nc c=1 wc c,iu (t)) iu (t)} if r r0 if r > r0 in Visual Studio .NET

Create QR Code in Visual Studio .NET nc c=1 wc c,iu (t)) iu (t)} if r r0 if r > r0
nc c=1 wc c,iu (t)) iu (t)} if r r0 if r > r0
Quick Response Code Scanner In .NET
Using Barcode Control SDK for .NET Control to generate, create, read, scan barcode image in VS .NET applications.
(1783)
QR Code JIS X 0510 Printer In .NET
Using Barcode creation for .NET Control to generate, create QR image in .NET applications.
where nc is the number of objectives, wc is the weight assigned to the c-th objective, and J is selected on the basis of the probability pc (t) = iJ (
QR Code Decoder In .NET
Using Barcode decoder for .NET framework Control to read, scan read, scan image in .NET applications.
u Ni nc c=1 wc c,iJ (t)) iJ (t) nc c=1 wc c,iu (t)) iu (t)
Make Bar Code In .NET
Using Barcode creator for VS .NET Control to generate, create bar code image in VS .NET applications.
(1784)
Scan Bar Code In .NET Framework
Using Barcode recognizer for .NET framework Control to read, scan read, scan image in VS .NET applications.
Local pheromone updates are as for the original ACS, but done separately for each objective: (1785) c,ij = (1 ) c,ij + 0 The global update changes to c,ij = (1 ) c,ij + c,ij where c,ij 15 10 = 5 0 if (i, j) best and second-best solution if (i, j) best solution if (i, j) second-best solution otherwise (1786)
Creating QR Code ISO/IEC18004 In C#
Using Barcode drawer for Visual Studio .NET Control to generate, create Quick Response Code image in Visual Studio .NET applications.
(1787)
Printing QR Code 2d Barcode In VS .NET
Using Barcode creation for ASP.NET Control to generate, create Quick Response Code image in ASP.NET applications.
with the best solutions above referring to non-dominated solutions An archive of non-dominated solutions is maintained Cardoso et al [105] extended the AS to solve MOPs in dynamically changing environments A pheromone matrix, c , and pheromone ampli cation coe cient, c , is
QR-Code Maker In Visual Basic .NET
Using Barcode creation for Visual Studio .NET Control to generate, create Denso QR Bar Code image in Visual Studio .NET applications.
17 Ant Algorithms
Code 128B Printer In VS .NET
Using Barcode creation for .NET Control to generate, create Code 128 Code Set A image in .NET applications.
maintained for each objective function fc The AS transition rule is changed to pij (t) =
Code 39 Full ASCII Printer In Visual Studio .NET
Using Barcode printer for VS .NET Control to generate, create Code39 image in Visual Studio .NET applications.
u Ni (t)
Paint Data Matrix 2d Barcode In Visual Studio .NET
Using Barcode generator for VS .NET Control to generate, create Data Matrix image in .NET framework applications.
ij (t) nc ( c,ij ) c c=1 iu (t) nc ( c,iu ) c c=1
Make Identcode In Visual Studio .NET
Using Barcode printer for .NET framework Control to generate, create Identcode image in VS .NET applications.
if j Ni (t) if j Ni (t)
Create UPCA In C#.NET
Using Barcode generation for .NET framework Control to generate, create GTIN - 12 image in .NET framework applications.
Q fk (x)
Make Barcode In .NET Framework
Using Barcode printer for ASP.NET Control to generate, create bar code image in ASP.NET applications.
(1788)
UPC-A Decoder In .NET
Using Barcode reader for VS .NET Control to read, scan read, scan image in VS .NET applications.
All visited links are updated by each ant with an amount
USS Code 39 Recognizer In VS .NET
Using Barcode decoder for .NET Control to read, scan read, scan image in Visual Studio .NET applications.
