed below. As a result, we construct an exact cubic-time algorithm which outputs a tree with the minimum cost of embedding into it and of embedding it into a given network (Theorem 1). We construct an algorithm that outputs a minimum embedding of a tree into a network, taking into account incomplete linear sorting; the algorithm depends linearly on the number of nodes in the network and is exact if the sorting cost is not less than the sum of the duplication cost and the loss cost (Theorem 3). We construct an exact approximately quadratic-time algorithm which, for arbitrary costs of SCJ operations, solves the problem of reconstruction of given structures on any two-star tree (Theorem 4). We construct an exact algorithm which reduced the problem of DCJ reconstruction of given structures on any star to a logarithmic-length sequence of SAT problems, each of them being of approximately quadratic size (Theorem 5). The theorems have rigorous and complete proofs of correctness and complexity of the algorithms, and are accompanied by numerical examples and numerous explanatory illustrations, including flowcharts. [ABSTRACT FROM AUTHOR]

The efficient management of complex production systems is a challenge in today’s logistics. In the field of intelligent and sustainable logistics, the optimization of production batches, especially in the context of a rapidly changing product range, requires fast and precise computational solutions. This paper explores the potential of quantum computers for solving these problems. Traditional computational methods are often limited when it comes to optimizing complex logistics systems. In response to these challenges, the paper proposes the use of a hybrid algorithm that combines quantum technologies with classical computational methods. Such integration allows the computational power of both types of technologies to be harnessed, leading to faster and more efficient identification of optimal solutions. In this work, we consider the knapsack problem, a classic NP-hard optimization problem that is commonly used to verify the effectiveness of new algorithm construction methods. The algorithm presented is based on the Branch and Bound method and aims to ensure solution optimality in the context of the non-determinism of quantum computers. Within the algorithm, computations are performed alternately on a classical processor and a quantum processor. In addition, the lower and upper bounds of the objective function are computed in constant time using the D-Wave quantum machine. [ABSTRACT FROM AUTHOR]

Business research practice is witnessing a surge in the integration of predictive modeling and prescriptive analysis. We describe a modeling framework JANOS that seamlessly integrates the two streams of analytics, allowing researchers and practitioners to embed machine learning models in an end-to-end optimization framework. JANOS allows for specifying a prescriptive model using standard optimization modeling elements such as constraints and variables. The key novelty lies in providing modeling constructs that enable the specification of commonly used predictive models within an optimization model, have the features of the predictive model as variables in the optimization model, and incorporate the output of the predictive models as part of the objective. The framework considers two sets of decision variables: regular and predicted. The relationship between the regular and the predicted variables is specified by the user as pretrained predictive models. JANOS currently supports linear regression, logistic regression, and neural network with rectified linear activation functions. In this paper, we demonstrate the flexibility of the framework through an example on scholarship allocation in a student enrollment problem and provide a numeric performance evaluation. Summary of Contribution. This paper describes a new software tool, JANOS, that integrates predictive modeling and discrete optimization to assist decision making. Specifically, the proposed solver takes as input user-specified pretrained predictive models and formulates optimization models directly over those predictive models by embedding them within an optimization model through linear transformations. [ABSTRACT FROM AUTHOR]

The order reduction method is an important approach to optimize higher-order binary Markov random fields (HoMRFs), which are widely used in information theory, machine learning and image analysis. It transforms an HoMRF into an equivalent and easier reduced first-order binary Markov random field (RMRF) by elaborately setting the coefficients and auxiliary variables of RMRF. However, designing order reduction methods is difficult, and no previous study has investigated this design issue. In this paper, we propose an order reduction design framework to study this problem for the first time. Through study, we find that the design difficulty mainly lies in that the coefficients and variables of RMRF must be set simultaneously. Therefore, the proposed framework decomposes the design difficulty into two processes, and each process mainly considers the coefficients or auxiliary variables of RMRF. Some valuable properties are also proven. Based on our framework, a new family of 14 order reduction methods is provided. Experiments, such as synthetic data and image denoising, demonstrate the superiority of our method. [ABSTRACT FROM AUTHOR]

This article highlights synergies between quantum information science (QIS) and operations research for QIS-curious operations researchers (and vice versa), and the author challenges the community to discover more. History: This "Challenge" paper was invited by the Editor in Chief and based on the topics raised by the author at his plenary address at the 2022 INFORMS Computing Society Conference in Tampa, Florida. Funding: This material is based on work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Accelerated Research in Quantum Computing, Fundamental Algorithmic Research for Quantum Computing. This article has been authored by an employee of National Technology & Engineering Solutions of Sandia, LLC, under Contract DE-NA0003525 with the U.S. Department of Energy (DOE). [ABSTRACT FROM AUTHOR]

