We present an Improved implementation of the Wagner-Whitin algorithm for economic lot-sizing problems based on the planning-horizon theorem and the Economic- Part-Period concept. The proposed method of this paper reduces the burden of the computations significantly in two different cases. We first assume there is no backlogging and inventory holding and set-up costs are fixed. The second model of this paper considers WWA when backlogging, inventory holding and set-up costs cannot be fixed. The preliminary results also indicate that the execution time for the proposed method is approximately linear in the number of periods in the planning-horizon.

Hyperspectral (HS) imaging is a significant tool in remote sensing applications. HS sensors measure the reflected light from the surface of objects in hundreds or thousands of spectral bands، called HS images. Increasing the number of these bands produces huge data، which have to be transmitted to a terrestrial station for further processing. In some applications، HS images have to be sent instantly to the station requiring a high bandwidth between the sensors and the station. Most of the time، the bandwidth between the satellite and the station is narrowed limiting the amount of data that can be transmitted، and brings the idea of Compressive Sensing (CS) into the minds. In addition to the large amount of data، in these images، mixed pixels are another issue to be considered. Despite of their high spectral resolution، their spatial resolution is low causing a mixture of spectra in each pixel، but not a pure spectrum. As a result، the analysis of mixed pixels or Spectral Unmixing (SU) technique has been introduced to decompose mixed pixels into a set of endmembers and abundance fraction maps. The endmembers are extracted from spectral signatures related to different materials، and the abundance fractions are the proportions of the endmembers in each pixel. In recent years، due to the large amount of data and consequently the difficulties of real-time signal processing، and also having the ability of image compression، methods of Compressive Sensing and Unmixing (CSU) have been introduced. Two assumptions have been considered in these methods: the finite number of elements in each pixel and the low variation of abundance fractions. HYCA algorithm is one of the methods trying to compress these kinds of data with their inherent features. One of the sensible characteristics of this algorithm is to utilize spatial information for better reconstruction of the data. In fact، HYCA algorithm splits the data cube into non-overlapping square windows and assumes that spectral vectors are similar inside each window. In this study، a real-time method is proposed، which uses the spectral information (non-neighborhood pixels) in addition to the spatial information. The proposed structure can be divided into two parts: transmitting information into the satellites and information recovery into the stations. In the satellites، firstly، to utilize the spectral information، a new real-time clustering method is proposed، wherein the similarity between the entire pixels is not restricted to any specific form such as square window. Figure 3 shows a segmented real HS image. It can be seen that the considering square form limits the capability of the HYCA algorithm and the similarity can be found in the both neighborhood and non-neighborhood pixels. Secondly، to utilize similarity in each cluster، different measurement matrices are used. By doing this، various samples can be achieved for each cluster and further information are extracted. On the other hand، usage of different measurement matrices may affect the system stability. As a matter of fact، generating the different measurement matrices is not simple and increases complexity into the transmitters. Therefore، it conflicts with the aim of CS theory، reducing complexity into the transmitters. As a result، in the proposed method، the number of the clusters is determined by the number of the producible measurement matrices. Figure 4 shows the schematic of the proposed structure in the satellites. In the stations، we follow HYCA procedure in equation 8 and 9، but the different similar pixels are applied to the both equations. By doing this، we reach to the Improved HYCA algorithm. Finally، the proposed structure is shown in the Table 1. To evaluate the proposed method، both real and simulated data have been used in this article. In addition، normalized mean-square error is considered as an error criteria. For the simulated data، in constant measurement sizes، the effects of the additive noise، and for real data، the effects of measurement sizes have been investigated. Besides، the proposed method has been compared with HYCA and C-HYCA and some of the traditional CS based methods. The experimental results show the superiority of the proposed method in terms of signal to noise ratios and the measurement sizes، up to in the simulated data and in the real data، which makes it suitable in the real-world applications.

Imperialist Competitive algorithm (ICA) is considered as prime meta-heuristic algorithm to find the general optimal solution in optimization problems. This paper presents a use of ICA for automatic clustering of huge unlabeled data sets. By using proper structure for each of the chromosomes and the ICA، at run time، the suggested method (ACICA) finds the optimum number of clusters while optimal clustering of the data simultaneously. To increase the accuracy and speed of convergence، the structure of ICA changes. The proposed algorithm requires no background knowledge to classify the data. In addition، the proposed method is more accurate in comparison with other clustering methods based on evolutionary algorithms. DB and CS cluster validity measurements are used as the objective function. To demonstrate the superiority of the proposed method، the average of fitness function and the number of clusters determined by the proposed method is compared with three automatic clustering algorithms based on evolutionary algorithms.

Clustering is a method of data analysis and one of the important methods in data mining that has been considered by researchers in many fields as well as in many disciplines. In this paper, we propose combining WOA with BA for data clustering. To assess the efficiency of the proposed method, it has been applied in data clustering. In the proposed method, first, by examining BA thoroughly, the weaknesses of this algorithm in exploitation and exploration are identified. The proposed method focuses on improving BA exploitation. Therefore, in the proposed method, instead of the random selection step, one solution is selected from the best solutions, and some of the dimensions of the position vector in BA are replaced We change some of the best solutions with the step of reducing the encircled mechanism and updating the WOA spiral, and finally, after selecting the best exploitation between the two stages of WOA exploitation and BA exploitation, the desired changes are applied on solutions. We evaluate the performance of the proposed method in comparison with other meta-heuristic algorithms in the data clustering discussion using six datasets. The results of these experiments show that the proposed method is statistically much better than the standard BA and also the proposed method is better than the WOA. Overall, the proposed method was more robust and better than the Harmony Search algorithm (HAS), Artificial Bee Colony (ABC), WOA and BA.

The bat algorithm is an example of meta-heuristic algorithms from the collective swarm intelligence, which is based on the echolocation behavior of bats. This algorithm preserves the diversity of the solution by using a frequency tuning method that can quickly and efficiently shift from exploration to exploitation. Therefore, when a fast and accurate solution is needed, this algorithm becomes an efficient optimizer for any application. Although the bat algorithm has many practical benefits, it also has some disadvantages. One of these disadvantages that reduces its efficiency is being trapped in the local optimum. To solve the mentioned problem in this research, the position and speed of the initial population is updated in three ways with different formulas, this makes the final answer of the problem not trapped in the local optimum and diversity occurs in the population. In this article, the performance of the Improved bat algorithm on 11 sample objective functions has been investigated and compared with other similar algorithms, and finally the results show the superiority and accuracy of this algorithm compared to similar samples.

In this paper, a new algorithm which is the result of combination of cellular learning automata (CLA) and shuffled frog leap algorithm (SFLA) is proposed for optimization of functions in continuous, static environments. In the frog leaping algorithm, every frog represents a feasible solution within the problem space. In the proposed algorithm, each memeplex of frogs is placed in a cell of CLA. Learning automata in each cell acts as the brain of memeplex and will determine the strategy of motion and search. The proposed algorithm along with the standard SFLA and two global and local versions of particle swarm optimization algorithm have been tested in 30-dimensional space on five standard merit functions. Experimental results show that the proposed algorithm has a performance of the introduced algorithm is due to the control of search behavior of frogs during the optimization process.