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17
Analysis of Different MMAS ACO Algorithms on Unimodal Functions and Plateaus
, 2008
"... Recently, the first rigorous runtime analyses of ACO algorithms appeared, covering variants of the MAXMIN ant system and their runtime on pseudoBoolean functions. Interestingly, a variant called 1ANT is very sensitive to the evaporation factor while Gutjahr and Sebastiani proved partly opposite ..."
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Cited by 12 (6 self)
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Recently, the first rigorous runtime analyses of ACO algorithms appeared, covering variants of the MAXMIN ant system and their runtime on pseudoBoolean functions. Interestingly, a variant called 1ANT is very sensitive to the evaporation factor while Gutjahr and Sebastiani proved partly opposite results for their variant called MMASbs. These algorithms differ in their update mechanisms and, moreover, MMASbs only accepts strict improvements in contrast to the 1ANT. The motivation for this work is manifold. Firstly, we prove that the different behavior of the 1ANT and MMASbs results from the different update mechanisms. Secondly, we improve results by Gutjahr and Sebastiani and extend their analyses to the important class of unimodal functions. Thirdly, we compare MMASbs with a variant that also accepts equally fit solutions as this enables the exploration of plateaus. For wellknown plateau functions we show theoretically and experimentally that accepting equally fit solutions drastically reduces the optimization time.
Refined runtime analysis of a basic ant colony optimization algorithm
 In IEEE Congress on Evolutionary Computation 2007
, 2007
"... Neumann and Witt (2006) analyzed the runtime of the basic ant colony optimization (ACO) algorithm 1Ant on pseudoboolean optimization problems. For the problem OneMax they showed how the runtime depends on the evaporation factor. In particular, they proved a phase transition from exponential to poly ..."
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Cited by 11 (1 self)
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Neumann and Witt (2006) analyzed the runtime of the basic ant colony optimization (ACO) algorithm 1Ant on pseudoboolean optimization problems. For the problem OneMax they showed how the runtime depends on the evaporation factor. In particular, they proved a phase transition from exponential to polynomial runtime. In this work, we simplify the view on this problem by an appropriate translation of the pheromone model. This results in a profound simplification of the pheromone update rule and, by that, a refinement of the results of Neumann and Witt. In particular, we show how the exponential runtime bound gradually changes to a polynomial bound inside the phase of transition. 1
Rigorous Analyses for the Combination of Ant Colony Optimization and Local Search
, 2008
"... Ant colony optimization (ACO) is a metaheuristic that produces good results for a wide range of combinatorial optimization problems. Often such successful applications use a combination of ACO and local search procedures that improve the solutions constructed by the ants. In this paper, we study t ..."
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Cited by 10 (5 self)
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Ant colony optimization (ACO) is a metaheuristic that produces good results for a wide range of combinatorial optimization problems. Often such successful applications use a combination of ACO and local search procedures that improve the solutions constructed by the ants. In this paper, we study this combination from a theoretical point of view and point out situations where introducing local search into an ACO algorithm enhances the optimization process significantly. On the other hand, we illustrate the drawback that such a combination might have by showing that this may prevent an ACO algorithm from obtaining optimal solutions.
Runtime Analysis of Binary PSO
"... We investigate the runtime of the Binary Particle Swarm Optimization (PSO) algorithm introduced by Kennedy and Eberhart (1997). The Binary PSO maintains a global best solution and a swarm of particles. Each particle consists of a current position, an own best position and a velocity vector used in a ..."
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Cited by 5 (2 self)
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We investigate the runtime of the Binary Particle Swarm Optimization (PSO) algorithm introduced by Kennedy and Eberhart (1997). The Binary PSO maintains a global best solution and a swarm of particles. Each particle consists of a current position, an own best position and a velocity vector used in a probabilistic process to update the particle’s position. We present lower bounds for swarms of polynomial size. To prove upper bounds, we transfer a fitnesslevel argument wellestablished for evolutionary algorithms (EAs) to PSO. This method is applied to estimate the expected runtime on the class of unimodal functions. A simple variant of the Binary PSO is considered in more detail. The 1PSO only maintains one particle, hence own best and global best solutions coincide. Despite its simplicity, the 1PSO is surprisingly efficient. A detailed analysis for the function OneMax shows that the 1PSO is competitive to EAs.
Running Time Analysis of Ant Colony Optimization for Shortest Path Problems
, 2011
"... Ant Colony Optimization (ACO) is a modern and very popular optimization paradigm inspired by the ability of ant colonies to find shortest paths between their nest and a food source. Despite its popularity, the theory of ACO is still in its infancy and a solid theoretical foundation is needed. We pre ..."
