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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]

Introduces a series of articles which appeared in the January 2005 issue. Reference to the papers presented at the 5th International Conference on Optimization: Techniques and Applications in Hong Kong, China; Claim that the papers were divided into three categories which are nonlinear optimization, scheduling and discrete optimization and engineering optimization.

This paper describes efficient algorithms for determining how buffer space should be allocated in a flow line. We analyze two problems: a primal problem, which minimizes total buffer space subject to a production rate constraint; and a dual problem, which maximizes production rate subject to a total buffer space constraint. The dual problem is solved by means of a gradient method, and the primal problem is solved using the dual solution. Numerical results are presented. Profit optimization problems are natural generalizations of the primal and dual problems, and we show how they can be solved using essentially the same algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new in-plane XYθz nano-positioning stage that utilizes piezoelectric actuators and flexure mechanisms. The proposed stage has an aperture and is compact, which facilitates its application in measurement equipment, especially those used for biological specimens. The stage has four piezoelectric actuators and four bridge-type flexure mechanisms, which are used to amplify the small motions produced by the piezoelectric actuators. This paper describes the modeling and design optimization of the stage, which has X- and Y-direction motion ranges of 300 μm and a θz-direction motion range of ±3.9 mrad. The stage measures 150 × 150 × 23 mm, and its aperture is 50 × 50 mm. [ABSTRACT FROM AUTHOR]

Based on both white response and connotation expression are geometric progression in the most primitive grey differential equation of GM(1,1)x(0)(k)+ax(1)(k) = b, this paper begins with generation of the time response function's grey derivative at discrete points. Through derivative's definition, establishing a new GM(1,1) by optimizing grey derivative and background value. Then, getting the best coefficient c by introducing criterion function and it has proved that the new expression has the whitened exponent law coincident property and the whitened coefficient coincident property in theory. Finally, some examples show the new model has higher prediction precision. [ABSTRACT FROM AUTHOR]

Recently, a semidefinite and semi-infinite linear programming problem (SDSIP), its dual (DSDSIP), and uniform LP duality between (SDSIP) and (DSDSIP) were proposed and studied by Li et al. (Optimization 52:507-528,2003). In this paper, we show that (SDSIP) is an ordinary linear semi-infinite program and, therefore, all the existing results regarding duality and uniform LP duality for linear semi-infinite programs can be applied to (SDSIP). By this approach, the main results of Li et al. (Optimization 52:507-528, 2003) can be obtained easily. [ABSTRACT FROM AUTHOR]

In this paper we discuss scenario reduction methods for risk-averse stochastic optimization problems. Scenario reduction techniques have received some attention in the literature and are used by practitioners, as such methods allow for an approximation of the random variables in the problem with a moderate number of scenarios, which in turn make the optimization problem easier to solve. The majority of works for scenario reduction are designed for classical risk-neutral stochastic optimization problems; however, it is intuitive that in the risk-averse case one is more concerned with scenarios that correspond to high cost. By building upon the notion of effective scenarios recently introduced in the literature, we formalize that intuitive idea and propose a scenario reduction technique for stochastic optimization problems where the objective function is a Conditional Value-at-Risk. Numerical results presented with problems from the literature illustrate the performance of the method and indicate the cases where we expect it to perform well. [ABSTRACT FROM AUTHOR]

Decision problems involving multiple agents invariably lead to conflict and gaming. In recent years, multi-agent systems have been analyzed using approaches that explicitly assign to each agent a unique objective function and set of decision variables; the system is defined by a set of common constraints that affect all agents. The decisions made by each agent in these approaches affect the decisions made by the others and their objectives. When strategies are selected simultaneously, in a noncooperative manner, solutions are defined as equilibrium points [13,51] so that at optimality no player can do better by unilaterally altering his choice. There are other types of noncooperative decision problems, though, where there is a hierarchical ordering of the agents, and one set has the authority to strongly influence the preferences of the other agents. Such situations are analyzed using a concept known as a Stackelberg strategy [13,14,46]. The hierarchical optimization problem [11,16,23] conceptually extends the open-loop Stackelberg model to K players. In this paper, we provide a brief introduction and survey of recent work in the literature, and summarize the contributions of this volume. It should be noted that the survey is not meant to be exhaustive, but rather to place recent papers in context. [ABSTRACT FROM AUTHOR]

