Proposed Initialization Algorithm Research Articles

An improved sequential insertion algorithm and tabu search to vehicle routing problem with time windows

The vehicle routing problem (VRP) is a well-researched problem in the operations re- search literature. This paper studies a vehicle routing problem with time windows. Based on Solomon’s research, an improved sequential initialization algorithm, Solomon i1 with DTWC (Solomon i1 with Dynamic Time Windows Compatibility), is proposed in this paper to construct feasible initial solutions with higher quality in less calculation time. A tabu search with VNS (Variable Neighborhood Search) and the Metropolis criterion is used to further optimize the solutions that the proposed initialization algorithm provides. We run computational experiments on cases of well-known problems. Results show that compared to the initialization method before the change, our improved initialization approach performs well in terms of providing a better feasible initialization solution in less time, with an average 10% improvement in solution quality and an average 34% computational time savings. The proposed initialization algorithm’s superiority is also demonstrated by the tabu search’s better performance on the initial solutions it produces.

Optimal control of a rate-based modelled batch distillation column: Initialization strategy

Batch distillation columns are dynamic processes represented by a system of differential and algebraic equations (DAE). Their optimal control problem can be solved through orthogonal collocation, which is an effective discretization method with accurate approximations to the behavior of state and control variables. Convergence of such technique is greatly improved by providing good initial values and bounds of the variables. Thus, this work proposes a strategy to estimate the initial values for a sieve trays batch distillation column modeled with a rate-based approach. During the initialization procedure, the modeling equations are solved under a steady state assumption by using the GAMS modeling environment. An experimental pilot scale batch distillation column was used as the case-study to evaluate the proposed initialization algorithm. This column was used to separate a mixture of methanol and ethanol. The initialization results for the state profiles show good agreement with the experimental results.

Development of new seed with modified validity measures for k-means clustering

Conventional k-means clustering is the widely used partitional method, mainly adapted to machine learning and pattern recognition problems. This algorithm is highly sensitive to initial centroid points, but it cannot guarantee to arrive at a better solution because initial centroids are computed randomly for the given cluster. In this paper, we have developed a new initialization method for k-means clustering. We have also made an effort to improve the Dunn Index and introduced a new validity ratio based on the silhouette index. The sum of squared error, Dunn Index, silhouette index, modified Dunn Index, and silhouette validity ratio were used as criteria to evaluate the performance of the initialization algorithm. Various benchmark datasets have been used to assess the effectiveness of the proposed initialization algorithm, and we compared the results with conventional k-means and k-means++ algorithms. The results have shown that the sum of squared error and number of iterations obtained by our proposed initialization algorithm are minimum. A precision chart is used to test the consistency of the initialization algorithm. The comparative analysis, based on the modified Dunn Index, and silhouette validity ratio have proved that the proposed initialization algorithm has performed better than the other initialization algorithms.

A new initialization and performance measure for the rough k-means clustering

A new initialization algorithm is proposed in this study to address the issue of random initialization in the rough k-means clustering algorithm refined by Peters. A new means to choose appropriate zeta values in Peters algorithm is proposed. Also, a new performance measure S/O [within-variance (S)/total-variance (O)] index has been introduced for the rough clustering algorithm. The performance criteria such as root-mean-square standard deviation, S/O index, and running time complexity are used to validate the performance of the proposed and random initialization with that of Peters. In addition, other popular initialization algorithms like k-means++, Peters Π, Bradley, and Ioannis are also herein compared. It is found that our proposed initialization algorithm has performed better than the existing initialization algorithms with Peters refined rough k-means clustering algorithm on different datasets with varying zeta values.

An efficient initialization mechanism of neurons for Winner Takes All Neural Network implemented in the CMOS technology

The paper presents a new initialization mechanism based on a Convex Combination Method (CCM) for Kohonen self-organizing Neural Networks (NNs) realized in the CMOS technology. A proper selection of initial values of the neuron weights exhibits a strong impact on the quality of the overall learning process. Unfortunately, in case of real input data, e.g. biomedical data, proper initialization is not easy to perform, as an exact data distribution is usually unknown. Bad initialization causes that even 70%–80% of neurons remain inactive, which increases the quantization error and thus limits the classification abilities of the NN. The proposed initialization algorithm has a couple of important advantages. Firstly, it does not require a knowledge of data distribution in the input data space. Secondly, there is no necessity for an initial polarization of the neuron weights before starting the learning process. This feature is very convenient in case of transistor level realizations. In this case the programming lines, which in other approaches occupy a large chip area, are not required. We proposed a modification of the original CCM algorithm. A new parameter which in the proposed analog CMOS realization is represented by an external current, allows to fit the behavior of the mechanism to NNs containing different numbers of neurons. The investigations show that the modified CCM operates properly for the NN containing even 250 neurons. A single CCM block realized in the CMOS 180nm technology occupies an area of 300μm2 and dissipates an average power of 20μW and at data rate of up to 20MHz.