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The purpose of the paper is to give a survey of methods, partly derived by the author in joint work with other researchers, concerning the problem of constructing e-optimal strategies for partially observable MDPs. The methods basically consist in transforming the problem into one of approximation: Starting from the original problem a sequence of approximating problems is constructed such that: (i) For each approximating problem an optimal strategy can actually be computed, (ii) Given ϵ » 0, there exists an approximating problem such that the optimal strategy for the latter is ϵ-optimal for the original problem. [ABSTRACT FROM AUTHOR]

In this paper a parametric optimization problem for a linear neutral system with two delays with an integral quadratic performance index is formulated and solved. The method of computing of a performance index value bases on determining of a Lyapunov functional defined on a state space such that its value for an initial state is equal to a performance index value. In the paper a form of a Lyapunov functional is assumed and a method of computing its coefficients is given. An example illustrating the application of discussed theory is presented. It concerns the system with a PD-controller designed to control a plant with two delays both retarded and neutral type. For such system a value of considered performance index is determined. [ABSTRACT FROM AUTHOR]

The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding, and collaborative filtering. Although specific instances can often be solved with specialized algorithms, the general affine rank minimization problem is NP-hard because it contains vector cardinality minimization as a special case. In this paper, we show that if a certain restricted isometry property holds for the linear transformation defining the constraints, the minimum-rank solution can be recovered by solving a convex optimization problem, namely, the minimization of the nuclear norm over the given affine space. We present several random ensembles of equations where the restricted isometry property holds with overwhelming probability, provided the codimension of the subspace is sufficiently large. The techniques used in our analysis have strong parallels in the compressed sensing framework. We discuss how affine rank minimization generalizes this preexisting concept and outline a dictionary relating concepts from cardinality minimization to those of rank minimization. We also discuss several algorithmic approaches to minimizing the nuclear norm and illustrate our results with numerical examples. [ABSTRACT FROM AUTHOR]

Emerging applications for networked and cooperative robots motivate the study of motion coordination for groups of agents. For example, it is envisioned that groups of agents will perform a variety of useful tasks including surveillance, exploration, and environmental monitoring. This paper deals with basic interactions among mobile agents such as "move away from the closest other agent" or "move toward the furthest vertex of your own Voronoi polygon." These simple interactions amount to distributed dynamical systems because their implementation requires only minimal information about neighboring agents. We characterize the close relationship between these distributed dynamical systems and the disk-covering and sphere-packing cost functions from geometric optimization. Our main results are as follows: (i) we characterize the smoothness properties of these geometric cost functions, (ii) we show that the interaction laws are variations of the nonsmooth gradient of the cost functions, and (iii) we establish various asymptotic convergence properties of the laws. The technical approach relies on concepts from computational geometry, nonsmooth analysis, and nonsmooth stability theory. [ABSTRACT FROM AUTHOR]

Abstract: Ecological expert knowledge is often based on qualitative rules consisting of linguistic terms such as ‘low’, ‘moderate’ or ‘high’. Since fuzzy systems transform these rules and terms into a mathematical framework, they allow implementing this expert knowledge in ecological models. However, the development of a reliable knowledge base is complex and time consuming. Recent research has shown that complementing fuzzy systems by data-driven techniques can solve this knowledge acquisition bottleneck. In this paper, a heuristic nearest ascent hill-climbing algorithm for rule base optimisation is applied to construct a fuzzy rule-based habitat suitability model for spawning European grayling (Thymallus thymallus L.) in the Aare river (Bern, Switzerland). Optimisation of the fuzzy rule-based model was based on two different training criteria, the weighted correctly classified instances and Cohen''s Kappa. The ecological relevance of the results was assessed by comparing the optimised rule bases with a rule base derived from ecological expert knowledge. Optimisation based on Kappa appeared to generate acceptable results (CCI=0.70; Kappa=0.32) and was more practical than optimisation based on since the latter required fine tuning of a weight parameter, which accounted for the species prevalence. The optimal rules showed 74% similarity with the rules derived from expert knowledge, while 84% of all model errors was due to false positive predictions of the model. These errors might be due to the impact of variables, which were not included in this study on grayling presence and thus are not necessarily a model error. The habitat suitability model optimised in this paper is able to predict the effect of different impacts on the river system and to select the optimal restoration option. Hence, it could be a valuable decision support tool for river managers and ease the discussion between stakeholders. [Copyright &y& Elsevier]

