**Developed one Multiobjective Simulated Annealing Algorithm, AMOSA***(paper has been published in IEEE Transactions on Evolutionary Computation)*. The program is being updated. Download a preliminary version of the program from here.**Please fill in some information (those are summarized in the form given below) before downloading the Code.****Note that the code should not be used for any business purpose.**

**Sanghamitra Bandyopadhyay, Sriparna Saha, Ujjwal Maulik and Kalyanmoy Deb. A Simulated Annealing Based
Multi-objective Optimization Algorithm: AMOSA , IEEE Transactions on
Evolutionary Computation, Volume 12, No. 3, JUNE 2008, Pages 269-283.**

**Results of MCVGAPS Clustering Technique accepted in:
**

**Sriparna Saha and Sanghamitra Bandyopadhyay. Application of a Multiseed Based Clustering Technique for Automatic Satellite Image Segmentation , IEEE Geoscience and Remote Sensing Letters, (accepted).**

**Some Literature Studies (not included in the final paper due to page restriction):**

[1] M. Tyagi, F. Bovolo, A. Mehra, S. Chaudhuri, and L. Bruzzone, A context-sensitive clustering technique based on graph-cut initialization and expectation-maximization algorithm, IEEE Geoscience and Remote Sensing Letters, vol. 5, no. 1, pp. 21 25, January 2008.

[2] G. Bilgin, S. Erturk, and T. Yildirim, Unsupervised classification of hyperspectral-image data using fuzzy approaches that spatially exploit membership relations, IEEE Geoscience and Remote Sensing Letters, vol. 5, no. 4, pp. 673 677, October 2008.

[3] C. Wemmert, A. Puissant, G. Forestier, and P. Gancarski, Multireso- lution remote sensing image clustering, IEEE Geoscience and Remote Sensing Letters, vol. 6, no. 3, pp. 533 537, July, 2009.

[4] A. Marcal and L. Castro, Hierarchical clustering of multispectral images using combined spectral and spatial criteria, IEEE Geoscience and Remote Sensing Letters, vol. 2, no. 1, pp. 59 63, January 2005.

[5] Y. Tarabalka, J. A. Benediktsson, and J. Chanussot, Spectralspatial classification of hyperspectral imagery based on partitional clustering techniques, IEEE Transactions on Geoscience and Remote Sensing, vol. 47, no. 8, pp. 29732987, Aug., 2009.

[6] S. Bandyopadhyay, U. Maulik, and A. Mukhopadhyay, Multiobjective genetic clustering for pixel classification in remote sensing imagery, IEEE Transactions on Geoscience and Remote Sensing, vol. 45, no. 5, pp. 1506 1511, May, 2007.

**Complexity analysis of MCVGAPS Clustering Technique:**

1) Initialization of GA needs

2) For assignment of points to different clusters total time needed is

3) Selection step of the GA requires

4) Mutation and Crossover require

So in general total time complexity becomes

**Results**

**IRS Image of Mumbai:**

The segmentation automatically identified by the proposed MCVGAPS clustering technique is shown in following Figure.

Number of centers per clusters automatically evolved by MCVGAPS clustering technique are 6, 4, 3, 4, 3 and 5, respectively. It can be seen from the figure that the water (Arabian sea) surrounding Mumbai gets differentiated into three distinct regions, based on the difference in their spectral properties. The islands, dockyard have mostly been correctly identified in the image. GAPS-clustering with Sym-index gets its optimal value for K=6. MCVGAPS clustering with PS-index, I-index and XB-index as objective functions get their optimum values for K=6, K=5 and K=3, respectively. Following figure demonstrates the Mumbai image clustered using the FCM technique when K=6 is given a priori.

Subtractive clustering technique automatically yields K=4 clusters from this data set. In order to show the effectiveness of MCVGAPS clustering technique quantitatively, I index and XB-index values are again calculated. I index values obtained by the MCVGAPS, FCM, GAPS with Sym-index and Subtractive clustering techniques are 205.36, 23.057, 180.45 and 60.65, respectively. Similarly XB-index values obtained by the MCVGAPS, FCM, GAPS with Sym-index and Subtractive clustering techniques are 1.028, 4.67, 2.9 and 9.15, respectively. Each algorithm is executed five times for these image data sets and the best values over these five runs are reported here. Smaller value of XB-index and larger value of I index correspond to good clustering. The values again establish the effectiveness of MCVGAPS clustering technique. The values again show that the segmentation provided by MCVGAPS clustering is much better than those of FCM-clustering, GAPS clustering optimizing Sym-index and subtractive clustering technique.

**SPOT Image of Kolkata:**

Bridge detected by MCVGAPS cluststreing technique: