Abstract: This paper proposes a mathematical model and
examines the performance of an exact algorithm for a location–
transportation problems in humanitarian relief. The model determines
the number and location of distribution centers in a relief network,
the amount of relief supplies to be stocked at each distribution center
and the vehicles to take the supplies to meet the needs of disaster
victims under capacity restriction, transportation and budgetary
constraints. The computational experiments are conducted on the
various sizes of problems that are generated. Branch and bound
algorithm is applied for these problems. The results show that this
algorithm can solve problem sizes of up to three candidate locations
with five demand points and one candidate location with up to twenty
demand points without premature termination.
Abstract: An exact algorithm for a n-link manipulator movement amidst arbitrary unknown static obstacles is presented.
The algorithm guarantees the reaching of a target configuration of the manipulator in a finite number of steps. The algorithm is
reduced to a finite number of calls of a subroutine for planning a trajectory in the presence of known forbidden states. The polynomial approximation algorithm which is used as the subroutine is presented. The results of the exact algorithm
implementation for the control of a seven link (7 degrees of
freedom, 7DOF) manipulator are given.
Abstract: Some fast exact algorithms for the maximum weight clique problem have been proposed. Östergard’s algorithm is one of them. Kumlander says his algorithm is faster than it. But we confirmed that the straightforwardly implemented Kumlander’s algorithm is slower than O¨ sterga˚rd’s algorithm. We propose some improvements on Kumlander’s algorithm.
Abstract: In this paper, we study the knapsack sharing problem, a variant of the well-known NP-Hard single knapsack problem. We investigate the use of a tree search for optimally solving the problem. The used method combines two complementary phases: a reduction interval search phase and a branch and bound procedure one. First, the reduction phase applies a polynomial reduction strategy; that is used for decomposing the problem into a series of knapsack problems. Second, the tree search procedure is applied in order to attain a set of optimal capacities characterizing the knapsack problems. Finally, the performance of the proposed optimal algorithm is evaluated on a set of instances of the literature and its runtime is compared to the best exact algorithm of the literature.
Abstract: Wavelet transform or wavelet analysis is a recently
developed mathematical tool in applied mathematics. In numerical
analysis, wavelets also serve as a Galerkin basis to solve partial
differential equations. Haar transform or Haar wavelet transform has
been used as a simplest and earliest example for orthonormal wavelet
transform. Since its popularity in wavelet analysis, there are several
definitions and various generalizations or algorithms for calculating
Haar transform. Fast Haar transform, FHT, is one of the algorithms
which can reduce the tedious calculation works in Haar transform. In
this paper, we present a modified fast and exact algorithm for FHT,
namely Modified Fast Haar Transform, MFHT. The algorithm or
procedure proposed allows certain calculation in the process
decomposition be ignored without affecting the results.
Abstract: During the last years, the genomes of more and more
species have been sequenced, providing data for phylogenetic recon-
struction based on genome rearrangement measures. A main task in
all phylogenetic reconstruction algorithms is to solve the median of
three problem. Although this problem is NP-hard even for the sim-
plest distance measures, there are exact algorithms for the breakpoint
median and the reversal median that are fast enough for practical use.
In this paper, this approach is extended to the transposition median as
well as to the weighted reversal and transposition median. Although
there is no exact polynomial algorithm known even for the pairwise
distances, we will show that it is in most cases possible to solve
these problems exactly within reasonable time by using a branch and
bound algorithm.