Search

Applying generative adversarial networks (GANs) to text-related tasks is challenging due to the discrete nature of language. One line of research resolves this issue by employing reinforcement learning (RL) and optimizing the next-word sampling policy directly in a discrete action space. Such methods compute the rewards from complete sentences and avoid error accumulation due to exposure bias. Other approaches employ approximation techniques that map the text to continuous representation in order to circumvent the non-differentiable discrete process. Particularly, autoencoder-based methods effectively produce robust representations that can model complex discrete structures. In this article, we propose a novel text GAN architecture that promotes the collaborative training of the continuous-space and discrete-space methods. Our method employs an autoencoder to learn an implicit data manifold, providing a learning objective for adversarial training in a continuous space. Furthermore, the complete textual output is directly evaluated and updated via RL in a discrete space. The collaborative interplay between the two adversarial trainings effectively regularize the text representations in different spaces. The experimental results on three standard benchmark datasets show that our model substantially outperforms state-of-the-art text GANs with respect to quality, diversity, and global consistency.

Optimizing the Content Delivery Network system configuration has been addressed as an interesting problem for the system owners. They want to minimize the investment cost while guaranteeing their system's quality. Several works have resolved this problem as a single-objective optimization (SOO) problem with heuristic methods. These approaches usually aggregate the objectives into a scalar function and resolve the problem with SOO algorithms. A typical drawback of these approaches is that they cannot capture the trade-off between the objectives, which usually leads to a sub-optimal solution. To overcome this drawback, this paper considers the problem as a discrete multiobjective problem and resolves it with meta-heuristic techniques, namely Bayesian optimization (BO) and evolutionary methods. More importantly, we also propose an empirical method to improve the convergence speed of the standard BO methods in discrete space. Our experiments show that our proposed method can dramatically improve the rate of convergence. Moreover, we apply our method to a real CDN system and compare our solution with the system's current solution. Our experimental results show that our proposed solution can save about 39% of the current cost with the same internal traffic.

Humans can communicate emotions through a plethora of facial expressions, each with its own intensity, nuances and ambiguities. The generation of such variety by means of conditional GANs is limited to the expressions encoded in the used label system. These limitations are caused either due to burdensome labelling demand or the confounded label space. On the other hand, learning from inexpensive and intuitive basic categorical emotion labels leads to limited emotion variability. In this paper, we propose a novel GAN-based framework that learns an expressive and interpretable conditional space (usable as a label space) of emotions, instead of conditioning on handcrafted labels. Our framework only uses the categorical labels of basic emotions to learn jointly the conditional space as well as emotion manipulation. Such learning can benefit from the image variability within discrete labels, especially when the intrinsic labels reside beyond the discrete space of the defined. Our experiments demonstrate the effectiveness of the proposed framework, by allowing us to control and generate a gamut of complex and compound emotions while using only the basic categorical emotion labels during training. Our source code is available at https://github.com/stefanodapolito/GANmut.

In this paper, we present a gradient descent and Metropolis-Hastings (MH) principle based low-complexity, highly parallelizable, near-optimal MIMO demodulation framework. The optimal maximum-likelihood (ML) demodulation is a discrete optimization problem and is computationally infeasible for large MIMO dimensions. Many continuous-relaxed versions of ML, such as least-squares (LS) demodulation, have closed-form solutions but are highly suboptimal to ML. However, the continuous surface of, for example, LS cost function can serve as a proxy for the discontinuous staircase-like surface of the ML cost function. The key idea in this work is to search for the ML solution by performing an MH random walk around the gradient-descent direction of the LS surface (scheme referred hereafter as MHGD). In MH algorithm, a Markov Chain Monte Carlo (MCMC) technique, first a random perturbation over the previous state is proposed. Then, the proposal is accepted/rejected with non-zero probability. In MHGD, gradient-descent and MH work synergistically-gradient-descent shows the likely directions to MH making it very efficient and MH navigates the discrete space, which the gradient-descent alone cannot. To achieve near-ML performance, MHGD uses a preconditioner on the gradient and channel-matrix based covariance for the MH random step. The complexity of MHGD algorithm is comparable or lower than the well-known low-complexity, near-ML algorithms. But more importantly, MHGD is highly parallelizable, has simple vectorizable operations, scalable to very large MIMO due to the use of gradients, and can also be extended to distributed computing paradigm. Simulations demonstrate the aforementioned strengths and salient features of near-ML MHGD algorithm.

