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Purpose: The time required by the algorithms for general layouts to solve the large-scale two-dimensional cutting problems may become unaffordable. So this paper presents an exact algorithm to solve above problems. Design/methodology/approach: The algorithm uses the dynamic programming algorithm to generate the optimal homogenous strips, solves the knapsack problem to determine the optimal layout of the homogenous strip in the composite strip and the composite strip in the segment, and optimally selects the enumerated segments to compose the three-stage layout. Findings: The algorithm not only meets the shearing and punching process need, but also achieves good results within reasonable time. Originality/value: The algorithm is tested through 43 large-scale benchmark problems. The number of optimal solutions is 39 for this paper's algorithm; the rate of the rest 4 problem's solution value and the optimal solution is 99. 9%, and the average consumed time is only 2. 18seconds. This paper's pattern is used to simplify the cutting process. Compared with the classic three-stage, the two-segment and the T-shape algorithms, the solutions of the algorithm are better than that of the above three algorithms. Experimental results show that the algorithm to solve a large-scale piece packing quickly and efficiency. [ABSTRACT FROM AUTHOR]

The concept of the tropical algebra was first introduced to solve problems in mathematical economy such as optimization and approximation problems. In this paper, the concept of tropical algebra is used to build an image filtering algorithm. By using this concept, the lowest and highest pixel values are considered in determining the new pixel value. In addition, adaptive window will also be implemented to help the filtering process become more effective at high density noise. Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM) are used to evaluate the output image quality produced by the filtering method. In this experiment, the performance of proposed method and existing methods such as switching median filter (SMF), adaptive fuzzy noise switching median filter (NAFSM), modified decision based on unsymmetric trimmed median filter (MDBUTMF), adaptive type-2 fuzzy filter (AT2FF)), based on pixel density filters (BPDF), different applied median filters (DAMF), and tropical SVD filters (TSVD) will be compared. PSNR and SSIM results show that the proposed method outperforms most existing methods: SMF (27.13/0.7954), NAFSM (29.11/0.8459), MDBTUMF (29.18/0.8462), AT2FF (28.10/0.8159), BPDF (25.65/0.7545), DAMF (31.20/0.8833), TSVD (28.39/0.7906), and proposed (31.26/0.8827). [ABSTRACT FROM AUTHOR]

In this paper we propose an efficient method for solving the spherically constrained homogeneous polynomial optimization problem. The new approach has the following three main ingredients. First, we establish a block coordinate descent type search method for nonlinear optimization, with the novelty being that we accept only a block update that achieves the maximum improvement, hence the name of our new search method: maximum block improvement (MBI). Convergence of the sequence produced by the MBI method to a stationary point is proved. Second, we establish that maximizing a homogeneous polynomial over a sphere is equivalent to its tensor relaxation problem; thus we can maximize a homogeneous polynomial function over a sphere by its tensor relaxation via the MBI approach. Third, we propose a scheme to reach a KKT point of the polynomial optimization, provided that a stationary solution for the relaxed tensor problem is available. Numerical experiments have shown that our new method works very efficiently: for a majority of the test instances that we have experimented with, the method finds the global optimal solution at a low computational cost. [ABSTRACT FROM AUTHOR]

Several lifetime distributions have played an important role to fit survival data. However, for some of these models, the computation of maximum likelihood estimators is quite difficult due to presence of flat regions in the search space, among other factors. Several well-known derivative-based optimization tools are unsuitable for obtaining such estimates. To circumvent this problem, we introduce the AdequacyModel computational library version 2.0.0 for the R statistical environment with two major contributions: a general optimization technique based on the Particle Swarm Optimization (PSO) method (with a minor modification of the original algorithm) and a set of statistical measures for assessment of the adequacy of the fitted model. This library is very useful for researchers in probability and statistics and has been cited in various papers in these areas. It serves as the basis for the Newdistns library (version 2.1) published in an impact journal in the area of computational statistics, see . It is also the basis of the Wrapped library (version 2.0), see . A third package making use of the AdequacyModel library can be found in . In addition, the proposed library has proved to be very useful for maximizing log-likelihood functions with complex search regions. The library provides a greater control of the optimization process by introducing a stop criterion based on a minimum number of iterations and the variance of a given proportion of optimal values. We emphasize that the new library can be used not only in statistics but in physics and mathematics as proved in several examples throughout the paper. [ABSTRACT FROM AUTHOR]

The process of inferring parameter values from experimental data can be a cumbersome task. In addition, the collection of experimental data can be time consuming and costly. This paper covers both these issues by addressing the following question: “Which experimental outputs should be measured to ensure that unique model parameters can be calculated?”. Stated formally, we examine the topic of minimal output sets that guarantee a model’s structural identifiability. To that end, we introduce an algorithm that guides a researcher as to which model outputs to measure. Our algorithm consists of an iterative structural identifiability analysis and can determine multiple minimal output sets of a model. This choice in different output sets offers researchers flexibility during experimental design. Our method can determine minimal output sets of large differential equation models within short computational times. [ABSTRACT FROM AUTHOR]

