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In this paper, we introduce new classes of nonsmooth second-order cone-convex functions and respective generalizations in terms of first and second-order directional derivative. These classes encapsulate several already existing classes of cone-convex functions and their weaker variants. Second-order KKT type sufficient optimality conditions and duality results for a nonsmooth vector optimization problem are proved using these functions. The results have been supported by examples. [ABSTRACT FROM AUTHOR]

This paper deals with a robust multiobjective optimization problem involving nonsmooth/nonconvex real-valued functions. Under an appropriate constraint qualification, we establish necessary optimality conditions for weakly robust efficient solutions of the considered problem. These optimality conditions are presented in terms of Karush-Kuhn-Tucker multipliers and convexificators of the related functions. Examples illustrating our findings are also given. [ABSTRACT FROM AUTHOR]

The problem of finding the maximum number of d-vertices cliques (d = 3) in d-partite graph (d = 3) when graph density q is lower than 1 is an important problem in combinatorial optimization and it is one of many NP-complete problems. For this problem a meta-heuristic algorithm has been developed, namely an ant colony optimization algorithm. In this paper a new development of this ant algorithm and experimental results are presented. The problem of finding the maximum number of 3-vertices cliques can be encountered in computer image analysis, computer vision applications, automation and robotic vision systems. The optimal solution of this problem boils down to finding a set of 3-vertices cliques in a 3-partite graph and this set should have cardinality as high as possible. The elaborated ant colony algorithm can be easily modified for d-dimensional problems, that is for finding the maximum number of d-vertices cliques in a d-partite graph. [ABSTRACT FROM AUTHOR]

The paper is devoted to the analysis of a graph transformation, pertinent for the transport and logistic systems and their planning and management. Namely, we consider, for a given graph, representing some existing transport or logistic system, its transformation to a (non-equivalent) so-called "hub-and-spoke" structure, known from both literature and practice of transportation and logistics. This structure is supposed to bring benefits in terms of functioning and economic performance of the respective systems. The transformation into the "hub-and-spoke" is not only non-equivalent (regarding the original graph of the system), but is also, in general, non unique. The structure sought is composed of two kinds of elements - nodes of the graph (stations, airports, havens, etc.), namely: the subgraph of hubs, which, in principle, ought to constitute a complete sub-graph (a clique), and the "spokes", i.e. the subsets of nodes, each of which is connected in the ultimate structure only with one of the hubs. The paper proposes a relaxation of the hub-and-spoke structure by allowing the hub subgraph not to be complete, but at least connected, with a definite "degree of completeness" (alpha), from where the name of "alpha-clique". It is shown how such structures can be obtained and what are the resulting benefits for various assumptions, regarding such structures. The benefits are measured here with travel times. The desired structures are sought with an evolutionary algorithm. It is shown on an academic example how the results vary and how the conclusions, relevant for practical purposes, can be drawn from such analyses, done with the methods here presented. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with a constrained set-valued optimization problem (P) . Using support functions, we give necessary optimality conditions in terms of Karush-Kuhn-Tucker (KKT) multipliers and approximations. Under generalized convexity, we investigate sufficient optimality conditions. An example illustrating our findings is also given. [ABSTRACT FROM AUTHOR]

Recently, boiler plants are have been the subject of intensive investigations in the context of energy-saving technologies and management for power saving and reduction of emissions. Mod- ern boiler design offers several benefits with this respect. In the past, improper design of boilers has been the cause of explosions which led to the loss of life and property. Modern designs attempt to avoid such mishaps. This paper presents a novel Self-Adaptive Whale Optimization Algorithm (SAWOA) for improving the learning char- acteristic of the neural network, the major intention being to model the characteristics of the boiler plant and so to effectively predict the boiler behaviour. The performance analysis of the introduced model has been carried out using the three test cases with consideration of several parameters. In the experimental analysis, the introduced technique is compared with the existing ones, based on such ap- proaches as Neural Model (NM), Firefly (FF-NM), Adaptive Firefly NM (AFF-NM), and Whale Optimization Algorithm-NM (WOA- NM). In this comparison, the error, i.e. the difference between the actual and the predicted value, was used, and the results revealed that the error is lower for the introduced technique under different experimental scenarios. The experimental results demonstrate that the performance level of SAWOA is by 18% better than those of NM, FF-NM, and AFF-NM, and by 3.74% better than that of WOA-NM. This confirms the quality of performance of the proposed approach regarding boiler plants. [ABSTRACT FROM AUTHOR]