Graph Convolutional Network (GCN) is adopted to tackle the problem of convolution operation in non-Euclidean space. Previous works on GCN have made some progress, however, one of their limitations is that the design of Adjacency Matrix (AM) as GCN input requires domain knowledge and such process is cumbersome, tedious and error-prone. In addition, entries of a fixed Adjacency Matrix are generally designed as binary values (i.e., ones and zeros) which can not reflect the real relationship between nodes. Meanwhile, many applications require a weighted and dynamic Adjacency Matrix instead of an unweighted and fixed AM, and there are few works focusing on designing a more flexible Adjacency Matrix. To that end, we propose an end-to-end algorithm to improve the GCN performance by focusing on the Adjacency Matrix. We first provide a calculation method called node information entropy to update the matrix. Then, we perform the search strategy in a continuous space and introduce the Deep Deterministic Policy Gradient (DDPG) method to overcome the drawback of the discrete space search. Finally, we integrate the GCN and reinforcement learning into an end-to-end framework. Our method can automatically define the Adjacency Matrix without prior knowledge. At the same time, the proposed approach can deal with any size of the matrix and provide a better AM for network. Four popular datasets are selected to evaluate the capability of our algorithm. The method in this paper achieves the state-of-the-art performance on Cora and Pubmed datasets, with the accuracy of 84.6% and 81.6% respectively.

In order to improve the performance of model predictive torque control (MPTC) for induction motor (IM), this paper proposed the use of discrete space vector modulation (DSVM). In traditional MPTC, the application of one voltage vector is performed during the whole control cycle, which requires a small sampling time for proper operation. The application of the voltage vector can be performed in a discrete manner by using the DSVM to increase the sampling time required for the control. Nevertheless, DSVM increase considerable the computational burden of the controller, for this reason, this paper proposed a methodology to reduce the number of voltage vectors of DSVM evaluated in MPTC to keep computational burden feasible. Simulation results on a commercial IM are presented to prove the effectiveness of the proposed method.

An algorithm for calculating the number of broken interatomic bonds for a hexagonal close-packed crystal lattice cut by an arbitrary plane is proposed. This challenge occurs in surface energy calculation, modeling strength and surface properties, the crystal growth simulation, and other problems of solid-state and surface physics. The dimension and complexity of this problem are so great that it cannot be solved without involving a computer with a proper software. In the paper, the geometry of the HCP lattice was analyzed. This made it possible to represent the lattice as an integer discrete space and to construct an integer metric in it. Such representation allowed us to develop an exact, fully integer algorithm for solving the problem. The algorithm was implemented as a PC application. In addition to the number of broken bonds, the application calculates the reticular density, builds 3D models of the HCP lattice cross-section by a given plane. The analysis of the time complexity of the algorithm and test results are also given.

Aiming at the problem of green logistics vehicle path optimization with the smallest carbon dioxide emissions, this paper proposes the Hybrid Discrete Differential Evolution (HDDE) algorithm. For the HDDE algorithm, adopt the integer-arranged encoding method and then encode the client as initial individual. Firstly, the mutation operation aims at reflecting the direction and degree of mutation preferably, by defining addition, subtraction and multiplication operation of the differential mutation operator based on permutation method, and simultaneously bringing in incremental subsequence position transformation; secondly, the method of partial cross mapping is to avoid the illegal offspring caused by the traditional single-point crossover; finally, combined with the 2-opt local search algorithm, the discrete differential evolution algorithm is prevented this operation from the local optimal solution so as to apply and solve the path optimization problem in discrete space all the times. Compared with the original discrete differential evolution algorithm and particle swarm optimization algorithm, the experimental results indicate: this algorithm has smaller minimum, average and standard deviation, which search for the minimum value as soon as possible and hardly become local optimum, as well as the better convergence performance which shows the algorithm will achieve a smaller carbon emission path and better effect of optimization in this paper.

This paper studied the solution of the traveling salesman problem (TSP), a discrete particle swarm optimization algorithm (DPSO) model for solving this problem under dynamic topology was established. As to the discreteness and order of the TSP solution, a new coding method was designed, which included the time series connection between cities, the mapping relationship between particles and actual problems was established. And aiming at the premature convergence of the algorithm, a dynamic topology strategy based on particle mass clustering was designed to adjust the flight space of the particles. By introducing the gradient learning coefficient, the convergence speed of the algorithm and the probability of obtaining the optimal solution were improved. The simulation results showed that the proposed algorithm model can be applied to the optimization of TSP in discrete space.

