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Abstract: Borodin, Nielsen and Rackoff  introduced the class of priority algorithms as a framework for modeling deterministic greedy-like algorithms. In this paper we address the effect of randomization in greedy-like algorithms. More specifically, we consider approximation ratios within the context of randomized priority algorithms. As case studies, we prove inapproximation results for two well-studied optimization problems, namely facility location and makespan scheduling. [Copyright &y& Elsevier]

Abstract: Many real problems can be modeled to the problems with a hierarchical structure, and bilevel programming is a useful tool to solve the hierarchical optimization problems. So the bilevel programming is widely applied, and numerous methods have been proposed to solve this programming. In this paper, we propose an approximate programming algorithm to solve bilevel nonlinear programming problem. Finally, the example illustrates the feasibility of the proposed algorithm. [Copyright &y& Elsevier]

Abstract: In this paper, by solving the relaxed quasiconcave programming problem in outcome space, a new global optimization algorithm for convex multiplicative programming is presented. Two kinds of techniques are employed to establish the algorithm. The first one is outer approximation technique which is applied to shrink relaxation area of quasiconcave programming problem and to compute appropriate feasible points and to raise the capacity of bounding. And the other one is branch and bound technique which is used to guarantee global optimization. Some numerical results are presented to demonstrate the effectiveness and feasibility of the proposed algorithm. [Copyright &y& Elsevier]

Abstract: We consider a class of global optimization problems, in which the objective function is Lebesgue integrable. In this paper, we present a sufficient and necessary condition for computing the essential infimum. This optimality condition can be used to design algorithms for solving the global optimization problem. [Copyright &y& Elsevier]

Abstract: We consider in this paper the scheduling of families of jobs in which both processing and delivery are coordinated together. Only one vehicle is available to deliver the jobs to specified customers. The jobs can be processed together to form processing batches on the machine and setups of batches are required when the machine is changing from one family to another. Jobs from different families cannot be transported together by the vehicle. The objective is to minimize the time when the vehicle finishes delivering the last delivery batch to its customer and returns to the machine. We propose an -time optimal algorithm for the scheduling problem under the group technology assumption. For the scheduling problem without the group technology assumption, we show that the problem is NP-hard and give an -time dynamic programming algorithm, where is the number of jobs, and is the number of families; we also provide a heuristic algorithm with a performance ratio of 3/2. [Copyright &y& Elsevier]

Abstract: This paper develops an optimal solution procedure for the multi-period online fulfillment assignment problem to determine how many and which of a retailer/e-tailer’s capacitated regional warehouse locations should be set up to handle online sales over a finite planning horizon. To reduce the number of candidate solutions in each period, dominance rules from the facility location literature are extended to handle the nonlinear holding and backorder cost implications of our problem. Computational results indicate that multi-period considerations can play a major role in determining the optimal set of online fulfillment locations. In 92% of our test problems, the multi-period solution incorporated fewer openings and closings than myopic single period solutions. To illustrate the use of the model under changing demands, the multi-period solution yielded different supply chain configurations than the myopic single period solution in over 37% of the periods. [Copyright &y& Elsevier]

Abstract: This paper compares the performances of two different optimisation techniques for solving inverse problems; the first one deals with the Hierarchical Asynchronous Parallel Evolutionary Algorithms software (HAPEA) and the second is implemented with a game strategy named Nash-EA. The HAPEA software is based on a hierarchical topology and asynchronous parallel computation. The Nash-EA methodology is introduced as a distributed virtual game and consists of splitting the wing design variables–aerofoil sections–supervised by players optimising their own strategy. The HAPEA and Nash-EA software methodologies are applied to a single objective aerodynamic ONERA M6 wing reconstruction. Numerical results from the two approaches are compared in terms of the quality of model and computational expense and demonstrate the superiority of the distributed Nash-EA methodology in a parallel environment for a similar design quality. [Copyright &y& Elsevier]

Abstract: In this paper we propose a primal-dual path-following interior-point algorithm for second-order cone optimization. The algorithm is based on a new technique for finding the search directions and the strategy of the central path. At each iteration, we use only full Nesterov–Todd step. Moreover, we derive the currently best known iteration bound for the algorithm with small-update method, namely, , where N denotes the number of second-order cones in the problem formulation and the desired accuracy. [Copyright &y& Elsevier]

