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Abstract: We show that the main results in the recent paper [4] by Sadiq Basha (2012) are not real generalizations but particular cases of existing fixed point theorems in the literature. [Copyright &y& Elsevier]

Abstract: In this paper, we focus on the proposed algorithms to solve a linear programming problem with the convex combination of the max–min and the max–average composition and the max–star composition, respectively. They have been proposed by Ghodousian and Khorram [A. Ghodousian, E. Khorram, Solving a linear programming problem with the convex combination of the max–min and the max–average fuzzy relation equations, Appl. Math. Comput. 180 (2006) 411–418] and Khorram et al. [E. Khorram, A. Ghodousian, A. Abbasi Molai, Solving linear optimization problems with max–star composition equation constraints, Appl. Math. Comput. 179 (2006) 654–661], respectively. Firstly, we show that the “Tabular method algorithm” in the first paper and the “First procedure” in the second paper may not lead to the optimal solutions of the two models in some cases. Secondly, we generalize the proposed algorithm by Abbasi Molai and Khorram [A. Abbasi Molai, E. Khorram, A modified algorithm for solving the proposed models by Ghodousian and Khorram and Khorram and Ghodousian, Appl. Math. Comput. 190 (2007) 1161–1167] to solve the two models. In fact, it modifies the presented algorithms in the two papers. Finally, some numerical examples are given to illustrate the purposes. [Copyright &y& Elsevier]

Abstract: The aim of this note is to show that the optimization algorithm proposed in may not lead to the optimal solution in some cases. In fact, the optimization problem remains open if we do not apply the branch-and-bound method to solve it or compute all the objective values of minimal solutions of the feasible domain. [Copyright &y& Elsevier]

Abstract: A counterexample is provided in this short note to show that some of local convergence theorems established in [D.K.R. Babajee, M.Z. Dauhoo, An analysis of the properties of the variants of Newton’s method with third order convergence, Appl. Math. Comput. 183 (2006) 659–684] are not always true. Some mistakes in the proofs of these theorems are pointed out. [Copyright &y& Elsevier]

Abstract: The aim of this short note is to show on a numerical example that one of the two optimization algorithms proposed in [E. Khorram, A. Ghodousian, Linear objective function optimization with fuzzy relation equation constraints regarding max-av composition, Appl. Math. Comput. 173 (2006) 872–886] may not lead to the optimal solution in some cases. Besides it will be pointed out that the other algorithm (correct, but unfortunately ineffective for larger problems) proposed in [E. Khorram, A. Ghodousian, Linear objective function optimization with fuzzy relation equation constraints regarding max-av composition, Appl. Math. Comput. 173 (2006) 872–886] can be extended to a wider class of non-convex optimization problems. [Copyright &y& Elsevier]

In this paper, we first present a modified Chambolle–Pock primal-dual method (MCPPDM) to solve a convex composite optimization problem which minimizes the sum of two convex functions with one composed by a linear operator. It is well known that the Chambolle–Pock primal-dual method (CPPDM) with the combination parameter being 1 is an application of the proximal point algorithm and thus is convergent, however, when the combination parameter is not 1, the method may be not convergent. To choose flexibly the combination parameter, we develop a slightly modified version with little additional computation cost. In CPPDM, one variable is updated twice but another variable is updated only once at each iteration. However, in the modified version, two variables are respectively updated twice at each iteration. Another main task of this paper is that we reformulate some well-known sparse recovery problems as special cases of the convex composite optimization problem and then apply MCPPDM to address these sparse recovery problems. A large number of numerical experiments have demonstrated that the efficiency of the proposed method is generally comparable or superior to that of existing well-known methods such as the linearized alternating direction method of multipliers and the graph projection splitting algorithm in terms of solution quality and run time. [ABSTRACT FROM AUTHOR]

Many practical problems involve the search for the global extremum in the space of the system parameters. The functions to be optimized are often highly multiextremal, black-box with unknown analytical representations, and hard to evaluate even in the case of one parameter to be adjusted in the presence of non-linear constraints. The interest of both the stochastic (in particular, metaheuristic) and mathematical programming (in particular, deterministic) communities to the comparison of metaheuristic and deterministic classes of methods is well recognized. Although both the communities have a huge number of journal and proceedings papers, a few of them are really dedicated to a systematic comparison of the methods belonging to these two classes. This paper meets the requirement of such a comparison between nature-inspired metaheuristic and deterministic algorithms (more than 125,000 launches of the methods have been performed) and presents an attempt (beneficial to practical fields including engineering design) to bring together two rather disjoint communities of metaheuristic and mathematical programming researchers and applied users. [ABSTRACT FROM AUTHOR]

This paper studies the parameter tuning problem for a class of extended disturbance observers (EDO) and the EDO-based sliding mode control (SMC). Based on a H 2 optimization technique, analytical solutions for the parameter tuning of the EDO and the EDO-based SMC are obtained. The conditions under which higher-order EDOs are strictly better than lower-order EDOs are derived analytically. Furthermore, the steady-state performance of the EDO-based SMC is analyzed, where it is shown that the improvement of the tracking accuracy of the EDO can reduce the sensitivity of the state variables and the control input with respect to the controller parameters. This implies that the SMC parameter tuning requirement can be reduced if a high tracking accuracy of the EDO is guaranteed. Finally, the application to the active structural control problem of an offshore wind turbine is studied and the effectiveness of the obtained results is demonstrated based on a National Renewable Energy Laboratory (NREL) 5MW baseline offshore wind turbine. • Parameter tuning for an extended disturbance observer and sliding mode control is studied. • Analytical solutions are derived based on a H 2 optimization method. • Conditions for higher-order EDOs being better than the lower-order ones are obtained. • Influence of the EDO on the steady-state behavior of a sliding mode control is analyzed. • The effectiveness is verified via the application of an offshore wind turbine. [ABSTRACT FROM AUTHOR]