Recently Dekker and Hordijk [3,4] introduced conditions for the existence of deterministic Blackwell optimal policies in denumerable Markov decision chains with unbounded rewards. These conditions include ii-uniform geometric recurrence. The μ-uniform geometric recurrence property also implies the existence of average optimal policies, a solution to the average optimality equation with explicit formula's and convergence of the value iteration algorithm for average rewards. For this reason, the verification of μ-uniform geometric convergence is also useful in cases where average and α-discounted rewards are considered. On the other hand, μ-uniform geometric recurrence is a heavy condition on the Markov decision chain structure for negative dynamic programming problems. The verification of μ-uniform geometric recurrence for the Markov chain induced by some deterministic policy together with results by Sennott [14] yields the existence of a deterministic policy that minimizes the expected average cost for non-negative immediate cost functions. In this paper μ-uniform geometric recurrence will be proved for two queueing models: the K competing queues and the two centre open Jackson network with control of the service rates. [ABSTRACT FROM AUTHOR]

The issue of adapting the best solution to handle the varying demand for electricity is one of the active areas of research in power system domain. Combined Economic Emission Dispatch (CEED) problem has become a vital issue as it focuses on both the economy and emission objectives with necessary constraints. The stability of the power system is also considered as an important factor in the performance of the power system. Optimization Techniques can be utilized to deal with the CEED as it provides optimal solution for the required parameters. A majority of the optimization techniques are slow for such complex optimization tasks and are not suitable for on-line use. This paper presents an effective optimization algorithm, for solving security constrained CEED problem. Also, the power system stability plays an important role in power system. Voltage stability is focused in this approach which has an impact on the performance of the entire power system. In this paper, an efficient optimization technique called Improved Search Exploration and Sensibility based Artificial Bee Colony (ISESABC) Optimization is used to solve the CEED problem. The performance of the proposed approach is compared with the other optimization techniques. The experimental result shows that the proposed system results in better solution for CEED problem with the maintenance of system stability. [ABSTRACT FROM AUTHOR]

In this paper, we address the problem of determining the optimum antenna configuration for a multi-input multi-output (MIMO) system at any given signal-to-noise ratio (SNR). We used two-level differential evolution (DE) algorithm that finds both an appropriate expression among a set of candidate expressions within the list of the optimization software used, and the parameter values ( coefficients) belonging to the selected expression. The results of the proposed expression are compared with the results of high SNR approximation, asymptotic approach and optimum antenna number ratios. It is shown that the numerical outcomes produced by the new expression exhibit very good agreement with the optimum antenna number ratios, and this agreement is almost independent of the specific value of SNR. Copyright © 2010 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract  Dynamic optimization problems challenge traditional evolutionary algorithms seriously since they, once converged, cannot adapt quickly to environmental changes. This paper investigates the application of memetic algorithms, a class of hybrid evolutionary algorithms, for dynamic optimization problems. An adaptive hill climbing method is proposed as the local search technique in the framework of memetic algorithms, which combines the features of greedy crossover-based hill climbing and steepest mutation-based hill climbing. In order to address the convergence problem, two diversity maintaining methods, called adaptive dual mapping and triggered random immigrants, respectively, are also introduced into the proposed memetic algorithm for dynamic optimization problems. Based on a series of dynamic problems generated from several stationary benchmark problems, experiments are carried out to investigate the performance of the proposed memetic algorithm in comparison with some peer evolutionary algorithms. The experimental results show the efficiency of the proposed memetic algorithm in dynamic environments. [ABSTRACT FROM AUTHOR]

This paper tackles a power minimization problem of interleave-division multiple-access (IDMA) systems over a fading multiple-access channel. The problem is minimizing the total power received by the receiver while keeping the bit error rates (BERs) of all users below a predefined value. The original formulation of the problem has highly nonlinear and implicitly defined functions, which render most existing optimization methods incapable. A new formulation is proposed in this paper, whose solution can effectively be obtained by a branch-and-bound (B&B) technique. An algorithm is devised based on B&B, and its effectiveness is also demonstrated by numerical experiments of systems with a moderate numbers of users. [ABSTRACT FROM AUTHOR]

In this paper, we propose a fast and efficient adaptive transmission algorithm for the Mobile WiMAX system. In our algorithm, we select the position of the boundary between the downlink and uplink subframes, the positions of the service, flows within the frame, the coding and modulation schemes, and the transmission power values. Our algorithm gains high spectral efficiency, satisfies quality-of-service (QoS) requirements for the service flows, and has low computational complexity. The algorithm includes a frame boundary position optimization procedure, downlink and uplink optimization procedures, as well as a procedure that selects a transmission power value that enables satisfaction of the QoS requirements. All these procedures are novel, efficient, and fast. We evaluate the adaptive transmission algorithm by performing a system-level simulation of the Mobile WiMAX system with multisector topology. We show that our algorithm has high spectral efficiency and low computational complexity, enabling QoS provisioning. [ABSTRACT FROM AUTHOR]