In this paper, we are proposing two novel swarm intelligence approaches for solving discrete problems. Two different continuous evolutionary algorithms inspired by the behaviour of elephants, namely elephant herding optimization and elephant swarm water search algorithm, are studied and analysed in order to propose discrete versions of the latter called discrete elephant herding optimization and discrete elephant swarm water search algorithm. As an illustration of how our proposals can work on discrete problems, a case study on association rule mining is carried out where the proposed discrete algorithms are modelled and applied on the problem in order to extract interesting association rules from large‐scale databases. Extensive experiments on eight different real‐life and relevant datasets with various sizes showed that both our proposals yield good results that compete and sometimes outperform state of the art algorithms. [ABSTRACT FROM AUTHOR]

This paper presents an algorithm for the optimization of the design of reinforced concrete (RC) road bridges, taking into account the current conditions in Cuba. The use of RC is chosen over the common solutions due to the current high economic cost of prestressing steel. The optimization problem is formulated to find the minimum direct cost, defining constraints based on the AASTHO-LRFD 2014 and NC-207:2019 standards. The algorithm is created to properly obtain practical solutions from the engineering point of view, involving the use of discrete variables. The optimization method used is Biogeography-Based Optimization. A sensitivity analysis of the parameters of this method is performed. The results indicate that the typical projects currently used can be considerably improved to enhance their economic indexes. Based on these results, some specific design recommendations are given. In addition, future research lines are suggested based on the deficiencies of the proposed methodology. [ABSTRACT FROM AUTHOR]

This paper proposes a novel optimization approach of the quantum-behaved binary firefly algorithm with a gravitational search algorithm (QBFA-GSA) for discrete feature optimization, which is utilized for the application of human activity recognition. The firefly algorithm (FA) and gravitational search algorithm (GSA) are recently introduced meta-heuristic algorithms that are efficient for optimizing the continuous solution set. The binarized version of the proposed approach enables it to optimize the discrete features and quantum behavior ensures the better diversity of the final optimized features. In the proposed QBFA-GSA approach, the features are optimized by following the combined advantageous attributes of FA and GSA in which the search space is initially explored by firefly agents until the current firefly finds the brighter firefly and further these agents adapt the attributes of GSA to complete the process. These optimized features are passed to deep neural networks (DNN) for the classification of human activities. Here, DNN models of deep convolutional neural networks (DCNN) and DCNN extended with residual blocks (DCNN-RB) are incorporated. The evaluation experiments for human activity recognition are conducted on a benchmark dataset of UCF-101, which is a composition of 101 different activities. The experimental results of the proposed QBFA-GSA approach are superlative to state-of-art techniques, which indicate that the proposed approach is efficient to optimize the features. [ABSTRACT FROM AUTHOR]

Optimization problems are prevalent in almost all areas and hence optimization algorithms are crucial for a myriad of real-world applications. Deterministic optimization algorithms tend to be computationally costly and time-consuming. Hence, heuristic and metaheuristic algorithms are more favoured as they provide near-optimal solutions in an acceptable amount of time. Swarm intelligence algorithms are being increasingly used for optimization problems owing to their simplicity and good performance. The Dragonfly Algorithm (DA) is one which is inspired by the swarming behaviours of dragonflies, and it has been proven to have a superior performance than other algorithms in multiple applications. Hence, it is worth considering its application to the traveling salesman problem which is a predominant discrete optimization problem. The original DA is only suitable for solving continuous optimization problems and, although there is a binary version of the algorithm, it is not easily adapted for solving discrete optimization problems like TSP. We have previously proposed a discrete adapted DA algorithm suitable for TSP. However, it has low effectiveness, and it has not been used for large TSP problems. In this paper, we propose an optimized discrete adapted DA by using the steepest ascent hill climbing algorithm as a local search. The algorithm is applied to a TSP problem modelling a package delivery system in the Kuala Lumpur area and to benchmark TSP problems, and it is found to have a higher effectiveness than the discrete adapted DA and some other swarm intelligence algorithms. It also has a higher efficiency than the discrete adapted DA. [ABSTRACT FROM AUTHOR]

Unsupervised hashing has been extensively applied in large-scale multi-modal retrieval by mapping original data from heterogeneous modalities into unified binary codes. However, there still remain challenges especially how to balance the individual modality-specific representations and common representation preserving intrinsic linkages among heterogeneous modalities. In this paper, we propose a novel fast U nsupervised M ulti-modal H ashing based on P iecewise L earning, denoted as UMHPL , to deal with the mentioned issue. Initially, we formulate the problem as matrix factorization to derive the individual modality-specific latent representations and common latent representation with consensus matrices in a brief time. To maintain the integrality of multi-modal data, we integrate them by adaptive weight factors and nuclear norm minimization. Subsequently, we establish a connection between the individual modality-specific latent representations and common latent representation based on the piecewise hash learning framework to reinforce the discriminative competency of model, which leads the hash codes more compact. Finally, an effective discrete optimization algorithm in mathematical logic and functional analysis is proposed. Comprehensive experiments on Wiki, MIRFlirck, NUS-WIDE, and MSCOCO datasets demonstrate the superior performance of UMHPL to state-of-the-art hashing methods. [ABSTRACT FROM AUTHOR]