• We propose a fast error estimation method for LRBF for the first time. • Based on the error estimation method, we propose an adaptive shape parameter selection strategy for LRBF for the first time, and give a complete process. • A particle swarm optimization algorithm is used to realize the complete process proposed above, and the feasibility of this method is verified by using test functions and multi type boundary problems. Radial basis function (RBF) is a basis function suitable for scattered data interpolation and high dimensional function interpolation, wherein the independent shape parameters have a direct impact on the accuracy of calculation results. Research in this field is mostly concerned with the shape parameter selection strategy based on the premise of global distribution or block regional distribution. In this paper, a shape parameter selection strategy is proposed, which is used for the local RBF collocation method (LRBF) for solving partial differential equations. It overcomes many limitations of the traditional methods applied to LRBF. In this strategy, a set of twin matrices similar to the interpolation matrix are constructed to evaluate the error of the model. In addition, the penalty term contained in the twin matrix is used to relax the influence of the far end region on the target node. Since the objective problem is nonlinear, a particle swarm optimization algorithm (PSO) is employed to minimize the training objective and adjust the shape parameters of the basis function at each iteration. Extensive numerical results showed the effectiveness of the error estimation strategy, by providing a good shape parameter and better solution accuracy. At the end of the paper, the generality of the shape parameter optimization framework based on this strategy is discussed through three examples. [ABSTRACT FROM AUTHOR]

• This paper introduces a bilevel problem for identifying parameters in generalized total variation and anisotropic tensor. • The existence of the solution for the bilevel model has been proved. • A rigorous primal-dual algorithm is applied to the optimization problem to identify the desired parameters. • Representative experiments have been carried-out and many comparison have been checked to show the efficiency of the proposed model. This paper investigates a novel variational optimization model for image denoising. Within this work, a bilevel optimization technique with a suitable mathematical background is proposed to detect automatically three crucial parameters: α 0 , α 1 and θ. The parameters α 0 , α 1 control the Total Generalized Variation (TGV) regularization while the parameter θ is related to the anisotropic diffusive tensor. A proper selection of these parameters represents a challenging task. Since these parameters are always related to a better approximation of the image gradient and texture, their computation plays a major role in preserving the image features. Analytically, we include results on the approximation of these parameters as well as the resolution of the encountered bilevel problem in a suitable framework. In addition, to resolve the PDE-constrained minimization problem, a modified primal-dual algorithm is proposed. Finally, numerical results are provided to remove noise and simultaneously keep safe fine details and important features with numerous comparisons to show the performance of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, we provide a novel fractional particle swarm optimization (FPSO) algorithm. The traditional PSO is one of the most well-known bio-inspired algorithms used in optimization problems, which basically consists of a number of particles that collectively move in search of the global optimum. Nevertheless, despite its success over the past 20 years, the PSO is also known to be unable to converge, and even stagnate, in many complex problems with multiple local optima. In order to overcome this drawback, this paper proposes a modified version of the PSO algorithm, considering a fractional calculus approach. Stability results evaluation is carried out to analytically prove the convergence of the fractional extensions. This is naturally followed by simulation results to test the fractional-based PSOs under several well-known objective functions, thus highlighting the relationship between the fractional order velocity and position of particles with the convergence of the algorithm. Experimental results show that the FPSO and its variants significantly outperform the traditional PSO. [ABSTRACT FROM AUTHOR]

This paper concerns the process of computing the underlying function of a given set of data points. In many cases, it is not possible to obtain an analytical solution for this problem so the goal is transformed into that of computing a meta-model instead. In this paper we seek to compute a smooth meta-model of such points based on local-support free-form parametric curves. Given an initial parameterization, our method applies a particle-based metaheuristic approach to determine optimal values for the breakpoints and poles of the fitting curve, which is well-known to be a continuous nonlinear optimization problem. The performance of our approach is evaluated by its application to two illustrative examples: a synthetic academic shape and a real-world shape. Our experimental results show that the proposed scheme performs very well, even for shapes with underlying functions exhibiting challenging features, such as self-intersections and sharp changes of curvature. Comparative results show that our approach outperforms previous approaches in terms of generality and fitting error accuracy. [ABSTRACT FROM AUTHOR]

This paper investigates the Pareto optimization scheduling problem on a single machine with two competing agents A and B in which agent A wants to minimize the number of tardy A -jobs and agent B wants to minimize the maximum cost of B -jobs. In the literature, the constrained optimization problem of minimizing the number of tardy A -jobs under the restriction that the maximum cost of B -jobs is bounded is solved in polynomial time. This implies that the corresponding Pareto optimization scheduling problem can be solved in a weakly polynomial time. In this paper, by presenting a new algorithm for the constrained optimization problem, we provide a strongly polynomial-time algorithm for the corresponding Pareto optimization scheduling problem. Experimentation results show that the proposed algorithm for the considered problem is efficient. [ABSTRACT FROM AUTHOR]

Bidirectional inductive power transfer (BIPT) system facilitates contactless power transfer between two sides and across an air-gap, through weak magnetic coupling. Typically, this system is nonlinear high order system which includes nonlinear switch components and resonant networks, developing of accurate model is a challenging task. In this paper, a novel technique for parameter identification of a BIPT system is presented by using chaotic-enhanced fruit fly optimization algorithm (CFOA). The fruit fly optimization algorithm (FOA) is a new meta-heuristic technique based on the swarm behavior of the fruit fly. This paper proposes a novel CFOA, which employs chaotic sequence to enhance the global optimization capacity of original FOA. The parameter identification of the BIPT system is formalized as a multi-dimensional optimization problem, and an objective function is established minimizing the errors between the estimated and measured values. All the 11 parameters of this system ( L pi , L T , L si , L so , C T , C s , M, R pi , R T , R si and R so ) can be identified simultaneously using measured input–output data. Simulations show that the proposed parameter identification technique is robust to measurements noise and variation of operation condition and thus it is suitable for practical application. [ABSTRACT FROM AUTHOR]