This paper proposes a novel estimator named minimum-variance pseudo-unbiased reduced-rank estimator (MVPURE) for the linear regression model, designed specially for the case where the model matrix is ill-conditioned and the unknown deterministic parameter vector to be estimated is subjected to known linear constraints. As a natural generalization of the Gauss-Markov (BLUE) estimator, the MV-PURE estimator is a solution of the following hierarchical nonconvex constrained optimization problem directly related to the mean square error expression. In the first-stage optimization, under a rank constraint, we minimize simultaneously all unitarily invariant norms of an operator applied to the unknown parameter vector in view of suppressing bias of the proposed estimator. Then, in the second-stage optimization, among all pseudo-unbiased reduced-rank estimators defined as the solutions of the first-stage optimization, we find the one achieving minimum variance. We derive a closed algebraic form of the MV-PURE estimator and show that well-known estimators-the Gauss-Markov (BLUE) estimator, the generalized Marquardt's reduced-rank estimator, and the minimum-variance conditionally unbiased affine estimator subject to linear restrictions-are all special cases of the MV-PURE estimator. We demonstrate the effectiveness of the proposed estimator in a numerical example, where we employ the MV-PURE estimator to the ill-conditioned problem of reconstructing a 2-D image subjected to linear constraints from blurred, noisy observation. This example demonstrates that the MV-PURE estimator outperforms all aforementioned estimators, as it achieves smaller mean square error for all values of signal-to-noise ratio. [ABSTRACT FROM AUTHOR]

The economic dispatch has the objective of generation allocation to the power generators in such a manner that the total fuel cost is minimized while all operating constraints are satisfied. Conventional optimization methods assume generator cost curves to be continuous and monotonically increasing, but modern generators have a variety of nonlinearities in their cost curves making this assumption inaccurate, and the resulting approximate dispatches cause a lot of revenue loss. Evolutionary methods like particle swarm optimization perform better for such problems as no convexity assumptions are imposed, but these methods converge to sub-optimum solutions prematurely, particularly for multimodal problems. To handle the problem of premature convergence, this paper proposes to apply a novel self-organizing hierarchical particle swarm optimization (SOH̱PSO) for the nonconvex economic dispatch (NCED). The performance further improves when time-varying acceleration coefficients are included. The results show that the proposed approach outperforms previous methods for NCED. [ABSTRACT FROM AUTHOR]

Active Appearance Models (AAMs) are generative, parametric models that have been successfully used in the past to model deformable objects such as human faces. The original AAMs formulation was 2D, but they have recently been extended to include a 3D shape model. A variety of single-view algorithms exist for fitting and constructing 3D AAMs but one area that has not been studied is multi-view algorithms. In this paper we present multi-view algorithms for both fitting and constructing 3D AAMs. Fitting an AAM to an image consists of minimizing the error between the input image and the closest model instance; i.e. solving a nonlinear optimization problem. In the first part of the paper we describe an algorithm for fitting a single AAM to multiple images, captured simultaneously by cameras with arbitrary locations, rotations, and response functions. This algorithm uses the scaled orthographic imaging model used by previous authors, and in the process of fitting computes, or calibrates, the scaled orthographic camera matrices. In the second part of the paper we describe an extension of this algorithm to calibrate weak perspective (or full perspective) camera models for each of the cameras. In essence, we use the human face as a (non-rigid) calibration grid. We demonstrate that the performance of this algorithm is roughly comparable to a standard algorithm using a calibration grid. In the third part of the paper, we show how camera calibration improves the performance of AAM fitting. A variety of non-rigid structure-from-motion algorithms, both single-view and multi-view, have been proposed that can be used to construct the corresponding 3D non-rigid shape models of a 2D AAM. In the final part of the paper, we show that constructing a 3D face model using non-rigid structure-from-motion suffers from the Bas-Relief ambiguity and may result in a “scaled” (stretched/compressed) model. We outline a robust non-rigid motion-stereo algorithm for calibrated multi-view 3D AAM construction and show how using calibrated multi-view motion-stereo can eliminate the Bas-Relief ambiguity and yield face models with higher 3D fidelity. [ABSTRACT FROM AUTHOR]

