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

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

24 2

24 2 Optimization with ant colonies The Ant-Based Control (ABC) [102] algorithm was the first attempt to apply an ACO algorithm to a routing problem. A network can be represented by a directed graph. Here are ants used to build routing tables. The AntNet [13] is another ant-based algorithm used for a routing problem. The population-based Ant-Colony Optimization (PACO) [44] represents a new approach to problem solving compared to the standard ACO algorithms. Instead of the pheromone trails the PACO algorithm updates and maintains a population of solutions. 2.6 ACO-based algorithms for numerical optimization So far there were only few ant-based approaches proposed for numerical optimization problems. The first one was the Continuous ACO (CACO) [8]. It comprises two levels: global and local. The CACO uses the ant-colony framework to perform local searches, whereas global search is handled by a GA. It was 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 and 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 was proposed by Socha [104] and is called the Extended Ant-Colony Optimization (eACO). As it is an extension of a generic ACO, it can solve mixed discrete-continuous optimization problems. In the case of numerical optimization problems, the domain can change 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 ant-based algorithms usually do, the ants generate a random number according to a certain probability density function. As mentioned before, the probability distribution can be either discrete or continuous. In this way the eACO is capable of solving continuous and mixed-variable optimization problems.

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

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