The paper deals with the problem of power quality and its solution. Passive or active compensators are usually used to reduce distortions of voltage and current waveforms. Active power filters seem to be the best choice if the effect of compensation is the only criterion. However, the financial cost of such a solution put the potential investors off. The paper shows that the cost could be reduced considerably if the optimization of active power filter allocation, as well as their nominal currents, is carried out. Two cases have been considered – active power filters with a classical control algorithm, which operates locally and aims at obtaining sinusoidal shape of waveforms in the point of installation, and active power filters with a modified control algorithm, which aims at reduction of waveform distortions in all nodes of an analyzed power system. Goal functions and optimization problems for both cases have been defined. [ABSTRACT FROM AUTHOR]

E-learning is a knowledge management concept where content creators have to arrange a set of learning resources, to present them in a clear and comprehensive way to the learners. In this paper, we formulate a new approach for obtaining better learning paths for different learners groups as a constraint satisfaction problem (CSP) in which meta-data and competencies are used to define the relationships between the learning objects (LOs), where the course materials are used to formulate LOs sequence. The main aim of this paper is to obtain a dynamic learning path for the considered CSP problem by using the swarm intelligence technique, which is a sub-set of the artificial intelligence technique. Further, the proposed model is tested in a simulated environment, which gives an optimized LO sequencing. The simulation results reveal that the artificial ants gives solution to the proposed problem in an optimized way. More precisely, suitable learning path can be obtained by applying ant colony optimization (ACO) technique. From the obtained results it is concluded that the proposed model supports the e-learning portal administrator in getting benefits in terms of less processing time and minimal sequencing cost. [ABSTRACT FROM AUTHOR]

In this work, first we introduce several notions of invexity and pseudoinvexity for a locally Lipschitz function by means of the generalized Jacobian. We study relationships between these concepts, in particular the implications between preinvexity and invexity. Next, we obtain necessary and sufficient optimality conditions for efficient and weak efficient solutions of finite-dimensional (non necessarily Pareto) vector optimization problems with locally Lipschitz objective functions through solutions of vector variational-like inequality problems. These conditions are stated via the generalized Jacobian and under pseudoinvexity hypotheses, and they show that a vector optimization problem can be reformulated as a vector variational-like inequality problem. This work extends and improves several previous papers, where the objective function of the vector optimization problem is assumed to be differentiable, or being locally Lipschitz, the authors consider the componentwise subdifferential based on the Clarke’s generalized gradients of the components of the objective function. Throughout the paper some simple examples are given in order to illustrate the main concepts and results. [ABSTRACT FROM AUTHOR]

Real life optimization problems involve a number of constraints arising out of user requirements, physical laws, statutory requirements, resource limitations etc. Such constraints are routinely evaluated using computationally expensive analysis i.e., solvers relying on finite element methods, computational fluid dynamics, computational electro magnetic, etc. Existing optimization approaches adopt a full evaluation policy , i.e., all the constraints corresponding to a solution are evaluated throughout the course of search. Furthermore, a common sequence of constraint evaluation is used for all the solutions. In this paper, we introduce a novel scheme for constraint handling, wherein every solution is assigned a random sequence of constraints and the evaluation process is aborted whenever a constraint is violated. The solutions are sorted based on two measures i.e., the number of satisfied constraints and the violation measure. The number of satisfied constraints takes precedence over the amount of violation and the most efficient sequence of constraint evaluation is evolved during the course of search. The performance of the proposed scheme is rigorously compared with other state of the art constraint handling methods using single objective inequality constrained test problems of CEC-2006 and CEC-2010 . The constraint handling approach is generic and can be easily used for the solution of constrained multiobjective optimization problems or even problems with equality constraints. A bi-objective welded beam design problem, a tri-objective car side impact problem and an equality constrained optimization problem of CEC-2006 is solved as an illustration. The results clearly highlight potential savings offered by the proposed strategy and more importantly the paper provides a detailed insight on why such a strategy performs better than others. [ABSTRACT FROM AUTHOR]

Several algorithms inspired in recent years by the swarm behavior of honeybees have been developed for a variety of practical applications. The Bees Algorithm (BA) is one of these swarm-based algorithms that imitate the intelligent behaviors of honeybees. The present paper proposes a Novel Bees Algorithm (NBA) that uses a stochastic self-adaptive neighborhood ( ssngh ) search to improve the original BA. The ssngh automatically and dynamically reflects swarm convergence conditions and frees its settings. Additionally, this paper tests two additional designs for bee relocation as well as the effect on algorithm performance of using fewer recruited bees. Experimental results are compared using 23 benchmark functions. Results demonstrate that the proposed NBA not only frees the parameter settings of the neighborhood ranges of BA but also significantly improves upon the convergence performance of the original BA. Additionally, experimental results indicate that the NBA outperforms the artificial bee colony (ABC) algorithm on 12 benchmark functions, while the ABC outperforms the NBA on only 8 benchmark functions. [ABSTRACT FROM AUTHOR]