Critical dimension (CD) variation caused by defocus is largely systematic with dense lines ‘smiling’ through focus while isolated lines ‘frown.’ In this paper, we propose a new design methodology that allows explicit compensation of focus-dependent CD variation, in particular, either within a cell (self-compensated cells) or across cells in a critical path (self-compensated design). By creating iso and dense variants for each library cell, we can achieve designs that are more robust to focus variation. Optimization with a mixture of dense and iso cell variants is possible, both for area and leakage power in timing constraints (critical delay), with the latter an interesting complement to existing leakage-reduction techniques, such as dual-Vth. We implement both a heuristic and mixed-integer linear-programming (MILP) solution methods to address this optimization and experimentally compare their results. Results indicate that designing with a self-compensated cell library incurs 12% area penalty and 6% leakage increase over a baseline library while compensating for focus-dependent CD variation (i.e., the design meets timing constraints across a large range of focus variation). We observe 27% area penalty and 7% leakage increase at the worst case defocus condition using only single-pitch cells. The area penalty of circuits after using both the heuristic and MILP optimization approaches is reduced to 3% while maintaining timing. We also apply the optimization to leakage, which traditionally shows very large variability due to its exponential relationship with gate CD. We conclude that a mixed iso/dense library that is combined with a sensitivity-based optimization approach yields much better area/timing/leakage tradeoffs than using a self-compensated cell library alone. Self-compensated designs show 25% less leakage power on average at the worst defocus condition compared to a design employing a conventional library for the benchmarks studied. [ABSTRACT FROM AUTHOR]

This short correspondence is a reply to a recently published paper by Verlinde et al. in which the authors empirically compared fuzzy and nonfuzzy association analysis and, on the basis of their results, questioned the usefulness of a fuzzy approach. Although we highly welcome the critical examination of the topic and definitely agree that fuzzy extensions of existing methods call for a thorough justification, the empirical comparison presented in the aforementioned paper is in our opinion not objective and extensive enough to fully warrant the conclusions drawn from the results. Apart from some general comments on the claims raised in their paper, we present empirical results based on an alternative experimental setup that lead to different conclusions. [ABSTRACT FROM AUTHOR]

This paper deals with a problem of guaranteed (robust) financial decision-making under model uncertainty. An efficient method is proposed for determining optimal robust portfolios of risky financial instruments in the presence of ambiguity (uncertainty) on the probabilistic model of the returns. Specifically, it is assumed that a nominal discrete return distribution is given, while the true distribution is only known to lie within a distance d from the nominal one, where the distance is measured according to the Kullback-Leibler divergence. The goal in this setting is to compute portfolios that are worst-case optimal in the mean-risk sense, that is, to determine portfolios that minimize the maximum with respect to all the allowable distributions of a weighted risk-mean objective. The analysis in the paper considers both the standard variance measure of risk and the absolute deviation measure. [ABSTRACT FROM AUTHOR]

The metaheuristic technique of Ant Colony Search has been revised here in order to deal with dynamic search optimization problems having a large search space and mixed integer variables. The problem to which it has been applied is an electrical distribution systems management problem. This kind of issues is indeed getting increasingly complicated due to the introduction of new energy trading strategies, new environmental constraints and new technologies. In particular, in this paper, the problem of finding the optimal reinforcement strategy to provide reliable and economic service to customers in a given time frame is investigated. Utilities indeed need efficient software tools to take decisions in this new complex scenario. In past times, utilities project the load growth for several years and then estimate when the capacity limit will be exceeded. Designers then consider some feasible alternatives and select the optimal one in terms of performance and costs. In this paper, the Distributed Generation, DG, technology considered in compound solutions with the installation of feeder and substations is viewed as a new option for solving distribution systems capacity problems, along several years. The objective to be minimized is therefore the overall cost of distribution systems reinforcement strategy in a given timeframe. An application on a medium size network is carried out using the proposed technique that allows the identification of optimal paths in extremely large or non-finite spaces. The proposed algorithm uses an adaptive parameter in order to push exploration or exploitation as the search procedure stops in a local minimum. The algorithm allows the easy investigation of these kinds of complex problems, and allows to make useful comparisons as the intervention strategy and type of DO sources vary. [ABSTRACT FROM AUTHOR]

In this paper we use the penalty approach to study three constrained minimization problems. A penalty function is said to have the exact penalty property [J.-B. Hiriart-Urruty and C. Lemarechal, Convex Analysis and Minimization Algorithms, 2 vols., Springer-Verlag, Berlin, 1993] if there exists a penalty coefficient for which a solution of an unconstrained penalized problem is a solution of the corresponding constrained problem. In this paper we establish a very simple sufficient condition for the exact penalty property. [ABSTRACT FROM AUTHOR]