One of the most important aspect of evacuation management system, when it comes to organizing a safer large-scale gathering is crowd dynamics. Utilizing evacuation simulation of crowd dynamics during egress, for planning efficient crowd control can minimize crowd disaster to a great extent. Most of the previous studies on evacuation models have been done over a discrete space which have neglected the uncertainty aspect of an agent's decision making, especially when it comes to panic situations. This study proposes a model for evacuation simulation under uncertainty conditions in a continuous space via computer simulations. It will focus on developing an intelligent simulation model utilizing one of the artificial intelligence techniques which is fuzzy logic. Social Force Model will be taken as the base for basic agent motion. Membership functions such as distance from the exit, familiarity and visibility of the exit, density of crowd around the exit are incorporated in the fuzzy logic system to model the system. From our findings, it can be deduced that factors such as density, distance, and familiarity all considerably affect the time of evacuation of agents from the threat place. Indeed, uncertainty aspect influences agents' decision making, thus affecting the result of evacuation time.

Path planning of polyhedrons by rolling on edges includes arbitrary relocation, obstacle avoidance and goal achievement. These tasks have various applications in robotics fields such as autonomous vehicles, navigation and robotic surgery. This paper reviewed path planning approaches applied to rolling contact with different types of polyhedral parts. The advantages and disadvantages of some mainstream algorithms were analyzed and compared. We further pointed out the directions of future research on rolling polyhedron path planning in discrete space.

Fuzzy extractors (Dodis et al., Eurocrypt 2004) convert repeated noisy readings of a high-entropy source into the same uniformly distributed key. The functionality of a fuzzy extractor outputs the key when provided with a value close to the original reading of the source. A necessary condition for security, called fuzzy min-entropy, is that the probability of every ball of values of the noisy source is small.Many noisy sources are best modeled using continuous metric spaces. To build continuous-source fuzzy extractors, prior work assumes that the system designer has a good model of the distribution (Verbitskiy et al., IEEE TIFS 2010). However, it is impossible to build an accurate model of a high entropy distribution just by sampling from the distribution.Model inaccuracy may be a serious problem. We demonstrate a family of continuous distributions ${\mathcal{W}}$ that is impossible to secure. No fuzzy extractor designed for ${\mathcal{W}}$ extracts a meaningful key from an average element of ${\mathcal{W}}$. This impossibility result is despite the fact that each element $W \in {\mathcal{W}}$ has high fuzzy min-entropy. We show a qualitatively stronger negative result for secure sketches, which are used to construct most fuzzy extractors.Our results are for the Euclidean metric and are information-theoretic in nature. To the best of our knowledge all continuous-source fuzzy extractors argue information-theoretic security.Fuller, Reyzin, and Smith showed comparable negative results for a discrete metric space equipped with the Hamming metric (Asiacrypt 2016). Continuous Euclidean space necessitates new techniques.

We capitalize on the Wasserstein distance to obtain two information-theoretic bounds on the generalization error of learning algorithms. First, we specialize the Wasserstein distance into total variation, by using the discrete metric. In this case we derive a generalization bound and, from a strong data-processing inequality, show how to narrow the bound by adding Gaussian noise to the output hypothesis. Second, we consider the Wasserstein distance under a generic metric. In this case we derive a generalization bound by exploiting the geometric nature of the Kantorovich-Rubinstein duality theorem. We illustrate the use of these bounds with examples. Our bounds can handle certain cases in which existing bounds via mutual information fail.

Aiming at the unknown obstacle environment, an online obstacle avoidance method, which is based on the model-based artificial potential field (MAPF) method and only depends on the information detected by onboard sensors, is proposed. First, the entire mission space is discretized. According to the relative position relation between the detection sector and the detected obstacle surface in the discrete space, the virtual repulsive potential fields (VRPFs) and the corresponding total force fields are constructed to make the robot avoid the detected obstacles and gradually move to the destination. Then, to avoid the local optimum, the memory mechanism for VRPFs and its corresponding path planning solution are introduced. Finally, the effectiveness of the proposed method is demonstrated by the simulation.

Graph clustering has wide applications in different areas such as machine learning, bioinformatics, data mining, social networks and understanding a software. Since it is an NP-hard problem, most approaches use the meta-heuristic and search-based evolutionary methods for solving it. Inspired by optimization algorithms like krill herd (KH) and genetic algorithm (GA), this paper proposes a new graph clustering algorithm. KH is an effective algorithm to solve continuous space optimization problems. It imitates individual and group behavior of krills and, normally, it cannot solve discrete space problems. GA is an evolutionary algorithm that uses search techniques to find near-optimal solutions. However, the main disadvantage of the GA is the lack of strong and effective information flow between generations as well as the lack of local search. In the proposed evolutionary algorithm, we have combined strengths of these two algorithms, e.g., adopting the cycle and GA operators, using swarm intelligence, and inspiring the Krill's movements, we got better results for the graph clustering problem. Initial results of the proposed algorithms on a number of software graphs showed that the clustering results obtained from the proposed algorithm are of higher quality compared to other considered algorithms.