The approach of Iredi et al [405] discussed above makes use of a di erent heuristic matrix for each objective (refer to equation (1782)) Bar n and Schaerer [49] devela oped a di erent approach based on ACS, as a variation of the approach developed by Gambardella et al [303] A single colony is used, with a single pheromone matrix, but one heuristic matrix for each objective Assuming two objectives, the ACS transition rule changes to j=
Data Matrix Creator In VB.NET
Using Barcode maker for .NET Control to generate, create Data Matrix 2d barcode image in .NET applications.
arg maxu Ni (t) { iu (t) 1,iu (t) 2,iu J (1 )
Painting EAN 13 In VB.NET
Using Barcode drawer for .NET Control to generate, create EAN13 image in .NET applications.
(t)} if r r0 if r > r0
Barcode Encoder In .NET
Using Barcode creation for ASP.NET Control to generate, create barcode image in ASP.NET applications.
(1789)
USS Code 39 Generation In Visual Basic .NET
Using Barcode creator for Visual Studio .NET Control to generate, create ANSI/AIM Code 39 image in VS .NET applications.
where [0, 1] and J is selected on the basis of the probability, pk (t) iJ =
iJ (t) 1,iJ (t) 2,iJ (1 )
(1 ) (t) u Ni iu (t) 1,iu (t) 2,iu
(1790)
For the local update rule, the constant 0 is initially calculated using 0 = 1 f 1f 2 (1791)
where f 1 and f 2 are the average objective values over a set of heuristically obtained solutions (prior to the execution of the ant algorithm) for the two objectives respectively The constant is, however, changed over time At each iteration, 0 is calculated using equation (1791), but calculated over the current set of non-dominated solutions If 0 > 0 , then pheromone trails are initialized to 0 = 0 ; otherwise, the global pheromone update is applied with respect to each solution x P, where P is the set on non-dominated solutions: ij = (1 ) ij + f1 (x)f2 (x) (1792)
Dynamic Environments
For dynamic optimization problems (refer to Section A9), the search space changes over time A current good solution may not be a good solution after a change in the environment has occurred Ant algorithms may not be able to track changing environments due to pheromone concentrations that become too strong [77] If most of the ants have already settled on the same solution, the high pheromone concentrations on the links representing that solution cause that solution to be constructed by all future ants with very high probability even though a change has occurred To enable
174 Advanced Topics
ACO algorithms to track changing environments, mechanisms have to be employed to favor exploration For example, using the transition probability of ACS (refer to equation (1718)), exploration is increased by selecting a small value for r0 and increasing This will force more random transition decisions, where the new, updated heuristic information creates a bias towards the selection of links that are more desirable according to the changed environment An alternative is to use an update rule where only those links that form part of a solution have their pheromone updated, including an evaporation component similar to the local update rule of ACS (refer to Section 1715) Over time the pheromone concentrations on the frequently used links decrease, and these links become less favorable Less frequently used links will then be explored A very simple strategy is to reinitialize pheromone after change detection, but to keep a reference to the previous best solution found If the location of an environment change can be identi ed, the pheromone of links in the neighborhood can be reinitialized to a maximum value, forcing these links to be more desirable If these links turn out to represent bad solution components, reinforcement will be small (since it is usually proportional to the quality of the solution), and over time desirability of the links reduces due to evaporation Guntsch and Middendorf [340] proposed to repair solutions when a change occurred This can be done by applying a local search procedure to all solutions Alternatively, components a ected by change are deleted from the solution, connecting the predecessor and successor of the deleted component New components (not yet used in the solution) are then inserted on the basis of a greedy algorithm The position where a new component is inserted is the position that causes the least cost increase, or highest cost decrease (depending on the objective) Sim and Sun [791] used a multiple colony system, where colonies are repelled by the pheromone of other colonies to promote exploration in the case of changing environments Other approaches to cope with changing environments change the pheromone update rules to favor exploration: Li and Gong [520] modify both the local and global update rules The local update rule is changed to ij (t + 1) = (1 1 ( ij (t))) ij (t) + ij (t) where 1 ( ij ) is a monotonically increasing function of ij , eg 1 ( ij ) = where > 0 The dynamic changing evaporation constant has the e ect that high pheromone values are decreased more than low pheromone values In the event of an environment change, and if a solution is no longer the best solution, the pheromone concentrations on the corresponding links decrease over time 1 1+ e ( ij + ) (1794) (1793)