The paper presents an improved sample based rule- probability estimation that is an important indicator of the rule quality and credibility in systems of machine learning. It concerns rules obtained, e.g., with the use of decision trees and rough set theory. Particular rules are frequently supported only by a small or very small number of data pieces. The rule probability is mostly investigated with the use of global estimators such as the frequency-, the Laplace-, or the m-estimator constructed for the full probability interval [0,1]. The paper shows that precision of the rule probability estimation can be considerably increased by the use of m-estimators which are specialized for the interval [phmin, phmax] given by the problem expert. The paper also presents a new interpretation of the m-estimator parameters that can be optimized in the estimators. [ABSTRACT FROM AUTHOR]

The paper describes an analytical study of open two node (tandem) network models with blocking. Here, a specific tandem configuration is chosen: the first node is treated as an infinite server (IS - often referred to as the ample-server), meaning that any incoming task can find at least one empty line for service in this node, and the second node has several parallel lines that can serve input task streams simultaneously. Between these two nodes there is a buffer with finite capacity. In this type of network, if the buffer is full, the accumulation of new tasks by the second node is temporarily suspended (blocking factor) and tasks must wait at the first node until the transmission process is resumed. In this paper, the two-node model is investigated using two different methods. The first is the multi-step exact algorithm, involving a numerical part for solving a set of linear equations, and the second is an approximate algorithm using a product form solution. The numerical part is used for solving a system of linear equations and for calculating the state probability vector. Finally, after comparing both algorithms, some recommendations as to when each method can be used are given. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of locating coated inclusions in a 2D dimensional conductor material in order to obtain a suitable thermal environment. The mathematical model is described by elliptic partial differential equation with linear boundary condition, including heat transfer coefficient. A shape optimization problem is formulated by introducing a cost functional to solve the problem under consideration. The shape sensitivity analysis is rigorously performed for the problem by means of a Lagrangian formulation. The optimization problem is solved by means of gradient-based strategy and numerical experiments are carried out to demonstrate the feasibility of the approach. [ABSTRACT FROM AUTHOR]

The paper considers parametric optimal control problems with bang-bang control vector function. For this problem we give regularity and second-order optimality conditions at the nominal solution which are sufficient to: (i) existence and local uniqueness of extremals, (ii) local structure stability, (iii) strong local optimality, under parameter perturbations. Here "local" means in a L∞- neighbourhood of the nominal trajectory, regardless of the control values. Stability results were obtained by the first author using the shooting approach, while optimality results were obtained by the other authors, using the Hamiltonian approach. The paper, combining both approaches, allows to unify the assumptions and to close some gaps between optimality and stability results. [ABSTRACT FROM AUTHOR]

In this paper, multiobjective variational programming problem is considered. Mond-Weir type higher order duality results are established by using the efficiency of higher order as the optimization tool. In order to prove these results, we propose the notion of generalized higher order (F,p, θ, m, h)-invexity. [ABSTRACT FROM AUTHOR]

The Topological Derivative has been recognized as a powerful tool in obtaining the optimal topology for several kinds of engineering problems. This derivative provides the sensitivity of the cost functional for a boundary value problem for nucleation of a small hole or a small inclusion at a given point of the domain of integration. In this paper, we present a topological asymptotic analysis with respect to the size of singular domain perturbation for a coupled nonlinear PDEs system with an obstacle on the boundary. The domain decomposition method, referring to the Steklov-Poincaré pseudo-differential operator, is employed for the asymptotic study of boundary value problem with respect to the size of singular domain perturbation. The method is based on the observation that the known expansion of the energy functional in the ring coincides with the expansion of the Steklov-Poincaré operator on the boundary of the truncated domain with respect to the small parameter, which measures the size of perturbation. In this way, the singular perturbation of the domain is reduced to the regular perturbation of the Steklov-Poincaré mapping for the ring. The topological derivative for a tracking type shape functional is evaluated so as to obtain the useful formula for application in the numerical methods of shape and topology optimization. [ABSTRACT FROM AUTHOR]