Abstract: The power method is an algorithm for computing the largest eigenvalue of matrix A in absolute value. To find the other eigenvalues one can apply the power method to the matrix for some shift σ. This scheme is called the inverse iteration method. Both of these two methods produce a convergence sequence and the limit is approximated by one of the iterates. In the chosen iterate, it may be difficult to estimate the global error, consisting of the truncation error and the round-off error. In this paper, by using the CESTAC method and the CADNA library, we propose a method for computing the optimal iterate, the iterate for which the global error is minimal. In the proposed method the accuracy of the computed eigenvalue may also be estimated. Some numerical examples are given to show the efficiency of the method. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce a vector-valued Tikhonov-type regularization algorithm for an extended-valued multiobjective optimization problem. Under some mild conditions, we prove that any sequence generated by this algorithm converges to a weak Pareto optimal solution of the multiobjective optimization problem. Our results improve and generalize some known results. [Copyright &y& Elsevier]

Abstract: In this paper, by means of a new efficient identification technique of active constraints and the method of strongly sub-feasible direction, we propose a new sequential system of linear equations (SSLE) algorithm for solving inequality constrained optimization problems, in which the initial point is arbitrary. At each iteration, we first yield the working set by a pivoting operation and a generalized projection; then, three or four reduced linear equations with a same coefficient are solved to obtain the search direction. After a finite number of iterations, the algorithm can produced a feasible iteration point, and it becomes the method of feasible directions. Moreover, after finitely many iterations, the working set becomes independent of the iterates and is essentially the same as the active set of the KKT point. Under some mild conditions, the proposed algorithm is proved to be globally, strongly and superlinearly convergent. Finally, some preliminary numerical experiments are reported to show that the algorithm is practicable and effective. [Copyright &y& Elsevier]

Abstract: In this paper, a new filled function which has better properties is proposed for identifying a global minimum point for a general class of nonlinear programming problems within a closed bounded domain. An algorithm for unconstrained global optimization is developed from the new filled function. Theoretical and numerical properties of the proposed filled function are investigated. The implementation of the algorithm on seven test problems is reported with satisfactory numerical results. [Copyright &y& Elsevier]

Abstract: This paper considers two semi-online scheduling problems, one with known optimal value and the other with known total sum, on two uniform machines with a machine speed ratio of . For the first problem, we provide an optimal algorithm for , and improved algorithms or/and lower bounds for , over which the optimal algorithm is unknown. As a result, the largest gap between the competitive ratio and the lower bound decreases to 0.02192. For the second problem, we also present algorithms and lower bounds for . The largest gap between the competitive ratio and the lower bound is 0.01762, and the length of the interval over which the optimal algorithm is unknown is 0.47382. Our algorithms and lower bounds for these two problems provide insights into their differences, which are unusual from the viewpoint of the known results on these two semi-online scheduling problems in the literature. [Copyright &y& Elsevier]

Abstract: In this paper, we present a nonmonotone conic trust region method based on line search technique for unconstrained optimization. The new algorithm can be regarded as a combination of nonmonotone technique, line search technique and conic trust region method. When a trial step is not accepted, the method does not resolve the trust region subproblem but generates an iterative point whose steplength satisfies some line search condition. The function value can only be allowed to increase when trial steps are not accepted in close succession of iterations. The local and global convergence properties are proved under reasonable assumptions. Numerical experiments are conducted to compare this method with the existing methods. [Copyright &y& Elsevier]

Abstract: Recently, an efficient reversible lossless data hiding algorithm by Ni et al. was presented. Their fast algorithm can recover the original image without any distortion and its PSNR lower bound is higher than that of all existing reversible data hiding algorithms. Instead of selecting the peak-valley pairs in a greedy way, this paper presents a dynamic programming-based reversible data hiding algorithm to determine the most suitable peak-valley pairs such that the embedding capacity object can be maximized. Based on some artificial map images, experimental results demonstrate that our proposed algorithm has 9% embedding capacity improvement ratio and has the similar image quality performance when compared to Ni et al.’s algorithm although it has some execution-time degradation. For natural images, the embedding capacity of Ni et al.’s algorithm is very close to the maximal embedding capacity obtained by our proposed algorithm. Furthermore, the comparison between our proposed dynamic programming-based algorithm and the reversible data hiding algorithm by Chang et al. is investigated. [Copyright &y& Elsevier]