Engineering design problems involve meeting system’s performance requirements such as reliability which is in close relation to appropriate selection of components and determination of a system level architecture. In this paper a new nonlinear redundancy allocation model with the choice of redundancy strategy and component types is presented. The redundancy strategies can be in forms of active and cold standby. Also there is a choice for no redundancy strategy. We assume that time to failure follows Erlang distribution which is parameterized in terms of shape and scale parameters which are usually determined deterministically. In this paper we release the deterministic assumption of the scale parameter since in reality the estimation of this parameter accompanies with uncertainty. Also, the cost and weights are not known exactly due to estimation uncertainties and fluctuations. The uncertain proposed model maximizes the system’s reliability, which is converted into a deterministic multi-objective model maximizing left bound and center of intervals. Finally, a numerical example is presented to show the performance of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: Recently a regret portfolio optimization approach is proposed by minimizing the difference between the maximum return and the sum of each portfolio return which can efficiently overcome the drawback that the classical portfolio optimization model cannot catch the core of the risk diversification. In this paper, we generalize the regret portfolio optimization approach by considering to minimize the weighted sum of the difference between the return and the sum of each portfolio return. We suppose that the decision-maker is ambiguous about the choice of weights and he choose a robust optimization approach to cope with this ambiguity. Then we aim at minimizing the maximization of the weighted sum of the difference between the return and the sum of each portfolio return, where the maximization is to be taken in all the possible distributions of the weights. We call this generalization as worst-case discounted regret portfolio optimization. In general the solution for this problem is NP hard and some approximation method is often proposed. In this paper, we suppose that the decision maker gets across some parts of information about the uncertain distributions of the weights, for example the first-order, support set and affine first-order information. By applying the duality of the semi-infinite programming, the worst-case discounted regret portfolio optimization problem with the uncertain distributions can be equivalently reformulated to a linear optimization problem, then the established solution approaches for linear optimization can all be applied to our setting. An example of a portfolio optimization problem is given to show the efficiency of our methods and the results demonstrate that our methods can satisfy the diversified property under the uncertain distributions of the weights. [Copyright &y& Elsevier]

Abstract: There are many evolutionary algorithms for numerical optimization problems. However, the universality and robustness of existing algorithms are still unsatisfactory, and the performance of these algorithms deteriorates significantly as the dimensionality of the optimization problems increases. In this paper, an ensemble of evolution algorithm based on self-adaptive learning population search techniques (EEA-SLPS) is presented to overcome these defects on the numerical optimization problems. The EEA-SLPS integrates three self-adaptive learning based stochastic search algorithms which are termed as sub-algorithms. In the EEA-SLPS, the population is divided into three sub-populations, and the sub-algorithms are employed to evolve the sub-populations in parallel. Among the three sub-algorithms, one is designed in this paper and the other two are proposed by relevant literature, and eighteen information exchanging manners (IEMs) between sub-populations are investigated in order to make use of the sub-algorithms efficiently. We have found the most suitable IEM for the EEA-SLPS according to experimental investigations. Finally, the EEA-SLPS is tested on a suite of 26 bound-constrained functions with low and high dimensionality. The experimental results indicate that the universality and robustness performance of EEA-SLPS is better. Meanwhile, the results clearly verify the advantages of EEA-SLPS on the numerical optimization problems with low or high dimensionality. [Copyright &y& Elsevier]

Abstract: The aim of the paper is to show relations between two different types of optimization problems: multiple criteria dynamic programming (MCDP) and integer linear programming (ILP) in a form of multiple knapsack (MK) problem. Moreover, the paper presents how to use MCDP methods in order to solve (MK) problems. [Copyright &y& Elsevier]

Abstract: In this paper we introduce a new Jacobi–Davidson type eigenvalue solver for a set of commuting matrices, called JDCOMM, used for the global optimization of so-called Minkowski-norm dominated polynomials in several variables. The Stetter–Möller matrix method yields such a set of real non-symmetric commuting matrices since it reformulates the optimization problem as an eigenvalue problem. A drawback of this approach is that the matrix most relevant for computing the global optimum of the polynomial under investigation is usually large and only moderately sparse. However, the other matrices are generally much sparser and have the same eigenvectors because of the commutativity. This fact is used to design the JDCOMM method for this problem: the most relevant matrix is used only in the outer loop and the sparser matrices are exploited in the solution of the correction equation in the inner loop to greatly improve the efficiency of the method. Some numerical examples demonstrate that the method proposed in this paper is more efficient than approaches that work on the main matrix (standard Jacobi–Davidson and implicitly restarted Arnoldi), as well as conventional solvers for computing the global optimum, i.e., SOSTOOLS, GloptiPoly, and PHCpack. [Copyright &y& Elsevier]

• Discrete time Consensus Based Optimization (CBO) algorithm on a convex set is introduced. • The error between optimal value and consensus value is rigorously calculated and further extended from previous paper. • Portfolio optimization problem was solved using our proposed constrained CBO algorithm. In this paper, we propose a predictor-corrector type Consensus Based Optimization(CBO) algorithm on a convex feasible set. Our proposed algorithm generalizes the CBO algorithm in [11] to tackle a constrained optimization problem for the global minima of the non-convex function defined on a convex domain. As a practical application of the proposed algorithm, we study the portfolio optimization problem in finance. In this application, we introduce an objective function to choose the optimal weight on each asset in an asset-bundle, which yields the maximal expected returns given a certain level of risks. Simulation results show that our proposed predictor-corrector type model is successful in finding the optimal value. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we generalize the classical primal–dual logarithmic barrier method for linear optimization to convex quadratic optimization over symmetric cone by using Euclidean Jordan algebras. The symmetrization of the search directions used in this paper is based on the Nesterov–Todd scaling scheme, and only full Nesterov–Todd step is used at each iteration. We derive the iteration bound that matches the currently best known iteration bound for small-update methods, namely, . Some preliminary numerical results are provided to demonstrate the computational performance of the proposed algorithm. [Copyright &y& Elsevier]