Several recent papers have proposed the use of grids for solving unconstrained optimisation problems. Grid-based methods typically generate a sequence of grid local minimisers which converges to stationary points under mild conditions. In this paper the location and number of grid local minimisers is calculated for strictly convex quadratic functions in two dimensions with certain types of grids. These calculations show it is possible to construct a grid with an arbitrary number of grid local minimisers. The furthest of these can be an arbitrary distance from the quadratic's minimiser. These results have important implications for the design of practical grid-based algorithms. Grids based on conjugate directions do not suffer from these problems. For such grids only the grid points closest (depending on the choice of metric) to the minimiser are grid local minimisers. Furthermore, conjugate grids are shown to be reasonably stable under mild perturbations so that in practice, only approximately conjugate grids are required. [ABSTRACT FROM AUTHOR]

The condition-based approach for consensus solvability consists of identifying sets of input vectors, called conditions, for which there exists an asynchronous protocol solving consensus despite the occurrence of up to f process crashes. This paper investigates $\mathcal{C}_f$ , the largest set of conditions which allow us to solve the consensus problem in an asynchronous shared memory system.The first part of the paper shows that $\mathcal{C}_f$ is made up of a hierarchy of classes of conditions, $\mathcal{C}^{[d]}_f$ where d is a parameter (called degree of the condition), starting with $d = \min(n-f,\allowbreak f)$ and ending with d = 0, where $\mathcal{C}^{[0]}_f = \mathcal{C}_f$ . We prove that each one is strictly contained in the previous one: $\mathcal{C}^{[d]}_f\subset\mathcal{C}^{[d-1]}_f$ . Various properties of the hierarchy are also derived. It is shown that a class can be characterized in two equivalent but complementary ways: one is convenient for designing protocols while the other is for analyzing the class properties. The paper also defines a linear family of conditions that can be used to derive many specific conditions. In particular, for each d, two natural conditions are presented.The second part of the paper is devoted to the design of efficient condition-based protocols. A generic condition-based protocol is presented. This protocol can be instantiated with any condition C, $C\in\mathcal{C}^{[d]}_f$ , and requires at most $(2n + 1) \lceil{\log_2(\lceil{(f-d)/2\rceil} + 1)}$ shared memory read/write operations per process in the synchronization part of the protocol. Thus, the value ( f- d) represents the ? difficulty? of the class $\mathcal{C}^{[d]}_f$ . An improvement of the protocol for the conditions in $\mathcal{C}^{[0]}_f$ is also presented. [ABSTRACT FROM AUTHOR]

Optimization models and methods have been used extensively in the forest industry. In this paper we describe the general wood-flow in forestry and a variety of planning problems. These cover planning periods from a fraction of a second to more than one hundred years. The problems are modelled using linear, integer and nonlinear models. Solution methods used depend on the required solution time and include for example dynamic programming, LP methods, branch & bound methods, heuristics and column generation. The importance of modelling and qualitative information is also discussed. [ABSTRACT FROM AUTHOR]

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

In this paper, we propose a new predictor-corrector interior-point algorithm for linear programming based on a wide neighbourhood. In each iteration, the algorithm computes the Ai-Zhang's predictor direction (SIAM J. Optim. 16(2):400-417, ) and a new corrector direction, in an attempt to improve its performance. We drive that the duality gap reduces in both predictor and corrector steps. Moreover, we also prove that the complexity of the algorithm coincides with the best iteration bound for small neighbourhood algorithms. Finally, some numerical experiments are provided which reveal capability and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In the present paper, we consider the inequality constrained vector problem with continuously Fréchet differentiable objective functions and constraints. We obtain second-order necessary optimality conditions of Karush-Kuhn-Tucker type for weak efficiency. A new second-order constraint qualification of Zangwill type is introduced. It is applied in the optimality conditions. Some connections with other constraint qualifications are established. [ABSTRACT FROM AUTHOR]

Because public systems problems are frequently ill-defined and have fuzzy constraints and vague multiple objectives, their solution by means of formal optimization models is not widely accepted. This paper will explore the modes (both useful and otherwise) in which optimization has been applied to such problems. The need for optimization models which somehow "fit" the decision-makers' methods and backgrounds will be discussed. Several other aspects of public systems optimization will be considered, in a somewhat random fashion. This paper will raise more questions than answers. [ABSTRACT FROM AUTHOR]