Abstract: Scalarization of the multiobjective programming problems with fuzzy coefficients using the embedding theorem and the concept of convex cone (ordering cone) is proposed in this paper. Since the set of all fuzzy numbers can be embedded into a normed space, this motivation naturally inspires us to invoke the scalarization techniques in vector optimization problems to evaluate the multiobjective programming problems with fuzzy coefficients. Two solution concepts are proposed in this paper by considering different convex cones. [Copyright &y& Elsevier]

During the last years nature inspired intelligent techniques have become attractive for analyzing large data sets and solving complex optimization problems. In this paper, one of the most interesting of them, the Ant Colony Optimization (ACO), is used for the construction of a hybrid algorithmic scheme which effectively handles the Pap Smear Cell classification problem. This algorithmic approach is properly combined with a number of nearest neighbor based approaches for performing the requested classification task, through the solution of the so-called optimal feature subset selection problem. The proposed complete algorithmic scheme is tested in two sets of data. The first one consists of 917 images of pap smear cells and the second set consists of 500 images, classified carefully by expert cyto-technicians and doctors. Each cell is described by 20 numerical features, and the cells fall into seven (7) classes, four (4) representing normal cells and three (3) abnormal cases. Nevertheless, from the medical diagnosis viewpoint, a minimum requirement corresponds to the general two-class problem of correct separation between normal from abnormal cells. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we suggest and analyze a new inexact proximal point method for solving general variational inequalities, which can be considered as an implicit predictor–corrector method. An easily measurable error term is proposed with further relaxed error bound and an optimal step length is obtained by maximizing the profit-function and is dependent on the previous points. Our results include several known and new techniques for solving variational inequalities and related optimization problems. Results obtained in this paper can be viewed as an important improvement and refinement of the previously known results. Preliminary numerical experiments are included to illustrate the advantage and efficiency of the proposed method. [Copyright &y& Elsevier]

Abstract: A rank-niche evolution strategy (RNES) algorithm has been developed in this paper to solve unconstrained multiobjective optimization problems. A required number of Pareto-optimal solutions can be generated by the algorithm in a single run. In addition to the operations of recombination, mutation and selection used in original evolution strategy (ES), an external elite set which contains a given number of non-dominated elites is updated and trimmed by a clustering technique to maintain a uniformly distributed Pareto front. The fitness function for each individual contains the information of rank and crowding status. The selection operation using this fitness function considers the superiority and distribution simultaneously. Eight test problems illustrated in other papers are used to test RNES. For some test problems the Pareto-optimal solutions obtained by RNES are better than those obtained by GA-based algorithms. [Copyright &y& Elsevier]

The purpose of this paper is to extend, as much as possible, the modern theory of condition numbers for conic convex optimization: ... to the more general nonconic format: ... where P is any closed convex set, not necessarily a cone, which we call the ground-set. Although any convex problem can be transformed to conic form, such transformations are neither unique nor natural given the natural description of many problems, thereby diminishing the relevance of data-based condition number theory. Herein we extend the modern theory of condition numbers to the problem format (GPd). As a byproduct, we are able to state and prove natural extensions of many theorems from the conic-based theory of condition numbers to this broader problem format. [ABSTRACT FROM AUTHOR]

This paper describes an algorithm, based on a recently proposed method due to D.D. Morrison, for solving constrained optimization problems, and shows that it compares favorably with existing methods in several examples. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we consider a class of non-standard time optimal control problems involving a dynamical system consisting of multiple subsystems evolving over different time horizons. Different subsystems are required to reach their respective target sets at different termination times. The goal is to minimize the maximum of these termination times. By introducing a discrete variable to represent the system termination ordering, we reformulate this problem as a discrete optimization problem. A discrete filled function method is developed to solve this discrete optimization problem. For illustration, a numerical example is solved. [Copyright &y& Elsevier]