Purpose: In this article, a practical design methodology is proposed for discrete sizing optimization of high-rise concrete buildings with a focus on large-scale and real-life structures. Design/methodology/approach: This framework relies on a computationally efficient approximation of the constraint and objective functions using a radial basis function model with a linear tail, also called the combined response surface methodology (RSM) in this article. Considering both the code-stipulated constraints and other construction requirements, three sub-optimization problems were constructed based on the relaxation model of the original problem, and then the structural weight could be automatically minimized under multiple constraints and loading scenarios. After modulization, the obtained results could meet the discretization requirements. By integrating the commercially available ETABS, a dedicated optimization software program with an independent interface was developed and details for practical software development were also presented in this paper. Findings: The proposed framework was used to optimize different high-rise concrete buildings, and case studies showed that material usage could be saved by up to 12.8% compared to the conventional design, and the over-limit constraints could be adjusted, which proved the feasibility and effectiveness. Originality/value: This methodology can therefore be applied by engineers to explore the optimal distribution of dimensions for high-rise buildings and to reduce material usage for a more sustainable design. [ABSTRACT FROM AUTHOR]

In the last decade, decision diagrams (DDs) have been the basis for a large array of novel approaches for modeling and solving optimization problems. Many techniques now use DDs as a key tool to achieve state-of-the-art performance within other optimization paradigms, such as integer programming and constraint programming. This paper provides a survey of the use of DDs in discrete optimization, particularly focusing on recent developments. We classify these works into two groups based on the type of diagram (i.e., exact or approximate) and present a thorough description of their use. We discuss the main advantages of DDs, point out major challenges, and provide directions for future work. [ABSTRACT FROM AUTHOR]

The minimum stretch spanning tree problem for a connected graph G is to find a spanning tree T of G such that the maximum distance in T between two adjacent vertices of G is minimized, where the minimum value is called the tree-stretch of G. This paper presents the tree-stretch of a graph constructed by the Cartesian product of two trees. This result is a generalization of the result for the grid graphs obtained by Lin and Lin (L. Lin, Y. Lin, The minimum stretch spanning tree problem for typical graphs, Acta Mathematicae Applicatae Sinica, English Series, 37(3) (2021) 510–522). Then, we give the tree-stretch of the k -th power of a tree. [ABSTRACT FROM AUTHOR]

[Display omitted] • Proposed a novel two-step label embedding semantic-guided hashing method. • Proposed a fast alternative optimization strategy to address the non-convex problem. • Evaluated the effectiveness of the proposed method via three famous datasets. Hashing technologies have been widely used for information retrieval tasks due to their efficient retrieval and storage capabilities. Generally, most of the current supervised learning only utilizes labels to construct a binary similarity matrix of instance pairs and ignores the rich semantic information contained in the labels. Indeed, the reason why supervised hashing is better than unsupervised hashing is that the labels itself has strong discriminative information. Therefore, how to effectively explore the label information is one of the ways to improve the performance of retrieval tasks. In addition, existing hashing methods have the problems of high time consumption and weak scalability when facing large-scale data. To remedy these problems, in this paper, we present a flexible two-step label embedding hashing method named L abel E mbedding S emantic- G uided H ashing (LESGH). In the first step, LESGH leverages an asymmetric discrete learning framework to learn discriminative compact hash codes only from label information, and adds the constraints of bit-balance and bit-decorrelation to boost the quality of the hash code generation. In the second step, LESGH learns the hash projection function through the generated hash codes in the first step. Moreover, an effective and fast iterative discrete optimization algorithm is presented to solve the discrete problem instead of using the relaxation-based scheme. In doing so, we can not only simplify the optimization process, but also easily scale to large-scale data. We conduct several experiments on three public datasets, i.e., WIKI, MIRFlickr and NUS-WIDE, demonstrate that LESGH can improve the retrieval performance over the compared state-of-the-art baselines. [ABSTRACT FROM AUTHOR]

This paper presents several strategies to tune the parameters of metaheuristic methods for (discrete) design optimization of reinforced concrete (RC) structures. A novel utility metric is proposed, based on the area under the average performance curve. The process of modelling, analysis and design of realistic RC structures leads to objective functions for which the evaluation is computationally very expensive. To avoid costly simulations, two types of surrogate models are used. The first one consists of the creation of a database containing all possible solutions. The second one uses benchmark functions to create a discrete sub-space of them, simulating the main features of realistic problems. Parameter tuning of four metaheuristics is performed based on two strategies. The main difference between them is the parameter control established to perform partial assessments. The simplest strategy is suitable to tune good "generalist" methods, i.e., methods with good performance regardless the parameter configuration. The other one is more expensive, but is well suited to assess any method. Tuning results prove that Biogeography-Based Optimization, a relatively new evolutionary algorithm, outperforms other methods such as GA or PSO for such optimization problems, due to its particular approach of applying recombination and mutation operators. [ABSTRACT FROM AUTHOR]