Abstract  The study and research of evolutionary algorithms (EAs) is getting great attention in recent years. Although EAs have earned extensive acceptance through numerous successful applications in many fields, the problem of finding the best combination of evolutionary parameters especially for population size that need the manual settings by the user is still unresolved. In this paper, our system is focusing on differential evolution (DE) and its control parameters. To overcome the problem, two new systems were carried out for the self-adaptive population size to test two different methodologies (absolute encoding and relative encoding) in DE and compared their performances against the original DE. Fifty runs are conducted for every 20 well-known benchmark problems to test on every proposed algorithm in this paper to achieve the function optimization without explicit parameter tuning in DE. The empirical testing results showed that DE with self-adaptive population size using relative encoding performed well in terms of the average performance as well as stability compared to absolute encoding version as well as the original DE. [ABSTRACT FROM AUTHOR]

This paper concentrates on high-level data-flow optimization and synthesis techniques for datapath intensive designs such as those in Digital Signal Processing (DSP), computer graphics and embedded systems applications, which are modeled as polynomial computations over Z2^{n_1 } \times Z2^{n_2 } \times \cdots \times Z2^{n_d } to Z2^m . Our main contribution in this paper is proposing an optimization method based on functional decomposition of multivariate polynomial in the form of f(x) = g(x) \;o \;h(x) + f0 = g(h(x)) + f0 to obtain good building blocks, and vanishing polynomials over Z2^m to add/delete redundancy to/from given polynomial functions to extract further common sub-expressions. Experimental results for combinational implementation of the designs have shown an average saving of 38.85 and 18.85 percent in the number of gates and critical path delay, respectively, compared with the state-of-the-art techniques. Regarding the comparison with our previous works, the area and delay are improved by 10.87 and 11.22 percent, respectively. Furthermore, experimental results of sequential implementations have shown an average saving of 39.26 and 34.70 percent in the area and the latency, respectively, compared with the state-of-the-art techniques. [ABSTRACT FROM PUBLISHER]

A generalized 3-dimensional assignment problem is a decisionmaking process that involves allocating limited resources to a set of tasks over time, where the objective is to optimize a cost function subject to a set of generalized assignment constraints. The 3- dimensional (3-D) assignment problems are known to be NP-hard. In this paper, we propose a novel approach to efficiently solve an m-best 3-D assignment problem with non-unity right-hand side constraints (also referred to simply as 3-D assignment problem), where m may be large (as many as 104 solutions), by decomposing it into two sequential phases. In phase I, we partition the original problem space into a series of subproblems via Murty's m-best search space decomposition procedure. Modifications previously proposed in the literature for the 2-dimensional (2-D) assignment problem are applied to optimize the search space decomposition for the 3- D assignment problem. In phase II, we solve each subproblem by using Lagrangian relaxation and solving the 3-D assignment problem as a combination of relaxed 2-D assignment problems and 2-D transportation problems. The 2-D assignment problem is solved by the JVC or auction algorithms and the 2-D transportation problem is solved by the simplex-based transportation, Transauction or RELAX-IV algorithms. The sequence of relaxed 2-D problems are interchangeable, while adhering to the relaxed constraints. We validate and compare the performance and utility of the proposed algorithms and search space decomposition optimizations via extensive numerical experiments. Overall, the fully optimized algorithm took less than 50 seconds, on average, to obtain 104 soutions for a tensor of dimension 30X30X8. [ABSTRACT FROM AUTHOR]

This paper is concerned with a linear fractional problem of the form: max[sub x] min[sub y] F(X, Y) = (cX + dY + α)/(fX + gY + β), subject to AX + BY less than or equal to b; X, Y greater than or equal to O. This problem represents a generalization of a problem considered in the literature in which F(X, Y) is assumed to be linear. A number of results for the linear case are extended; and, in particular, it is shown that this fractional max-min problem is equivalent to a quasi-convex programming problem whose optimal solution lies at a vertex of the feasible region. Using these results, we develop an algorithm for solving this problem. The paper concludes with a numerical example. [ABSTRACT FROM AUTHOR]

In this paper, an anti-jamming method, which turns the single objective optimization problem into a multi-objective optimization problem by utilizing 2-norm, is proposed. The proposed jamming suppression method can reduce the wide nulls and wrong nulls problems, which are generated by the common adaptive nulling methods. Therefore a better signal-noise-ratio (SNR) can be achieved, especially when the jammers are close to satellite signals. It can also improve the robustness of the algorithm. The effectiveness of the proposed method is evaluated by simulation and practical outdoor experiments with the GPS L1 band C/A signals. The experimental results show that with the dedicated method, the nulls targeting at the corresponding jammers become narrower and the wrong nulls can be eliminated. [ABSTRACT FROM AUTHOR]

This paper deals with the multiplicative finite-field matrix channel, a discrete memoryless channel whose input and output are matrices (over a finite field) related by a multiplicative transfer matrix. The model considered here assumes that all transfer matrices with the same rank are equiprobable, so that the channel is completely characterized by the rank distribution of the transfer matrix. This model is seen to be more flexible than previously proposed ones in describing random linear network coding systems subject to link erasures, while still being sufficiently simple to allow tractability. The model is also conservative in the sense that its capacity provides a lower bound on the capacity of any channel with the same rank distribution. A main contribution is to express the channel capacity as the solution of a convex optimization problem which can be easily solved by numerical computation. For the special case of constant-rank input, a closed-form expression for the capacity is obtained. The behavior of the channel for asymptotically large field size or packet length is studied, and it is shown that constant-rank input suffices in this case. Finally, it is proved that the well-known approach of treating inputs and outputs as subspaces is information-lossless even in this more general model. [ABSTRACT FROM AUTHOR]