The conventional finite set-predictive torque control (FS-PTC) of permanent magnet synchronous motor (PMSM) is known for its easy implementation, fast torque performance, and capability to include the constraints and nonlinearities. However, the most notable problems in the classical FS-PTC are the long calculation time and large current and torque ripples. This paper presents a simple FS-PTC with discrete space vector modulation (DSVM) and a deadbeat control (DBC) for PMSM drives. In this method, the DSVM is utilized to increase the number of virtual voltage vectors without the need for complex lookup tables or initialization requirement. The proposed DBC strategy is designed aiming to reduce the computation burden while widening the selected zones of candidate voltage vectors in the prediction steps. The proposed FCS-PTC of PMSM has also other advantages; such as reduction of torque and flux ripples, constant switching frequency owing to the use of DSVM, robustness against parameter variations due to the increase of candidate voltage vectors considered in the cost function, and easy implementation. The effectiveness of the proposed control strategy is verified by simulation results using PSIM software package.

This paper proposes an improved finite control set model predictive control (FCS-MPC) algorithm based on virtual space vector to reduce computational burden, and achieve a constant switching frequency for two-level three-phase inverters. The voltage vector reference is calculated in a 60° coordinate system according to the principle of deadbeat (DB) technique. A large number of virtual voltage vectors synthesized by discrete space vector modulation (DSVM) is utilized to approach the voltage vector reference. To avoid enumerating all the virtual voltage vectors from a look-up table, an algebraic way using the voltage vector reference is adopted to calculate the three candidate vectors. Then, a cost function is defined to select the optimal voltage vector among them. This new method greatly improves the computation efficiency since plenty of multiply operation is eliminated in the 60° coordinate system. Moreover, a fixed switching frequency is achieved since the durations of each switch states has been calculated. Experimental results under a two-level three-phase inverter verify the effectiveness of the proposed control strategy.

Problems with multiple optimal solutions widely exist in the real world. In some applications, it is required to locate multiple optima. However, most studies are dedicated to the continuous multi-solution optimization, while few works contribute to the discrete multi-solution optimization. To promote the multi-solution research in the discrete area, we design a benchmark test suite for multi-solution traveling salesman problems and propose two evaluation indicators. Further, in order to solve the problems, the genetic algorithm is incorporated with a niching technique defined in the discrete space. The proposed algorithm is compared with an existing algorithm. Experimental results demonstrate that the proposed algorithm outperforms the compared algorithm concerning the quality and diversity of obtained solutions.

The articles considers the matters relevant to the assessment of the reaction of integral strain gauges (ISGs) for the analysis of pressure and deformations occurring because of cyclical workload on the surface of metal constructions and machinery details. It is pointed out that the images of the reaction of ISGs can be considered as identifiable objects with vaguely defined structure. The author outlines the necessity to implement specialized algorithms for preliminary processing of ISG reaction images used for the creation of a feature space of the object in question based on the definition of geometrical and morphological parameters of an image. The article describes an algorithm of skeletization of ISG reaction images given maintained coherence. Computer realization is presented afterwards.

This paper presents a novel model predictive control (MPC) method with discrete space vector modulation (DSVM) to balance neutral-point voltage of Vienna-type rectifier. With the virtual vectors, more feasible voltage vectors can be used for the MPC method to reduce input current ripple. Meanwhile, compared with the normal finite control set MPC (FCS-MPC) neutral-point balancing control method, which the predictive neutral-point voltage difference is added to cost function, the proposed DSVM-MPC method just selects the optimal redundant small vector without calculating predictive neutral-point voltage, so it is simple to realize. The proposed DSVM-MPC method only takes real and virtual feasible vectors into account after judging the current sector, which can reduce the amount of MPC calculation of three-level rectifier. The DSVM-MPC method with selected small vectors can improve the ability of balancing and the performance of input current. The proposed DSVM-MPC method is investigated through simulations and validated through experimental results with a laboratory prototype.