Abstract: In this paper we present some new results related to the higher order sigma point filter (HOSPoF), introduced in [1] for filtering nonlinear multivariate time series. This paper makes two distinct contributions. Firstly, we propose a new algorithm to generate a discrete statistical distribution to match exactly a specified mean vector, a specified covariance matrix, the average of specified marginal skewness and the average of specified marginal kurtosis. Both the sigma points and the probability weights are given in closed-form and no numerical optimization is required. Combined with HOSPoF, this random sigma point generation algorithm provides a new method for generating proposal density which propagates the information about higher order moments. A numerical example on nonlinear, multivariate time series involving real financial market data demonstrates the utility of this new algorithm. Secondly, we show that HOSPoF achieves a higher order estimation accuracy as compared to UKF for smooth scalar nonlinearities. We believe that this new filter provides a new and powerful alternative heuristic to existing filtering algorithms and is useful especially in econometrics and in engineering applications. [Copyright &y& Elsevier]

Abstract: This paper introduces the Backtracking Search Optimization Algorithm (BSA), a new evolutionary algorithm (EA) for solving real-valued numerical optimization problems. EAs are popular stochastic search algorithms that are widely used to solve non-linear, non-differentiable and complex numerical optimization problems. Current research aims at mitigating the effects of problems that are frequently encountered in EAs, such as excessive sensitivity to control parameters, premature convergence and slow computation. In this vein, development of BSA was motivated by studies that attempt to develop simpler and more effective search algorithms. Unlike many search algorithms, BSA has a single control parameter. Moreover, BSA’s problem-solving performance is not over sensitive to the initial value of this parameter. BSA has a simple structure that is effective, fast and capable of solving multimodal problems and that enables it to easily adapt to different numerical optimization problems. BSA’s strategy for generating a trial population includes two new crossover and mutation operators. BSA’s strategies for generating trial populations and controlling the amplitude of the search-direction matrix and search-space boundaries give it very powerful exploration and exploitation capabilities. In particular, BSA possesses a memory in which it stores a population from a randomly chosen previous generation for use in generating the search-direction matrix. Thus, BSA’s memory allows it to take advantage of experiences gained from previous generations when it generates a trial preparation. This paper uses the Wilcoxon Signed-Rank Test to statistically compare BSA’s effectiveness in solving numerical optimization problems with the performances of six widely used EA algorithms: PSO, CMAES, ABC, JDE, CLPSO and SADE. The comparison, which uses 75 boundary-constrained benchmark problems and three constrained real-world benchmark problems, shows that in general, BSA can solve the benchmark problems more successfully than the comparison algorithms. [Copyright &y& Elsevier]

Abstract: Consider the Hermitian matrix function subject to a consistent system of matrix equations where means conjugate transpose. In this paper we first establish explicit expansion formulas to calculate the global maximal and minimal ranks and inertias of the Hermitian matrix function , then we use the derived formulas to give necessary and sufficient conditions for system (0.1) to have Re-nonnegative definite, Re-nonpositive definite, Re-positive definite, and Re-negative definite solutions. Moreover, as another application of the derived formulas, we establish necessary and sufficient conditions for the solvability to the system of matrix equations and provide an expression of the general solution to (0.2) when it is solvable. The findings of this paper widely extend the known results in the literature. [Copyright &y& Elsevier]

Abstract: Decision making in engineering is becoming increasingly complex due to the large number of alternatives and multiple conflicting goals. Powerful decision-support expert systems powered by suitable software are increasingly necessary. In this paper, the multiple attribute decision method known as analytical hierarchy process (AHP), which uses pairwise comparisons with numerical judgments, is considered. Since judgments may lack a minimum level of consistency, mechanisms to improve consistency are necessary. A method to achieve consistency through optimisation is described in this paper. This method has the major advantage of depending on just n decision variables – the number of compared elements – and so is less computationally expensive than other optimisation methods, and can be easily implemented in virtually any existing computer environment. The proposed approach is exemplified by considering a simplified version of one of the most important problems faced by water supply managers, namely, the minimisation of water loss. [Copyright &y& Elsevier]

Abstract: This paper shows how advanced numerical methods can help to improve the thermal efficiency of walls made up of multi-holed bricks with large recesses. In order to get this objective, a new methodology based on different numerical simulations is presented here. With the help of the finite element analysis (FEA), we present an optimization procedure in order to determine the best candidate brick with large recesses from the thermal point of view. With respect to the ecological design and the energy saving for housing and industrial structures, there is also a great interest in light building materials with good physical and thermal behaviours, which fulfils all thermal requirements of the new CTE Spanish rule for further energy savings. On one hand, we want to validate the numerical analysis procedure, based on the simulation of three-dimensional walls by the finite element method (FEM). On the other hand, we have analyzed the material conductivity for different compositions of the light concrete. The FEM technique is used for finding accurate solutions of the heat transfer equation in walls made up of light concrete multi-holed bricks with large recesses. Mathematically, the non-linearity is due to the radiation boundary condition inside the inner recesses of the bricks. Next, the thermal optimization of the walls is carried out from the FEM technique of several hollow brick geometries using the average mass overall thermal efficiency and the equivalent thermal conductivity. In order to select the appropriate wall satisfying the CTE requirements, detailed instructions are obtained and indicated to the readers. Finally, conclusions of this paper are exposed. [Copyright &y& Elsevier]

Abstract: In the paper [A. Rababah, S. Mann, Iterative process for G 2-multi degree reduction of Bézier curves, Applied Mathematics and Computation 217 (2011) 8126–8133], Rababah and Mann proposed an iterative method for multi-degree reduction of Bézier curves with C 1 and G 2-continuity at the endpoints. In this paper, we provide a theoretical proof for the existence of the unique solution in the first step of the iterative process, while the proof in their paper applies only in some special cases. Also, we give a complete convergence proof for the iterative method. We solve the problem by using convex quadratic optimization. [Copyright &y& Elsevier]