For the global optimization problems with continuous variables, evolutionary algorithms (EAs) are often used to find the approximate solutions. The number of generations for an EA to find the approximate solutions, called the first hitting time, is an important index to measure the performance of the EA. However, calculating the first hitting time is still difficult in theory. This paper proposes some new drift conditions that are used to estimate the upper bound of the first hitting times of EAs for finding the approximate solutions. Two case studies are given to show how to apply these conditions to estimate the first hitting times. [ABSTRACT FROM AUTHOR]

This paper deals with a parametric family of convex semi-infinite optimization problems for which linear perturbations of the objective function and continuous perturbations of the right-hand side of the constraint system are allowed. In this context, Cánovas et al. (SIAM J. Optim. 18:717–732, []) introduced a sufficient condition (called ENC in the present paper) for the strong Lipschitz stability of the optimal set mapping. Now, we show that ENC also entails high stability for the minimal subsets of indices involved in the KKT conditions, yielding a nice behavior not only for the optimal set mapping, but also for its inverse. Roughly speaking, points near optimal solutions are optimal for proximal parameters. In particular, this fact leads us to a remarkable simplification of a certain expression for the (metric) regularity modulus given in Cánovas et al. (J. Glob. Optim. 41:1–13, []) (and based on Ioffe (Usp. Mat. Nauk 55(3):103–162, []; Control Cybern. 32:543–554, [])), which provides a key step in further research oriented to find more computable expressions of this regularity modulus. [ABSTRACT FROM AUTHOR]

The majorize-minimize (MM) optimization technique has received considerable attention in signal and image processing applications, as well as in statistics literature. At each iteration of an MM algorithm, one constructs a tangent majorant function that majorizes the given cost function and is equal to it at the current iterate. The next iterate is obtained by minimizing this tangent majorant function, resulting in a sequence of iterates that reduces the cost function monotonically. A well-known special case of MM methods are expectation-maximization algorithms. In this paper, we expand on previous analyses of MM, due to Fessler and Hero, that allowed the tangent majorants to be constructed in iteration-dependent ways. Also, this paper overcomes an error in one of those earlier analyses. There are three main aspects in which our analysis builds upon previous work. First, our treatment relaxes many assumptions related to the structure of the cost function, feasible set, and tangent majorants. For example, the cost function can be nonconvex and the feasible set for the problem can be any convex set. Second, we propose convergence conditions, based on upper curvature bounds, that can be easier to verify than more standard continuity conditions. Furthermore, these conditions allow for considerable design freedom in the iteration-dependent behavior of the algorithm. Finally, we give an original characterization of the local region of convergence of MM algorithms based on connected (e.g., convex) tangent majorants. For such algorithms, cost function minimizers will locally attract the iterates over larger neighborhoods than typically is guaranteed with other methods. This expanded treatment widens the scope of the MM algorithm designs that can be considered for signal and image processing applications, allows us to verify the convergent behavior of previously published algorithms, and gives a fuller understanding overall of how these algorithms behave. [ABSTRACT FROM AUTHOR]

Because the orbital periods for planetary orbital transfers are of order hour, the primary objective of an optimal trajectory is to minimize the propellant consumption. In this paper, we present a systematic investigation of optimal trajectories for planetary orbital transfer. Major results on thrust control, propellant consumption, and flight time are presented with particular reference to LEO-to-GEO transfer. The following results were obtained with the sequential gradient-restoration algorithm in either single-subarc form or multiple-subarc form: (i) For minimum propellant consumption, the thrust direction is tangent to the flight path. The thrust magnitude has a three-subarc form: powered flight with maximum thrust is followed by coasting flight, which is followed by powered flight with maximum thrust. (ii) The flight time is determined mainly by the thrust-to-weight ratio. A transfer via chemical engines is relatively short: usually, it requires less than one cycle to achieve the mission, which involves a large portion of coasting flight. A transfer via electrical engines is relatively long: usually, it requires a multicycle spiral trajectory to achieve the mission, which involves a large portion of powered flight, mostly in the first subarc. (iii) The propellant consumption is determined mainly by the specific impulse: the electrical engine is more efficient than the chemical engine, resulting in lower propellant consumption and higher payload. [ABSTRACT FROM AUTHOR]

In this paper, we attempt to investigate a class of constrained nonsmooth convex optimization problems, that is, piecewise C² convex objectives with smooth convex inequality constraints. By using the Moreau-Yosida regularization, we convert these problems into unconstrained smooth convex programs. Then, we investigate the second-order properties of the Moreau-Yosida regularization n. By introducing the (GAIPCQ) qualification, we show that the gradient of the regularized function n is piecewise smooth, thereby, semismooth. [ABSTRACT FROM AUTHOR]

In this paper we study a method for global optimization of increasing positively homogeneous functions over the unit simplex, which is a version of the cutting angle method. Some properties of the auxiliary subproblem are studied and a special algorithm for its solution is proposed. A cutting angle method based on this algorithm allows one to find an approximate solution of some problems of global optimization with 50 variables. Results of numerical experiments are discussed. [ABSTRACT FROM AUTHOR]

