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 International Journal of Mathematical Education in Science and Technology       (Followers: 6) International Journal of Mathematics in Operational Research       (Followers: 1) International Journal of Medical Engineering and Informatics       (Followers: 5) International Journal of Micro Air Vehicles       (Followers: 3) International Journal of Microwave and Wireless Technologies       (Followers: 1) International Journal of Microwave Science and Technology       (Followers: 2) International Journal of Mobile Network Design and Innovation       (Followers: 3) International Journal of Multiphase Flow       (Followers: 2) International Journal of Nanomanufacturing       (Followers: 1) International Journal of Nanoscience       (Followers: 1) International Journal of Nanotechnology       (Followers: 5) International Journal of Navigation and Observation       (Followers: 5) International Journal of Network Management International Journal of Nonlinear Sciences and Numerical Simulation       (Followers: 1) International Journal of Numerical Methods for Heat & Fluid Flow       (Followers: 7) International Journal of Optics       (Followers: 1) International Journal of Organisational Design and Engineering       (Followers: 8) International Journal of Pattern Recognition and Artificial Intelligence       (Followers: 6) International Journal of Pavement Engineering       (Followers: 2) International Journal of Physical Modelling in Geotechnics       (Followers: 3) International Journal of Plasticity       (Followers: 6) International Journal of Plastics Technology International Journal of Polymer Analysis and Characterization       (Followers: 3) International Journal of Polymer Science       (Followers: 16) International Journal of Precision Engineering and Manufacturing       (Followers: 6) International Journal of Precision Technology International Journal of Pressure Vessels and Piping       (Followers: 2) International Journal of Production Economics       (Followers: 10) International Journal of Quality and Innovation       (Followers: 3) International Journal of Quality Engineering and Technology       (Followers: 2) International Journal of Quantum Information International Journal of Rapid Manufacturing       (Followers: 2) International Journal of Reliability, Quality and Safety Engineering       (Followers: 4) International Journal of Renewable Energy Technology       (Followers: 7) International Journal of Robust and Nonlinear Control       (Followers: 2) International Journal of Science Engineering and Advance Technology International Journal of Sediment Research       (Followers: 1) International Journal of Self-Propagating High-Temperature Synthesis       (Followers: 2) International Journal of Signal and Imaging Systems Engineering International Journal of Six Sigma and Competitive Advantage International Journal of Social Robotics       (Followers: 1) International Journal of Software Engineering and Knowledge Engineering     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  (Followers: 4) International Journal of Thermodynamics       (Followers: 1) International Journal of Turbo & Jet-Engines International Journal of Ultra Wideband Communications and Systems International Journal of Vehicle Autonomous Systems       (Followers: 1) International Journal of Vehicle Design       (Followers: 6) International Journal of Vehicle Information and Communication Systems       (Followers: 2) International Journal of Vehicle Noise and Vibration       (Followers: 3) International Journal of Vehicle Safety       (Followers: 4) International Journal of Vehicular Technology       (Followers: 2) International Journal of Virtual Technology and Multimedia       (Followers: 4) International Journal of Wavelets, Multiresolution and Information Processing International Journal on Artificial Intelligence Tools       (Followers: 4) International Nano Letters       (Followers: 6) International Review of Applied Sciences and Engineering Inverse Problems in Science and Engineering 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 Journal of Global Optimization    [6 followers]  Follow        Hybrid journal (It can contain Open Access articles)      ISSN (Print) 1573-2916 - ISSN (Online) 0925-5001      Published by Springer-Verlag  [2210 journals]   [SJR: 1.149]   [H-I: 46]
• Column generation bounds for numerical microaggregation
• Abstract: The biggest challenge when disclosing private data is to share information contained in databases while protecting people from being individually identified. Microaggregation is a family of methods for statistical disclosure control. The principle of microaggregation is that confidentiality rules permit the publication of individual records if they are partitioned into groups of size larger or equal to a fixed threshold value, where none is more representative than the others in the same group. The application of such rules leads to replacing individual values by those computed from small groups (microaggregates), before data publication. This work proposes a column generation algorithm for numerical microaggregation in which its pricing problem is solved by a specialized branch-and-bound. The algorithm is able to find, for the first time, lower bounds for instances of three real-world datasets commonly used in the literature. Furthermore, new best known solutions are obtained for these instances by means of a simple heuristic method with the columns generated.
PubDate: 2014-10-01