Due to the exponential growth of multimedia data, multi-modal hashing as a promising technique to make cross-view retrieval scalable is attracting more and more attention. However, most of the existing multi-modal hashing methods either divide the learning process unnaturally into two separate stages or treat the discrete optimization problem simplistically as a continuous one, which leads to suboptimal results. Recently, a few discrete multi-modal hashing methods that try to address such issues have emerged, but they still ignore several important discrete constraints (such as the balance and decorrelation of hash bits). In this paper, we overcome those limitations by proposing a novel method named “Enhanced Discrete Multi-modal Hashing (EDMH)” which learns binary codes and hashing functions simultaneously from the pairwise similarity matrix of data, under the aforementioned discrete constraints. Although the model of EDMH looks a lot more complex than the other models for multi-modal hashing, we are actually able to develop a fast iterative learning algorithm for it, since the subproblems of its optimization all have closed-form solutions after introducing a couple of auxiliary variables. Our experimental results on three real-world datasets have revealed the usefulness of those previously ignored discrete constraints and demonstrated that EDMH not only performs much better than state-of-the-art competitors according to several retrieval metrics but also runs much faster than most of them. [ABSTRACT FROM AUTHOR]

This paper proposes two novel approaches to perform more suitable sensitivity analyses for discrete topology optimization methods. To properly support them, we introduce a more formal description of the Bi-directional Evolutionary Structural Optimization (BESO) method, in which the sensitivity analysis is based on finite variations of the objective function. The proposed approaches are compared to a naive strategy; to the conventional strategy, referred to as First-Order Continuous Interpolation (FOCI) approach; and to a strategy previously developed by other researchers, referred to as High-Order Continuous Interpolation (HOCI) approach. The novel Woodbury Sensitivity (WS) approach provides exact sensitivity values and is a better alternative to HOCI. Although HOCI and WS approaches may be computationally prohibitive, they provide useful expressions for a better understanding of the problem. The novel Conjugate Gradient Sensitivity (CGS) approach provides sensitivity values with arbitrary precision and is computationally viable for a small number of steps. The CGS approach is a better alternative to FOCI since, for appropriate initial conditions, it is always more accurate than the conventional strategy. The standard compliance minimization problem with volume constraint is considered to illustrate the methodology. Numerical examples are presented together with a broad discussion about BESO-type methods. [ABSTRACT FROM AUTHOR]

Supervised cross-modal hashing has attracted much attention. However, there are still some challenges, e.g., how to effectively embed the label information into binary codes, how to avoid using a large similarity matrix and make a model scalable to large-scale datasets, how to efficiently solve the binary optimization problem. To address these challenges, in this paper, we present a novel supervised cross-modal hashing method, i.e., scalaBle Asymmetric discreTe Cross-modal Hashing, BATCH for short. It leverages collective matrix factorization to learn a common latent space for the labels and different modalities, and embeds the labels into binary codes by minimizing a distance-distance difference problem. Furthermore, it builds a connection between the common latent space and the hash codes by an asymmetric strategy. In the light of this, it can perform cross-modal retrieval and embed more similarity information into the binary codes. In addition, it introduces a quantization minimization term and orthogonal constraints into the optimization problem, and generates the binary codes discretely. Therefore, the quantization error and redundancy may be much reduced. Moreover, it is a two-step method, making the optimization simple and scalable to large-scale datasets. Extensive experimental results on three benchmark datasets demonstrate that BATCH outperforms some state-of-the-art cross-modal hashing methods in terms of accuracy and efficiency. [ABSTRACT FROM AUTHOR]

Hashing methods have been extensively applied to efficient multimedia data indexing and retrieval on account of the explosion of multimedia data. Cross-modal hashing usually learns binary codes by mapping multi-modal data into a common Hamming space. Most supervised methods utilize relation information like class labels as pairwise similarities of cross-modal data pair to narrow intra-modal and inter-modal gap. In this paper, we propose a novel supervised cross-modal hashing method dubbed Subspace Relation Learning for Cross-modal Hashing (SRLCH), which exploits relation information of labels in semantic space to make similar data from different modalities closer in the low-dimension Hamming subspace. SRLCH preserves the modality relationships, the discrete constraints and nonlinear structures, while admitting a closed-form binary codes solution, which effectively enhances the training efficiency. An iterative alternative optimization algorithm is developed to simultaneously learn both hash functions and unified binary codes. With these binary codes and hash functions, we can index multimedia data and search them in an efficient way. Evaluations in two cross-modal retrieval tasks on several widely-used datasets show that the proposed SRLCH outperforms most cross-modal hashing methods. Theoretical analysis also illustrates reasons for our method’s promotion in subspace relation learning. [ABSTRACT FROM AUTHOR]

