(*^ ::[ Information = "This is a Mathematica Notebook file. It contains ASCII text, and can be transferred by email, ftp, or other text-file transfer utility. It should be read or edited using a copy of Mathematica or MathReader. If you received this as email, use your mail application or copy/paste to save everything from the line containing (*^ down to the line containing ^*) into a plain text file. On some systems you may have to give the file a name ending with ".ma" to allow Mathematica to recognize it as a Notebook. The line below identifies what version of Mathematica created this file, but it can be opened using any other version as well."; FrontEndVersion = "Macintosh Mathematica Notebook Front End Version 2.2"; MacintoshStandardFontEncoding; fontset = title, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, e8, 24, "Times"; fontset = subtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, e6, 18, "Times"; fontset = subsubtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, italic, e6, 14, "Times"; fontset = section, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, grayBox, M22, bold, a20, 18, "Times"; fontset = subsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, blackBox, M19, bold, a15, 14, "Times"; fontset = subsubsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, whiteBox, M18, bold, a12, 12, "Times"; fontset = text, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; fontset = smalltext, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 10, "Times"; fontset = input, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeInput, M42, N23, bold, L-5, 12, "Courier"; fontset = output, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-5, 12, "Courier"; fontset = message, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, R65535, L-5, 12, "Courier"; fontset = print, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-5, 12, "Courier"; fontset = info, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, B65535, L-5, 12, "Courier"; fontset = postscript, PostScript, formatAsPostScript, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeGraphics, M7, l34, w282, h287, 12, "Courier"; fontset = name, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, italic, 10, "Geneva"; fontset = header, inactive, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; fontset = leftheader, inactive, L2, 12, "Times"; fontset = footer, inactive, noKeepOnOnePage, preserveAspect, center, M7, 12, "Times"; fontset = leftfooter, inactive, L2, 12, "Times"; fontset = help, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 10, "Times"; fontset = clipboard, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; fontset = completions, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; fontset = special1, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; fontset = special2, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; fontset = special3, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; fontset = special4, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; fontset = special5, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; paletteColors = 128; showRuler; automaticGrouping; currentKernel; ] :[font = input; inactive; preserveAspect] from Exploring Neural Networks with Mathematica © Jacques J. Vidal, 1995 ;[s] 2:0,2;82,1;83,-1; 3:0,12,10,Courier,1,12,0,0,0;1,18,14,Times,1,18,0,0,0;1,12,9,Times,1,12,0,0,0; :[font = input; inactive; preserveAspect] Flexmap Networks ;[s] 1:0,1;18,-1; 