Since its inception in 1995, many improvements to the original particle swarm optimization (PSO) algorithm have been developed. This paper reviews one class of such PSO variations, i.e. PSO algorithms that make use of crossover operators. The review is supplemented with a more extensive sensitivity analysis of the crossover PSO algorithms than provided in the original publications. Two adaptations of a parent-centric crossover PSO algorithm are provided, resulting in improvements with respect to solution accuracy compared to the original parent-centric PSO algorithms. The paper then provides an extensive empirical analysis on a large benchmark of minimization problems, with the objective to identify those crossover PSO algorithms that perform best with respect to accuracy, success rate, and efficiency. [ABSTRACT FROM AUTHOR]

Waveform design is a pivotal component of the fully adaptive radar construct. In this paper, we consider waveform design for radar space time adaptive processing (STAP), accounting for the waveform dependence of the clutter correlation matrix. Due to this dependence, in general, the joint problem of receiver filter optimization and radar waveform design becomes an intractable, nonconvex optimization problem, Nevertheless, it is, however, shown to be individually convex either in the filter or in the waveform variables. We derive constrained versions of a) the alternating minimization algorithm, b) proximal alternating minimization, and c) the constant modulus alternating minimization, which, at each step, iteratively optimizes either the STAP filter or the waveform independently. A fast and slow time model permits waveform design in radar STAP, but the primary bottleneck is the computational complexity of the algorithms. [ABSTRACT FROM PUBLISHER]

In this paper, foundations of a new approach for solving vector optimization problems are introduced. Generalized Lagrangian duality, related for the first time with vector optimization, provides new scalarization techniques and allows for the generation of efficient solutions for problems which are not required to satisfy any convexity assumptions. [ABSTRACT FROM AUTHOR]

Generalized linear latent variable models (GLLVM) are popular tools for modeling multivariate, correlated responses. Such data are often encountered, for instance, in ecological studies, where presence-absences, counts, or biomass of interacting species are collected from a set of sites. Until very recently, the main challenge in fitting GLLVMs has been the lack of computationally efficient estimation methods. For likelihood based estimation, several closed form approximations for the marginal likelihood of GLLVMs have been proposed, but their efficient implementations have been lacking in the literature. To fill this gap, we show in this paper how to obtain computationally convenient estimation algorithms based on a combination of either the Laplace approximation method or variational approximation method, and automatic optimization techniques implemented in software. An extensive set of simulation studies is used to assess the performances of different methods, from which it is shown that the variational approximation method used in conjunction with automatic optimization offers a powerful tool for estimation. [ABSTRACT FROM AUTHOR]

Abstract Multi-population based nature-inspired optimization algorithms have attracted wide research interests in the last decade, and become one of the frequently used methods to handle real-world optimization problems. Considering the importance and value of multi-population methods and its applications, we believe it is the right time to provide a comprehensive survey of the published work, and also to discuss several aspects for the future research. The purpose of this paper is to summarize the published techniques related to the multi-population methods in nature-inspired optimization algorithms. Beginning with the concept of multi-population optimization, we review basic and important issues in the multi-population methods and discuss their applications in science and engineering. Finally, this paper presents several interesting open problems with future research directions for multi-population optimization methods. [ABSTRACT FROM AUTHOR]

Abstract Grey Wolf Optimizer (GWO) algorithm is a relatively new algorithm in the field of swarm intelligence for solving continuous optimization problems as well as real world optimization problems. The Grey Wolf Optimizer is the only algorithm in the category of swam intelligence which is based on leadership hierarchy. This paper has three important aspects- Firstly, for improving the search ability by grey wolf a modified algorithm RW-GWO based on random walk has been proposed. Secondly, its performance is exhibited in comparison with GWO and state of art algorithms GSA, CS, BBO and SOS on IEEE CEC 2014 benchmark problems. A non-parametric test Wilcoxon and Performance Index Analysis has been performed to observe the impact of improving the leaders in the proposed algorithm. The results presented in this paper demonstrate that the proposed algorithm provide a better leadership to search a prey by grey wolves. The third aspect of the paper is to use the proposed algorithm and GWO on real life application problems. It is concluded from this article that RW-GWO algorithm is an efficient and reliable algorithm for solving not only continuous optimization problems but also for real life optimization problems. [ABSTRACT FROM AUTHOR]

The Semi-Infinite Simplex Algorithm (SISA) with applications to so called Semi-Infinite Linear Programs (SILP) with capacity constraints as a direct analog to column generating techniques in linear programming methods ofwas presented by the author in 1978. Later in 1981, the SISA for SILP in partially ordered spaces was described with more algebraic framework in terms of feasible basic solutions, extreme points and so on. Now this paper has two aims: to reflect the history of one branch of the so-called Leipzig-Optimization-Tree with roots J. Focke/A. Göpfert / R. Klötzler and to demonstrate some applications of the Simplex Algorithm. [ABSTRACT FROM AUTHOR]