Portal frames are single-story frame buildings including columns and rafters, and their rafters can be either curved or pitched. These are used widely in the construction of industrial buildings, warehouses, gyms, fire stations, agricultural buildings, hangars, etc. The construction cost of these frames considerably depends on their weight. In the present research, the discrete optimum design of two types of portal frames including planar steel Curved Roof Frame (CRF) and Pitched Roof Frame (PRF) with tapered I-section members are presented. The optimal design aims to minimize the weight of these frame structures while satisfying some design constraints based on the requirements of ANSI/AISC 360-16 and ASCE 7-10. Four population-based metaheuristic optimization algorithms are applied to the optimal design of these frames. These algorithms consist of Teaching-Learning-Based Optimization (TLBO), Enhanced Colliding Bodies Optimization (ECBO), Shuffled Shepherd Optimization Algorithm (SSOA), and Water Strider Algorithm (WSA). Two main objectives are followed in this paper. The first one deals with comparing the optimized weight of the CRF and PRF structures with the same dimensions for height and span in two different span lengths (16.0 m and 32.0 m), and the second one is related to comparing the performance of the considered metaheuristics in the optimum design of these portal frames. The obtained results reveal that CRF is more economical than PRF in the fair comparison. Moreover, comparing the results acquired by SSOA with those of other considered metaheuristics reveals that SSOA has better performance for the optimal design of these portal frames. [ABSTRACT FROM AUTHOR]

The paper is based on using methods of continuous mathematics in discrete problems. Three new approaches to solving scheduling theory problems are considered, namely, a metric approach, an interpolation approach, and a combined one (metric interpolation). Metric interpolation is a mix of the other two approaches and combines their advantages. Each of these approaches permits one to reduce the time required for solving the corresponding problems and calculate the values of the guaranteed absolute error of the objective function. [ABSTRACT FROM AUTHOR]

Software defined network (SDN) has shown significant advantages in numerous real-life aspects with separating the control plane from the data plane that provides programmable management for networks. However, with the increase in the network size, a single controller of SDN imposes considerable limitations on various features. Therefore, in networks with immense scalability, multiple controllers are essential. Specifying the optimal number of controllers and their deployment place is known as the controller placement problem (CPP), which affects the network's performance. In the present paper, a novel controller placement algorithm has been introduced using the advantages of nature-inspired optimization algorithms and network portioning. Firstly, the Manta Ray Foraging Optimization (MRFO) and Salp Swarm Algorithm (SSA) have been discretized to solve CPP. Three new operators comprising a two-point swap, random insert, and half points crossover operators were introduced to discretized the algorithms. Afterward, the resulting discrete MRFO and SSA algorithms were hybridized in a promoting manner. Next, the proposed discrete algorithm has been evaluated on six well-known software-defined networks with a different number of controllers. In addition, the networks have been chosen from various sizes to evaluate the scalability of the proposed algorithm. The proposed algorithm has been compared with several other state-of-the-art algorithms regarding network propagation delay and convergence rate in experiments. The findings indicated the effectiveness of the contributions and the superiority of the proposed algorithm over the competitor algorithms. [ABSTRACT FROM AUTHOR]

A major issue while conceiving or parameterizing an optimization heuristic is to ensure an appropriate balance between exploitation and exploration of the search. Evolution strategies and neighborhood-based metaheuristics constitute relevant high-level frameworks, which ease the problem solving but are often complex to configure. Moreover, their effective behavior, according to the particularities of the search landscapes, remains difficult to grasp. In this paper, we deeply investigate the sampled walk search algorithm, which is a local search equivalent of the (1 , λ) -evolution strategy, considering that the neighborhood relation describes mutation possibilities. We specifically designed experiments to better understand the behavior of such a strategy offering a fine way to deal with the exploration versus exploitation dilemma. The main contribution is the analysis of search trajectories by evaluating and visualizing both their width (exploration) and their height (exploitation). More generally, we aim at bringing insights about the behavior of the (1 , λ) -ES in a discrete optimization context and within a fitness landscape perspective. [ABSTRACT FROM AUTHOR]

