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Stigmergy as an Approach to Metaheuristic Optimization - Computer ...

24 2 **Optimization** with **an**t colonies The Ant-B**as**ed Control (ABC) [102] algorithm w**as** the first attempt **to** apply **an** ACO algorithm **to** a routing problem. A network c**an** be represented by a directed graph. Here are **an**ts used **to** build routing tables. The AntNet [13] is **an**other **an**t-b**as**ed algorithm used for a routing problem. The population-b**as**ed Ant-Colony **Optimization** (PACO) [44] represents a new approach **to** problem solving compared **to** the st**an**dard ACO algorithms. Instead of the pheromone trails the PACO algorithm updates **an**d maintains a population of solutions. 2.6 ACO-b**as**ed algorithms for numerical optimization So far there were only few **an**t-b**as**ed approaches proposed for numerical optimization problems. The first one w**as** the Continuous ACO (CACO) [8]. It comprises two levels: global **an**d local. The CACO uses the **an**t-colony framework **to** perform local searches, where**as** global search is h**an**dled by a GA. It w**as** later followed by the Continuous Interacting Ant Colony (CIAC) [28], the Aggregation Pheromone System [119], the Improved Ant-Colony Algorithm [14], the Extended ACO for continuous **an**d mixedvariable [104], etc. Although these algorithms draw inspiration from the ACO metaheuristic, they do not follow it closely. One of the few algorithms that follow the ACO metaheuristic w**as** proposed by Socha [104] **an**d is called the Extended Ant-Colony **Optimization** (eACO). As it is **an** extension of a generic ACO, it c**an** solve mixed discrete-continuous optimization problems. In the c**as**e of numerical optimization problems, the domain c**an** ch**an**ge from discrete **to** continuous. The only adaptation needed is a move from using the discrete probability distribution **to** a continuous one. Instead of choosing a new component at step i, like **an**t-b**as**ed algorithms usually do, the **an**ts generate a r**an**dom number according **to** a certain probability density function. As mentioned before, the probability distribution c**an** be either discrete or continuous. In this way the eACO is capable of solving continuous **an**d mixed-variable optimization problems.

2.7 Applications of **an**t-colony optimization algorithms 25 2.7 Applications of **an**t-colony optimization algorithms In Table 2.1 different applications of **an**t-colony optimization algorithms are shown (partially adapted from [23]). Of course, Table 2.1 c**an**not present a complete overview, Table 2.1 Applications of **an**t-colony optimization algorithms. Problem name / Authors Algorithm name Year Traveling salesm**an** Dorigo, M**an**iezzo **an**d Colorni AS 1991 Gambardella **an**d Dorigo Ant-Q 1995 Dorigo **an**d Gambardella ACS **an**d ACS-3-opt 1996 Stützle **an**d Hoos MMAS 1997 Bullnheimer, Hartl **an**d Strauss ASr**an**k 1997 Guntsch **an**d Middendorf PACO 2002 Quadratic **as**signment M**an**iezzo, Colorni **an**d Dorigo AS-QAP 1994 Gambardela, Taillard **an**d Dorigo HAS-QAP 1997 Stützle **an**d Hoos MMAS-QAP 1997 M**an**iezzo ANTS-QAP 1998 M**an**iezzo **an**d Colorni AS-QAP 1999 Scheduling problems Colorni, Dorigo **an**d M**an**iezzo AS-JSP 1994 Stützle AS-FSP 1997 Bauer et al. ACS-SMTTP 1999 den Besten, Stützle **an**d Dorigo AS-VRP 1997 Vehicle routing Bullnheimer, Hartl **an**d Strauss AS-VRP 1997 Gambardella, Taillard **an**d Agazzi HAS-VRP 1999 Connection-oriented network routing Schoonderwoerd et al. ABC 1996 Di Caro **an**d Dorigo AntNet-FS 1998 Bonabeau et al. ABC-smart **an**ts 1998 Connection-less network routing Di Caro **an**d Dorigo AntNet **an**d AntNet-FA 1997 v**an** der Put **an**d Rothkr**an**tz ABC-backward 1998 Sequential ordering Gambardella **an**d Dorigo HAS-SOP 1997 Shortest common supersequence Michel **an**d Middendorf AS-SCS 1998 Frequency **as**signment M**an**iezzo **an**d Carbonaro ANTS-FAP 1998 Generalized **as**signment Ramalhinho, Lorenço **an**d Serra MMAS-GAP 1998 Multiple knapsack Leguizamón **an**d Michalewicz AS-MKP 1999 Optical network routing Navarro Varela **an**d Sinclair ACO-VWP 1999 Redund**an**cy allocation Li**an**g **an**d Smith ACO-RAP 1999 Mesh partitioning Korošec **an**d Šilc ACO 2002 Multi-criteria optimization Guntsch **an**d Middendorf PACO 2003 Multi-parameter optimization Bilchev **an**d Parmee CACO 1995 Monmarché, Venturini, **an**d Slim**an**e API 2000 Dréo **an**d Siary CIAC 2002 Socha eACO 2004 Korošec **an**d Šilc MASA 2005 Korošec **an**d Šilc DASA 2006

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128 Acknowledgements

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140 Index Covariance Matrix Adaptat

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142 Index TSP, see Traveling Salesm

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144 List of Algorithms

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160 Selected publications Izbrane o