Abstract: In this paper, we use the third order shear deformation theory of Reddy [Reddy JN. Mechanics of laminated composite plates and shells. CRC Press; 2004] with a meshless numerical method to analyze the static deformation of composite plates and shells. Numerical results are compared with Navier solutions in various examples. The meshless collocation method based on radial basis functions requires a user-defined shape parameter than can compromise the quality of the solution when poorly chosen. To improve the choice of this shape parameter, we apply an optimization technique based on the leave-one-out cross validation analysis to obtain the shape parameter in a given interval. The results obtained were significantly better than those produced with a user-defined shape parameter. [Copyright &y& Elsevier]

Abstract: The aim of the paper is to report a systematic methodology which is used to evaluate and improve the ride comfort. An accurate model is necessary for further investigation and optimization. The vehicle dynamics model of tractor with tandem suspension is modeled and simulated in dynamics software ADAMS, which is redeveloped to add a function of automatic parametric modeling and simulation. The modeling methods of nonlinear characteristic components and various road excitation inputs, which can be simply seen as the implementation means for the model solution, are introduced. A new index called annoyance rate is presented to indicate the quantitative correlation between objective method and subjective comment. The quantitative correlation between them, which is quite different from the qualitative “comfortable” or “uncomfortable” results attained by objective evaluation, can be defined by function and regarded as a basis to scientifically evaluate and improve the ride comfort. According to the request of performance-based design, the parameter sensitive analysis and structure optimization have been carried out to find the trade-off among ride comfort, maneuverability and safety. The approach has proved to be very effective for predicting and improving the ride comfort by experiment results. The methodology can be also used for any other specific category of vehicle. [Copyright &y& Elsevier]

Abstract: Optimization design is the most important key technique of Air-breathing Hypersonic Cruise Vehicle (HCV). To improve the design level and get better integrated performances of HCV, this paper researches the integrated optimization design method of waverider hypersonic cruise vehicle. In the optimization design, Multi-Objective Genetic Algorithms (MOGA) is selected as the optimization algorithm, and the shape parameters of aircraft are as design variables. Some performances, such as aerodynamics, aeroheating, radar cross section (RCS), airframe/scramjet integration, and volume of airframe, trimmed characteristic, static stability and maneuverability at cruise phase are selected as the objectives. When the optimization process finishes, the Pareto front side is got, in which many Pareto solutions whose integrated performances are more excellent than basic configuration are found. According to the design idea, we choose a Pareto solution from the Pareto front side as the recommended shape configuration for further research. To validate the aerodynamics of recommended configuration, wind tunnel test is done. And the comparison results show that the optimization design is successful. [Copyright &y& Elsevier]

Abstract: Bilevel programming has been proposed for dealing with decision processes involving two decision makers with a hierarchical structure. They are characterised by the existence of two optimisation problems in which the constraint region of the upper level problem is implicitly determined by the lower level optimisation problem. In this paper we focus on the class of bilevel problems in which the upper level objective function is linear multiplicative, the lower level one is linear and the common constraint region is a bounded polyhedron. After replacing the lower level problem by its Karush–Kuhn–Tucker conditions, the existence of an extreme point which solves the problem is proved by using a penalty function approach. Besides, an algorithm based on the successive introduction of valid cutting planes is developed obtaining a global optimal solution. Finally, we generalise the problem by including upper level constraints which involve both level variables. [Copyright &y& Elsevier]

Abstract: This paper deals with a special case of multicriteria optimization problems. The problems studied come from the medical domain and are of a very important practical relevance. One of the problems refers to the ranking of treatments for the Trigeminal Neuralgia. The second problem refers to a hierarchy of risk factors for Bronchial Asthma. The most common way to deal with a multiobjective optimization problem is to apply Pareto dominance relationship between solutions. But in the cases studied here, a decision cannot be made just by using Pareto dominance. In one of the experiments, all the potential solutions are nondominated (and we need to clearly find a hierarchy of these solutions) and in the second experiment most of the solutions are nondominated between them. We propose a novel multiple criteria procedure and then an evolutionary scheme is applied for solving the problems. Results obtained by the proposed approach in a very simple way are same as the results (or even better) obtained by applying weighted-sum method. The advantage of the proposed technique is that it does not require any additional information about the problem (like weights for each criteria in the case of weighted-sumapproach). [Copyright &y& Elsevier]