This paper presents the application of a logic-based modelling language and integer programming framework for multicriteria optimisation proposed by Pinto and Rustem [12] to solve a bond portfolio problem. This application requires the analysis of conflicting objectives. The relevant information that should be taken into consideration during the solution search process can be better represented in terms of algebraic and logical relationships. The bond portfolio problem is introduced and the deterministic case is described based on the model by Nauss [9]. A logic-based model for a fictitious example is given, and finally the paper illustrates how one can interactively address the multiplicity of objectives. [ABSTRACT FROM AUTHOR]

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

This paper considers the solution of the problem: infƒ[ y. x(y)] s.t. γ ϵ R[y,x(y)]⊆ Ek, where x(y) solves: min F(x, y) s.t. x ϵ (x, y) ⊆ En. In order to obtain local solutions, a first-order algorithm, which uses {dx(y)/dy} for solving a special case of the implicitly defined y-problem. is given. The derivative is obtained from {dx(y, r)/dy}. where r is a penalty function parameter and {x(y, r)} are approximations to the solution of the x-problem given by a sequential minimization algorithm. Conditions are stated under which x( y, r) and {dx( y, r)/dy} exist. The computation of {dx( y, r)/dy} requires the availability of ∇y F (x, y) and the partial derivatives of the other functions defining the set R(x, y) with respect to the parameters y. [ABSTRACT FROM AUTHOR]

Due to the complexity of optimum replacement problems over finite time horizons various asymptotic criteria based upon fixed age replacement policies have been employed in the literature and in practice. In this paper the relationships between the optimum policies under three alternative cost criteria are considered. An ordering of the accounting costs under two of these is obtained, and for distributions with Increasing Hazard Rate an ordering of the optimum replacement time is derived. For a finite time horizon the policies are compared to the optimal sequential and fixed-age replacement polices through the example of a gamma distribution previously investigated by Barlow and Proschan (1962, 1965). [ABSTRACT FROM AUTHOR]

This paper, which is presented in two parts, is a contribution to the theory of fractional programming, i.e. maximization of quotients subject to constraints. In Part 1, duality theory for linear and concave-convex fractional programs is developed and related to recent results by Bector, Craven-Mond, Jagannathan, Sharma-Swarup, et al. Basic duality theorems of linear, quadratic and convex programming are extended. In Part II Dinkelbach's algorithm solving fractional programs is considered. The rate of convergence as well as a priori and a posteriori error estimates are determined. In view of these results the stopping rule of the algorithm is changed. Also the starting rule is modified using duality as introduced in Part I. Furthermore a second algorithm is proposed. In contrast to Dinkelbach's procedure the rate of convergence is still controllable. Error estimates are obtained too. [ABSTRACT FROM AUTHOR]

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

Abstract This paper proposes a novel decomposition method based on user-preference and developed a variation of the decomposition based multi-objective optimization algorithm (MOEA/D) targeting only solutions in a small region of the Pareto-front defined by the preference information supplied by the decision maker (DM). This is particularly advantageous for solving multi-objective optimization problems (MOPs) with more than 3 objectives, i.e., many-objective optimization problems (MaOPs). As the number of objectives increases, the ability of an EMO algorithm to approximate the entire Pareto front (PF) is rapidly diminishing. In this paper, we first propose a novel scalarizing function making use of a series of new reference points derived from a reference point specified by the DM in the preference model. Based on this scalarizing function, we then develop a user-preference-based EMO algorithm, namely R-MOEA/D. One key merit of R-MOEA/D is that it does not rely on an estimation of the ideal point, which may impact significantly the performances of state-of-the-art decomposition based EMO algorithms. Our experimental results on multi-objective and many-objective benchmark problems have shown that R-MOEA/D provides a more direct and efficient search towards the preferred PF region, resulting in competitive performances. In an interactive setting when the DM changes the reference point during optimization, R-MOEA/D has a faster response speed and performance than the compared algorithms, showing its robustness and adaptability to changes of the preference model. Furthermore, the effectiveness of R-MOEA/D is verified on a real-world problem of reservoir flood control operations. [ABSTRACT FROM AUTHOR]

In this paper we examine optimal sample sizes using a formal Bayesian decision-theoretic approach, in which auditors seek to maximize expected utility subject to a budgetary constraint. The results are presented for finite and infinite population models based on a linear loss function and the prior distribution mean error rates for audit populations taken from the GA study. As with GA, the sampling designs are for compliance tests. Our results indicate that the formal Bayesian approach can provide optimal sample sizes which differ from those found using the informal approach, and that the optimal sample sizes may be larger for the finite model. [ABSTRACT FROM AUTHOR]