Ant Colony Optimization (ACO) is a stochastic search method that mimics the social behavior of real ant colonies, managing to establish the shortest route to the feeding sources and back. Such algorithms have been developed to arrive at near-optimal solutions to large-scale optimization problems, for which traditional mathematical techniques may fail. In this paper, the semi-random start procedure is applied. A new kind of evaluation of start nodes of the ants is developed and several starting strategies are prepared and combined. The idea of semi-random start is related to a better management of the ants. This new technique is tested on the Multiple Knapsack Problem (MKP). A Comparison among the strategies applied is presented in terms of quality of the results. A comparison is also carried out between the new evaluation and the existing one. Based on this comparative analysis, the performance of the algorithm is discussed. The study presents the idea that should be beneficial to both practitioners and researchers involved in solving optimization problems. [ABSTRACT FROM AUTHOR]

This paper concerns an energy efficient global path planning algorithm for a four-wheeled mobile robot (4WMR). First, the appropriate graph search methods for robot path planning are described. The A* heuristic algorithm is chosen to find an optimal path on a 2D tile-decomposed map. Various criteria of optimization in path planning, like mobility, distance, or energy are reviewed. The adequate terrain representation is introduced. Each cell in the map includes information about ground height and type. Tire-ground interface for every terrain type is characterized by coefficients of friction and rolling resistance. The goal of the elaborated algorithm is to find an energy minimizing route for the given environment, based on the robot dynamics, its motor characteristics, and power supply constraints. The cost is introduced as a function of electrical energy consumption of each motor and other robot devices. A simulation study was performed in order to investigate the power consumption level for diverse terrain. Two 1600 m2 test maps, representing field and urban environments, were decomposed into 20x20 equal-sized square-shaped elements. Several simulation experiments have been carried out to highlight the differences between energy consumption of the classic shortest path approach, where cost function is represented as the path length, and the energy efficient planning method, where cost is related to electrical energy consumed during robot motion. [ABSTRACT FROM AUTHOR]

Cost-efficient project management based on Critical Chain Method (CCPM) is investigated in this paper. This is a variant of the resource-constrained project scheduling problem (RCPSP) when resources are only partially available and a deadline is given, but the cost of the project should be minimized. RCPSP is a well- known NP-hard problem but originally it does not take into con- sideration the initial resource workload. A metaheuristic algorithm driven by a metric of a gain was adapted to solve the problem when applied to CCPM. Refinement methods enhancing the quality of the results are developed. The improvement expands the search space by inserting the task in place of an already allocated task, if a better allocation can be found for it. The increase of computation time is reduced by distributed calculations. The computational experiments showed significant efficiency of the approach, in comparison with the greedy methods and with genetic algorithm, as well as high reduction of time needed to obtain the results. [ABSTRACT FROM AUTHOR]

The paper presents a new, relatively simple proof of Pontryagin's maximum principle for the canonical problem of optimal control, with equality and inequality constraints imposed on the trajectory endpoints. The proof combines together two ideas, which appeared separately in the earlier works: application of the Karush-John conditions for finite-dimensional problems, and using packages of needle variations. [ABSTRACT FROM AUTHOR]

In this paper, we introduce four new classes of open sets in general Euclidean space RN. It is shown that every such class of open sets is compact under the Hausdorff distance. The result is applied to a shape optimization problem of p-Laplacian equation. The existence of the optimal solution is presented. [ABSTRACT FROM AUTHOR]

The well-known problem of price-based coordinability is studied for the case of a multiagent system in which information regarding the goals of the interacting subsystems is asymmetric. The paper illustrates how the uniformprice-based coordination rules may create incentives to anticipate the values of coordination signals and, thus, why the coordinability condition cannot be satisfied under asymmetric information. For this purpose a comparison is given of Nash equilibrium outcomes that are reachable individually by price-anticipating agents in two noncooperative games. These games are induced by the uniform-price-based coordination mechanism and are referred to as payment-bidding auction and demand-bidding auction. The analysis presented shows that in the games considered some of the agents may improve payoffs and allocations by applying the price-anticipating bidding strategies. However, the payment-bidding auction cannot be strictly dominated by the demand-bidding auction with respect to the resource allocation levels individually received by each agent. The derived results of theoretic considerations are illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

In this paper an abstract linear-quadratic optimal control problem governed by an evolution equation is considered. To solve this problem numerically a reduced-order approach based on proper orthogonal decomposition (POD) is applied. The error between the POD suboptimal control and the optimal control of the original problem is controlled by an a-posteriori error analysis. However, if the POD basis has bad approximation properties, a huge number of POD basis function is required to solve the reduced-order problem with the desired accuracy. To overcome this problem, optimality system POD (OS-POD) is utilized, where the POD basis is chosen with respect to the optimization criteria. [ABSTRACT FROM AUTHOR]