To adapt to the uncertainty of the real environment and solve the problem of high efficiency and high quality, this study comprehensively considers a variety of uncertainty factors, focusing on modeling and solving a hybrid flow-shop scheduling problem by two-stage stochastic programming (HFSP-TSP). First, this paper uses a two-stage scenario tree to describe the uncertain factors, the probabilities and values are obtained under different discrete production scenarios, and stochastic programming theory is used to formulate a mixed-integer linear programming (MILP) model for HFSP-TSP. Second, based on a general discrete optimization algorithm framework, that is, pointer-based discrete differential evolution (PDDE) algorithm, a novel variant (H-PDDE) is proposed for effectively solving the HFSP-TSP. It adopts a permutation scheduling decoding method and introduces three new improvement strategies: the strategy of inconsistent code length of individuals in the population, adding local search in discrete mutation operation, using a heuristic algorithm to generate the initial population. Finally, computational experiments were conducted to illustrate the proposed mathematical model and optimization algorithm. The computational results show that the H-PDDE can solve the HFSP-TSP more effectively than existing algorithms and conventional PDDE variants. The stochastic programming model is increasingly superior to the deterministic model in an uncertain environment. The source code of the H-PDDE algorithm and its data files can be found at https://github.com/huangyiping-ai/H-PDDE-algorithm.git , which is publicly available. [ABSTRACT FROM AUTHOR]

• A user-friendly Abaqus/CAE plug-in tool is developed to rapidly estimate crashworthiness by inputting geometry parameters of these multi-cell tubes. • The offset and zoom can optimize the crashworthiness of the 0th order hybrid tubes. • The crashworthiness of first-order hybrid tubes can be enhanced by self-similar inspired double space-filling. • COPRAS and discrete optimization method are used for design and optimization. Self-similar inspired multi-cell tubes have been widely used in energy absorbing devices due to their flexible and feasible design strategy. In this paper, a novel multi-cell hexagonal tube is constructed by space-filling and cross-section topological design of self-similar inspired multi-cell tubes. A user-friendly plug-in tool is developed in Abaqus/CAE to rapidly estimate the crashworthiness of these multi-cell tubes by taking as input the geometry of these multi-cell tubes. The discrete robust optimization algorithm and multi-object decision-making method (COPRAS) are used to select the optimal cross-section topology of the self-similar inspired multi-cell hexagonal tubes. In addition, the effect of different space-filling strategies and the number and layout of ribs on the crashworthiness of these multi-cell tubes are studied. The results show that the crashworthiness of these multi-cell structures can be further improved by double space-filling. Hence, these design strategies and optimization methods proposed in this paper can be used in the topology optimization of the multi-cell tubes. [ABSTRACT FROM AUTHOR]

Over the last few years, social recommendation has attracted tremendous attention due to the ever-growing online social platform such as Twitter and Facebook. However, as the number of users increases rapidly, recommendation efficiency has become the bottleneck of many existing social recommender systems due to the computation and storage of real-valued models. For addressing the efficiency problem, recent researches resolve it by introducing hashing technique into social recommender systems. By mapping real values to discrete values, the computational speed is guaranteed as well as the storage cost is reduced. Nevertheless, these methods suffer from two critical limitations: (1) The inevitable quantization loss brought by hash function decreases recommendation accuracy to a certain extent. (2) The original social relations contain massive noise that may result in sub-optimal accuracy of recommendation without considering the fact that people can only pay attention to a small number of their friends. Therefore, to tackle the above limitations and have a better tradeoff between accuracy and efficiency, in this paper, we propose a novel social recommendation method called Discrete Limited Attentional Collaborative Filtering (DLACF), which models recommendation objective with limited attention as a constrained mix-integer optimization problem. Since the original problem is NP-hard, we further devise a computationally efficient optimization algorithm to learn the binary codes as well as to estimate the best influential friends. Experimental results conducted on two real-world datasets demonstrate the effectiveness of our proposed model, achieving the averaged improvement of 118.7% and 54.7% compared to state-of-the-art discrete methods. [ABSTRACT FROM AUTHOR]

Fuel cell longevity management is the key issue for the vehicle application as it is extremely susceptible to operating circumstances. Hybridizing the fuel cells with the power batteries forming a fuel cell hybrid electric vehicle (FCHEV) is prospective solution. However, the lifetime competition mechanism existing between the two different power sources makes it difficult to balance the system lifetime economy in real-time against driving conditions. Therefore, this paper proposes a new discrete optimization approach derived from min–max game theory to describe the mapping relationship between the output power of the power source with the complicated operating conditions so as to realize the real-time aging quantification of both the fuel cell and batteries in FCHEVs. Meanwhile, under the proposed discrete optimization method, the degradation interaction between fuel cell and battery is well established to decouple the lifetime competition between the two power sources with the consideration of system economy. In addition, an empirical-data-driven battery lifetime real-time model is developed to describe the battery degradation regarding its life stages. The real-time performance of the proposed aging model, as well as the discrete optimization approach, is verified by hardware in the loop experiment benefiting in both fuel cell and battery degradation reduction and energy consumption economy. • A real-time battery lifetime model is designed to be used in vehicle system. • The lifetime competition mechanism between the fuel cell and battery is investigated. • Hydrogen safety is considered by avoiding rapidly hydrogen tank pressure change. • Fuel cell lifetime is extended by keeping it working in high-efficiency region. [ABSTRACT FROM AUTHOR]