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Cited by 5 (4 self)
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Ant Colony Optimization (ACO) is a modern and very popular optimization paradigm inspired by the ability of ant colonies to find shortest paths between their nest and a food source. Despite its popularity, the theory of ACO is still in its infancy and a solid theoretical foundation is needed. We present bounds on the running time of different ACO systems for shortest path problems. First, we improve previous results by Attiratanasunthron and Fakcharoenphol [Information Processing Letters, 105(3):88–92, 2008] for singledestination shortest paths and extend their results from DAGs to arbitrary directed graphs. Our upper bound is asymptotically tight for large evaporation factors, holds with high probability, and transfers to the allpairs shortest paths problem. There, a simple mechanism for exchanging information between ants with different destinations yields a significant improvement. A comparison with evolutionary and genetic approaches indicates that ACO is among the best known metaheuristics for the allpairs shortest paths problem.
Running Time Analysis of ACO Systems for Shortest Path Problems
"... Ant Colony Optimization (ACO) is inspired by the ability of ant colonies to find shortest paths between their nest and a food source. We analyze the running time of different ACO systems for shortest path problems. First, we improve running time bounds by Attiratanasunthron and Fakcharoenphol [Infor ..."
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Cited by 4 (2 self)
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Ant Colony Optimization (ACO) is inspired by the ability of ant colonies to find shortest paths between their nest and a food source. We analyze the running time of different ACO systems for shortest path problems. First, we improve running time bounds by Attiratanasunthron and Fakcharoenphol [Information Processing Letters, 105(3):88–92, 2008] for singledestination shortest paths and extend their results for acyclic graphs to arbitrary graphs. Our upper bound is asymptotically tight for large evaporation factors, holds with high probability, and transfers to the allpairs shortest paths problem. There, a simple mechanism for exchanging information between ants with different destinations yields a significant improvement. Our results indicate that ACO is the best known metaheuristic for the allpairs shortest paths problem.
Runtime Analysis of a Binary Particle Swarm Optimizer
"... We investigate the runtime of a Binary Particle Swarm Optimizer (PSO) for optimizing pseudoBoolean functions f: {0, 1} n → R. The Binary PSO maintains a swarm of particles searching for good solutions. Each particle consists of a current position from {0, 1} n, an own best position and a velocity v ..."
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Cited by 3 (2 self)
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We investigate the runtime of a Binary Particle Swarm Optimizer (PSO) for optimizing pseudoBoolean functions f: {0, 1} n → R. The Binary PSO maintains a swarm of particles searching for good solutions. Each particle consists of a current position from {0, 1} n, an own best position and a velocity vector used in a probabilistic process to update its current position. The velocities for a particle are then updated in the direction of its own best position and the position of the best particle in the swarm. We present a lower bound for the time needed to optimize any function with unique optimum. To prove upper bounds, we transfer a fitnesslevel argument wellestablished for evolutionary algorithms (EAs) to PSO. This method is applied to estimate the expected runtime on the class of unimodal functions. A simple variant of the Binary PSO is considered in more detail on the test function OneMax, showing that there the Binary PSO is competitive to EAs. An additional experimental comparison reveals further insights.
How single ant aco systems optimize pseudoboolean functions
 In Parallel Problem Solving from Nature ? PPSN X, USA, Atlanta, 2008, LNCS 5199
"... We undertake a rigorous experimental analysis of the optimization behavior of the two most studied single ant ACO systems on several pseudoboolean functions. By tracking the behavior of the underlying random processes rather than just regarding the resulting optimization time, we gain additional in ..."
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We undertake a rigorous experimental analysis of the optimization behavior of the two most studied single ant ACO systems on several pseudoboolean functions. By tracking the behavior of the underlying random processes rather than just regarding the resulting optimization time, we gain additional insight into these systems. A main finding is that in those cases where the single ant ACO system performs well, it basically simulates the much simpler (1+1) evolutionary algorithm. 1
Simple maxmin ant systems and the optimization of linear pseudoboolean functions
 Proc. of Foundations of Genetic Algorithms (FOGA
, 2011
"... With this paper, we contribute to the understanding of ant colony optimization (ACO) algorithms by formally analyzing their runtime behavior. We study simple MAXMIN ant systems on the class of linear pseudoBoolean functions defined on binary strings of length n. Our investigations point out how ..."
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With this paper, we contribute to the understanding of ant colony optimization (ACO) algorithms by formally analyzing their runtime behavior. We study simple MAXMIN ant systems on the class of linear pseudoBoolean functions defined on binary strings of length n. Our investigations point out how the progress according to function values is stored in the pheromones. We provide a general upper bound of O((n3 logn)/ρ) on the running time for two ACO variants on all linear functions, where ρ determines the pheromone update strength. Furthermore, we show improved bounds for two wellknown linear pseudoBoolean functions called OneMax and BinVal and give additional insights using an experimental study.