Discretization continuous feature is an important task to handle the problems with real values in machine learning. In order to construct a classifier using a discrete space, it is required for many supervised classification algorithms to perform with discretized features. In this paper, we presents the supervised classification model based on Hidden Markov Model (HMM) developed recently and we review several discretization methods reported in the litterature. We take 9 benchmarking study data set to evaluate the performance and study the effect of discretization methods on the assessment of the proposed learning algorithm. Three metrics performance including accuracy, Area under curve and squared loss are used to investigate the powerful class prediction and to show the capability of HMM classifier in presence of available data.

A method is proposed for torque control of permanent magnet synchronous motors with lower switching frequency than SVM-based methods. This method takes the advantages of discrete SVM while a complicated switching table is avoided. Owing to the Deadbeat stator current control, the proposed control does not require stator flux estimation. Compared to the conventional Deadbeat methods using SVM operating in linear range of inverter, the proposed method possesses better DC link voltage utilization. Therefore, faster torque response could be achieved. The simulation results for a permanent magnet synchronous motor shows a lower switching frequency than the one of the SVM-based Deadbeat method and a better steady state performance compared to existing model predictive current control method.

One important challenge in the current research of UAVs is the obstacle avoidance feature, a highly demanded capability in all kinds of UAV applications. Different algorithms that perform sampling tasks in continuous or discrete spaces are widely used in path planning. The Probabilistic Roadmap (PRM) and Rapidly Exploring Random Tree (RRT) variants have a stochastic essence, which allows them to obtain a response even in wide and complex environments. However, they present disadvantages related to computational cost and time convergence of results. In this paper a survey on sampling-based planners is presented, comparing algorithms with continuous and discrete sampling in 3D environments. On the other hand, two new variants are introduced: the Exact Cell Decomposition on Probabilistic Roadmap (ECD-PRM), as an extension of PRM method, and the Modified Adaptive Cell Decomposition (MACD) performing a reduced space decomposition. The comparison is performed attending to several criteria such as path cost, number of generated nodes and number of control points in the final path, whenever it has been reached.

In the next years, the launch of new satellites with Hyperspectral (HS) sensors will guarantee the availability of regular multitemporal HS datasets. In order to exploit the dense sampling of the spectrum of HS sensors to discriminate multiple land-cover changes ad-hoc techniques are required. In this paper we propose a novel method for unsupervised multiple Change Detection (CD) in HS multitemporal images based on binary Spectral Change Vectors (SCVs). In greater detail, the method discriminates between unchanged and changed areas in order to focus only on the latter ones. Then, it converts the real valued SCVs in a binary form to work in a discrete high dimensional space. The binary SCVs are clustered following an hierarchical tree structure where each leaf represent a kind of change. The tree also highlights how the different changes are related among each other. The proposed approach has been tested on a multitemporal dataset acquired over an agricultural area. Experimental results confirmed that the binary SCVs allows us to detect and discriminate multiple changes by working in a simpler discrete space.

The power system is a crucial infrastructure which supports computer systems that affect many aspects of our daily lives, and thus a constant target of hackers' malicious attacks. An unidentifiable attack is a new type of bad data injection attack on power systems that confuses the control center software by manipulating measurement data so that there exist multiple feasible solutions for state estimation and thus no deterministic state estimation solution can be produced. To reveal and defend against this type of attacks, these multiple feasible solutions must be solved in advance. This paper proposes a fast and reliable algorithm to reveal such unidentifiable attacks. The algorithm combines the angle modulated particle swarm optimization (AMPSO) and the dormant measurement technique. The AMPSO is employed to reduce the complex high-dimensional binary search problem defined in discrete space to a simple four-dimensional search problem defined in continuous space; the dormant measurement technique is used to avoid repeated computation of state estimation. Simulation results using the IEEE 14-bus and 30-bus systems show that our proposed method produces multiple feasible solutions fast and reliably.

Representation of the surrounding environment is a vital task for a mobile robot. Many applications for mobile robots in urban environments may be considered such as self-driving cars, delivery drones or assistive robots. In contrast to the conventional methods, in this paper a Non Uniform Rational B-Spline (NURBS) based technique is represented for 3D mapping of the surrounding environment. While in the state of the art techniques, the robot's environment is expressed in a discrete space, the proposed method is mainly developed for representation of environment in a continuous space. Exploiting the information theory, the generated representation has much lower complexity and more compression capability in relation to some state of the art techniques. In addition to representation in a lower dimensional space, the NURBS based representation is invariant against 3D geometric transformations. Furthermore, the NURBS based representation can be employed for obstacle avoidance and navigation. The applicability of the proposed algorithm is investigated in some urban environments through some publicly available data sets. It has been shown by some experiments that the proposed method has better visual representation and much better data compression compared to some state-of-the-art methods.