This paper introduces a generalization of the frequently discussed problem of finding the optimum redundancy that maximizes the reliability of a network of components. Past work has restricted consideration to arrangements of redundant components called series-parallel networks. This paper allows a much broader class of arrangements called series-parallelseries networks. It is important to consider such arrangements for realistic situations in which components have more than one failure mode, or the combination of parallel paths introduces a failure probability. A dynamic programming algorithm is used to solve the more general problem for the case in which there are no constraints on the optimum solution. The algorithm is extended to handle multiple constraints using dominance and a variety of elimination methods to reduce the storage required in a compurer implementation of the algorithm. Problems with as many as 15 serial components and three constraints have been solved with reasonable digital computer computation times. [ABSTRACT FROM AUTHOR]

Generalizing both mixed-integer linear optimization and convex optimization, mixed-integer convex optimization possesses broad modeling power but has seen relatively few advances in general-purpose solvers in recent years. In this paper, we intend to provide a broadly accessible introduction to our recent work in developing algorithms and software for this problem class. Our approach is based on constructing polyhedral outer approximations of the convex constraints, resulting in a global solution by solving a finite number of mixed-integer linear and continuous convex subproblems. The key advance we present is to strengthen the polyhedral approximations by constructing them in a higher-dimensional space. In order to automate this extended formulation we rely on the algebraic modeling technique of disciplined convex programming (DCP), and for generality and ease of implementation we use conic representations of the convex constraints. Although our framework requires a manual translation of existing models into DCP form, after performing this transformation on the MINLPLIB2 benchmark library we were able to solve a number of unsolved instances and on many other instances achieve superior performance compared with state-of-the-art solvers like Bonmin, SCIP, and Artelys Knitro. [ABSTRACT FROM AUTHOR]

Reaction networks are systems in which the populations of a finite number of species evolve through predefined interactions. Such networks are found as modeling tools in many biological disciplines such as biochemistry, ecology, epidemiology, immunology, systems biology and synthetic biology. It is now well-established that, for small population sizes, stochastic models for biochemical reaction networks are necessary to capture randomness in the interactions. The tools for analyzing such models, however, still lag far behind their deterministic counterparts. In this paper, we bridge this gap by developing a constructive framework for examining the long-term behavior and stability properties of the reaction dynamics in a stochastic setting. In particular, we address the problems of determining ergodicity of the reaction dynamics, which is analogous to having a globally attracting fixed point for deterministic dynamics. We also examine when the statistical moments of the underlying process remain bounded with time and when they converge to their steady state values. The framework we develop relies on a blend of ideas from probability theory, linear algebra and optimization theory. We demonstrate that the stability properties of a wide class of biological networks can be assessed from our sufficient theoretical conditions that can be recast as efficient and scalable linear programs, well-known for their tractability. It is notably shown that the computational complexity is often linear in the number of species. We illustrate the validity, the efficiency and the wide applicability of our results on several reaction networks arising in biochemistry, systems biology, epidemiology and ecology. The biological implications of the results as well as an example of a non-ergodic biological network are also discussed. [ABSTRACT FROM AUTHOR]

Existing approaches to template-based visual tracking, in which the objective is to continuously estimate the spatial transformation parameters of an object template over video frames, have primarily been based on deterministic optimization, which as is well-known can result in convergence to local optima. To overcome this limitation of the deterministic optimization approach, in this paper we present a novel particle filtering approach to template-based visual tracking. We formulate the problem as a particle filtering problem on matrix Lie groups, specifically the three-dimensional Special Linear group SL(3) and the two-dimensional affine group Aff(2). Computational performance and robustness are enhanced through a number of features: (i) Gaussian importance functions on the groups are iteratively constructed via local linearization; (ii) the inverse formulation of the Jacobian calculation is used; (iii) template resizing is performed; and (iv) parent-child particles are developed and used. Extensive experimental results using challenging video sequences demonstrate the enhanced performance and robustness of our particle filtering-based approach to template-based visual tracking. We also show that our approach outperforms several state-of-the-art template-based visual tracking methods via experiments using the publicly available benchmark data set. [ABSTRACT FROM PUBLISHER]

In this paper, we consider solving a set of global optimization problems in parallel. The proposed novel algorithm provides uniform convergence to the set of solutions for all problems treated simultaneously. The current accuracy for each particular solution is estimated by the difference in each coordinate from the point of global decision. The main statement is given in the corresponding theorem. For the sake of illustration some computational results with hundreds of multidimensional global problems are provided. [ABSTRACT FROM AUTHOR]