In this paper we propose a nonlinear Generalized Disjunctive Programming model to optimize the 2-dimensional continuous location and allocation of the potential facilities based on their maximum capacity and the given coordinates of the suppliers and customers. The model belongs to the class of Capacitated Multi-facility Weber Problem. We propose a bilevel decomposition algorithm that iteratively solves a discretized MILP version of the model, and its nonconvex NLP for a fixed selection of discrete variables. Based on the bounding properties of the subproblems, ϵ-convergence is proved for this algorithm. We apply the proposed method to random instances varying from 2 suppliers and 2 customers to 40 suppliers and 40 customers, from one type of facility to 3 different types, and from 2 to 32 potential facilities. The results show that the algorithm is more effective at finding global optimal solutions than general purpose global optimization solvers tested. [ABSTRACT FROM AUTHOR]

Bat algorithm (BA) is a new approach designed by imitating bat's behavior of searching and capturing preys. The existing results have demonstrated the effectiveness and efficiency in comparison with other heuristic algorithms such as genetic algorithms and particle swarm optimization. In this paper, we design a novel framework for bat algorithm named two-stage bat algorithm (TSBA) using a trade-off strategy which balances the relationship between exploration and exploitation at the most extent. Inspired by the multi-population methods (e.g., artificial bee colony), we not only concern some technologies to avoid premature inevitably encountered when using BA, but also use a trade-off strategy to improve the comprehensive search performance for optimization. Some typical test sets which consist of 27 benchmark functions are utilized in comparative experiment, and the simulation results in terms of convergence rate and accuracy illustrate that the TSBA has a competitive performance than other swarm intelligent optimization algorithms. In addition, the proposed algorithm will not lend to the tremendous increase in computing time and thus will be a powerful tool in practical applications. [ABSTRACT FROM AUTHOR]

This paper presents the conic scalarization method for scalarization of nonlinear multi-objective optimization problems. We introduce a special class of monotonically increasing sublinear scalarizing functions and show that the zero sublevel set of every function from this class is a convex closed and pointed cone which contains the negative ordering cone. We introduce the notion of a separable cone and show that two closed cones (one of them is separable) having only the vertex in common can be separated by a zero sublevel set of some function from this class. It is shown that the scalar optimization problem constructed by using these functions, enables to characterize the complete set of efficient and properly efficient solutions of multi-objective problems without convexity and boundedness conditions. By choosing a suitable scalarizing parameter set consisting of a weighting vector, an augmentation parameter, and a reference point, decision maker may guarantee a most preferred efficient or properly efficient solution. [ABSTRACT FROM AUTHOR]

This paper introduces novel numerical solution strategies for generalized semi-infinite optimization problems (GSIP), a class of mathematical optimization problems which occur naturally in the context of design centering problems, robust optimization problems, and many fields of engineering science. GSIPs can be regarded as bilevel optimization problems, where a parametric lower-level maximization problem has to be solved in order to check feasibility of the upper level minimization problem. The current paper discusses several strategies to reformulate this class of problems into equivalent finite minimization problems by exploiting the concept of Wolfe duality for convex lower level problems. Here, the main contribution is the discussion of the non-degeneracy of the corresponding formulations under various assumptions. Finally, these non-degenerate reformulations of the original GSIP allow us to apply standard nonlinear optimization algorithms. [ABSTRACT FROM AUTHOR]

This paper discusses several areas of research conducted by Vyacheslav Tanaev (1940-2002), mainly on scheduling. His contribution to the parametric decomposition of optimization problems is also addressed. For each area we focus on the most important results obtained by V.S. Tanaev and trace how his research has been advanced. [ABSTRACT FROM AUTHOR]

In this paper, a modified degree-based strategy is proposed for pinning control of complex networks under constrained control capacity. Limited by the total control strength, the pinning strategy design problem is reconsidered as a constrained optimization problem. To provide a fast and effective solution, a decrease-and-conquer approach has been designed to assign the best control strengths to the pinned highest-degree nodes. Simulation results have demonstrated that the obtained strategy provides an outperformed control effect on various kinds of complex networks, as compared with strategies derived from degree, betweenness or closeness using evenly-distributed control strength. [ABSTRACT FROM AUTHOR]