• Extended formulations for convex envelopes
• Abstract: In this work we derive explicit descriptions for the convex envelope of nonlinear functions that are component-wise concave on a subset of the variables and convex on the other variables. These functions account for more than 30 % of all nonlinearities in common benchmark libraries. To overcome the combinatorial difficulties in deriving the convex envelope description given by the component-wise concave part of the functions, we consider an extended formulation of the convex envelope based on the Reformulation–Linearization-Technique introduced by Sherali and Adams (SIAM J Discret Math 3(3):411–430, 1990). Computational results are reported showing that the extended formulation strategy is a useful tool in global optimization.
PubDate: 2014-10-01

• Influence of ensemble surrogate models and sampling strategy on the
solution quality of algorithms for computationally expensive
black-box global optimization problems
• Abstract: This paper examines the influence of two major aspects on the solution quality of surrogate model algorithms for computationally expensive black-box global optimization problems, namely the surrogate model choice and the method of iteratively selecting sample points. A random sampling strategy (algorithm SO-M-c) and a strategy where the minimum point of the response surface is used as new sample point (algorithm SO-M-s) are compared in numerical experiments. Various surrogate models and their combinations have been used within the SO-M-c and SO-M-s sampling frameworks. The Dempster–Shafer Theory approach used in the algorithm by Müller and Piché (J Glob Optim 51:79–104, 2011) has been used for combining the surrogate models. The algorithms are numerically compared on 13 deterministic literature test problems with 2–30 dimensions, an application problem that deals with groundwater bioremediation, and an application that arises in energy generation using tethered kites. NOMAD and the particle swarm pattern search algorithm (PSWARM), which are derivative-free optimization methods, have been included in the comparison. The algorithms have also been compared to a kriging method that uses the expected improvement as sampling strategy (FEI), which is similar to the Efficient Global Optimization (EGO) algorithm. Data and performance profiles show that surrogate model combinations containing the cubic radial basis function (RBF) model work best regardless of the sampling strategy, whereas using only a polynomial regression model should be avoided. Kriging and combinations including kriging perform in general worse than when RBF models are used. NOMAD, PSWARM, and FEI perform for most problems worse than SO-M-s and SO-M-c. Within the scope of this study a Matlab toolbox has been developed that allows the user to choose, among others, between various sampling strategies and surrogate models and their combinations. The open source toolbox is available from the authors upon request.
PubDate: 2014-10-01

• Stabilizer-based symmetry breaking constraints for mathematical programs
• Abstract: Mathematical programs whose formulation is symmetric often take a long time to solve using Branch-and-Bound type algorithms, because of the several symmetric optima. A simple technique used in these cases is to adjoin symmetry breaking constraints to the formulation before solving the problem. These constraints: (a) aim to guarantee that at least one optimum is feasible, whilst making some of the symmetric optima infeasible; and (b) are usually associated to the different orbits of the action of the formulation group on the set of variable indices. In general, one cannot adjoin symmetry breaking constraints from more than one orbit. In Liberti (Math Program A 131:273–304, doi:10.1007/s10107-010-0351-0, 2012), some (restrictive) sufficient conditions are presented which make it possible to adjoin such constraints from several orbits at the same time. In this paper we present a new, less restrictive method for the same task, and show it performs better computationally.
PubDate: 2014-10-01

• Discretization orders for protein side chains
• Abstract: Proteins are important molecules that are widely studied in biology. Since their three-dimensional conformations can give clues about their function, an optimal methodology for the identification of such conformations has been researched for many years. Experiments of Nuclear Magnetic Resonance (NMR) are able to estimate distances between some pairs of atoms forming the protein, and the problem of identifying the possible conformations satisfying the available distance constraints is known in the scientific literature as the Molecular Distance Geometry Problem (MDGP). When some particular assumptions are satisfied, MDGP instances can be discretized, and solved by employing an ad-hoc algorithm, named the interval Branch & Prune. When dealing with molecules such as proteins, whose chemical structure is known, a priori information can be exploited for generating atomic orderings that allow for the discretization. In previous publications, we presented a handcrafted order for the protein backbones. In this work, we propose 20 new orders for the 20 side chains that can be present in proteins. Computational experiments on artificial and real instances from NMR show the usefulness of the proposed orders.
PubDate: 2014-10-01

