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PDF Artificial Intelligence in Networking: Ant Colony Optimization

Ant Colony Optimization is aimed at doing just that Packet Switching and Circuit Switching There are two different techniques currently used by computers to send information across the global internet circuit switching and packet switching Circuit switching is often compared to a telephone call because it follows the same basic principles

PDF Optimization

The complex social behaviors of ants have been much studied by science and these behavior patterns can provide models for solving difficult combinatorial develop algorithms inspired by one aspect of ant behavior the ability to find what paths has become the field of ant colony optimization (ACO) the most successful technique based on ant behavi

  • What is ant colony optimization?

    Ant Colony Optimization technique is purely inspired from the foraging behaviour of ant colonies, first introduced by Marco Dorigo in the 1990s. Ants are eusocial insects that prefer community survival and sustaining rather than as individual species. They communicate with each other using sound, touch and pheromone.

Marco Dorigo and Thomas Stützle

The complex social behaviors of ants have been much studied by science, and these behavior patterns can provide models for solving difficult combinatorial develop algorithms inspired by one aspect of ant behavior, the ability to find what paths, has become the field of ant colony optimization (ACO), the most successful technique based on ant behavi

1 From Real to Artificial Ants

I am lost Where is the line? —A Bug’s Life, Walt Disney, 1998 Ant colonies, and more generally social insect societies, are distributed systems that, in spite of the simplicity of their individuals, present a highly structured social orga-nization. As a result of this organization, ant colonies can accomplish complex tasks that in some cases far

2 The Ant Colony Optimization Metaheuristic

A metaheuristic refers to a master strategy that guides and modifies other heuristics to produce solutions beyond those that are normally generated in a quest for local optimality. —Tabu Search, Fred Glover and Manuel Laguna, 1998 Combinatorial optimization problems are intriguing because they are often easy to state but very di‰cult to solve. Many

A W

set of constraints. The solutions belonging to the set ~ S S of candidate solutions that satisfy the constraints are called feasible solutions. The goal is to find a glob- W ally optimal feasible solution s . For minimization problems this consists in finding a solution s S ~ with minimum cost, that is, a solution such that f ðs Þ f ðsÞ for all S;

P ðS; ; WÞ,

and a parameter , does a feasible solution s ~ S exist such that f ðsÞ , in case % A % P was a minimization problem? It is clear that solving the search version a of a combi-natorial problem implies being able to give the solution of the corresponding decision problem, while the opposite is not true in general. This means that is at least as P hard

P 1⁄4 N P

ing P 1⁄4 N P implies proving that all problems in N P can be solved in polynomial time. On this subject, a particularly important role is played by polynomial time reduc-tions. Intuitively, a polynomial time reduction is a procedure that transforms a prob-lem into another one by a polynomial time algorithm. The interesting point is that if problem

WðtÞ.

9 In some cases a cost, or the estimate of a cost, Jðx tÞ can be associated with states ; other than candidate solutions. If xj can be obtained by adding solution components to a state xi, then Jðxi; tÞ Jðxj;tÞ. Note that Jðs tÞ gðs tÞ. a ; 1 ; Given this formulation, artificial ants build solutions by performing randomized walks on the completely

h i A

is satisfied, then the ant stops. When an ant builds a can-didate solution, moves to infeasible states are forbidden in most applications, either through the use of the ant’s memory, or via appropriately defined heuristic values h. It selects a move by applying a probabilistic decision rule. The probabilistic 9 deci-sion rule is a function of (1) t

4 Ant Colony Optimization Theory

In theory, there is no di¤erence between theory and practice. But in practice, there is a di¤erence —Author unknown The brief history of the ant colony optimization metaheuristic is mainly a history of experimental research. Trial and error guided all early researchers and still guides most of the ongoing research e¤orts. This is the typical situa

A M 1⁄4

sumption is needed in order to guarantee that the sampling can concentrate in the proximity of any solution, the optimal solution in particular. Additionally, we assume that the model structure is fixed, and that the model space M is parameterized by a vector T Rw, where is a w-dimensional pa- web2.qatar.cmu.edu

5 Ant Colony Optimization for N P-Hard Problems

We shall refer to a problem as intractable if it is so hard that no polynomial time algorithm can possibly solve it. —Computers and Intractability, Michael R. Garey & David S. Johnson, 1979 This chapter gives an overview of selected applications of ACO to di¤erent N P-hard optimization problems. The chapter is intended to serve as a guide to how AC

l k tl1⁄2hl

AN where k N is the feasible neighborhood of ant k before adding component i; N k consists of all columns that cover at least one still uncovered row. An ant has com-pleted a solution when all rows are covered. AS-SCP-HRTB uses essentially the same way of constructing solutions with the only di¤erence that in a first stage an ant adds l randomly ch

W h

component yj; e to ant k’s partial solution e is the partial solution after adding i sk and f ðskÞ is the number of con- web2.qatar.cmu.edu

X t yi; d

h ih yj; e i: yi; d sk h iA This sum gives the desirability of assigning the value e to variable yj. Pheromone update The pheromone update follows the general rules of MMAS with the exception that more than one ant may deposit pheromone. In particular, in MMAS-CSP all iteration-best ants deposit an amount 1 f ðskÞ of pheromone, = favoring in this w

2 ð6 : Þ

In this way, ants adapt their exploration activity to the varying data tra‰c distribution. While traveling toward their destination nodes, the forward ants keep memory of their paths and of the tra‰c conditions found. The identifier of every visited node i and the time elapsed since the launching time to arrive at this i-th node are stored in a mem

x ð0 1

; ; Rþ: ð6 9 : Þ Squashing the r-values allows the system to be more sensitive in rewarding good (high) values of r, while having the tendency to saturate the rewards for bad (near to zero) r-values: the scale is compressed for lower values and expanded in the upper part. In such a way an emphasis is put on good results. 6.3 The Experimental Settin

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