Abstract: Spatial planning is an important and complex activity. It includes land use planning and resource allocation as basic components. An abundance of papers can be found in the literature related to each one of these two aspects separately. On the contrary, a much smaller number of research reports deal with both aspects simultaneously. This paper presents an innovative evolutionary algorithm for treating combined land use planning and resource allocation problems. The new algorithm performs optimization on a cellular automaton domain, applying suitable transition rules on the individual neighbourhoods. The optimization process is multi-objective, based on non-domination criteria and self-organizing. It produces a Pareto front thus offering an advantage to the decision maker, in comparison to methods based on weighted-sum objective functions. Moreover, the present multi-objective self-organizing algorithm (MOSOA) can handle both local and global spatial constraints. A combined land use and water allocation problem is treated, in order to illustrate the cellular automaton optimization approach. Water is allocated after pumping from an aquifer, thus contributing a nonlinearity to the objective function. The problem is bi-objective aiming at (a) the minimization of soil and groundwater pollution and (b) the maximization of economic profit. An ecological and a socioeconomic constraint are imposed: (a) Groundwater levels at selected places are kept above prescribed thresholds. (b) Land use quota is predefined. MOSOA is compared to a standard multi-objective genetic algorithm and is shown to yield better results both with respect to the Pareto front and to the degree of compactness. The latter is a highly desirable feature of a land use pattern. In the land use literature, compactness is part of the objective function or of the constraints. In contrast, the present approach renders compactness as an emergent result. [Copyright &y& Elsevier]

Highlights • A modified leaky ReLU scheme (MLRS) for topology optimization with multiple materials is proposed. • A sequence of modified leaky ReLU functions are used for the material property interpolation. • No extra design variables will be introduced when implementing MLRS for multiple material topology optimization. • The sensitivity of objective and constraint functions is easy to derive. Abstract Based on the leaky rectified linear unit (ReLU) function, the paper proposes a modified leaky ReLU scheme (MLRS) for topology optimization with multiple materials. A continuous function formed by sequence of modified leaky ReLU functions are used for the material property interpolation. No extra design variables will be introduced for whatever number of materials considered. Thus, the computational cost is independent to material types. Since the modified leaky ReLU function only consists of two linear functions, the sensitivity of objective and constraint functions is easy to derive. Besides, the sensitivity of MSRL stays a proper constant number even when the design variable is sufficiently small, which may help the convergence. The discontinuous points of derivatives can be jumped across smoothly so that stable transitions can be guaranteed from one type of material to another. An optimal criteria (OC) based solution method is derived from the KKT condition, and an interior point method based solution procedure is introduced for more complex cases. The proposed method is general and straightforward, and is compatible with the existing optimization algorithms. Numerical examples including structural and thermal topology optimization are used to verify the proposed method. The results demonstrate its efficiency and stability. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we propose an iterative method based on reduced-space approximations for unconstrained optimization problems. The method works as follows: among iterations, samples are taken about the current solution by using, for instance, a Normal distribution; for all samples, gradients are computed (approximated) in order to build reduced-spaces onto which descent directions of cost functions are estimated. By using such directions, intermediate solutions are updated. The overall process is repeated until some stopping criterion is satisfied. The convergence of the proposed method is theoretically proven by using classic assumptions in the line search context. Experimental tests are performed by using well-known benchmark optimization problems and a non-linear data assimilation problem. The results reveal that, as the number of sample points increase, gradient norms go faster towards zero and even more, in the data assimilation context, error norms are decreased by several order of magnitudes with regard to prior errors when the assimilation step is performed by means of the proposed formulation. [ABSTRACT FROM AUTHOR]

Abstract: This paper concerns the memoryless quasi-Newton method, that is precisely the quasi-Newton method for which the approximation to the inverse of Hessian, at each step, is updated from the identity matrix. Hence its search direction can be computed without the storage of matrices. In this paper, a scaled memoryless symmetric rank one (SR1) method for solving large-scale unconstrained optimization problems is developed. The basic idea is to incorporate the SR1 update within the framework of the memoryless quasi-Newton method. However, it is well-known that the SR1 update may not preserve positive definiteness even when updated from a positive definite matrix. Therefore we propose the memoryless SR1 method, which is updated from a positive scaled of the identity, where the scaling factor is derived in such a way that positive definiteness of the updating matrices are preserved and at the same time improves the condition of the scaled memoryless SR1 update. Under very mild conditions it is shown that, for strictly convex objective functions, the method is globally convergent with a linear rate of convergence. Numerical results show that the optimally scaled memoryless SR1 method is very encouraging. [Copyright &y& Elsevier]

Abstract: In this paper we study the profit-maximization problem, considering maximum constraints for the general case of m-inputs and using the Cobb–Douglas model for the production function. To do so, we previously study the firm’s cost minimization problem, proposing an equivalent infimal convolution problem for exponential-type functions. This study provides an analytical expression of the production cost function, which is found to be a piece-wise potential. Moreover, we prove that this solution belongs to class C 1. Using this cost function, we obtain the explicit expression of maximum profit. Finally, we illustrate the results obtained in this paper with an example. [Copyright &y& Elsevier]

Abstract: This paper proposes a mathematical model to plan the financial strategy of a large company. The model links the philosophy of new behavioural economics with the multiple criteria decision making paradigm. Within this theoretical approach, the proposed model is supported by more realistic behavioral hypotheses. After formulating the initial multi-objective programming model, it has, due to its underlying computational difficulties, to be transformed into an easily computable extended compromise programming model. The functional and empirical potential of the model is illustrated with the help of a case study concerning a “stock market quoted” Spanish company operating in the energy sector. This paper shows how such an approach can open up new prospects for research linking economic problems with applied mathematics. [Copyright &y& Elsevier]

