Ant Colony Optimization-2

8/22/2019 Ant Colony Optimization-2

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Ant Colony Optimization

Optimisation Methods


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Overview


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ACO Concept

Ants (blind) navigate from nest tofood source

Shortest path is discovered viapheromone trails

each ant moves at random

pheromone is deposited on path

ants detect lead ants path, inclined to

follow more pheromone on path increases

probability of path being followed


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ACO System

Virtual trail accumulated on pathsegments

Starting node selected at random

Path selected at random

based on amount of trail present on possiblepaths from starting node

higher probability for paths with more trail

Ant reaches next node, selects next path

Continues until reaches starting node

Finished tour is a solution


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ACO System, cont.

A completed tour is analyzed for optimality Trail amount adjusted to favor better

solutions better solutions receive more trail

worse solutions receive less trail

higher probability of ant selecting path that ispart of a better-performing tour

New cycle is performed

Repeated until most ants select the same

tour on every cycle (convergence tosolution)


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ACO System, cont.

Often applied to TSP (Travelling SalesmanProblem): shortest path betweenn nodes

Algorithm in Pseudocode: InitializeTrail

Do While(Stopping Criteria Not Satisfied) Cycle

Loop Do Until(Each Ant Completes a Tour) Tour

Loop

Local Trail Update

End Do

Analyze Tours

Global Trail Update

End Do


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Background

Discrete optimization problemsdifficult to solve

Soft computing techniquesdeveloped in past ten years:

Genetic algorithms (GAs)

based on natural selection and genetics

Ant Colony Optimization (ACO)

modeling ant colony behavior


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Background, cont.

Developed by Marco Dorigo (Milan,Italy), and others in early 1990s

Some common applications: Quadratic assignment problems

Scheduling problems Dynamic routing problems in networks

Theoretical analysis difficult algorithm is based on a series of random

decisions (by artificial ants) probability of decisions changes on each

iteration


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Implementation


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Ant Algorithms


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Ant Algorithms


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Implementation

Can be used for both Static andDynamic Combinatorial optimizationproblems

Convergence is guaranteed, althoughthe speed is unknown

Value

Solution


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The Algorithm

Ant Colony Algorithms are typicallyuse to solve minimum cost problems.

We may usually have N nodes andAundirected arcs

There are two working modes for theants: either forwards or backwards.

Pheromones are only deposited in

backward mode.


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The Algorithm

The ants memory allows them toretrace the path it has followed whilesearching for the destination node

Before moving backward on theirmemorized path, they eliminate anyloops from it. While movingbackwards, the ants leave

pheromones on the arcs theytraversed.


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The Algorithm

The ants evaluate the cost of thepaths they have traversed.

The shorter paths will receive agreater deposit of pheromones. Anevaporation rule will be tied with thepheromones, which will reduce thechance for poor quality solutions.


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The Algorithm

At the beginning of the searchprocess, a constant amount ofpheromone is assigned to all arcs.When located at a node i an ant k

uses the pheromone trail to computethe probability of choosingjas thenext node:

where is the neighborhood of ant kwhen in node i.

0

ki

ij k

ikilij l N

k

i

if j N p

if j N

k

iN


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The Algorithm

When the arc (i,j) is traversed , thepheromone value changes as follows:

By using this rule, the probabilityincreases that forthcoming ants willuse this arc.

k

ij ij


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The Algorithm

After each ant khas moved to thenext node, the pheromonesevaporate by the following equationto all the arcs:

where is a parameter. Aniteration is a completer cycleinvolving ants movement,pheromone evaporation, andpheromone deposit.

(1 ) , ( , )ij ijp i j A

(0,1]p


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Steps for Solving a Problem by ACO

1. Represent the problem in the form of sets ofcomponents and transitions, or by a set of weightedgraphs, on which ants can build solutions

2. Define the meaning of the pheromone trails3. Define the heuristic preference for the ant while

constructing a solution4. If possible implement a efficient local searchalgorithm for the problem to be solved.

5. Choose a specific ACO algorithm and apply toproblem being solved

6. Tune the parameter of the ACO algorithm.


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Applications

Efficiently Solves NP hard Problems Routing

TSP (Traveling Salesman Problem)

Vehicle Routing

Sequential Ordering Assignment

QAP (Quadratic Assignment Problem)

Graph Coloring

Generalized Assignment Frequency Assignment

University Course Time Scheduling

43

52

1


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Applications

Scheduling

Job Shop Open Shop Flow Shop Total tardiness (weighted/non-weighted) Project Scheduling

Group Shop Subset

Multi-Knapsack Max Independent Set Redundancy Allocation

Set Covering Weight Constrained Graph Tree partition Arc-weighted L cardinality tree Maximum Clique


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Applications

Other

Shortest Common Sequence

Constraint Satisfaction

2D-HP protein folding

Bin Packing

Machine Learning Classification Rules

Bayesian networks

Fuzzy systems

Network Routing

Connection oriented network routing

Connection network routing

Optical network routing


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Advantages andDisadvantages


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Advantages and Disadvantages

For TSPs (Traveling Salesman Problem), relatively efficient

for a small number of nodes, TSPs can be solved byexhaustive search

for a large number of nodes, TSPs are verycomputationally difficult to solve (NP-hard) exponential time to convergence

Performs better against other global optimizationtechniques for TSP (neural net, genetic algorithms,simulated annealing)

Compared to GAs (Genetic Algorithms):

retains memory of entire colony instead of previous

generation only less affected by poor initial solutions (due to

combination of random path selection and colonymemory)


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Advantages and Disadvantages, cont.

Can be used in dynamic applications(adapts to changes such as new distances,etc.)

Has been applied to a wide variety ofapplications

As with GAs, good choice for constrained

discrete problems (not a gradient-basedalgorithm)


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Theoretical analysis is difficult: Due to sequences of random decisions

(not independent)

Probability distribution changes by

iteration Research is experimental rather than

theoretical

Convergence is guaranteed, but time toconvergence uncertain


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Tradeoffs in evaluating convergence: In NP-hard problems, need high-quality

solutions quickly focus is on quality ofsolutions

In dynamic network routing problems, needsolutions for changing conditions focus is

on effective evaluation of alternative paths

Coding is somewhat complicated, notstraightforward

Pheromone trail additions/deletions, globalupdates and local updates Large number of different ACO algorithms to

exploit different problem characteristics

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Ant Colony Optimization-2