The discrete topology optimization method is widely used because of its high degree of freedom and high problem-solving efficiency. However, one of its main drawbacks is that the output graphic is constituted of a 0–1 matrix leading to rough boundaries and implicit structures, which are difficult to be manufactured. Aiming to transform the implicit rough boundary into the explicit smooth boundary in discrete topology optimization, an effective structural boundary processing method based on support vector machine (SVM) is proposed in this paper. In this method, SVM is used for processing the boundaries obtained by the Solid Isotropic Material with Penalization (SIMP) and discrete level-set methods, respectively. With the SVM method, the clear structural boundaries are obtained and can be used in CAD directly. In order to make structural boundaries more smooth, data filtering on boundaries is employed. The effectiveness of the proposed method is illustrated by the experimental examples. Results show that the proposed method can obtain clear and smooth structural boundaries in discrete topology optimization.

Particle Swarm Optimization (PSO) successfully finds a solution as shown in various literatures. In some problems creating on discrete space, adjustment control-parameter may be difficult to modify a reach of optimum solution. The paper proposes an approach applying roulette wheel selection to PSO, which can help PSO escape from a local solution. This approach tested on both continuous and discrete space by finding solution of 12-numerical functions and an engineering-problem. The experiment result showed that the proposed technique can help PSO getting the best result both problem spaces, the performance improvement but also maintain easily to implementation.

In order to find an optimal solution of a research problem, the problem parameters are encoded in discrete space (e.g. bits or integers). Genetic algorithm (GA) performs the discrete space by binary chromosome. Particle swarm optimization (PSO) uses probability and sigmoid function to convert the next bird's velocity into binary bit. Flower pollination algorithm (FPA) is quite new and also has a few number of the paper implements to discrete space. This research uses a cut-off parameter applied on FPA. The main objective is to examine the performance of the algorithms on discrete space and calculate velocity of PSO as well as Levy fight movement of FPA when using discrete parameter. The experiment used eight-numerical functions to test conversion from a real value to a bit value and measure the effectiveness of each algorithm. Experiment result showed that FPA could perform better than PSO and GA.

This paper presents a scenario-case approach to coordinated control of heterogeneous ensembles of unmanned aerial vehicles, which is based on repeatability of vehicle's activity of interactions as the coordination stereotypes for similar situations. In this approach, each case contains scenarios of activity for each role in the ensemble. Description of situations is generalized to a spatial configuration defined on discrete space. The case for execution is selected based on spatial configuration; the scenarios that contains in this case are corrected dynamically due to observed events. The coordinated control of vehicles ensemble is implemented as three-layer system, which allows each vehicle makes relevant decisions in real time situations.

In this paper, we propose a PSO algorithm with transition probability based on Hamming distance for solving planar graph coloring problems. PSO was originally intended to handle only continuous optimization problems. To apply PSO to discrete problems, the standard arithmetic operators of PSO need to be redefined over discrete space. In this work, we propose a new algorithm that uses transition probability based on Hamming distance into PSO. The experimental results show that the new algorithm can get higher success rate and smaller average iterations than a Genetic Algorithm and the conventional PSO.

This paper focuses on the problem of hyper-graph matching, by accounting for both unary and higher-order affinity terms. Our method is in line with the linear approximate framework while the problem is iteratively solved in discrete space. It is empirically found more efficient than many extant continuous methods. Moreover, it avoids unknown accuracy loss by heuristic rounding step from the continuous approaches. Under weak assumptions, we prove the iterative discrete gradient assignment in general will trap into a degenerating case - an m-circle solution path where m is the order of the problem. A tailored adaptive relaxation mechanism is devised to detect the degenerating case and makes the algorithm converge to a fixed point in discrete space. Evaluations on both synthetic and real-world data corroborate the efficiency of our method.