• Upper bounding in inner regions for global optimization under inequality
constraints
• Abstract: In deterministic continuous constrained global optimization, upper bounding the objective function generally resorts to local minimization at several nodes/iterations of the branch and bound. We propose in this paper an alternative approach when the constraints are inequalities and the feasible space has a non-null volume. First, we extract an inner region, i.e., an entirely feasible convex polyhedron or box in which all points satisfy the constraints. Second, we select a point inside the extracted inner region and update the upper bound with its cost. We describe in this paper two original inner region extraction algorithms implemented in our interval B&B called IbexOpt (AAAI, pp 99–104, 2011). They apply to nonconvex constraints involving mathematical operators like , $$+\; \bullet ,\; /,\; power,\; sqrt,\; exp,\; log,\; sin$$ . This upper bounding shows very good performance obtained on medium-sized systems proposed in the COCONUT suite.
PubDate: 2014-10-01

• A filter-based artificial fish swarm algorithm for constrained global
optimization: theoretical and practical issues
• Abstract: This paper presents a filter-based artificial fish swarm algorithm for solving nonconvex constrained global optimization problems. Convergence to an $$\varepsilon$$ -global minimizer is guaranteed. At each iteration $$k$$ , the algorithm requires a $$(\rho ^{(k)},\varepsilon ^{(k)})$$ -global minimizer of a bound constrained bi-objective subproblem, where as $$k\rightarrow \infty$$ , $$\rho ^{(k)}\rightarrow 0$$ gives the constraint violation tolerance and $$\varepsilon ^{(k)} \rightarrow \varepsilon$$ is the error bound defining the accuracy required for the solution. The subproblems are solved by a population-based heuristic known as artificial fish swarm algorithm. Each subproblem relies on the approximate solution of the previous one, randomly generated new points to explore the search space for a global solution, and the filter methodology to accept non-dominated trial points. Convergence to a $$(\rho ^{(k)},\varepsilon ^{(k)})$$ -global minimizer with probability one is guaranteed by probability theory. Preliminary numerical experiments show that the algorithm is very competitive when compared with known deterministic and stochastic methods.
PubDate: 2014-10-01

• Abstract: The restriction (prohibition) of certain turns at intersections is a very common task employed by the managers of urban traffic networks. Surprisingly, this approach has received little attention in the research literature. The turning restriction design problem (TRDP) involves finding a set of turning restrictions at intersections to promote flow in a congested urban traffic network. This article uses a successive linear approximation (SLA) method for identifying approximate solutions to a nonlinear model of the TRDP. It aims to adjust the current turning restriction regime in a given network in order to minimize total user travel cost when route choice is driven by user equilibrium principles. Novel features of the method include the facts that it is based on link capacity-based arc travel costs and there is a budget constraint on the total cost of all turning restriction alterations. It has been tested using standard network examples from the literature. One of the tests utilized a multi-start approach which improved the solutions produced by the SLA method. The method was also employed to identify turning restrictions for an actual medium-sized urban traffic network in Brazil. Computational experience with the proposed method is promising.
PubDate: 2014-10-01

• Global optimization workshop 2012
• PubDate: 2014-10-01

• An integer linear programming formulation and heuristics for the minmax
relative regret robust shortest path problem
• Abstract: The well-known Shortest Path problem (SP) consists in finding a shortest path from a source to a destination such that the total cost is minimized. The SP models practical and theoretical problems. However, several shortest path applications rely on uncertain data. The Robust Shortest Path problem (RSP) is a generalization of SP. In the former, the cost of each arc is defined by an interval of possible values for the arc cost. The objective is to minimize the maximum relative regret of the path from the source to the destination. This problem is known as the minmax relative regret RSP and it is NP-Hard. We propose a mixed integer linear programming formulation for this problem. The CPLEX branch-and-bound algorithm based on this formulation is able to find optimal solutions for all instances with 100 nodes, and has an average gap of 17 % on the instances with up to 1,500 nodes. We also develop heuristics with emphasis on providing efficient and scalable methods for solving large instances for the minmax relative regret RSP, based on Pilot method and random-key genetic algorithms. To the best of our knowledge, this is the first work to propose a linear formulation, an exact algorithm and metaheuristics for the minmax relative regret RSP.
PubDate: 2014-10-01