Abstract: In this paper, we first complement an inappropriate mathematical error on the total cost in two previous published research papers in inventory field. Then an arithmetic–geometric inequality method is proposed not only to simplify the algebraic method of completing prefect squares, but also to complement their shortcomings. In addition, we also provide a closed-form optimal solution to the integrated vendor–buyer inventory system without using complex derivatives. Finally, the proposed method seems to be easy-to-understand and simple-to-apply by individuals who are not familiar with differential calculus. [Copyright &y& Elsevier]

Abstract: The simulated annealing (SA) algorithm is a well-established optimization technique which has found applications in many research areas. However, the SA algorithm is limited in its application due to the high computational cost and the difficulties in determining the annealing schedule. This paper demonstrates that the temperature parallel simulated annealing (TPSA) algorithm, a parallel implementation of the SA algorithm, shows great promise to overcome these limitations when applied to continuous functions. The TPSA algorithm greatly reduces the computational time due to its parallel nature, and avoids the determination of the annealing schedule by fixing the temperatures during the annealing process. The main contributions of this paper are threefold. First, this paper explains a simple and effective way to determine the temperatures by applying the concept of critical temperature (T C ). Second, this paper presents systematic tests of the TPSA algorithm on various continuous functions, demonstrating comparable performance as well-established sequential SA algorithms. Third, this paper demonstrates the application of the TPSA algorithm on a difficult practical inverse problem, namely the hyperspectral tomography problem. The results and conclusions presented in this work provide are expected to be useful for the further development and expanded applications of the TPSA algorithm. [Copyright &y& Elsevier]

Abstract: This paper introduces the notion of mixed leadership in nonzero-sum differential games, where there is no fixed hierarchy in decision making with respect to the players. Whether a particular player is leader or follower depends on the instrument variable s/he is controlling, and it is possible for a player to be both leader and follower, depending on the control variable. The paper studies two-player open-loop differential games in this framework, and obtains a complete set of equations (differential and algebraic) which yield the controls in the mixed-leadership Stackelberg solution. The underlying differential equations are coupled and have mixed-boundary conditions. The paper also discusses the special case of linear-quadratic differential games, in which case solutions to the coupled differential equations can be expressed in terms of solutions to coupled Riccati differential equations which are independent of the state trajectory. [ABSTRACT FROM AUTHOR]

Abstract: Bees algorithm (BA) is a new member of meta-heuristics. BA tries to model natural behavior of honey bees in food foraging. Honey bees use several mechanisms like waggle dance to optimally locate food sources and to search new ones. This makes them a good candidate for developing new algorithms for solving optimization problems. In this paper a brief review of BA is first given, afterwards development of a BA for solving generalized assignment problems (GAP) with an ejection chain neighborhood mechanism is presented. GAP is a NP-hard problem. Many meta-heuristic algorithms were proposed for its solution. So far BA is generally applied to continuous optimization. In order to investigate the performance of BA on a complex integer optimization problem, an attempt is made in this paper. An extensive computational study is carried out and the results are compared with several algorithms from the literature. [Copyright &y& Elsevier]

Abstract: In real-life projects, both the trade-off between the project cost and the project completion time, and the uncertainty of the environment are considerable aspects for decision-makers. However, the research on the time-cost trade-off problem seldom concerns stochastic environments. Besides, optimizing the expected value of the objective is the exclusive decision-making criterion in the existing models for the stochastic time-cost trade-off problem. In this paper, two newly developed alternative stochastic time-cost trade-off models are proposed, in which the philosophies of chance-constrained programming and dependent-chance programming are adopted for decision-making. In addition, a hybrid intelligent algorithm integrating stochastic simulations and genetic algorithm is designed to search the quasi-optimal schedules under different decision-making criteria. The goal of the paper is to reveal how to obtain the optimal balance of the project completion time and the project cost in stochastic environments. [Copyright &y& Elsevier]

Abstract: Multiagent systems have been studied and widely used in the field of artificial intelligence and computer science to catalyze computation intelligence. In this paper, a multiagent evolutionary algorithm called RAER based on the ERA multiagent modeling pattern is proposed, where ERA has the same architecture as Swarm including three parts of Environment, Reactive rules and Agents. RAER integrates a novel roulette inversion operator (RIO) proposed in this paper and theoretically proved to conquer the irrationality of the inversion operator (IO) designed by John Holland when used for real code stochastic optimization algorithms. Experiments for numerical optimization of 4 benchmark functions show that the RIO operator bears better functioning than IO operator. And experiments for numerical optimization of 12 benchmark functions are used to examine the performance and scalability of RAER along the problem dimensions ranging 20–10000, results indicate that RAER outperforms other comparative algorithms significantly. Also, two engineering optimization problems of a stable linear system approximation and a welded beam design are used to examine the applicability of RAER. Results show that RAER has better search ability and faster convergence speed. Especially for the approximation problem, REAR can find the proper optima belonging to different fixed search areas, which is significantly better than other algorithms and shows that RAER can search the problem domains more thoroughly than other algorithms. Hence, RAER is efficient and practical. [Copyright &y& Elsevier]

Abstract: Dynamic bilinear recurrent neural network (D-BLRNN) with a dynamic learning gain and optimization layer by layer procedure is proposed and applied to MPEG video traffic prediction over ATM networks in this paper. Since the BLRNN is based on the bilinear polynomial, it has been more effectively used in modeling highly non-linear systems with time-series characteristics than the conventional multi-layered perceptron type neural network (MLPNN). D-BLRNN is proposed to enhance the prediction capability of the BLRNN further by introducing dynamic learning control and optimization layer by layer procedure. Since ATM networks have a bursty nature because of their variable bit rate (VBR) and MPEG video traffic has a typical VBR characteristics, the proposed D-BLRNN can be an optimal candidate for the MPEG traffic prediction problem. In the experiment, the proposed D-BLRNN is applied to a real world MPEG traffic problem (‘MPEG.data’ from the movie ‘Star Wars’) as an on-line learning and a prediction problem. When compared with other prediction schemes including MLPNN and pipelined recursive neural network, the D-BLRNN improves the prediction error by 60% or more in most cases. The results may imply that the D-BLRNN based predictor proposed in this paper is promising and practically reliable tool for predicting bursty sources including real-time MPEG video traffic. [Copyright &y& Elsevier]

