An Adaptive Dynamic Ant System Based on Acceleration for TSP

Abstract

Ant System (AS) is a novel simulated evolutionary algorithm which shows many good characters, but it has some typical shortcomings, such as high time complexity, stagnation behavior. An Ant Adaptive Dynamic Ant System (ADAS) based on Acceleration is proposed, which is improved from AS by modifying the pheromone updating rule and the transition rule with evenness of solution, interesting and acceleration. Simulation shows that the ADAS can solve the contradictory between convergence speed and stagnation behavior efficiently and has a better solution.

New Ant Colony Optimization Algorithm for the Traveling Salesman Problem

“…In this algorithm, the pheromone updates according to the following equation: (8) To diversify the search process, the pheromone values of all paths should be limited to an interval [ min , max ], which is as follows: (9) where min and max are the pheromone extent values, which can be determined from experiments. A detailed description of min and max can be found in reference [6].…”

“…However, as a heuristic algorithm, the AS has several shortcomings [1], including slow convergence and difficulty in expanding the search space. To solve the TSP well, several scholars have proposed many corrective algorithms for ACOs, such as the elitist AS [3], the ant colony system [4], the rank-based AS [5], the max-min AS [6], the novel max-min AS [7], the adaptive dynamic AS [8], the moderate AS [9], an improved ACO algorithm [10], the cooperative genetic AS [11], a hybrid method of ant colony optimization and the genetic algorithm (ACO-GA) [12], a hybrid method of ant colony optimization and the cuckoo search algorithm (ACO-CS) [12], a hybrid max-min ant system integrated with an inequality constraint on four vertices and three lines (HMMAS) [13], a modified AS [14], a nearest neighbor ant colony system (NNACS) [15], a hybrid elitist-ant system (HEAS) [16], a hybrid method based on ant colony optimization and the 3-Opt * Email: wgaowh@163.com algorithm (ACO-3Opt) [17], and a parallel ACO algorithm based on a quantum dynamic mechanism [18], and so on. The details of these algorithms are as follows.…”

“…However, its convergence rate needs to be improved. The adaptive dynamic AS [8] improved AS by modifying the pheromone updating rule and the transition rule with evenness of solution, interesting and acceleration to avoid premature convergence. However, this does not solve the problem of slow convergence.…”

Modified ant colony optimization with improved tour construction and pheromone updating strategies for traveling salesman problem

“…However, for its intractable nature, a lot of heuristic approaches have been proposed to solve TSP, and using those methods, the very short tours which cannot be guaranteed to be minimal can be found. These methods include greedy algorithm (Hoos and Stützle 2005), stimulated annealing (Meer 2007;Zhan et al 2016), tabu search (Fiechter 1994;Misevičius et al 2005), neural network (Créput and Koukam 2009;Mulder and Wunch 2003), genetic algorithm (Cunkas and Ozsaglam 2009;Khan et al 2009;Tsai et al 2014), particle swarm optimization (Cunkas and Ozsaglam 2009;Shi et al 2007), ACO (Dorigo and Gambardella 1997;Guo and Liu 2011;Mei et al 2009), etc. Currently, many other new metaheuristic optimization algorithms have been applied to solve it too, such as quantum heuristic algorithm (Bang et al 2012), artificial bee colony algorithm (Kıran et al 2013;Meng et al 2016;Wong et al 2008), shrinking blob algorithm (Jones and Adamatzky 2014), discrete cuckoo search algorithm (Ouaarab et al 2014), African buffalo optimization (Odili and Kahar 2016), discrete bat algorithm (Saji and Riffi 2016), fruit fly optimization algorithm (Huang et al 2017), artificial atom algorithm (Yildirim and Karci 2018), black hole algorithm (Hatamlou 2018), symbiotic organisms search algorithm , and a minimum spanning tree-based heuristic (Kumar et al 2018).…”

“…However, as one heuristic algorithm, ant system has some shortcomings, including slow convergence, low efficiency, and hard to expand the hunting zone, etc. Thus, to improve ant system, some scholars proposed many corrective algorithms of ACO, such as elitist-ant system (Dorigo et al 1996), ant colony system (Dorigo and Gambardella 1997), rank-based ant system (Bullnheimer et al 1999), ant colony algorithm with mutation (Wu et al 1999), max-min ant system (Stützle and Hoos 2000), ant colony optimization with mutation and dynamic pheromone updating (Zhu and Yang 2004), adaptive dynamic ant system (Mei et al 2009), moderate ant system (Guo and Liu 2011), modified ant system (Yan et al 2017), nearest neighbor ant colony system (Thill and Kuo 2018), modified ant colony optimization algorithm (Oonsrikaw and Thammano 2018).…”