• Finding multiple roots of a box-constrained system of nonlinear equations
with a biased random-key genetic algorithm
• Abstract: Several numerical methods for solving nonlinear systems of equations assume that derivative information is available. Furthermore, these approaches usually do not consider the problem of finding all solutions to a nonlinear system. Rather, most methods output a single solution. In this paper, we address the problem of finding all roots of a system of equations. Our method makes use of a biased random-key genetic algorithm (BRKGA). Given a nonlinear system, we construct a corresponding optimization problem, which we solve multiple times, making use of a BRKGA, with areas of repulsion around roots that have already been found. The heuristic makes no use of derivative information. We illustrate the approach on seven nonlinear equations systems with multiple roots from the literature.
PubDate: 2014-10-01

• Modeling and solving the bi-objective minimum diameter-cost spanning tree
problem
• Abstract: The bi-objective minimum diameter-cost spanning tree problem (bi-MDCST) seeks spanning trees with minimum total cost and minimum diameter. The bi-objective version generalizes the well-known bounded diameter minimum spanning tree problem. The bi-MDCST is a NP-hard problem and models several practical applications in transportation and network design. We propose a bi-objective multiflow formulation for the problem and effective multi-objective metaheuristics: a multi-objective evolutionary algorithm and a fast nondominated sorting genetic algorithm. Some guidelines on how to optimize the problem whenever a priority order can be established between the two objectives are provided. In addition, we present bi-MDCST polynomial cases and theoretical bounds on the search space. Results are reported for four representative test sets.
PubDate: 2014-10-01

• A new hybrid classical-quantum algorithm for continuous global
optimization problems
• Abstract: Grover’s algorithm can be employed in global optimization methods providing, in some cases, a quadratic speedup over classical algorithms. This paper describes a new method for continuous global optimization problems that uses a classical algorithm for finding a local minimum and Grover’s algorithm to escape from this local minimum. Such algorithms will be useful when quantum computers of reasonable size are available. Simulations with testbed functions and comparisons with algorithms from the literature are presented.
PubDate: 2014-10-01

• Optimal rank-sparsity decomposition
• Abstract: We describe a branch-and-bound (b&b) method aimed at searching for an exact solution of the fundamental problem of decomposing a matrix into the sum of a sparse matrix and a low-rank matrix. Previous heuristic techniques employed convex and nonconvex optimization. We leverage and extend those ideas, within a spatial b&b framework, aimed at exact global optimization. Our work may serve to (i) gather evidence to assess the true quality of the previous heuristic techniques, and (ii) provide software to routinely calculate global optima or at least better solutions for moderate-sized instances coming from applications.
PubDate: 2014-10-01

• Integrating nonlinear branch-and-bound and outer approximation for convex
Mixed Integer Nonlinear Programming
• Abstract: In this paper, we present a new hybrid algorithm for convex Mixed Integer Nonlinear Programming (MINLP). The proposed hybrid algorithm is an improved version of the classical nonlinear branch-and-bound (BB) procedure, where the enhancements are obtained with the application of the outer approximation algorithm on some nodes of the enumeration tree. The two methods are combined in such a way that each one collaborates to the convergence of the other. Computational experiments with benchmark instances of the MINLP problem show the good performance of the proposed algorithm, which is compared to the outer approximation algorithm, the nonlinear BB algorithm and the hybrid algorithm implemented in the solver Bonmin.
PubDate: 2014-10-01