The global exponential stability and the exponential convergence rate for time-delay systems with nonlinear uncertainties are investigated. A novel exponential stability criterion for the system is derived using the Lyapunov method. These stability conditions are formulated as linear matrix inequalities (LMIs), which can be easily solved by various convex optimization algorithms. The issue of exponential stability for time-delay systems with nonlinear uncertainties using generalized eigen value problem (GEVP) approach remains open, which motivates this paper. Numerical examples are given to illustrate the usefulness of our proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we consider the convex quadratic optimization problem with simultaneous perturbation in the right-hand side of the constraints and the linear term of the objective function with different parameters. The regions with invariant optimal partitions as well as the behaviour of the optimal value function on the regions are investigated. We show that identifying these regions can be done in polynomial time in the output size. An algorithm for identifying all invariancy regions is presented. Some implementation details as well as a numerical example are discussed. [ABSTRACT FROM AUTHOR]

The generation expansion planning (GEP) problem is defined as the problem of determining WHAT, WHEN, and WHERE new generation units should be installed over a planning horizon to satisfy the expected energy demand. This paper presents a framework to determine the number of new generating units (e.g., conventional steam units, coal units, combined cycle modules, nuclear plants, gas turbines, wind farms, and geothermal and hydro units), power generation capacity for those units, number of new circuits on the network, the voltage phase angle at each node, and the amount of required imported fuel for a single-period generation expansion plan. The resulting mathematical program is a mixed-integer bilinear multiobjective GEP model. The proposed framework includes a multiobjective evolutionary programming algorithm to obtain an approximation of the Pareto front for the multiobjective optimization problem and analytical hierarchy process to select the best alternative. A Mexican power system case study is utilized to illustrate the proposed framework. Results show coherent decisions given the objectives and scenarios considered. Some sensitivity analysis is presented when considering different fuel price scenarios. [ABSTRACT FROM AUTHOR]

In this paper we present our experience with the optimization of atomic clusters under the binary Lennard-Jones potential. This is a generalization of the single atom type Lennard-Jones model to the case in which atoms of two different types (and 'sizes') interact within the same cluster. This problem has a combinatorial structure which increases complexity and requires strategies to be revised in order to take into account such new aspects. Our approach has been a very effective one: we have been able not only to confirm most putative optima listed in the Cambridge Cluster Database, but also to find 95 improved solutions. [ABSTRACT FROM AUTHOR]

Different types of underestimation strategies are used in deterministic global optimization. In this paper, convexification and underestimation techniques applicable to problems containing signomial functions are studied. Especially, power transformation and exponential transformation (ET) will be considered in greater detail and some new theoretical results regarding the relation between the negative power transformation and the ET are given. The techniques are, furthermore, illustrated through examples and compared with other underestimating methods used in global optimization solvers such as αBB and BARON. [ABSTRACT FROM AUTHOR]

Liu and Tureli proposed a blind carrier frequency offset (CFO) estimation method for orthogonal frequency-division multiplexing (OFDM) systems, making use of null subcarriers. The optimal subcarrier placement that minimizes the Cramer-Rao bound (CRB) of the CFO estimation was reported by Ghogho et al. In this paper, we study the optimality of the null subcarrier placement from another perspective. We first show that the SNR of the CFO estimation using null subcarriers is a function of the null subcarrier placement. We then formulate the CFO-SNR optimization for the null subcarrier placement as a convex optimization problem for small CFO values and derive the optimal placement when the number of subcarriers is a multiple of the number of null subcarriers. In addition, we show that the SNR-optimal null subcarrier placement also minimizes the theoretical mean square error in the high SNR region. When the number of subcarriers is not a multiple of the number of null subcarriers, we propose a heuristic method for the null subcarrier placement that still achieves good performance in the CFO estimation. We also discuss the optimality of the null subcarrier placement in practical OFDM systems, where guard bands are required at both ends of the spectrum. [ABSTRACT FROM AUTHOR]

Abstract  The parameter determination of viscoelastic material is a multi-variable, multi-aim nonlinear optimization problem, which made the optimization process very complicated. In this paper a hybrid optimal algorithm was proposed to determine the viscoelastic parameters in the constitutive relation according to the experimentally obtained mechanical properties. This algorithm merges the Broydon–Fletcher–Goldfarb–Shanno search into a genetic algorithm framework as a basic operator in order to enhance the local search capability. The proposed hybrid algorithm not only can reduce the iterative times greatly but can abolish the limitation of initial parameter values. Nonlinear material characteristic curve-fitting was carried out using the proposed algorithm and other existing approaches. And the comparison results show this algorithm is accurate and effective. The numerical simulation and experimental study of viscoelastic cantilever beam also indicates that the finite element formulation and the calculative viscoelastic model parameters are reliable. The proposed optimization method can be extended to further complex parameter estimation researches. [ABSTRACT FROM AUTHOR]