Abstract: The optimization of parallel applications is difficult to achieve by classical optimization techniques because of their diversity and the variety of actual parallel and distributed platforms and/or environments. Adaptive algorithmic schemes, capable of dynamically changing the allocation of jobs during the execution to optimize global system behavior, are the best alternatives for solving this problem. In this paper, we focus on non-clairvoyant scheduling of parallel jobs with known resource requirements but unknown running times, with emphasis on the regulation of idle periods in the context of general list policies. We consider a new family of scheduling strategies based on two phases which successively combine sequential and parallel execution of jobs. We generalize known worst-case performance bounds by considering two extra parameters, in addition to the number of processors and maximum processor requirements considered in the literature, namely, job parallelization penalty and idle regulation factor. Furthermore, we prove that under certain conditions of idle regulation, the performance guarantee of parallel job scheduling in space-sharing mode can be improved. [Copyright &y& Elsevier]

Abstract: This paper presents an affine scaling optimal path approach in association with nonmonotonic interior backtracking line search technique for nonlinear optimization subject to linear constraints. We shall employ the eigensystem decomposition and affine scaling mapping to form affine scaling optimal curvilinear path very easily. By using interior backtracking line search technique, each iterate switches to trial step of strict interior feasibility. The nonmonotone criterion is used to speed up the convergence progress in the contours of objective function with large curvature. Theoretical analysis is given which prove that the proposed algorithm is globally convergent and has a local superlinear convergence rate under some reasonable conditions. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm. [Copyright &y& Elsevier]

Abstract: In this paper, one novel genetic algorithm dynamic chain-like agent genetic algorithm (CAGA) is proposed for solving global numerical optimization problem and feature selection problem. The CAGA combines the chain-like agent structure with dynamic neighboring genetic operators to get higher optimization capability. An agent in chain-like agent structure represents a candidate solution to the optimization problem. Any agent interacts with neighboring agents to evolve. With dynamic neighboring genetic operators, they compete and cooperate with their neighbors, and can use knowledge to increase energies. Global numerical optimization problem and feature selection problem are the most important problems for evolutionary algorithm, especially for genetic algorithm. Hence, the experiments of global numerical optimization and feature selection are necessary to verify the performance of genetic algorithms. Corresponding experiments have been done and show that CAGA is suitable for real coding and binary coding optimization problems, and has more precise and more stable optimization results. [Copyright &y& Elsevier]

Abstract: In this paper, an efficient approach to search for the global threshold of image using Gaussian mixture model is proposed. Firstly, a gray-level histogram of an image is represented as a function of the frequencies of gray-level. Then to fit the Gaussian mixtures to the histogram of image, the expectation maximization (EM) algorithm is developed to estimate the number of Gaussian mixture of such histograms and their corresponding parameterization. Finally, the optimal threshold which is the average of these Gaussian mixture means is chosen. And the experimental results show that the new algorithm performs better. [Copyright &y& Elsevier]

Abstract: Particle swarm optimization is a novel swarm-intelligence-based algorithm and a valid optimization technique. However, the algorithm suffers from the premature convergence problem when facing to complex optimization problem. In order to keep the balance between the global exploration and the local exploitation validly, the paper develops a knowledge-based cooperative particle swarm optimization (KCPSO). KCPSO mainly simulates the self-cognitive and self-learning process of evolutionary agents in special environment, and introduces a knowledge billboard to record varieties of search information. Moreover, KCPSO takes advantage of multi-swarm to maintain the swarm diversity and tries to guide their evolution by the shared information. Under the guide of the shared information, KCPSO manipulates each sub-swarm to go on with local exploitation in different local area, in which every particle follows a social learning behavior mode; at the same time, KCPSO carries out the global exploration through the escaping behavior and the cooperative behavior of the particles in different sub-swarms. KCPSO can maintain appropriate swarm diversity and alleviate the premature convergence validly. The proposed model was applied to some well-known benchmarks. The relative experimental results show KCPSO is a robust global optimization method for the complex multimodal functions. [Copyright &y& Elsevier]