We study the Prisoner's Dilemma in competitive environments with the aim to investigate if, and under which conditions, a cooperative behavior emerges in an agent population. In particular, agents are embedded in two different regions of space, i.e., A continuous space and a discrete space. The former is represented by a simple square, whereas the latter by a directed network. In both spaces, agents face by playing the Prisoner's Dilemma with their neighbors. In the continuous space, neighbors are identified by a rule based on the Euclidean distance among agents. Instead, in the network, agents have as neighbors those connected with them. In the proposed model, the competitiveness corresponds to the number of opponents each agent decides to face, i.e., Competitive agents faces many agents at each time step. Therefore, in the continuous space, the competitiveness is represented by the radius of each agent within it finds its opponents. Instead, in the discrete space, the competitiveness corresponds to the agent's out-degree, i.e., The number of neighbors connected with an arrow starting from the considered agent an directed to its neighbors. We study the evolution of the system over time in both spaces, analyzing also the degree distribution (both the in-degree and the out-degree) of the resulting directed network. It is worth to highlight that, as main result, we found the competitiveness strongly improves cooperation among agents in both domains. Furthermore, as cooperation emerges when the Prisoner's Dilemma is played over a network, several agents become hubs (i.e., Agents with a high out-degree).

International audience; The model of autonomous oblivious and anonymous mobile robots recently emerged as an attractive distributed computingabstraction that permits to assess the intrinsic difficulties of many fundamentals tasks, such as exploring orgathering in a discrete space. We present and implement a generic method for obtaining all possible protocols for aswarm of mobile robots operating in a particular discrete space. We use the exclusive perpetual exploration ofanonymous rings as a case study. Our method permits to discover new protocols that solve the problem, and to assessspecific optimization criteria (such as individual coverage, visits frequency, etc.) that are met by those protocols.To our knowledge, this is the first attempt to mechanize the discovery and fine-grained property testing ofdistributed mobile robot protocols.

Knapsack problem is famous NP-complete problem where one has to maximize the benefit of objects in a knapsack without exceeding its capacity. In this paper, a binary bacterial foraging optimization (BBFO) is proposed to find solutions of 0/1 knapsack problems. The original BFO chemotaxis equation is modified to operate in discrete space by using a mapping function, where some new variables and parameter, i.e., binary matrix y, logistic transformation S, and limiting transformation L is built to transform the bacterial position to a binary matrix. By using this schema, the proposed BBFO model can also be easily applied in other discrete problem solving. To further validate the efficiency of the BFO-based approach, an improved version BFO named BFO with linear decreasing chemotaxis step (BFO-LDC) is used to evaluate on six different instances. Comparisons with particle swarm optimization (PSO) and original BFO are presented and discussed.

In this paper, we propose an efficient method to reconstruct surface-from-gradients (SfG). Our method is formulated under the framework of discrete geometry processing. Unlike the existing SfG approaches, we transfer the continuous reconstruction problem into a discrete space and efficiently solve the problem via a sequence of least-square optimization steps. Our discrete formulation brings three advantages: 1) the reconstruction preserves sharp-features, 2) sparse/incomplete set of gradients can be well handled, and 3) domains of computation can have irregular boundaries. Our formulation is direct and easy to implement, and the comparisons with state-of-the-arts show the effectiveness of our method.

The aim of this paper is to investigate extremum problems with pay-off the total variational distance metric subject to linear functional constraints both defined on the space of probability measures, as well as related problems. Utilizing concepts from signed measures, the extremum probability measures of such problems are obtained in closed form, by identifying the partition of the support set and the mass of these extremum measures on the partition. The results are derived for abstract spaces, specifically, complete separable metric spaces, while the high level ideas are also discussed for denumerable spaces endowed with the discrete topology. © 2013 IEEE. 1204 1209

Summary form only given. Classes of asymptotic methods for the direct computation of discrete Green's functions are considered.

We revisit the formulation within the FDTD method of the Abraham-Lorentz model of a 1-electron atom coupling to an external electromagnetic field via the dipole interaction between the field and the moving charge. This classical problem is reformulated for a purely discrete space in discrete-time by specifying the electromagnetic potentials and the electron charge density only at discrete spatial points or edges in a mesh decomposition of space. A systematic simplicial complex structure is used which preserves classical field theorems such as Gauss's Law, Stokes' and Green's Theorems in the discrete domain. The role of the radiation reaction field which permeates the electron charge is identified.

The computational time complexity is an important topic in the theory of Evolutionary Algorithms (EAs). The analysis in continuous space function is rare nowadays in comparison to that in discrete space. In this paper, we extend the general drift theory to analyze the complexity of optimization problem in continuous space, by proposing a new version of Variable Drift-Johannsen theorem. Comparing with general drift analysis, we establish a tighter upper bound for continuous optimization by integration for every problem that is monotonic in drift. Finally, we apply the proposed theory to a continuous (1+1)EA algorithm which is the basic framework of evolutionary algorithm(EA) in continuous space. The continuous (1+1)EA is similar with (1+1)EA except for its elitism strategy. In addition, its solutions are transferred to continuous space and mutations are implemented randomly by obeying one single probability distribution. It means that the continuous (1+1)EA requires exponential time complexity. Both the upper and lower bounds of the (1+1)EA with the mutation of (0,1)-normal distribution are bounding above that of the (1+1)EA with the mutation of (?1,1)-uniform distribution. This means that the (1+1)EA with the mutation of (0,1)-normal distribution outperforms the (1+1)EA with the mutation of (?1,1)-uniform distribution in reaching the optimum of sphere function.