Abstract: The splitting spinning which is designed to split a rotational disk blank into two flanges, is one of newly rising, green flexible forming technologies, and it can be widely applied to manufacture a whole pulley or wheel in fields of aerospace, automobile and train. The investigation of forming parameters influencing on splitting spinning force can provide the foundation for the choice of equipments, the design of dies and the determination of processing parameters. This paper aims at developing a reasonable formula between splitting spinning force and forming parameters by the principal stress method, and then the reliability of the formula is verified by the comparisons with experimental data. Meanwhile, both a reasonable method of calculating the three-dimensional projected areas and a more effective method of solving the average angle in the deformation zone are presented. Furthermore, based on the formula, the laws of initial thickness and initial diameter of workpiece, diameter and splitting angle of splitting roller and feed ratio of splitting spinning influencing on splitting spinning force are investigated. The achievements may serve as an important guide for the determination and optimization of forming parameters of splitting spinning. [Copyright &y& Elsevier]

Abstract: Cold cross-wedge rolling process is utilized to enhance the surface hardness and the strength in a round shaped part. Main geometrical design parameters in a cold cross-wedge rolling die are the forming angle, the spreading angle, and the die height. General defects in this process are an excessive slip on the surface and a hole generation at the center point which is usually called as the Mannesmann hole defect. The friction coefficient and geometrical design variables affect occurrences of an excessive slip and/or a central hole generation. In this paper, effects of the forming angle and the friction coefficient on the initiation of the Mannesmann hole defect are analyzed by using a response surface method. Integrals of four different ductile fracture models are compared with a history of the effective plastic strain at the central point. It reveals that the maximum effective plastic strain at the point can be utilized to determine the initiation point of the ductile fracture in the cold cross-wedge rolling process. Optimization of design parameters for prevention of the Mannesmann hole defect initiation is carried out using a response surface method. As results, that the forming angle of 25° and the spreading angle of 1° can be proper design conditions with the prevention of occurrences of internal hole defect and an excessive slip. Optimum design specification is testified by the experimental result. [Copyright &y& Elsevier]

Abstract: The inverse optimization problem is to modify the weight (or cost, length, capacity and so on) such that a given feasible solution becomes an optimal solution. In this paper, we consider the inverse min–max spanning tree problem under the weighted sum-type Hamming distance. For the model considered, we present its combinatorial algorithm that runs in strongly polynomial times. [Copyright &y& Elsevier]

Abstract: In this paper, we study the inapproximability of the following NP-complete number theoretic optimization problems introduced by Rössner and Seifert [C. Rössner, J.P. Seifert, The complexity of approximate optima for greatest common divisor computations, in: Proceedings of the 2nd International Algorithmic Number Theory Symposium, ANTS-II, 1996, pp. 307–322]: Given numbers , find an -minimum GCD multiplier for , i.e., a vector with minimum satisfying . We show that assuming , it is NP-hard to approximate the Minimum GCD Multiplier in norm () within a factor for some constant where is the dimension of the given vector. This improves on the best previous result. The best result so far gave factor hardness by Rössner and Seifert [C. Rössner, J.P. Seifert, The complexity of approximate optima for greatest common divisor computations, in: Proceedings of the 2nd International Algorithmic Number Theory Symposium, ANTS-II, 1996, pp. 307–322], where is an arbitrarily small constant. [Copyright &y& Elsevier]

Abstract: In this paper, we establish the global estimates for divergence form elliptic equations in the Orlicz space , where Ω is a bounded Reifenberg domain in . Our result generalizes the estimates. [Copyright &y& Elsevier]

Abstract: This paper studies maximality and totality of stable functions in the category of stable bifinite domains. We present three main results as follows, [o] [(1)] every maximum-preserving function is a maximal element in the stable function spaces; [(2)] a maximal stable function f : D → E is maximum-preserving if D is maximum-separable and E is completely separable; and [(3)] a stable bifinite domain D is maximum-separable if and only if for any locally distributive stable bifinite domain E, each maximal stable function f : D → E is maximum-preserving. [Copyright &y& Elsevier]