We consider a global optimization problem for Lipschitz-continuous functions with an unknown Lipschitz constant. Our approach is based on the well-known DIRECT (DIviding RECTangles) algorithm and motivated by the diagonal partitioning strategy. One of the main advantages of the diagonal partitioning scheme is that the objective function is evaluated at two points at each hyper-rectangle and, therefore, more comprehensive information about the objective function is considered than using the central sampling strategy used in most DIRECT-type algorithms. In this paper, we introduce a new DIRECT-type algorithm, which we call BIRECT (BIsecting RECTangles). In this algorithm, a bisection is used instead of a trisection which is typical for diagonal-based and DIRECT-type algorithms. The bisection is preferable to the trisection because of the shapes of hyper-rectangles, but usual evaluation of the objective function at the center or at the endpoints of the diagonal are not favorable for bisection. In the proposed algorithm the objective function is evaluated at two points on the diagonal equidistant between themselves and the endpoints of a diagonal. This sampling strategy enables reuse of the sampling points in descendant hyper-rectangles. The developed algorithm gives very competitive numerical results compared to the DIRECT algorithm and its well know modifications. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of robust and efficient relative rotation averaging in the context of large-scale Structure from Motion. Relative rotation averaging finds global or absolute rotations for a set of cameras from a set of observed relative rotations between pairs of cameras. We propose a generalized framework of relative rotation averaging that can use different robust loss functions and jointly optimizes for all the unknown camera rotations. Our method uses a quasi-Newton optimization which results in an efficient iteratively reweighted least squares (IRLS) formulation that works in the Lie algebra of the 3D rotation group. We demonstrate the performance of our approach on a number of large-scale data sets. We show that our method outperforms existing methods in the literature both in terms of speed and accuracy. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a novel algorithm—parallel adaptive quantum genetic algorithm—which can rapidly determine the minimum control nodes of arbitrary networks with both control nodes and state nodes. The corresponding network can be fully controlled with the obtained control scheme. We transformed the network controllability issue into a combinational optimization problem based on the Popov-Belevitch-Hautus rank condition. A set of canonical networks and a list of real-world networks were experimented. Comparison results demonstrated that the algorithm was more ideal to optimize the controllability of networks, especially those larger-size networks. We demonstrated subsequently that there were links between the optimal control nodes and some network statistical characteristics. The proposed algorithm provides an effective approach to improve the controllability optimization of large networks or even extra-large networks with hundreds of thousands nodes. [ABSTRACT FROM AUTHOR]

Software test suites based on the concept of interaction testing are very useful for testing software components in an economical way. Test suites of this kind may be created using mathematical objects called covering arrays. A covering array, denoted by CA(N; t, k, v), is an N × k array over with the property that every N × t sub-array covers all t-tuples of at least once. Covering arrays can be used to test systems in which failures occur as a result of interactions among components or subsystems. They are often used in areas such as hardware Trojan detection, software testing, and network design. Because system testing is expensive, it is critical to reduce the amount of testing required. This paper addresses the Optimal Shortening of Covering ARrays (OSCAR) problem, an optimization problem whose objective is to construct, from an existing covering array matrix of uniform level, an array with dimensions of (N − δ) × (k − Δ) such that the number of missing t-tuples is minimized. Two applications of the OSCAR problem are (a) to produce smaller covering arrays from larger ones and (b) to obtain quasi-covering arrays (covering arrays in which the number of missing t-tuples is small) to be used as input to a meta-heuristic algorithm that produces covering arrays. In addition, it is proven that the OSCAR problem is NP-complete, and twelve different algorithms are proposed to solve it. An experiment was performed on 62 problem instances, and the results demonstrate the effectiveness of solving the OSCAR problem to facilitate the construction of new covering arrays. [ABSTRACT FROM AUTHOR]

Finding optimal Golomb rulers is an extremely challenging combinatorial problem. The distance between each pair of mark is unique in a Golomb ruler. For a given number of marks, an optimal Golomb ruler has the minimum length. Golomb rulers are used in application areas such as X-ray crystallography, radio astronomy, information theory, and pulse phase modulation. The most recent optimal Golomb ruler search algorithm hybridises a range of techniques such as greedy randomised adaptive search, scatter search, tabu search, clustering techniques, and constraint programming, and obtains optimal Golomb rulers of up to 16 marks with very low success rates. In this paper, we provide tight upper bounds for Golomb ruler marks and present heuristic-based effective domain reduction techniques. Using these along with tabu and configuration checking meta-heuristics, we then develop a constraint-based multi-point local search algorithm to perform a satisfaction search for optimal Golomb rulers of specified length. We then present an algorithm to perform an optimisation search that minimises the length using the satisfaction search repeatedly. Our satisfaction search finds optimal Golomb rulers of up to 19 marks while the optimisation search finds up to 17 marks. [ABSTRACT FROM AUTHOR]

A sophisticated method for node deployment can efficiently reduce the energy consumption of a Wireless Sensor Network (WSN) and prolong the corresponding network lifetime. Pioneers have proposed many node deployment based lifetime optimization methods for WSNs, however, the retransmission mechanism and the discrete power control strategy, which are widely used in practice and have large effect on the network energy consumption, are often neglected and assumed as a continuous one, respectively, in the previous studies. In this paper, both retransmission and discrete power control are considered together, and a more realistic energy-consumption-based network lifetime model for linear WSNs is provided. Using this model, we then propose a generic deployment-based optimization model that maximizes network lifetime under coverage, connectivity and transmission rate success constraints. The more accurate lifetime evaluation conduces to a longer optimal network lifetime in the realistic situation. To illustrate the effectiveness of our method, both one-tiered and two-tiered uniformly and non-uniformly distributed linear WSNs are optimized in our case studies, and the comparisons between our optimal results and those based on relatively inaccurate lifetime evaluation show the advantage of our method when investigating WSN lifetime optimization problems. [ABSTRACT FROM AUTHOR]

This paper specifies a detailed, fully type-based general method for translating the class of all pure, many-sorted algebras of a given constant-free type into an equivalent variety of single-sorted algebras of defined, constant-free type. The complexity of the identities defining the variety is a linear function of the number of sorts and the arity of the fundamental operations. [ABSTRACT FROM AUTHOR]