• We used quantum computing to optimize model predictive control of building HVAC systems. • We formulated mixed-integer non-linear programming as quadratic unconstrained binary optimization for quantum computer. • Solution of quantum computing was almost the same as traditional optimization method, but computing time was greatly reduced. • Quantum computing had the potential to solve large-scale non-linear optimization problems for building energy systems. Buildings contribute to more than 70% of overall U.S. electricity usage and greenhouse gas (GHG) emissions. HVAC systems in buildings often consume more than 40% of the total building energy usage. To reduce such high energy use, numerous control strategies including optimal and predictive controls have been developed and demonstrated. To achieve a near real-time solution, most previous research has simplified the non-linearity of building thermodynamics and provided an approximate optimal solution. The future HVAC control optimizes more connected devices in buildings, which requires a rapid and accurate response, not only to the building itself but also to the grid signals. It also poses the challenge of solving non-linear problems with discrete variables. With the recent development of quantum computers, this has become feasible. In this paper, we developed a new optimization solution based on quantum annealing for model predictive control (MPC) of a rooftop unit (RTU). Compared to traditional optimization methods, we obtained similar solutions with less than 2% differences and improved computational speed from hours to seconds. We also demonstrated an 80% reduction in total electricity consumption and a 21% reduction in electricity bills by considering day-ahead price time-of-use demand response signals. Quantum computing has proven capable of solving large-scale non-linear discrete optimization problems for building energy systems. [ABSTRACT FROM AUTHOR]

· COPRAS and discrete optimization method are proposed for design and optimization. · COPRAS effectively selects optimal solution from many conflicting design criteria. · Discrete optimization can circularly make mean analysis in optimization process. · The crashworthiness can be improved by filling the lattice in corner regions. Thin-walled tubes filled with ultra-light materials have attracted much attention due to excellent energy absorption characteristics. With the development of additive manufacturing technology, it is allowed to manufacture structures with complex geometry shapes as new filled materials. In this study, complex proportional assessment (COPRAS) and discrete optimization algorithm were proposed to design and optimize the topology of thin-walled tubes filled with lattice structures. Firstly, the finite element model verified by experiment was adopted to investigate the influence of cross-sectional configurations and octet truss lattice filling distributions on crashworthiness of hybrid structures. The results show that the cross-sectional configuration has a greater effect on specific energy absorption (SEA) and the lattice filling distribution has a greater effect on peak crushing force (PCF). Then, COPRAS was used to sort the crashworthiness of hybrid structures with different topologies and select the optimal solution. It was found that C3-L4 structure had the best crashworthiness among all design schemes, indicating that the better crashworthiness can be obtained by filling the lattice in the four corner regions of tube or increase the number of cells in corner regions. Finally, the discrete optimization algorithm based on successive orthogonal arrays was adopted to further improve the crashworthiness of hybrid structure. It was found that the thin-walled tubes with different thickness had greater energy absorption capacity than those with the same thickness. Hence, the method proposed in this paper can become an effective way for topology optimization of crashworthiness. [Display omitted] [ABSTRACT FROM AUTHOR]

The Optimal Reactive Power Flow (ORPF) problem has been used as an important computational tool for power system planning and operation. Its mixed-discrete version (DORPF) is formulated as a non-convex, non-linear optimization problem with discrete and continuous variables, which is aimed at minimizing the transmission losses while meeting the power demand and enforcing operational and physical limits of the system. Although the DORPF problem has been solved by a myriad of methods, some of them present regularization problems associated with poor matrix-conditioning in the optimal solution, some do not provide for rapid infeasibility detection and some do not provide effective ways for handling the discrete nature of the control variables. Although some of these complicating issues have been tackled separately in the literature by various studies, a method that addresses all these issues has not yet been proposed for solving the DORPF problem. In this paper, an integration of optimization approaches is proposed for handling all such complicating issues. The basis of this approach is a primal–dual penalty-interior-point method, which integrates the good properties of penalty methods (e.g. regularization effects on the constraints and rapid infeasibility detection) and interior-point methods (e.g. scalability and good convergence behavior), without suffering from their disadvantages. In the proposed approach, this method is integrated with a sinusoidal penalty function method for handling the discrete nature of the control variables of the DORPF problem, together with a specific inertia correction strategy designed to avoid local maximizers associated with such a penalty function. Numerical tests carried out with the IEEE 30-, 57-, 118- and 300-bus systems focus on showing that all the complicating issues have been addressed by the proposed method. Comparisons with the results obtained by interior-point methods are also provided. • An integration of approaches is proposed for handling mixed-discrete optimization problems. • A Primal–dual penalty-interior-point method is integrated with a sinusoidal penalty method and an inertia correction strategy. • The approach handles discrete variables, poor matrix-conditioning and has rapid infeasibility detection. • The approach is applied to solving a mixed-Discrete version of the Optimal Reactive Power Flow problem. • Systems up to 300 buses are solved and comparisons with interior-point methods are provided. [ABSTRACT FROM AUTHOR]

