Disconnected Skeleton: Shape at its Absolute Scale

We present a new skeletal representation along with a matching framework to address the deformable shape recognition problem. The disconnectedness arises as a result of excessive regularization that we use to describe a shape at an attainably coarse scale. Our motivation is to rely on the stable properties of the shape instead of inaccurately measured secondary details. The new representation does not suffer from the common instability problems of traditional connected skeletons, and the matching process gives quite successful results on a diverse database of 2D shapes. An important difference of our approach from the conventional use of the skeleton is that we replace the local coordinate frame with a global Euclidean frame supported by additional mechanisms to handle articulations and local boundary deformations. As a result, we can produce descriptions that are sensitive to any combination of changes in scale, position, orientation and articulation, as well as invariant ones.Comment: The work excluding {\S}V and {\S}VI has first appeared in 2005 ICCV: Aslan, C., Tari, S.: An Axis-Based Representation for Recognition. In ICCV(2005) 1339- 1346.; Aslan, C., : Disconnected Skeletons for Shape Recognition. Masters thesis, Department of Computer Engineering, Middle East Technical University, May 200

A numerical method for functional Hammerstein integro-differential equations

In this paper, a numerical method is presented to solve functional Hammerstein integro-differential equations. The presented method combines the successive approximations method with trapezoidal quadrature rule and natural cubic spline interpolation to solve the mentioned equations. The existence and uniqueness of the problem is also investigated. The convergence and numerical stability of the problem are proved, and finally, the accuracy of the method is verified by presenting some numerical computations

Differential Transform Method for Solving the Two-dimensional Fredholm Integral Equations

In this paper, we develop the Differential Transform (DT) method in a new scheme to solve the two-dimensional Fredholm integral equations (2D-FIEs) of the second kind. The differential transform method is a procedure to obtain the coefficients of the Taylor expansion of the solution of differential and integral equations. So, one can obtain the Taylor expansion of the solution of arbitrary order and hence the solution of the given equation can be obtained with required accuracy. Here, we first give some basic definitions and properties about DT from references, and then we prove some theorems to extend the DT method for solving the 2D-FIEs. Then by using the DT, the 2D-FIE is converted to a system of linear algebraic equations whose unknowns are the coefficients of the Taylor expansion of the solution. Solving the system gives us an approximate solution. Finally, we give some examples to show the accuracy and efficiency of the presented method

Toward the Design of Efficient Move Strategies for Local Search

Despite the huge number of studies in the metaheuristic field, it remains difficult to understand the relative impact of their elementary components. A major aspect determining the general efficiency of metaheuristics resides in the way to exploit a neighborhood structure to move within a search space. In particular, the study of iterative improvement neighborhood searches (climbers) provides guidelines to better understand local searches behavior. Several studies clearly state that some climbing strategies are more suited than classical best and first improvement, on which most local searches are based. Here, we are interested in determining empirically climbing strategies that allow the attainment of high quality local optima. First, we study alternative move selection criteria that globally outperform best and first improvement. Unfortunately, these strategies are time-consuming and consequently reduce their possibilities of integration into advanced metaheuristics. Then, we investigate ways to reduce their computational cost by approximation. Empirical studies on NK landscapes allow the identification of move criteria that offer good tradeoffs between the quality of the local optima attained and the computational time needed to reach them

Sampled Walk and Binary Fitness Landscapes Exploration

In this paper we present and investigate partial neighborhood local searches, which only explore a sample of the neighborhood at each step of the search. We particularly focus on establishing link between the structure of optimization problems and the efficiency of such local search algorithms. In our experiments we compare partial neighborhood local searches to state-of-the-art tabu search and iterated local search and perform a parameter sensitivity analysis by observing the efficiency of partial neighborhood local searches with different size of neighborhood sample. In order to facilitate the extraction of links between instances structure and search algorithm behavior we restrain the scope to binary fitness landscapes, such as NK landscapes and landscapes derived from UBQP

Worst Improvement based Iterated Local Search

To solve combinatorial optimization problems, many metaheuristics use first or best improvement hill-climbing as intensification mechanism in order to find local optima. In particular, first improvement offers a good tradeoff between computation cost and quality of reached local optima. In this paper, we investigate a worst improvement-based moving strategy, never considered in the literature. Such a strategy is able to reach good local optima despite requiring a significant additional computation cost. Here, we investigate if such a pivoting rule can be efficient when considered within metaheuristics, and especially within iterated local search (ILS). In our experiments, we compare an ILS using a first improvement pivoting rule to an ILS using an approximated version of worst improvement pivoting rule. Both methods are launched with the same number of evaluations on bit-string based fitness landscapes. Results are analyzed using some landscapes’ features in order to determine if the worst improvement principle should be considered as a moving strategy in some cases