Abstract: Quantum-behaved particle swarm optimization (QPSO) algorithm is a global convergence guaranteed algorithms, which outperforms original PSO in search ability but has fewer parameters to control. In this paper, we propose an improved quantum-behaved particle swarm optimization with weighted mean best position according to fitness values of the particles. It is shown that the improved QPSO has faster local convergence speed, resulting in better balance between the global and local searching of the algorithm, and thus generating good performance. The proposed improved QPSO, called weighted QPSO (WQPSO) algorithm, is tested on several benchmark functions and compared with QPSO and standard PSO. The experiment results show the superiority of WQPSO. [Copyright &y& Elsevier]

Abstract: This paper presents a novel particle swarm optimization algorithm from the angle of ecological population evolution, called the ecological particle swarm optimization, or EPSO. Initially, ecological population competition model (EPCM) is presented. From the basis of the EPCM, the EPSO algorithm and its general framework are proposed; in which particle swarm system with ecological hierarchy and competition model is defined and two collocating strategies of inertia weight factor are considered. The convergence performance and population dynamics including population aggregation and population diversity of the proposed approach are discussed separately through empirical simulations with well-known benchmarks from the standard literature. [Copyright &y& Elsevier]

Abstract: In this paper, the dynamic multi-objective optimization problem (DMOP) is first approximated by a series of static multi-objective optimization problems (SMOPs) by dividing the time period into several equal subperiods. In each subperiod, the dynamic multi-objective optimization problem is seen as a static multi-objective optimization problem by taking the time parameter fixed. Then, to decrease the amount of computation and efficiently solve the static problems, each static multi-objective optimization problem is transformed into a two-objective optimization problem based on two re-defined objectives. Finally, a new crossover operator and mutation operator adapting to the environment changing are designed. Based on these techniques, a new evolutionary algorithm is proposed. The simulation results indicate that the proposed algorithm can effectively track the varying Pareto fronts with time. [Copyright &y& Elsevier]

Abstract: This paper proposes a new frame-based pattern search algorithm for unconstrained optimization. The implementation of filter leads the sequence of function values at iterates nonmonotonically decreasing and thus motivates us to consider nonmonotone technique. Furthermore, the use of these two techniques can improve the efficiency of general pattern search algorithms. The numerical results show that the new algorithm is practical and efficient. [Copyright &y& Elsevier]

Abstract: In this paper, we study the conditions in which the random hill-climbing algorithm (1 + 1)-EA compares favorably to other evolutionary algorithms (EAs) in terms of fitness function distribution at a given iteration and with respect to the average optimization time. Our approach is applicable when the reproduction operator of an evolutionary algorithm is dominated by the mutation operator of the (1 + 1)-EA. In this case one can extend the lower bounds obtained for the expected optimization time of the (1 + 1)-EA to other EAs based on the dominated reproduction operator. This method is demonstrated on the sorting problem with HAM landscape and the exchange mutation operator. We consider several simple examples where the (1 + 1)-EA is the best possible search strategy in the class of the EAs. [Copyright &y& Elsevier]

Abstract: In many countries the power systems are going to move toward creating a competitive structure for selling and buying electrical energy. These changes and the numerous advantages of the distributed generation units (DGs) in term of their technology enhancement and economical considerations have created more incentives to use these kinds of generators than before. Therefore, it is necessary to study the impact of DGs on the power systems, especially on the distribution networks. The distribution feeder reconfiguration (DFR) is one of the most important control schemes in the distribution networks, which can be affected by DGs. This paper presents a new approach to DFR at the distribution networks considering DGs. The main objective of the DFR is to minimize the deviation of the bus voltage, the number of switching operations and the total cost of the active power generated by DGs and distribution companies. Since the DFR is a nonlinear optimization problem, we apply the particle swarm optimization (PSO) approach to solve it. The feasibility of the proposed approach is demonstrated and compared with other evolutionary methods such as genetic algorithm (GA), Tabu search (TS) and differential evolution (DE) over a realistic distribution test system. [Copyright &y& Elsevier]