Stochastic methods attempt to solve problems that cannot be solved by deterministic methods with reasonable time complexity. Optimization algorithms benefit from stochastic methods; however, they do not guarantee to obtain the optimal solution. Many optimization algorithms have been proposed for solving problems with continuous nature; nevertheless, they are unable to solve discrete or binary problems. Adaptation and use of continuous optimization algorithms for solving discrete problems have gained growing popularity in recent decades. In this paper, the binary version of a recently proposed optimization algorithm, Battle Royale Optimization, which we named BinBRO, has been proposed. The proposed algorithm has been applied to two benchmark datasets: the uncapacitated facility location problem, and the maximum-cut graph problem, and has been compared with 6 other binary optimization algorithms, namely, Particle Swarm Optimization, different versions of Genetic Algorithm, and different versions of Artificial Bee Colony algorithm. The BinBRO-based algorithms could rank first among those algorithms when applying on all benchmark datasets of both problems, UFLP and Max-Cut. • We proposed a binary version of Battle Royale Optimization algorithm named BinBRO. • BinBRO performs as good as or better than existing binary optimization algorithms. • BinBRO provides a good balance between exploration and exploitation. [ABSTRACT FROM AUTHOR]

• Sensitivity of the optimal design found on a large-scale steel frame to the size of the discrete design domain is investigated. • The size of the discrete design space is adjusted through member grouping modifications and limiting the available set of discrete cross-sections. • A recently develop metaheuristic optimization algorithm is employed to explore and (subsequently) exploit the large solution space of candidate designs. • Several combinations of member groups and standard steel profile lists were numerically tested on a large-scale (real-world) 3D steel frame. • A reduction of approximately 33% in the optimal weight was observed between member group and steel profile list combinations generating the smallest and largest design spaces, respectively. This paper examines the effect of member grouping and selected pool size of discrete cross-sections on the optimal design of a large-scale steel frame structure. Member grouping is commonly applied to structural optimization problems to significantly reduce the solution space of candidate designs and improve the efficiency and robustness of the search to achieve near-optimum solutions. At the same time, discrete sets of cross-sectional steel shapes (profile lists) assigned to a particular member group are often limited to a subset of cross-sections to further limit the search space and ensure practicality in the final design. However, for large-scale structural systems (e.g., tall buildings), limiting the number of member groups coupled with the exclusion of lighter cross-sectional shapes may significantly impact the quality of the optimal solution (i.e., weight of the frame). This work presents a case study of a large-scale three-dimensional (3D) steel frame to evaluate the sensitivity of the optimal design to practical combinations of member groups and steel profile lists used in multi-story steel frames. A recently developed metaheuristic search algorithm was applied to the steel frame and independent optimization experiments were performed for 16 unique member grouping and profile list combinations (cases) to quantify their influence on the variability and quality of the optimal design. Results reveal a 33% difference in the optimal (final) weight between member group and profile list combinations producing the smallest and largest solution spaces. Yet, the lightest design (corresponding to the largest solution space) produced a greater number of unique steel shapes and required significantly higher computational cost. [ABSTRACT FROM AUTHOR]

• Different from the majority of related methods, DOCH is a discrete one. • By keeping the binary constraints, quantization error can be avoided. • By preserving the similarity in Hamming space, DOCH learns accurate hash codes. • Both time and space complexity are low and acceptable. • Extensive experiments demonstrate the superiority of DOCH. With the prevalence of multimedia content on the Web which usually continuously comes in a stream fashion, online cross-modal hashing methods have attracted extensive interest in recent years. However, most online hashing methods adopt a relaxation strategy or real-valued auxiliary variable strategy to avoid complex optimization of hash codes, leading to large quantization errors. In this paper, based on Discrete Latent Factor model-based cross-modal Hashing (DLFH), we propose a novel cross-modal online hashing method, i.e., Discrete Online Cross-modal Hashing (DOCH). To generate uniform high-quality hash codes of different modal, DOCH not only directly exploits the similarity between newly coming data and old existing data in the Hamming space, but also utilizes the fine-grained semantic information by label embedding. Moreover, DOCH can discretely learn hash codes by an efficient optimization algorithm. Extensive experiments conducted on two real-world datasets demonstrate the superiority of DOCH. [ABSTRACT FROM AUTHOR]