2:0,12,10,Courier,1,12,0,0,0;1,18,14,Times,1,18,0,0,0; :[font = subsubsection; inactive; preserveAspect; startGroup] Solving the TSP Problem with FLEXMAP Student Project by David Cummings,1991 :[font = text; inactive; preserveAspect] References for this Notebook: FLEXMAP: A Neural Network for the Traveling Salesman Problem With Linear Time and Space Complexity B. Fritze & P. Wilke, Proc. IJCNN, Singapore, 1991 :[font = text; inactive; preserveAspect; rightWrapOffset = 454] This is a Mathematica program that implements the FLEXMAP solution to the Traveling Salesman Problem described in: FLEXMAP - A Neural Network for the Traveling Salesman Problem with Linear Time and Space Complexity by Bernd Fritzke and Peter Wilke in the proceedings of the International Joint Conference on Neural Networks, Singapore, Nov. 18-21, 1991. The pseudo-code for the algorithm, based on the above article, is: 1.Layout the city locations on a 2D Map 2.Generate 3 random positions ("cells" or "units"), and connect them in a ring structure 3. Mark all cities "free" and cells "non-pnned" 4. DO, until there are no free cities DO ndist times or until there are no free cities Choose one of free cities at random IF city never chosen before, or if last best matching unit (bmu) for city is now pinned Compute distance from city to all non-pinned cells Identify cell with smallest distance to city Call it the bmu (best matching unit) for that city ELSE Use last bmu for this city and the r non-pinned neighbors on either side of this last bmu Compute distance from city to these 2r+1 cells Identify cell with smallest distance to city Call it the bmu for that city ENDIF IF new bmu is same as last bmu for this city Increment bmu-selected count for this city ELSE set bmu-selected count for this city = 1 ENDIF Save index of bmu for this city Add distance to this cell ( the bmu) entry in the error array IF bmu-selected count for this city is greater than the bmu-pin-criterion for this city Move cell to position of city Mark cell "pinned" Mark city "not free" ELSE Move bmu and its two neighbors (if not pinned) toward the city by epsilonBmu and epsilonNeighbor, respectively ENDIF ENDDO IF still at least one free city Locate cell with highest error variable (the black sheep) Locate furthest of black sheep's two neighbors Compute position halfway between black sheep and its furthest neighbor Add a new cell at that position init error variable of new cell to 1/3 theblack sheep's error variable plus 1/3 the neighbor's error variable Reduce black sheep's and neighbor's error variable to 2/3 of their values ENDIF ENDDO ;[s] 19:0,0;12,1;23,0;954,2;957,0;1317,2;1336,0;1427,2;1439,0;1509,2;1520,0;1583,2;1600,0;1763,3;1778,0;1782,2;1796,0;1940,2;1951,0;2335,-1; 4:10,13,9,Times,0,12,0,0,0;1,13,9,Times,2,12,0,0,0;7,13,9,Times,1,12,0,0,0;1,13,9,Times,4,12,0,0,0; :[font = text; inactive; preserveAspect; rightWrapOffset = 454] when this algorithm completes, the solution is obtained by following all pinned cells in the order within their ring structure Start with some data structure definitions: nCities is the number of cities nDist is the number of times we perform the "distribution step" before adding a new cell bmuPinCriterion is the number of times a cell must be selected as the bmu for a city before it is "pinned" to the city epsilonBmu and epsilonNeighbor are the fractions of distance used when moving cells toward a city ;[s] 11:0,0;173,1;180,0;206,1;212,0;296,1;311,0;416,1;426,0;431,1;446,0;514,-1; 2:6,13,9,Times,0,12,0,0,0;5,13,9,Times,1,12,0,0,0; :[font = input; preserveAspect] u := Random[]; :[font = input; preserveAspect] nCities = 40; :[font = input; preserveAspect; startGroup] nDist = 40 :[font = output; output; inactive; preserveAspect; endGroup] 40 ;[o] 40 :[font = input; preserveAspect; startGroup] bmuPinCriterion = nDist :[font = output; output; inactive; preserveAspect; endGroup] 40 ;[o] 40 :[font = input; preserveAspect] epsilonBmu = 0.05; epsilonNeighbor = 0.05; :[font = text; inactive; preserveAspect] Initialize arrays cities contains the coordinates of the cities errorArray contains the error values for the cells freeCityIndices contains the list of cities that are still free lastBmuIndexForCity stores the last bmu for each city cells contains the coordinates of the cells (initially there are 3) neighbors defines the order of the cells within the ring structure. It is essentially a linked list. For example, {{3,2}, {1,3}, {2,1}} means that the left and right neighbors of cell #1 are cells #3 and #2, respectively. The left and right neighbors of cell #2 are cells #1 and #3, respectively, etc. ;[s] 13:0,0;20,1;26,0;66,1;76,0;117,1;132,0;181,1;201,0;237,1;242,0;305,1;314,0;610,-1; 2:7,13,9,Times,0,12,0,0,0;6,13,9,Times,1,12,0,0,0; :[font = input; preserveAspect; startGroup] cities = Table[{u,u}, {nCities}] :[font = output; output; inactive; preserveAspect; endGroup] {{0.3356872873958907, 0.3549521999920246}, {0.0701703835176461, 0.05787198696433893}, {0.5342744485852058, 0.2113819913917167}, {0.7177498311228432, 0.7051085077381552}, {0.850439535169033, 0.7859092050410909}, {0.1936411519218162, 0.994293781890538}, {0.907468255879867, 0.4872620279227623}, {0.908761587771409, 0.5704974205193874}, {0.1963644441857866, 0.01948151597837579}, {0.1669776929228757, 0.2285017687588211}, {0.3655416282082136, 0.4883120804246937}, {0.7454337256566648, 0.956746260695351}, {0.02985434081232284, 0.133359880432669}, {0.6752633421390187, 0.898874273731012}, {0.4955798922271172, 0.921977889040952}, {0.957513511016176, 0.193765765992857}, {0.6451403570580844, 0.1360686839998614}, {0.7638723590943593, 0.199471984102319}, {0.7376721011782172, 0.6488066560770993}, {0.85511077132295, 0.6289745635829317}, {0.5413076569924306, 0.6293251400987235}, {0.6881330784000744, 0.4004727948241106}, {0.175766028784217, 0.1410130596740298}, {0.94269935274341, 0.4437265341287595}, {0.1459116879718941, 0.00765317924136074}, {0.2674360106043911, 0.5448522603977474}, {0.6503317957447771, 0.0856752902004084}, {0.3099224995882157, 0.3510864944048904}, {0.005191438686692731, 0.949606606200547}, {0.5460501404938566, 0.1516145103025714}, {0.2675193375084756, 0.3007999501234479}, {0.6909393691709064, 0.5226399467196399}, {0.726211680516045, 0.6714748100247245}, {0.002806290770832006, 0.1221671518955293}, {0.5504456517318282, 0.5304617503506947}, {0.06010693802742236, 0.6784406177667699}, {0.404533963759934, 0.5228085711093339}, {0.7926709274230314, 0.1335883573690225}, {0.7542021680151568, 0.4371332809089255}, {0.4827484278348157, 0.7825018629641321}} ;[o] {{0.335687, 0.354952}, {0.0701704, 0.057872}, {0.534274, 0.211382}, {0.71775, 0.705109}, {0.85044, 0.785909}, {0.193641, 0.994294}, {0.907468, 0.487262}, {0.908762, 0.570497}, {0.196364, 0.0194815}, {0.166978, 0.228502}, {0.365542, 0.488312}, {0.745434, 0.956746}, {0.0298543, 0.13336}, {0.675263, 0.898874}, {0.49558, 0.921978}, {0.957514, 0.193766}, {0.64514, 0.136069}, {0.763872, 0.199472}, {0.737672, 0.648807}, {0.855111, 0.628975}, {0.541308, 0.629325}, {0.688133, 