Abstract: This paper studies the approximation of nonstationary signals from natural life systems in time–frequency plane using a type of four-parameter Gabor atoms. These four parameters, i.e. the dilation, chirprate, modulation and translation, have clear physical meanings and to optimize these parameters is an extremely difficult task. In this paper, a fast procedure is introduced without explicitly exploring these parameters over the continuous search space. Here, these four parameters together with a phase parameter for real signal are assigned with random values across their full ranges, creating a large library of candidate Gabor atoms. Then a fast algorithm is used to select atoms from the library that best approximate the nonstationary signal. The computational complexity of the method is only linearly related with the library size, the number of signal points and the number of used atoms. The proposed method is applied to several benchmark problems from life systems, including the bat signals, EEG signals and speech signals. The simulation results confirm its efficacy. [Copyright &y& Elsevier]

Abstract: Stressed power systems, either due to increased loading or due to contingencies, often lead to situations where the systems are no longer remaining in security operating regions. Under such situations, the primary objective of the operator is to apply control actions to bring the systems back into the security operating regions. In the cases when systems are subjected to any kind of time delay or unavailability of control, systems may become unstable which is very dangerous situation for power systems. Flexible AC transmission systems (FACTS) devices can play very important role in power system security enhancement. One of the most effective FACTS devices is the thyristor controlled series capacitor (TCSC) which can smoothly and rapidly change its apparent reactance according to the system requirements. Due to the high capital investment of FACTS devices and to achieve a better utilization (satisfactory performance) of theses devices, it is necessary to locate these devices optimally in the power system. This paper mainly concerned with the enhancement of the system security against single contingencies via the optimal placement of TCSC. The paper deals with the application of two evolutionary optimization techniques namely, genetic algorithm (GA) and particle swarm optimization (PSO) for the optimal location and the optimal parameter setting of TCSC under single line contingency (N −1 Contingency). Contingency analysis is performed to detect and rank the severest line faulted contingencies in the power system. To validate the proposed techniques, simulations are performed on an IEEE 6-bus power system and an IEEE 14-bus power system. Encouraging results are obtained, which show that TCSC is one of the most effective series compensation devices that can significantly eliminate or minimize line overloads under single contingencies. Also the results indicate that both GA and PSO techniques can easily and successfully find out the optimal location and the optimal parameter settings of TCSC. [Copyright &y& Elsevier]

Abstract: Integrated water resources management (IWRM) is recognized worldwide as the reference paradigm to meet society’s long-term needs for water resources while maintaining essential ecological services and economic benefits. In previous publications [A. Castelletti, R. Soncini-Sessa, A procedural approach to strengthening integration and participation in water resource planning, Environmental Modelling & Software 21(10) (2006) 1455–1470; A. Castelletti, F. Pianosi, R. Soncini-Sessa, Integration, participation and optimal control in water resources planning and management, Applied Mathematics and Computation, (2007), doi:10.1016/j.amc.2007.09.069], the authors have already insisted on the need for a procedural approach to make the IWRM paradigm truly operational; they have emphasized the role played by dynamic optimization in rationalizing and facilitating the selection by the decision maker of a best compromise planning alternative. When planning alternatives also include management policies, as in the case of the water reservoir networks considered in this paper, the best compromise off-line policy resulting from the planning exercise has to be actually implemented in the daily management of the system. Here, again, dynamic optimization may play a central role, as it can be adopted on-line to improve the performance of the off-line policy by exploiting any new useful information available in real-time (e.g., inflow predictions, a power station being temporarily out of service, etc.). In this paper, this approach is explored through a real-world case study of a simple reservoir system. The off-line management policy computed in a previous planning process is refined on-line with a receding horizon control scheme combined with an inflow predictor. The results yield indications that the approach can provide significant advantages to cope with extreme events, particularly those occurring in unusual periods of the year. [Copyright &y& Elsevier]

Abstract: In a recent paper by Wang [Y.M. Wang, On lexicographic goal programming method for generating weights from inconsistent interval pair-wise comparison matrices. Applied Mathematics and Computation 173 (2006) 985–991], it is shown that lexicographic goal programming method results in different rankings for upper- and lower-triangular interval judgments arranged in a positive reciprocal pair-wise comparison matrix. This was unexpected from a prioritization point of view, because upper- and lower-triangular entries in reciprocal interval pair-wise comparison matrices essentially provide the same judgment information. A research question was posed at the same article: “Which ranking is true or more reliable?”. Motivated by this question, in this paper, we provide a post-optimality analysis to detect the most reliable priority vector among m vectors derived by lexicographical goal programming for an inconsistent interval pair-wise comparison matrix of order n. The method is based on violations in the order of preferences among the resultant priorities and runs in time. When there exists a tie between some vectors, we also illustrate a tie-breaking algorithm running in time, based on violations in the order of the preference intensities among the resultant priorities. We re-visited the examples discussed in the afore-mentioned article and validate the practical usability of this method. [Copyright &y& Elsevier]

Abstract: This paper is concerned with a new type of the classical Bernstein operators where the function is evaluated at intervals . We also make extensive study simultaneous approximation by the linear combination of these new Bernstein type operators . At the end of this paper we have given an other modification of these operators. [Copyright &y& Elsevier]