• Unified framework for the propagation of continuous-time enclosures for
parametric nonlinear ODEs
• Abstract: This paper presents a framework for constructing and analyzing enclosures of the reachable set of nonlinear ordinary differential equations using continuous-time set-propagation methods. The focus is on convex enclosures that can be characterized in terms of their support functions. A generalized differential inequality is introduced, whose solutions describe such support functions for a convex enclosure of the reachable set under mild conditions. It is shown that existing continuous-time bounding methods that are based on standard differential inequalities or ellipsoidal set propagation techniques can be recovered as special cases of this generalized differential inequality. A way of extending this approach for the construction of nonconvex enclosures is also described, which relies on Taylor models with convex remainder bounds. This unifying framework provides a means for analyzing the convergence properties of continuous-time enclosure methods. The enclosure techniques and convergence results are illustrated with numerical case studies throughout the paper, including a six-state dynamic model of anaerobic digestion.
PubDate: 2014-09-12

• Locating a median line with partial coverage distance
• Abstract: We generalize the classical median line location problem, where the sum of distances from a line to some given demand points is to be minimized, to a setting with partial coverage distance. In this setting, a demand point within a certain specified threshold distance $$r$$ of the line is considered covered and its partial coverage distance is considered to be zero, while non-covered demand points are penalized an amount proportional to their distance to the coverage region. The sum of partial coverage distances is to be minimized. We consider general norm distances as well as the vertical distance and extend classical properties of the median line location problem to the partial coverage case. We are finally able to derive a finite dominating set. While a simple enumeration of the finite dominating set takes $$O(m^3)$$ time, $$m$$ being the number of demand points, we show that this can be reduced to $$O(m^2\log m)$$ in the general case by plane sweeping techniques and even to $$O(m)$$ for the vertical distance and block norm distances by linear programming.
PubDate: 2014-09-09

• Some interesting properties for zero-forcing beamforming under per-antenna
power constraints in rural areas
• Abstract: Providing broadband services in the rural area is a challenging work. Multi-user multiple-input multiple-output (MU-MIMO) systems can be applied to increase spectral efficiency. One of the most commonly used method in MU-MIMO broadcast channel is zero-forcing beamforming (ZFBF) since it provides a good trade off between complexity and performance. In this paper, we consider the ZFBF under the per-antenna power constraints. Particularly, a deterministic line-of-sight modeling of the downlink channels is adopted. To reduce the computational complexity, we consider the problem in which all the equality constraints are eliminated. By examining the KKT optimality conditions and the properties of the channel, some interesting properties are revealed.
PubDate: 2014-09-02

• A canonical duality approach for the solution of affine quasi-variational
inequalities
• Abstract: We propose a new formulation of the Karush–Kunt–Tucker conditions of a particular class of quasi-variational inequalities. In order to reformulate the problem we use the Fisher–Burmeister complementarity function and canonical duality theory. We establish the conditions for a critical point of the new formulation to be a solution of the original quasi-variational inequality showing the potentiality of such approach in solving this class of problems. We test the obtained theoretical results with a simple heuristic that is demonstrated on several problems coming from the academy and various engineering applications.
PubDate: 2014-09-02

• Optimizing assortment and pricing of multiple retail categories with
cross-selling
• Abstract: This paper investigates the joint optimization of assortment and pricing decisions for complementary retail categories. Each category comprises substitutable items (e.g., different coffee brands) and the categories are related by cross-selling considerations that are empirically observed in marketing studies to be asymmetric in nature. That is, a subset of customers who purchase a product from a primary category (e.g., coffee) can opt to also buy from one or several complementary categories (e.g., sugar and/or coffee creamer). We propose a mixed-integer nonlinear program that maximizes the retailer’s profit by jointly optimizing assortment and pricing decisions for multiple categories under a classical deterministic maximum-surplus consumer choice model. A linear mixed-integer reformulation is developed which effectively enables an exact solution to relatively large problem instances using commercial optimization solvers. This is encouraging, because simpler product line optimization problems in the literature have posed significant computational challenges over the last decades and have been mostly tackled via heuristics. Moreover, our computational study indicates that overlooking cross-selling between retail categories can result in substantial profit losses, suboptimal (narrower) assortments, and inadequate prices.
PubDate: 2014-09-02

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