Abstract: In this paper, a robust algorithm is proposed for globally solving a nonconvex quadratic programming problem (P1) with several additional multiplicative constraints. To our knowledge, little progress has been made so far for globally solving problem (P1). The proposed algorithm is based on a robust solution approach that provides an essential -optimal solution. This solution is also stable under small perturbations of the constraints, and it turns out that such a robust optimal solution is adequately guaranteed to be feasible and to be close to the actual optimal solution. Convergence of the algorithm is shown and three solved sample problems are given to illustrate the robust stability and feasibility of the present algorithm. [Copyright &y& Elsevier]

Abstract: In this paper, a new adaptive differential evolution algorithm (ADEA) is proposed for multiobjective optimization problems. In ADEA, the variable parameter F based on the number of the current Pareto-front and the diversity of the current solutions is given for adjusting search size in every generation to find Pareto solutions in mutation operator, and the select operator combines the advantages of DE with the mechanisms of Pareto-based ranking and crowding distance sorting. ADEA is implemented on five classical multiobjective problems, the results illustrate that ADEA efficiently achieves two goals of multiobjective optimization problems: find the solutions converge to the true Pareto-front and uniform spread along the front. [Copyright &y& Elsevier]

Blocking artifact is a prevailing degradation caused by the block-based Discrete Cosine Transform (BDCT) coding technique under low bit-rate conditions. In this paper, we propose an efficient no-reference noticeable blockiness estimation algorithm for BDCT coded images. The difference on block boundaries is first measured and then transformed into the block discontinuity map. We consider the effects of luminance adaptation and texture masking on blocking and integrate them using a nonlinear operator to form an overall masking map. This map is finally incorporated with the discontinuity map to generate Noticeable Blockiness Map (NBM), which can be used to guide perceptual quality assessment, codec parameter optimization, post-processing, etc. We have demonstrated the validity of the NBM through its applications in no-reference image quality assessment and image deblocking. [Copyright &y& Elsevier]

Abstract: In this paper, we present a general algorithm for nonlinear programming which uses a slanting filter criterion for accepting the new iterates. Independently of how these iterates are computed, we prove that all accumulation points of the sequence generated by the algorithm are feasible. Computing the new iterates by the inexact restoration method, we prove stationarity of all accumulation points of the sequence. [Copyright &y& Elsevier]

Abstract: Particle swarm optimization (PSO) as an efficient and powerful problem-solving strategy has been widely used, but appropriate adjustment of its parameters usually requires a lot of time and labor. So a co-evolving framework is proposed to improve the robustness of the PSO. In this paper, within this framework the fuzzy rules for the manipulation of the inertia weights are co-evolved with the particles. And the simulation results on a suite of test functions show that the use of this co-evolving framework improves the performance of the PSO, especially the robustness against the dimensional variation of the test functions. [Copyright &y& Elsevier]

Abstract: Holonic manufacturing systems (HMS) is based on the notion of holon, an autonomous, cooperative and intelligent entity to provide a econfigurable, flexible and decentralized manufacturing environment to respond to changing needs and opportunities. A set of holons that cooperate to achieve a goal forms a holarchy. How to design a mechanism to form a holarchy to achieve a goal while minimizing the overall cost is a challenge. The objectives of this paper are to propose models and develop collaborative algorithms to guide the holons to form a holarchy to coherently move toward the desired goal state ultimately. We adopt contract net protocol (CNP) to model mutual selection of holons in forming a holarchy. We formulate a holarchy optimization problem to minimize the cost subject to the feasibility constraints. To analyze the feasibility of a holarchy, a Petri net (PN) model is proposed. As classical PN models do not take into account the cost involved in firing transitions, we augment the PN model with cost functions in the problem formulation. Due to the distributed architecture of HMS, the internal structure of each potential holarchy that acts as bidder in CNP is not available to the manager. A key issue is to determine the feasibility of a holarchy without constructing the whole PN model of the given hierarchy. We study the feasible conditions for a holarchy and propose a collaborative algorithm to analyze the feasibility and award contracts to holons without constructing the whole model of a holarchy. [Copyright &y& Elsevier]