In this paper we develop a general convergence theory for nonmonotone line searches in optimization algorithms. The advantage of this theory is that it is applicable to various step size rules that have been published in the past decades. This gives more insight into the structure of these step size rules and points to several relaxations of the hypotheses. Furthermore, it can be used in the framework of discretized infinite-dimensional optimization problems like optimal control problems and ties the discretized problems to the original problem formulation. [ABSTRACT FROM AUTHOR]

In this paper, a Hierarchical Trust Region Algorithm for solving PDE-constrained optimization problems is developed. A hierarchy of finite element meshes is used to define a hierarchy of quadratic models for the approximation of the discrete reduced cost functional on the finest mesh. The proposed algorithm simultaneously controls the choice of the model and the size of the trust region radius. Application of the trust region convergence theory allows for proving that every accumulation point of the sequence produced by the algorithm is a stationary point of the discretized problem. Numerical examples illustrate the behavior of the method and show a considerable reduction of computation time compared to the standard Newton trust region scheme. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to consider the regularity and convexity properties of a given type of approximately generalized convex functions, namely approximately Breckner s-convex functions (see the origin of the definition in Breckner, 1978). Our main result is a Bernstein-Doetsch type one. It is proved that the local boundedness of such a type of function from above at a point of its domain implies approximate convexity and stronger regularity properties of the function in question on the whole domain. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present the shape derivative for a wide array of objective functions using the incompressible Navier-Stokes equations as a state constraint. Most real world applications of computational fluid dynamics are shape optimization problems in nature, yet special shape optimization techniques are seldom used outside the field of elliptic partial differential equations and linear elasticity. This article tries to be self contained, also presenting many useful results from the literature. We conclude with a comparison of different objective functions for the shape optimization of an obstacle in a channel, which can be done quite conveniently when one knows the general form of the shape gradient. [ABSTRACT FROM AUTHOR]

The paper discusses incomplete sensitivity evaluations for shape optimization problems. It also shows how reduced order models can be introduced to extend the validity domain of the approach. [ABSTRACT FROM AUTHOR]

For continuous, uncertain, linear quadratic control system with delayed input, we consider a min-max control policy in which the elements of feedback are present. The feedback is introduced into control optimization by allowing a control to be corrected at a given set of correction points from the control interval. This helps to overcome the feasibility difficulties that arise with standard min-max techniques. We show that construction of the optimal policy involves a sequence of min-max optimizations formulated as dynamic programs that do not yield simple analytical solutions. That is why the paper is mainly focused on construction and justification of suboptimal control policy that can be effectively implemented. Simulated examples demonstrate the proposed approach. [ABSTRACT FROM AUTHOR]

The uncertain equivalence method (UE) is a newly proposed technique for elicitation of 1-D utilities in the case of monotonic preferences. Previous publications argue that the rationale behind the introduction of this technique is that UE estimates are not influenced by certainty effect, UE elicits points that well describe the curvature of the utility function, which is somewhat closer to the true function than the one of the lottery equivalence method (LE), and there is no increase in the width of the elicited UE uncertainty intervals compared to those of the certainty equivalence method (CE). This paper analyzes these assumptions quantitatively on the basis of empirical data from 104 volunteers who constructed their utility functions over monetary prizes using CE, LE and UE. The data was analyzed with the help of four one-tail statistical tests for paired samples. Results showed that: 1) UE results are not influenced by the certainty effect, unlike CE; 2) the UE utility function is more curved than that of LE, but that might be associated with the better selection of approximation nodes and not with the certainty effect; 3) the length of the UE uncertainty intervals is greater than that of the CE intervals, perhaps because of higher complexity of the method, but the increase is only by 30%. [ABSTRACT FROM AUTHOR]

In this paper we propose and evaluate a soft computing- based passage retrieval system for Question Answering Systems (QAS). FuzzyPR, our base-line passage retrieval system, employs a similarity measure that attempts to model accurately the question reformulation intuition. The similarity measure includes fuzzy logic-based models that evaluate efficiently the proximity of question terms and detect term variations occurring within a passage. Our experimental results using FuzzyPR on the TREC and CLEF corpora show that our novel passage retrieval system achieves better performance compared to other similar systems. Finally, we describe the performance results of OptFuzzyPR, an optimized version of FuzzyPR, created by optimizing the values of FuzzyPR system parameters using genetic algorithms. [ABSTRACT FROM AUTHOR]

