17 Ant Algorithms

Recognizing QR-Code In .NETUsing Barcode Control SDK for Visual Studio .NET Control to generate, create, read, scan barcode image in VS .NET applications.

the best path [216] The pheromone update equation changes to

Generate QR Code ISO/IEC18004 In .NET FrameworkUsing Barcode creator for Visual Studio .NET Control to generate, create Quick Response Code image in VS .NET applications.

e ij (t + 1) = ij (t) + ij (t) + ne ij (t)

Decoding QR Code In .NETUsing Barcode reader for VS .NET Control to read, scan read, scan image in .NET applications.

(1715)

Paint Barcode In Visual Studio .NETUsing Barcode generation for VS .NET Control to generate, create barcode image in VS .NET applications.

where

Scan Bar Code In .NETUsing Barcode reader for VS .NET Control to read, scan read, scan image in .NET applications.

e ij (t) =

Draw QR In C#.NETUsing Barcode generator for VS .NET Control to generate, create QR Code image in Visual Studio .NET applications.

Q f ( (t)) x

QR Maker In .NET FrameworkUsing Barcode encoder for ASP.NET Control to generate, create Quick Response Code image in ASP.NET applications.

if (i, j) x(t) otherwise

QR-Code Generation In VB.NETUsing Barcode drawer for Visual Studio .NET Control to generate, create QR-Code image in .NET applications.

(1716)

Make ECC200 In VS .NETUsing Barcode drawer for .NET Control to generate, create Data Matrix 2d barcode image in VS .NET applications.

and e is the number of elite ants In equation (1716), x(t) is the current best route, with f ( (t)) = mink=1,,nk {f (xk (t))} The elitist strategy has as its objective directx ing the search of all ants to construct a solution to contain links of the current best route

Code39 Generation In .NETUsing Barcode maker for .NET Control to generate, create Code-39 image in .NET framework applications.

Ant Colony System

GTIN - 12 Creation In .NET FrameworkUsing Barcode drawer for .NET Control to generate, create UPC Symbol image in .NET framework applications.

The ant colony system (ACS) was developed by Gambardella and Dorigo to improve the performance of AS [77, 215, 301] ACS di ers from AS in four aspects: (1) a di erent transition rule is used, (2) a di erent pheromone update rule is de ned, (3) local pheromone updates are introduced, and (4) candidate lists are used to favor speci c nodes Each of these modi cations is discussed next The ACS transition rule, also referred to as a pseudo-random-proportional action rule [301], was developed to explicitly balance the exploration and exploitation abilities of the algorithm Ant k, currently located at node i, selects the next node j to move to using the rule, j=

Generating 2 Of 7 Code In .NET FrameworkUsing Barcode maker for Visual Studio .NET Control to generate, create Ames code image in VS .NET applications.

arg maxu Nik (t) { iu (t) iu (t)} if r r0 J if r > r0

Create Barcode In .NETUsing Barcode generation for ASP.NET Control to generate, create bar code image in ASP.NET applications.

(1717)

USS Code 39 Drawer In VB.NETUsing Barcode printer for VS .NET Control to generate, create Code39 image in Visual Studio .NET applications.

where r U (0, 1), and r0 [0, 1] is a user-speci ed parameter; J Nik (t) is a node randomly selected according to probability pk (t) = iJ Nik (t) is a set of valid nodes to visit The transition rule in equation (1717) creates a bias towards nodes connected by short links and with a large amount of pheromone The parameter r0 is used to balance exploration and exploitation: if r r0 , the algorithm exploits by favoring the best edge; if r > r0 , the algorithm explores Therefore, the smaller the value of r0 , the less best links are exploited, while exploration is emphasized more It is important to note that the transition rule is the same as that of AS when r > r0 Also note that the ACS transition rule uses = 1, and is therefore omitted from equation (1718) Unlike AS, only the globally best ant (eg the ant that constructed the shortest path, x+ (t)) is allowed to reinforce pheromone concentrations on the links of the corresponding best path Pheromone is updated using the global update rule, ij (t + 1) = (1 1 ) ij (t) + 1 ij (t) (1719)

Generating EAN128 In JavaUsing Barcode maker for Java Control to generate, create EAN128 image in Java applications.

iJ (t) iJ (t)

Code 128 Code Set A Maker In JavaUsing Barcode printer for Java Control to generate, create Code 128 Code Set C image in Java applications.

k u Ni

Painting EAN / UCC - 14 In VB.NETUsing Barcode creation for VS .NET Control to generate, create UCC-128 image in VS .NET applications.

iu (t) iu (t)

Make UPCA In .NET FrameworkUsing Barcode maker for ASP.NET Control to generate, create UPC Symbol image in ASP.NET applications.

(1718)

Make Code-39 In JavaUsing Barcode maker for Java Control to generate, create Code39 image in Java applications.

171 Ant Colony Optimization Meta-Heuristic where ij (t) =

EAN 13 Printer In JavaUsing Barcode maker for Java Control to generate, create EAN13 image in Java applications.

1 f (x+ (t))

if (i, j) x+ (t) otherwise

(1720)

with f (x+ )(t) = |x+ (t)|, in the case of nding shortest paths The ACS global update rule causes the search to be more directed, by encouraging ants to search in the vicinity of the best solution found thus far This strategy favors exploitation, and is applied after all ants have constructed a solution Gambardella and Dorigo [215, 301] implemented two methods of selecting the path, x+ (t), namely iteration-best, where x+ (t) represents the best path found during the current iteration, t, denoted as x(t), and global-best, where x+ (t) represents the best path found from the rst iteration of the algorithm, denoted as x(t) For the global-best strategy, the search process exploits more by using more global information Pheromone evaporation is also treated slightly di erently to that of AS Referring to equation (1719), for small values of 1 , the existing pheromone concentrations on links evaporate slowly, while the in uence of the best route is dampened On the other hand, for large values of 1 , previous pheromone deposits evaporate rapidly, but the in uence of the best path is emphasized The e ect of large 1 is that previous experience is neglected in favor of more recent experiences Exploration is emphasized While the value of 1 is usually xed, a strategy where 1 is adjusted dynamically from large to small values will favor exploration in the initial iterations of the search, while focusing on exploiting the best found paths in the later iterations In addition to the global updating rule, ACS uses the local updating rule, ij (t) = (1 2 ) ij (t) + 2 0 (1721)

with 2 also in (0, 1), and 0 is a small positive constant Experimental results on di erent TSPs showed that 0 = (nG L) 1 provided good results [215]; nG is the number of nodes in graph G, and L is the length of a tour produced by a nearestneighbor heuristic for TSPs [737] (L can be any rough approximation to the optimal tour length [215]) ACS also rede nes the meaning of the neighborhood set from which next nodes are selected The set of nodes, Nik (t), is organized to contain a list of candidate nodes These candidate nodes are preferred nodes, to be visited rst Let nl < |Nik (t)| denote the number of nodes in the candidate list The nl nodes closest (in distance or cost) to node i are included in the candidate list and ordered by increasing distance When a next node is selected, the best node in the candidate list is selected If the candidate list is empty, then node j is selected from the remainder of Nik (t) Selection of a non-candidate node can be based on equation (1718), or alternatively the closest non-candidate j Nik (t) can be selected