Personalisation of web information systems (WISs) means customisation of the presented data content to the needs of users, restricting the available functionality to the goals and preferences of users, and tailoring the web presentation according to used devices and style options. This paper primarily concentrates on the customisation of functionality by making all those operations available to a user that are needed to achieve a specified goal, and by organising them in an action scheme called plot that is in accordance with the behavioural preferences of the user. Plots are formalised by algebraic expressions in Kleene algebras with tests (KATs). Then personalisation can be formalised as an optimisation problem with equational preference rules, for which a term rewriting approach is proposed. In a second step the approach is extended to conditional term rewriting thereby dispensing with the particular need to associate preference rules with user profiles. Finally, the approach is refined by taking content specifications via extended views and abstract programs on these views into account. This leads us to reformulating the personalisation problem in higher-order dynamic logic. [Copyright &y& Elsevier]

Abstract: A multiple-choice knapsack problem can be formulated as a discrete nonlinear knapsack problem (DNKP). A powerful method for solving DNKP is the dynamic programming solution approach. The use of this powerful approach however is limited since the growth of the number of decision variables and state variables requires an extensive computer memory storage and computational time. In this paper we developed a hybrid algorithm for improving the computational efficiency of the dynamic programming when it is applied for solving the DNKP. In the hybrid algorithm, three routines of the imbedded state, surrogate constraints, and bounding scheme are incorporated for increasing the efficiency of this solution approach. We then conducted an experimental study for comparing the computational efficiency of the hybrid algorithm with the imbedded state dynamic programming approach. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to propose and compare different one-dimensional maps as chaotic search patterns in the constraint nonlinear optimization problems. For this purpose, about 10 one-dimensional maps are introduced that can be used as search pattern in chaos optimization algorithms. We apply these maps in specific optimization algorithm (weighted gradient direction based chaos optimization algorithm) and compare them based on numerical simulation results. [Copyright &y& Elsevier]

Based on P systems, this paper proposes a new multi-objective optimization algorithm (PMOA). Similar to P systems, PMOA has a cell-like structure. The structure is dynamic and its membranes merge and divide at different stages. The key rule of a membrane is the communication rule which is derived from P systems. Mutation rules are important for the algorithm, which has different ranges of mutation in different membranes. The cooperation of the two rules contributes to the diversity of the population, the conquest of the multimodality of objective function and the convergence of algorithm. Moreover, the unique structure divides the whole population into several subpopulations, which decreases the computational complexity. Almost a dozen popular algorithms are compared using several test problems. Simulation results illustrate that the PMOA has the best performance. Its solutions are closer to the true Pareto-optimal front and distributed well. Moreover, it converges fast. [ABSTRACT FROM AUTHOR]

Abstract: This article presents an approach to solve the travelling salesman problem using linear optimisation with a suitable set of constraints. Such approaches are well known as Cutting Plane methods but previously applied algorithms still suffer from the NP-completeness of the problem causing an exponential number of computational steps in the worst case. The method presented in this paper both tolerates non-integer results for a dedicated class of solutions (symmetric solutions) and avoids other ones (asymmetric solutions). It is thus able to deal with the inherent complexity of the travelling salesman problem.Therefore the overall complexity of the optimisation algorithm remains polynomial in the worst case. [Copyright &y& Elsevier]

Abstract: This paper studies a successive partitioning group correction algorithm and its some modified algorithms for solving large scale sparse unconstrained optimization problems. The methods depend on a symmetric consistent partition of the columns of the Hessian matrix. A q-superlinear convergence result and an r-convergence rate estimate show that the methods have good local convergence properties. The numerical results show that the methods, especially the modified algorithms, may be competitive with some current used algorithms. [Copyright &y& Elsevier]

Abstract: Many practical problems can be formulated as constrained optimization problems. Due to the simple concept and easy implementation, the penalty function method has been one of the most common techniques to handle constraints. However, the performance of this technique greatly relies on the setting of penalty factors, which are usually determined by manual trial and error, and the suitable penalty factors are often problem-dependent and difficult to set. In this paper, a differential evolution approach based on a co-evolution mechanism, named CDE, is proposed to solve the constrained problems. First, a special penalty function is designed to handle the constraints. Second, a co-evolution model is presented and differential evolution (DE) is employed to perform evolutionary search in spaces of both solutions and penalty factors. Thus, the solutions and penalty factors evolve interactively and self-adaptively, and both the satisfactory solutions and suitable penalty factors can be obtained simultaneously. Simulation results based on several benchmark functions and three well-known constrained design problems as well as comparisons with some existed methods demonstrate the effectiveness, efficiency and robustness of the proposed method. [Copyright &y& Elsevier]