The Nonlinear Hybrid Dynamical Systems (NHDS) represent discrete event dynamics along with continuous dynamics. This paper is focused identification of the NHDS based on fuzzy c-means clustering approach for the open loop data classification according to its discrete dynamics. In the present work, a novel fuzzy function based selection of PWARX model algorithm applied for validation of identified parameters of the PieceWise affine Auto Regressive eXogeneous (PWARX) models which are separable and linear in the discrete space. The performance of the proposed selection method is demonstrated using the physical application.

Differential evolution (DE) was introduced by Stone and Price in 1995 as a population-based stochastic search technique for solving optimization problems in a continuous space. DE has been successfully applied to various real world numerical optimization problems. In recent years not only continuous real-valued function, the applications of DE on combinatorial optimization problems with discrete decision variables are reported. However, genetic operator in the standard DE can not directly applied to discrete space. In this paper, we propose a method to solve quadratic assignment problems (QAP) by DE. The QAP is a well-known combinatorial optimization problem with a wide variety of practical applications. It is NP-hard and is considered to be one of the most difficult problems. In the QAP, a candidate solution can represented a permutation of integer. The proposed method employs permutation representation for individuals in DE. Therefore, a individual vector is encoded directly as a permutation. In discrete space, to realize effcient solution search like standard DE which have continuous nature, we modify differential operator to handle permutation encoding. Additionally, in order to maintain diversity of population, restart strategy and tabu list are introduced to proposed method instead of crossover operator. Finally, we show the experimental results using instances of QAPLIB and the efficacy of proposed method.

This paper presents a method for learning 3D object templates from view labeled object images. The 3D template is defined in a joint appearance and geometry space composed of deformable planar part templates placed at different 3D positions and orientations. Appearance of each part template is represented by Gabor filters, which are hierarchically grouped into line segments and geometric shapes. AND-OR trees are further used to quantize the possible geometry and appearance of part templates, so that learning can be done on a subsampled discrete space. Using information gain as a criterion, the best 3D template can be searched through the AND-OR trees using one bottom-up pass and one top-down pass. Experiments on a new car dataset with diverse views show that the proposed method can learn meaningful 3D car templates, and give satisfactory detection and view estimation performance. Experiments are also performed on a public car dataset, which show comparable performance with recent methods.

The ant colony algorithm has been successfully used to solve discrete problems. However, its discrete nature restricts applications to the continuous domains. In this paper, we introduce two methods of ACO for solving continuous domains. The first method references the thought of ACO in discrete space and need to divide continuous space into several regions and the pheromone is assigned on each region discrete, the ants depend on the pheromone to construct the path and find the solution finally. Compared with the first method, the second one which the distribution of pheromone in definition domain is simulated with normal distribution has essential difference to the first one. In order to improve the solving ability of those two algorithms, the pattern search method will be used. Experimental results on a set of test functions show that those two algorithms can obtain the solution in continuous domains well.

One of the challenges in routing for dense Wireless Sensor Networks (WSN) is balancing the traffic over different paths. Load-balancing methods inspired by physical phenomena such as electrostatics and optics have been studied in recent years, and the proposed methods are promising in energy-critical routing applications. Such methods model information flow in continuous domain in order to benefit from well-established continuous space optimization methods; however, the existing literature on physics inspired approaches do not address the link between continuous and discrete space models. In this paper, we present a discretization method for linking continuous flow to discrete paths in a dense-WSN. We study a p-norm flow optimization method in continuous domain and show that a fixed-path routing is not sufficient to completely balance traffic load over the network. Our results show that a significant improvement in transport capacity can be achieved by using a dynamic path selection scheme and balancing the traffic over the selected paths.

We consider the stochastic optimization of a noisy convex loss function defined on p-dimensional grid of points in Euclidean space. We introduce the middle point discrete simultaneous perturbation stochastic approximation (DSPSA) algorithm to this discrete space. Consistent with other stochastic approximation methods, this method formally accommodates noisy measurements of the loss function.