Active learning is the process in which unlabeled instances are dynamically selected for expert labelling, and then a classifier is trained on the labeled data. Active learning is particularly useful when there is a large set of unlabeled instances, and acquiring a label is costly. In business scenarios such as direct marketing, active learning can be used to indicate which customer to approach such that the potential benefit from the approached customer can cover the cost of approach. This paper presents a new algorithm for cost-sensitive active learning using a conditional expectation estimator. The new estimator focuses on acquisitions that are likely to improve the profit. Moreover, we investigate simulated annealing techniques to combine exploration with exploitation in the classifier construction. Using five evaluation metrics, we evaluated the algorithm on four benchmark datasets. The results demonstrate the superiority of the proposed method compared to other algorithms. [ABSTRACT FROM AUTHOR]

Method materialization is a promising data access optimization technique for multiple applications, including, in particular object programming languages with persistence, object databases, distributed computing systems, object-relational data warehouses, multimedia data warehouses, and spatial data warehouses. A drawback of this technique is that the value of a materialized method becomes invalid when an object used for computing the value of the method is updated. As a consequence, a materialized value of the method has to be recomputed. The materialized value can be recomputed either immediately after updating the object or just before calling the method. The moment the method is recomputed bears a strong impact on the overall system performance. In this paper we propose a technique of predicting access to materialized methods and objects, for the purpose of selecting the most appropriate recomputation technique. The prediction technique is based on the Hidden Markov Model (HMM). The prediction technique was implemented and evaluated experimentally. Its performance characteristics were compared to: immediate recomputation, deferred recomputation, random recomputation, and to our previous prediction technique, called a PMAP. [ABSTRACT FROM AUTHOR]

The robust H∞ control problem is considered for a class of uncertain neutral system involving both state and control input time-varying delays. The uncertainties under consideration are nonlinear time-varying parameter perturbations. The methodology is based on the Lyapunov functional combined with a unified LMI approach, and a new delay-dependent criterion is proposed to guarantee the stabilization and disturbance attenuation of systems. Moreover, a convex optimization approach is used to solve the robust H∞ control disturbance attenuation problem. Finally, a numerical example is illustrated to show the validity of this paper. The simulation results reveal significant improvement over the recent results. [ABSTRACT FROM AUTHOR]

The paper gives second order sufficient conditions for the strong local optimality of a bang-singular extremal in a minimum time problem. The conditions are given in terms of regularity assumptions on the extremal and of the coercivity of the extended second variation associated to the minimum time problem with fixed end-points on the singular arc. The conditions are close to the necessary ones in the usual sense, namely we require strict inequalities where necessary conditions have mild inequalities. [ABSTRACT FROM AUTHOR]

An optimal control problem for 2d and 3d Stokes equations is investigated with pointwise inequality constraints on the state and the control. The paper is concerned with the full discretization of the control problem allowing for different types of discretization of both the control and the state. For instance, piecewise linear and continuous approximations of the control are included in the present theory. Under certain assumptions on the L∞-error of the finite element discretization of the state, error estimates for the control are derived which can be seen to be optimal since their order of convergence coincides with the one of the interpolation error. The assumptions of the L∞-finite-element-error can be verified for different numerical settings. Finally the results of two numerical experiments are presented. [ABSTRACT FROM AUTHOR]

The paper is devoted to stability investigation of optimal structure and switching points position for parametric bangbang control problem with special focus on simultaneous switches of two control components. In contrast to problems where only simple switches occur, the switching points in general are no longer differentiable functions of input parameters. Conditions for Lipschitz stability are found which generalize known sufficient optimality conditions to nonsmooth situation. The analysis makes use of backward shooting representation of extremals, and of generalized implicit function theorems. The Lipschitz properties are illustrated for an example by constructing backward parameterized family of extremals and providing first-order switching points prediction. [ABSTRACT FROM AUTHOR]

The paper deals with optimal control problems for semilinear elliptic and parabolic PDEs subject to pointwise state constraints. The main issue is that the controls are taken from a restricted control space. In the parabolic case, they are Rm -vector- valued functions of time, while they are vectors of Rm in elliptic problems. Under natural assumptions, first- and second-order sufficient optimality conditions are derived. The main result is the ex- tension of second-order sufficient conditions to semilinear parabolic equations in domains of arbitrary dimension. In the elliptic case, the problems can be handled by known results of semi-infinite optimization. Here, different examples are discussed that exhibit different forms of active sets and where second-order sufficient conditions are satisfied at the optimal solution. [ABSTRACT FROM AUTHOR]