In this paper we present a method of parameter optimization, relative trust-region learning, where the trust-region method and the relative optimization [M. Zibulevsky, Blind source separation with relative Newton method, in: Proceedings of the ICA, Nara, Japan, 2003, pp. 897–902] are jointly exploited. The relative trust-region method finds a direction and a step size with the help of a quadratic model of the objective function (as in the conventional trust-region methods) and updates parameters in a multiplicative fashion (as in the relative optimization). We apply this relative trust-region learning method to the problem of independent component analysis (ICA), which leads to the relative TR-ICA algorithm which turns out to possess the equivariant property (as in the relative gradient) and to achieve faster convergence than the relative gradient and even Newton-type algorithms. Empirical comparisons with several existing ICA algorithms demonstrate the useful behavior of the relative TR-ICA algorithm, such as the equivariant property and fast convergence. [Copyright &y& Elsevier]

Abstract: In this paper, a global optimization algorithm, which relies on the exponential variable transformation of the signomial geometric programming (SGP) and the Lagrangian duality of the transformed programming, is proposed for solving the signomial geometric programming (SGP). The difficulty in utilizing Lagrangian duality within a global optimization context is that the restricted Lagrangian function for a given estimate of the Lagrangian multipliers is often nonconvex. Minimizing a linear underestimation of the restricted Lagrangian overcomes this difficulty and facilitates the use of Lagrangian duality within a global optimization framework. In the new algorithm the lower bounds are obtained by minimizing the linear relaxation of restricted Lagrangian function for a given estimate of the Lagrange multipliers. A branch-and-bound algorithm is presented that relies on these Lagrangian relaxations to provide lower bounds and on the interval Newton method to facilitate convergence in the neighborhood of the global solution. Computational results show that the algorithm is efficient. [Copyright &y& Elsevier]

Abstract: In this paper we study the higher secant varieties of Grassmann varieties in relation to the functional Waring’s problem for alternating tensors and to the Alexander–Hirschowitz theorem. We show how to identify defective higher secant varieties of Grassmannians using a probabilistic method involving Terracini’s lemma, and we describe an algorithm which can compute, by numerical methods, dim (S s G(k, n)) for n ⩽14. Our main result is that, except for Grassmannians of lines, if n ⩽14 and (if n =14 we have studied the case k ⩽5) there are only the four known defective cases: S 2 G(2,6), S 2 G(3,7), S 3 G(3,7) and S 3 G(2,8). [Copyright &y& Elsevier]

Abstract: This paper presents several algorithms that compute border bases of a zero-dimensional ideal. The first relates to the FGLM algorithm as it uses a linear basis transformation. In particular, it is able to compute border bases that do not contain a reduced Gröbner basis. The second algorithm is based on a generic algorithm by Bernard Mourrain originally designed for computing an ideal basis that need not be a border basis. Our fully detailed algorithm computes a border basis of a zero-dimensional ideal from a given set of generators. To obtain concrete instructions we appeal to a degree-compatible term ordering and hence compute a border basis that contains the reduced -Gröbner basis. We show an example in which this computation actually has advantages over Buchberger''s algorithm. Moreover, we formulate and prove two optimizations of the Border Basis Algorithm which reduce the dimensions of the linear algebra subproblems. [Copyright &y& Elsevier]

Abstract: Stochastic searching methods have been applied widely to areas such as continuous and combinatorial optimization problems in a number of disciplines. Many existing methods solve these problems by navigating on the surface of the possibly rugged landscape. This kind of navigation is not very effective because the property of the landscape at different resolutions can be very different. Time spent at the beginning of the search on the detailed part of the landscape is often useless. Appropriate searching strategies should be adopted at different resolutions. In this paper, we propose a new probabilistic searching model for global optimization. The main contributions of the model are (1) to provide a basis for resolution control and smoothing of search space and (2) to introduce continuous memory into stochastic search. The basis of resolution control is achieved by dividing the search space into a finite number of n-dimensional partitions structurally. The number of partitions governs the resolution of the search space. The more the partitions, the finer is the search space and the more detailed and rugged is the landscape. The benefits are twofold. First, the rugged landscape problem can be smoothed, because the ruggedness is a matter of the number of partitions. Hence, the difficulty in search due to the ruggedness of the landscape can be controlled. Second, it provides a basis to implement algorithms that may change the ‘view’ of the landscape during the search process because we can dynamically divide the search space accordingly. Another important feature that we use is continuous memory. Throughout the search process, searching experience is continuously accumulated in order to shape the global picture of the search space guiding the future searching direction. We present results on the algorithm performance in handling numerical function optimization. The empirical results show that our new model is comparable to, and in many cases performs better than, that of the other advanced methods in terms of solution quality and computation required. [Copyright &y& Elsevier]