0.400473}, {0.175766, 0.141013}, {0.942699, 0.443727}, {0.145912, 0.00765318}, {0.267436, 0.544852}, {0.650332, 0.0856753}, {0.309922, 0.351086}, {0.00519144, 0.949607}, {0.54605, 0.151615}, {0.267519, 0.3008}, {0.690939, 0.52264}, {0.726212, 0.671475}, {0.00280629, 0.122167}, {0.550446, 0.530462}, {0.0601069, 0.678441}, {0.404534, 0.522809}, {0.792671, 0.133588}, {0.754202, 0.437133}, {0.482748, 0.782502}} :[font = input; preserveAspect; startGroup] errorArray = Table[0, {3}] :[font = output; output; inactive; preserveAspect; endGroup] {0, 0, 0} ;[o] {0, 0, 0} :[font = input; preserveAspect; startGroup] freeCityIndices = Range[nCities] :[font = output; output; inactive; preserveAspect; endGroup] {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40} ;[o] {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40} :[font = input; preserveAspect; startGroup] lastBmuIndexForCity = Table[0, {nCities}] :[font = output; output; inactive; preserveAspect; endGroup] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0} ;[o] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0} :[font = input; preserveAspect; startGroup] cells = Table[{u,u}, {3}] :[font = output; output; inactive; preserveAspect; endGroup] {{0.7490107293284641, 0.4875266747083784}, {0.936698287340959, 0.6308873526615608}, {0.4814913918199886, 0.1867267245849306}} ;[o] {{0.749011, 0.487527}, {0.936698, 0.630887}, {0.481491, 0.186727}} :[font = input; preserveAspect] neighbors = { {3,2}, {1,3}, {2,1}}; :[font = text; inactive; preserveAspect] A few more data structures: pinnedFlags is a list with one entry per cell. The flag is 0 if the cell is not pinned, otherwise it is set to 1. bmuSelectedCount contains the number of times the last bmu has been selected for each city. maxErrorValue and maxErrorIndex are used to store the highest value in the errorArray, and the index of the corresponding cell within the cells array. This allows to avoid searching the errorArray under some circumstances, in an attempt to keep the time complexity linear. numNeighbors is the number of neighbors on either side of the last bmu that are used for the distance computation ( r in the pseudo-code above). ;[s] 13:0,0;32,1;43,0;146,1;162,0;238,1;251,0;256,1;269,0;511,1;523,0;626,1;628,0;657,-1; 2:7,13,9,Times,0,12,0,0,0;6,13,9,Times,1,12,0,0,0; :[font = input; preserveAspect; startGroup] pinnedFlags = {0, 0, 0}; bmuSelectedCount = Table[0, {nCities}] :[font = output; output; inactive; preserveAspect; endGroup] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0} ;[o] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0} :[font = input; preserveAspect] maxErrorValue = 0; maxErrorIndex = 0; numNeighbors = 4; :[font = text; inactive; preserveAspect] Now we will display the cities (large circles) and the cells (small circles), with the cells connected to show the ring structure. :[font = input; preserveAspect; startGroup] Show[Graphics [ {PointSize[0.04],RGBColor[1,0,0], Map[Point, cities], PointSize[0.02],RGBColor[0,0,1], Map[Point, cells],RGBColor[0,1,0], Map[Line,Table [{cells[[i]],cells[[neighbors[[i,2]]]]}, {i,Dimensions[cells][[1]]}]]}], AxesOrigin ->{0,0}, Axes->Automatic, AspectRatio->1, PlotRange->{{0,1},{0,1}}] :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 282] %! %%Creator: Mathematica %%AspectRatio: 1 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations -0 1 0 1 [ [(0.2)] .2 0 0 2 Msboxa [(0.4)] .4 0 0 2 Msboxa [(0.6)] .6 0 0 2 Msboxa [(0.8)] .8 0 0 2 Msboxa [(1)] 1 0 0 2 Msboxa [(0)] -0.0125 