Abstract: In this paper, we extend the classes of generalized type I vector-valued functions introduced by Aghezzaf and Hachimi in [J. Global Optim. 18 (2000) 91–101] to generalized univex type I vector-valued functions and consider a multiple-objective optimization problem involving generalized type I univex functions. A number of Kuhn–Tucker type sufficient optimality conditions are obtained for a feasible solution to be an efficient solution. The Mond–Weir and general Mond–Weir type duality results are also presented. [Copyright &y& Elsevier]

Abstract: Metabolic networks are often approached through steady-state optimization formulations that are solved to interpret and predict the behavior of the network subject to changes in external fluxes or internal enzyme activity. The major question addressed in this paper is how to ensure that solutions to these steady-state optimization models for metabolic networks are implementable from a stability point of view. The stability of a dynamic system is closely related to matrix stability. Hence, it can be determined through the computation of the largest eigenvalue of a coefficient matrix. While it is straightforward to analyze the stability of a given system, the challenge is to redesign a metabolic network in a way that guarantees that the system will be stable around the new steady-state. For this purpose, we propose to model metabolic networks through classical optimization formulations, such as the classical -system representation, with an additional constraint to enforce stability within a prespecified neighborhood of the solution point. The proposed formulation is a bilevel optimization problem that is very difficult to solve. We develop a suitable global optimization algorithm to solve this problem after transforming it to a semi-infinite optimization problem. Computational results are presented, including application to tryptophan biosynthesis in bacteria and anaerobic fermentation in Saccharomyces cerevisiae. [Copyright &y& Elsevier]

The paper studies the problem of determining the measurements of a given number of sizes of apparel so as to maximize expected sales or minimize an index of discomfort. It develops general necessary conditions for optimization in one control body dimension and calculates optimal sizes for the special case where the population distribution is normal. [ABSTRACT FROM AUTHOR]

The problem of minimizing the total tardiness for a set of independent jobs on one machine is considered. Lawler has given a pseudo-polynomial-time algorithm to solve this problem. In spite of extensive research efforts for more than a decade, the question of whether it can be solved in polynomial time or it is NP-hard (in the ordinary sense) remained open. In this paper the problem is shown to be NP-hard (in the ordinary sense). [ABSTRACT FROM AUTHOR]

Constraint propagation techniques have heavily utilized interval arithmetic while the application of convex and concave relaxations has been mostly restricted to the domain of global optimization. Here, reverse McCormick propagation, a method to construct and improve McCormick relaxations using a directed acyclic graph representation of the constraints, is proposed. In particular, this allows the interpretation of constraints as implicitly defining set-valued mappings between variables, and allows the construction and improvement of relaxations of these mappings. Reverse McCormick propagation yields potentially tighter enclosures of the solutions of constraint satisfaction problems than reverse interval propagation. Ultimately, the relaxations of the objective of a non-convex program can be improved by incorporating information about the constraints. [ABSTRACT FROM AUTHOR]

We consider single-carrier and single-user transmissions over a frequency-selective channel. We address the problem of joint estimation of the channel and the carrier frequency offset using a known training sequence (TS). Since in general the TS that is optimum for CFO estimation is not optimum for channel estimation, here we design the TS to minimize the mean-square error on the soft estimates of the data symbols obtained using a Wiener equalizer after CFO compensation. Our design results apply to the general scenarios of correlated and/or Ricean channel taps. Simulations measuring the bit error rate show an interesting gain when using the proposed training schemes in lieu of standard schemes. [ABSTRACT FROM AUTHOR]

Provides an overview of direct search methods that can be used to solve multidimensional optimization problem in mathematics. Effectiveness of the method in quantifying function values; Challenge of solving constrained optimization problems with direct methods.

Consider the relative entropy between a posterior density for a parameter given a sample and a second posterior density for the same parameter, based on a different model and a different data set. Then the relative entropy can be minimized over the second sample to get a virtual sample that would make the second posterior as close as possible to the first in an informational sense. If the first posterior is based on a dependent dataset and the second posterior uses an independence model, the effective inferential power of the dependent sample is transferred into the independent sample by the optimization. Examples of this optimization are presented for models with nuisance parameters, finite mixture models, and models for correlated data. Our approach is also used to choose the effective parameter size in a Bayesian hierarchical model. [ABSTRACT FROM AUTHOR]