Abstract: Consider the problem of computing the smallest enclosing ball of a set of m balls in . This problem arises in many applications such as location analysis, military operations, and pattern recognition, etc. In this paper, we reformulate this problem as an unconstrained convex optimization problem involving the maximum function max{0, t}, and then develop a simple algorithm particularly suitable for problems in high dimensions. This algorithm could efficiently handle problems of dimension n up to 10,000 under a moderately large m, as well as problems of dimension m up to 10,000 under a moderately large n. Numerical results are given to show the efficiency of algorithm. [Copyright &y& Elsevier]

Abstract: Research on a new metaheuristic for optimization is often initially focused on proof-of-concept applications. It is only after experimental work has shown the practical interest of the method that researchers try to deepen their understanding of the method''s functioning not only through more and more sophisticated experiments but also by means of an effort to build a theory. Tackling questions such as “how and why the method works’’ is important, because finding an answer may help in improving its applicability. Ant colony optimization, which was introduced in the early 1990s as a novel technique for solving hard combinatorial optimization problems, finds itself currently at this point of its life cycle. With this article we provide a survey on theoretical results on ant colony optimization. First, we review some convergence results. Then we discuss relations between ant colony optimization algorithms and other approximate methods for optimization. Finally, we focus on some research efforts directed at gaining a deeper understanding of the behavior of ant colony optimization algorithms. Throughout the paper we identify some open questions with a certain interest of being solved in the near future. [Copyright &y& Elsevier]

Abstract: We consider a multiserver retrial queueing model with applications in service industries, in which customers arrive according to a Markovian arrival process (MAP). Any admitted customer either [(a)] gets service and leaves the system as a satisfied primary customer; or [(b)] gets service and becomes a secondary customer. The secondary customers leave the system either as satisfied or unsatisfied with their services. In this paper, we perform the steady state analysis of the model and also study the algorithmic aspects of this queueing model including an optimization problem. [Copyright &y& Elsevier]

Abstract: In this paper, the nonlinear dynamic system of continuous glycerol fermentations to 1,3-propanediol by klebsiella pneumoniae is investigated. Considering big errors between the experimental results and computational values in the previous works, we establish the parameter identification model for the system. The properties of the solutions for the nonlinear dynamic system are discussed and the identifiability of the parameters is proved. Finally the feasible optimization algorithm is constructed to find the optimal parameters for the system. [Copyright &y& Elsevier]

Abstract: In this paper we show that the unconstrained continuous global minimization problem cannot be solved by any algorithm, so we consider the box constrained continuous global minimization problem. We present a definition of filled function for the problem. Moreover, a new class of filled functions are constructed, which contains only one parameter. A randomized algorithm is designed to solve the box constrained continuous global minimization problem based on the filled function. Numerical experiments are presented to show the practicability of the algorithm. [Copyright &y& Elsevier]

Abstract: In this paper, a novel algorithm is proposed for solving multiobjective optimization problems. The proposed algorithm, multiobjective differential evolution (MODE), is applied to optimize industrial adiabatic styrene reactor considering productivity, selectivity and yield as the main objectives. Five combinations of the objectives are considered. Pareto set (a set of equally good solutions) obtained for all the cases is compared with results reported using non-dominated sorting genetic algorithm (NSGA). The results show that all objectives besides profit can be improved compared to those reported using NSGA and current operating conditions. The Pareto optimal front provides wide-ranging optimal operating conditions and an appropriate operating point can be selected based on the requirements of the user. [Copyright &y& Elsevier]