0 1 0 Msboxa [(0.2)] -0.0125 .2 1 0 Msboxa [(0.4)] -0.0125 .4 1 0 Msboxa [(0.6)] -0.0125 .6 1 0 Msboxa [(0.8)] -0.0125 .8 1 0 Msboxa [(1)] -0.0125 1 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 1.001 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .2 0 m .2 .00625 L s P [(0.2)] .2 0 0 2 Mshowa p .002 w .4 0 m .4 .00625 L s P [(0.4)] .4 0 0 2 Mshowa p .002 w .6 0 m .6 .00625 L s P [(0.6)] .6 0 0 2 Mshowa p .002 w .8 0 m .8 .00625 L s P [(0.8)] .8 0 0 2 Mshowa p .002 w 1 0 m 1 .00625 L s P [(1)] 1 0 0 2 Mshowa p .001 w .04 0 m .04 .00375 L s P p .001 w .08 0 m .08 .00375 L s P p .001 w .12 0 m .12 .00375 L s P p .001 w .16 0 m .16 .00375 L s P p .001 w .24 0 m .24 .00375 L s P p .001 w .28 0 m .28 .00375 L s P p .001 w .32 0 m .32 .00375 L s P p .001 w .36 0 m .36 .00375 L s P p .001 w .44 0 m .44 .00375 L s P p .001 w .48 0 m .48 .00375 L s P p .001 w .52 0 m .52 .00375 L s P p .001 w .56 0 m .56 .00375 L s P p .001 w .64 0 m .64 .00375 L s P p .001 w .68 0 m .68 .00375 L s P p .001 w .72 0 m .72 .00375 L s P p .001 w .76 0 m .76 .00375 L s P p .001 w .84 0 m .84 .00375 L s P p .001 w .88 0 m .88 .00375 L s P p .001 w .92 0 m .92 .00375 L s P p .001 w .96 0 m .96 .00375 L s P p .002 w 0 0 m 1 0 L s P p .002 w 0 0 m .00625 0 L s P [(0)] -0.0125 0 1 0 Mshowa p .002 w 0 .2 m .00625 .2 L s P [(0.2)] -0.0125 .2 1 0 Mshowa p .002 w 0 .4 m .00625 .4 L s P [(0.4)] -0.0125 .4 1 0 Mshowa p .002 w 0 .6 m .00625 .6 L s P [(0.6)] -0.0125 .6 1 0 Mshowa p .002 w 0 .8 m .00625 .8 L s P [(0.8)] -0.0125 .8 1 0 Mshowa p .002 w 0 1 m .00625 1 L s P [(1)] -0.0125 1 1 0 Mshowa p .001 w 0 .04 m .00375 .04 L s P p .001 w 0 .08 m .00375 .08 L s P p .001 w 0 .12 m .00375 .12 L s P p .001 w 0 .16 m .00375 .16 L s P p .001 w 0 .24 m .00375 .24 L s P p .001 w 0 .28 m .00375 .28 L s P p .001 w 0 .32 m .00375 .32 L s P p .001 w 0 .36 m .00375 .36 L s P p .001 w 0 .44 m .00375 .44 L s P p .001 w 0 .48 m .00375 .48 L s P p .001 w 0 .52 m .00375 .52 L s P p .001 w 0 .56 m .00375 .56 L s P p .001 w 0 .64 m .00375 .64 L s P p .001 w 0 .68 m .00375 .68 L s P p .001 w 0 .72 m .00375 .72 L s P p .001 w 0 .76 m .00375 .76 L s P p .001 w 0 .84 m .00375 .84 L s P p .001 w 0 .88 m .00375 .88 L s P p .001 w 0 .92 m .00375 .92 L s P p .001 w 0 .96 m .00375 .96 L s P p .002 w 0 0 m 0 1 L s P P 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath p 1 0 0 r p .04 w .33569 .35495 Mdot .07017 .05787 Mdot .53427 .21138 Mdot .71775 .70511 Mdot .85044 .78591 Mdot .19364 .99429 Mdot .90747 .48726 Mdot .90876 .5705 Mdot .19636 .01948 Mdot .16698 .2285 Mdot .36554 .48831 Mdot .74543 .95675 Mdot .02985 .13336 Mdot .67526 .89887 Mdot .49558 .92198 Mdot .95751 .19377 Mdot .64514 .13607 Mdot .76387 .19947 Mdot .73767 .64881 Mdot .85511 .62897 Mdot .54131 .62933 Mdot .68813 .40047 Mdot .17577 .14101 Mdot .9427 .44373 Mdot .14591 .00765 Mdot .26744 .54485 Mdot .65033 .08568 Mdot .30992 .35109 Mdot .00519 .94961 Mdot .54605 .15161 Mdot .26752 .3008 Mdot .69094 .52264 Mdot .72621 .67147 Mdot .00281 .12217 Mdot .55045 .53046 Mdot .06011 .67844 Mdot .40453 .52281 Mdot .79267 .13359 Mdot .7542 .43713 Mdot .48275 .7825 Mdot P 0 0 1 r p .02 w .74901 .48753 Mdot .9367 .63089 Mdot .48149 .18673 Mdot P 0 1 0 r p .004 w .74901 .48753 m .9367 .63089 L s .9367 .63089 m .48149 .18673 L s .48149 .18673 m .74901 .48753 L s P P % End of Graphics MathPictureEnd :[font = output; output; inactive; preserveAspect; endGroup] Graphics["<<>>"] ;[o] -Graphics- :[font = text; inactive; preserveAspect] A few functions