With XML becoming a ubiquitous language for data interoperability purposes in various domains, efficiently querying XML data is a critical issue. This has lead to the design of algebraic frameworks based on tree-shaped patterns akin to the tree-structured data model of XML. Tree patterns are graphic representations of queries over data trees. They are actually matched against an input data tree to answer a query. Since the turn of the 21st century, an astounding research effort has been focusing on tree pattern models and matching optimization (a primordial issue). This paper is a comprehensive survey of these topics, in which we outline and compare the various features of tree patterns. We also review and discuss the two main families of approaches for optimizing tree pattern matching, namely pattern tree minimization and holistic matching. We finally present actual tree pattern-based developments, to provide a global overview of this significant research topic. [ABSTRACT FROM AUTHOR]

This paper presents an interactive topology optimization application designed for hand-held devices running iOS or Android. The TopOpt app solves the 2D minimum compliance problem with interactive control of load and support positions as well as volume fraction. Thus, it is possible to change the problem settings on the fly and watch the design evolve to a new optimum in real time. The use of an interactive app makes it extremely simple to learn and understand the influence of load-directions, support conditions and volume fraction. The topology optimization kernel is written in C# and the graphical user interface is developed using the game engine Unity3D. The underlying code is inspired by the publicly available 88 and 99 line Matlab codes for topology optimization but does not utilize any low-level linear algebra routines such as BLAS or LAPACK. The TopOpt App can be downloaded on iOS devices from the Apple App Store, at Google Play for the Android platform, and a web-version can be run from . [ABSTRACT FROM AUTHOR]

The scheduling in grids is known to be a NP-hard problem. The distributed deployment of nodes, their heterogeneity and their fluctuations in terms of workload and availability make the design of an effective scheduling algorithm a very complex issue. The scientific literature has proposed several heuristics able to tackle this kind of optimization problem using techniques and strategies inspired by nature. The algorithms belonging to ant colony optimization (ACO) paradigm represent an example of these techniques: each one of these algorithms uses strategies inspired by the self-organization ability of real ants for building effective grid schedulers. In this paper, the authors propose an on line, non-clairvoyant, distributed scheduling solution for multi-broker grid based on the alienated ant algorithm (AAA), a new ACO inspired technique exploiting a 'non natural' behavior of ants and an inverse interpretation of pheromone trails. The paper introduces the proposed algorithm, explains the differences with other classical ACO approaches, and compares AAA with two different algorithms. The results of simulations show that the AAA guarantees good performance in terms of makespan, average queue waiting time and load balancing capability. [ABSTRACT FROM AUTHOR]

Semidefinite programming (SDP) is one of the most active areas in mathematical programming, due to varied applications and the availability of interior point algorithms. In this paper we propose a new pre-processing technique for SDP instances that exhibit algebraic symmetry. We present computational results to show that the solution times of certain SDP instances may be greatly reduced via the new approach. [ABSTRACT FROM AUTHOR]

In this paper, a new Runge-Kutta-Nyström method of fourth algebraic order is developed. The new method has zero phase-lag, zero amplification error and zero first integrals of the previous properties. Numerical results indicate that the new method is very efficient for solving numerically the Schrödinger equation. We note that for the first time in the literature we use the requirement of vanishing the first integrals of phase-lag and amplification error in the construction of efficient methods for the numerical solution of the Schrödinger equation. [ABSTRACT FROM AUTHOR]

In a 1966 paper by C.A.B. Smith, the short and long conjunctive sums of games are defined and methods are described for determining the theoretical winner of a game constructed using one type of these sums. In this paper, we develop a method for determining the winner of a game constructed using arbitrary combinations of these sums. [ABSTRACT FROM AUTHOR]

Polynomial equation systems arising from real applications often have associated combinatorial information, expressible as graphs and underlying matroids. To simplify the system and improve its numerical robustness before attempting to solve it with numeric-algebraic techniques, solvers can employ graph algorithms to extract substructures satisfying or optimizing various combinatorial properties. When there are underlying matroids, these algorithms can be greedy and efficient. In practice, correct and effective merging of the outputs of different graph algorithms to simultaneously satisfy their goals is a key challenge. This paper merges and improves two highly effective but separate graph-based algorithms that preprocess systems for resolving the relative position and orientation of a collection of incident rigid bodies. Such collections naturally arise in many situations, for example in the recombination of decomposed large geometric constraint systems. Each algorithm selects a subset of incidences, one to optimize algebraic complexity of a parametrized system, the other to obtain a well-formed system that is robust against numerical errors. Both algorithms are greedy and can be proven correct by revealing underlying matroids. The challenge is that the output of the first algorithm is not guaranteed to be extensible to a well-formed system, while the output of the second may not have optimal algebraic complexity. Here we show how to reconcile the two algorithms by revealing well-behaved maps between the associated matroids. [ABSTRACT FROM AUTHOR]