for the main program. distance computes the distance between two positions. getLeftNeighbors constructs a list of the r neighbors to the left of a cell. getRightNeighbors constructs a list of the r neighbors to the right of a cell. ;[s] 7:0,0;42,1;50,0;96,1;112,0;173,1;190,0;253,-1; 2:4,13,9,Times,0,12,0,0,0;3,13,9,Times,1,12,0,0,0; :[font = input; preserveAspect] distance[x_,y_] := Sqrt[Apply[Plus,(x - y)^2]] :[font = input; preserveAspect] getLeftNeighbors[x_,y_] := Module[{currX, nextX}, (y = {}; currX = x; Do[ nextX = neighbors[[currX,1]]; y = Union[y, Intersection[{nextX}, {nextX (1-pinnedFlags[[nextX]])}]]; currX = nextX; {numNeighbors}])] :[font = input; preserveAspect] getRightNeighbors[x_,y_] := Module[{currX, nextX}, (y = {}; currX = x; Do[ nextX = neighbors[[currX,2]]; y = Union[y, Intersection[{nextX}, {nextX (1-pinnedFlags[[nextX]])}]]; currX = nextX;, {numNeighbors}])] :[font = text; inactive; preserveAspect] Next is the main program. Record the CPU time used so far,to later determine how much CPU time has been used in this run. :[font = input; preserveAspect; startGroup] startTime = TimeUsed[] :[font = output; output; inactive; preserveAspect; endGroup] 30.78333333333334 ;[o] 30.7833 :[font = input; preserveAspect; startGroup] While [(Dimensions[freeCityIndices][[1]] > 0), For [i=1, (i < nDist) && (Dimensions[freeCityIndices][[1]] > 0), i++, numFreeCities = Dimensions[freeCityIndices][[1]]; tempRandom = Random[Integer, {1, numFreeCities}]; currCityIndex = freeCityIndices[[tempRandom]]; savedBmuIndexForCity = lastBmuIndexForCity[[currCityIndex]]; If [(savedBmuIndexForCity == 0) || (pinnedFlags[[savedBmuIndexForCity]] == 1), distancesToCells = Map[distance[cities[[currCityIndex]],#]&, cells]; distancesToCells = ReplacePart[distancesToCells, Infinity, Position[pinnedFlags,1]]; minDistance = Min[distancesToCells]; lastBmuIndexForCity[[currCityIndex]] = First [Flatten [ Position [distancesToCells,minDistance]]];, leftNeighbors = .; getLeftNeighbors[savedBmuIndexForCity, leftNeighbors]; rightNeighbors = .; getRightNeighbors[savedBmuIndexForCity, rightNeighbors]; limitedNeighbors = Union[leftNeighbors, {savedBmuIndexForCity}, rightNeighbors]; distancesToCells = Map[distance[cities[[currCityIndex]],#]&, cells[[limitedNeighbors]]]; minDistance = Min[distancesToCells]; indexOfMin = First[Flatten[Position [distancesToCells, minDistance]]]; lastBmuIndexForCity[[currCityIndex]] = limitedNeighbors[[indexOfMin]]]; newBmuIndexForCity = lastBmuIndexForCity[[currCityIndex]]; If [newBmuIndexForCity == savedBmuIndexForCity, bmuSelectedCount[[currCityIndex]] = bmuSelectedCount[[currCityIndex]] + 1, bmuSelectedCount[[currCityIndex]] = 1]; errorArray[[newBmuIndexForCity]] = errorArray[[newBmuIndexForCity]] + minDistance; If [errorArray[[newBmuIndexForCity]] > maxErrorValue, maxErrorValue = errorArray[[newBmuIndexForCity]]; maxErrorIndex = newBmuIndexForCity]; If [bmuSelectedCount[[currCityIndex]] >= bmuPinCriterion, cells[[newBmuIndexForCity]] = cities[[currCityIndex]]; pinnedFlags[[newBmuIndexForCity]] = 1; freeCityIndices = Delete [freeCityIndices, Position[freeCityIndices, currCityIndex]];, lNeighbor = neighbors[[newBmuIndexForCity,1]]; rtNeighbor = neighbors[[newBmuIndexForCity,2]]; cells[[newBmuIndexForCity]] = cells[[newBmuIndexForCity]] - (epsilonBmu (cells[[newBmuIndexForCity]] - cities[[currCityIndex]])); If [pinnedFlags[[lNeighbor]] == 0, cells[[lNeighbor]] = cells[[lNeighbor]] - (epsilonNeighbor (cells[[lNeighbor]] - cities[[currCityIndex]]))]; If [pinnedFlags[[rtNeighbor]] == 0, cells[[rtNeighbor]] = cells[[rtNeighbor]] - (epsilonNeighbor (cells[[rtNeighbor]] - cities[[currCityIndex]]))]]; ]; If [Dimensions[freeCityIndices][[1]] > 0, bothNeighbors = {neighbors[[maxErrorIndex,1]], neighbors[[maxErrorIndex,2]]}; bothDistances = Map[distance[cells[[maxErrorIndex]],#]&, cells[[bothNeighbors]]]; indexOfFurthest = First [Flatten [Position [bothDistances, Max[bothDistances]]]]; otherIndex = Abs[indexOfFurthest - 2] + 1; furthest = bothNeighbors[[indexOfFurthest]]; cells = Append[cells, cells[[maxErrorIndex]] - (0.5 (cells[[maxErrorIndex]] - cells[[furthest]]))]; pinnedFlags = Append[pinnedFlags, 0]; errorArray = Append[errorArray, (1/3) (errorArray[[maxErrorIndex]] + errorArray[[furthest]])]; errorArray[[maxErrorIndex]] = (2/3) errorArray[[maxErrorIndex]]; errorArray[[furthest]] = (2/3) errorArray[[furthest]]; tempIndex = neighbors[[maxErrorIndex, indexOfFurthest]]; newCellIndex = Dimensions[cells][[1]]; neighbors[[maxErrorIndex,indexOfFurthest]] = newCellIndex; neighbors[[tempIndex,otherIndex]] = newCellIndex; neighbors = Append [neighbors, {0,0}]; neighbors[[newCellIndex,indexOfFurthest]] = tempIndex; neighbors[[newCellIndex,otherIndex]] = maxErrorIndex; maxErrorIndex = First[Flatten[Position [errorArray, Max[errorArray]]]]; maxErrorValue = errorArray[[maxErrorIndex]]; Show[Graphics [ {PointSize[0.04],RGBColor[1,0,0], Map[Point, 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.54131 .62933 L s .76271 .193 m .75911 .19221 L s .36845 .48822 m .40453 .52281 L s .48916 .85224 m .48275 .7825 L s .77239 .64781 m .85511 .62897 L s .62293 .14667 m .53427 .21138 L s .81723 .14619 m .79267 .13359 L s .83153 .50248 m .7556 .5177 L s .34755 .39819 m .36384 .47531 L s .32097 .06726 m .19636 .01948 L s .88076 .59626 m .90876 .5705 L s .82382 .8234 m .85044 .78591 L s .60761 .47734 m .67096 .41792 L s .11054 .0315 m .07017 .05787 L s .13918 .14053 m .17577 .14101 L s .94423 .27718 m .95751 .19377 L s .0095 .93777 m .00519 .94961 L s P P % End of Graphics MathPictureEnd :[font = output; output; inactive; preserveAspect] 103.5833333333333 ;[o] 103.583 :[font = output; output; inactive; preserveAspect] 72.8 ;[o] 72.8 :[font = print; inactive; preserveAspect] ***** END OF RUN ***** :[font = output; output; inactive; locked; preserveAspect] 1232.933333333333333 ;[o] 1232.93 :[font = output; output; inactive; locked; preserveAspect] 243.45 ;[o] 243.45 :[font = print; inactive; locked; preserveAspect; endGroup] ***** END OF RUN ***** :[font = text; inactive; preserveAspect] Now display the final results, ignoring cells that have not been pinned to a city. :[font = input; preserveAspect; startGroup] orderedCells = {}; firstIndex = First[Flatten[Position[ pinnedFlags,1]]]; orderedCells = Append [orderedCells, {cells[[firstIndex]],0}]; nextIndex = neighbors[[firstIndex,2]]; While [nextIndex != firstIndex, If [pinnedFlags[[nextIndex]] == 1, orderedCells[[Dimensions[ orderedCells][[1]],2]] = cells[[nextIndex]]; orderedCells = Append [orderedCells, {cells[[nextIndex]], 0}]]; nextIndex = neighbors[[nextIndex,2]]]; orderedCells[[Dimensions[orderedCells][[1]],2]] = cells[[firstIndex]]; Show[Graphics [ {PointSize[0.04],RGBColor[1,0,0], Map[Point, cities], PointSize[0.02],RGBColor[0,0,1], Map[Point, cells[[Flatten[Position[ pinnedFlags,1]]]]], RGBColor[0,1,0],Map[Line,orderedCells]}], AxesOrigin ->{0,0}, Axes->Automatic, AspectRatio->1, PlotRange->{{0,1},{0,1}}] :[font 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