Differential Evolution (DE) is a simple and efficient optimizer, especially for continuous optimization. For these reasons DE has often been employed for solving various engineering problems. On the other hand, the DE structure has some limitations in the search logic, since it contains too narrow a set of exploration moves. This fact has inspired many computer scientists to improve upon DE by proposing modifications to the original algorithm. This paper presents a survey on DE and its recent advances. A classification, into two macro-groups, of the DE modifications is proposed here: (1) algorithms which integrate additional components within the DE structure, (2) algorithms which employ a modified DE structure. For each macro-group, four algorithms representative of the state-of-the-art in DE, have been selected for an in depth description of their working principles. In order to compare their performance, these eight algorithm have been tested on a set of benchmark problems. Experiments have been repeated for a (relatively) low dimensional case and a (relatively) high dimensional case. The working principles, differences and similarities of these recently proposed DE-based algorithms have also been highlighted throughout the paper. Although within both macro-groups, it is unclear whether there is a superiority of one algorithm with respect to the others, some conclusions can be drawn. At first, in order to improve upon the DE performance a modification which includes some additional and alternative search moves integrating those contained in a standard DE is necessary. These extra moves should assist the DE framework in detecting new promising search directions to be used by DE. Thus, a limited employment of these alternative moves appears to be the best option in successfully assisting DE. The successful extra moves are obtained in two ways: an increase in the exploitative pressure and the introduction of some randomization. This randomization should not be excessive though, since it would jeopardize the search. A proper increase in the randomization is crucial for obtaining significant improvements in the DE functioning. Numerical results show that, among the algorithms considered in this study, the most efficient additional components in a DE framework appear to be the population size reduction and the scale factor local search. Regarding the modified DE structures, the global and local neighborhood search and self-adaptive control parameter scheme, recently proposed in literature, seem to be the most promising modifications. [ABSTRACT FROM AUTHOR]

Niching is an important technique for multimodal optimization. Most existing niching methods require specification of certain niching parameters in order to perform well. These niching parameters, often used to inform a niching algorithm how far apart between two closest optima or the number of optima in the search space, are typically difficult to set as they are problem dependent. This paper describes a simple yet effective niching algorithm, a particle swarm optimization (PSO) algorithm using a ring neighborhood topology, which does not require any niching parameters. A PSO algorithm using the ring topology can operate as a niching algorithm by using individual particles' local memories to form a stable network retaining the best positions found so far, while these particles explore the search space more broadly. Given a reasonably large population uniformly distributed in the search space, PSO algorithms using the ring topology are able to form stable niches across different local neighborhoods, eventually locating multiple global/local optima. The complexity of these niching algorithms is only O(N), where N is the population size. Experimental results suggest that PSO algorithms using the ring topology are able to provide superior and more consistent performance over some existing PSO niching algorithms that require niching parameters. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the idea of incorporating preference information into evolutionary multi-objective optimization and propose a preference-based evolutionary approach that can be used as an integral part of an interactive algorithm. One algorithm is proposed in the paper. At each iteration, the decision maker is asked to give preference information in terms of his or her reference point consisting of desirable aspiration levels for objective functions. The information is used in an evolutionary algorithm to generate a new population by combining the fitness function and an achievement scalarizing function. In multi-objective optimization, achievement scalarizing functions are widely used to project a given reference point into the Pareto optimal set. In our approach, the next population is thus more concentrated in the area where more preferred alternatives are assumed to lie and the whole Pareto optimal set does not have to be generated with equal accuracy. The approach is demonstrated by numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the multiple-objective optimization problems, considering an improved definition of generalized type I univex function. Some optimality conditions as well as some duality relations are established. [ABSTRACT FROM AUTHOR]

In this paper, a new sequential quadratic programming (SQP) algorithm is proposed to solve the minimax problem which uses the idea of nonmonotonicity. The problem is transformed into an equivalent inequality constrained nonlinear optimization problem. In order to prevent the scaling problem, we do some modifications to the minimization problem. By the non-monotone SQP method, the new algorithm is globally convergent without using a penalty function. Furthermore, it is shown that the proposed method does not suffer from the Maratos effect, so the locally superlinear convergence is achieved. Numerical results suggest that our algorithm for solving the minmax problem is efficient and robust. [ABSTRACT FROM AUTHOR]

In a recent paper [3], D. Buhagiar and B. A. Pasynkov introduced the notion of a supercomplete space and established an internal characterization of these spaces. It is clear that the proof of this characterization actually characterizes c- $$ \mathcal{U} $$-supercomplete spaces. In this short note we state the correct formulation and give a counterexample. [ABSTRACT FROM AUTHOR]

We study graph properties that are testable for bounded-degree graphs in time independent of the input size. Our goal is to distinguish between graphs having a predetermined graph property and graphs that are far from every graph having that property. It is well known that in the bounded-degree graph model (where two graphs are considered "far" if they differ in ϵn edges for a positive constant ϵ), many graph properties cannot be tested even with a constant or even with a polylogarithmic number of queries. Therefore in this paper we focus our attention on testing graph properties for special classes of graphs. Specifically, we show that every hereditary graph property is testable with a constant number of queries provided that every sufficiently large induced subgraph of the input graph has poor expansion. This result implies that, for example, any hereditary property (e.g., k-colorability, H-freeness, etc.) is testable in the bounded-degree graph model for planar graphs, graphs with bounded genus, interval graphs, etc. No such results have been known before, and prior to our work, very few graph properties have been known to be testable with a constant number of queries for general graph classes in the bounded-degree graph model. [ABSTRACT FROM AUTHOR]