Ant Colony Optimization

Introduction

Original Background concerning natural phenomenon

what is Swarm intelligence？

• Collective system capable of accomplishing difficult tasks in dynamic and varied environments without any external guidance or control and with no central coordination

• Achieving a collective performance which could not normally be achieved by an individual acting alone

• Constituting a natural model particularly suited to distributed problem solving

“Stigmergic?”

Two individuals interact indirectly when one of them modifies the environment and the other responds to the new environment at a later time. This is stigmergy. the ACO is also called with autocatalytic positive

feedback algorithms.

Ant System

The ant system is first introduced by Marco Dorigo in 1992.there are some Inherent features:Inherent parallelism,Stochastic nature,Adaptivity,Use of positive feedback,Autocatalytic in nature.

suppose bi(t)(i=1,2,..,n) represent the number of ant in i city in t time,then m= b1(t)+b(t)+…+bn(t).τij(t) is pheromone function.tabuk is the ant k ‘s tabu list.

AS concrete step described below:

1)In the initial time of algorithm,randomly place m ants to n cities,meanwhile put the current city into frist city of the tabu list.

2)every ant independently select the next city according to the remain number of pheromone and heuristic information,update the tabu list until the all ants finish the first tour.

the probability of ant k transfer from city i to city j in time t.



Jk(i)={1,2,…n}-tabuk represent ant k allowed cities of next step;ηij(t) is a heuristic factor,represent the expectation of ant going from city i to city j.

3）When all ant finish a tour,all paths is updated by below fomula:



ρ(0<ρ<1)evaporation coefficient;△τij(t) represent pheromone’s augment of edge(i,j).

4)if meet the condition of terminate,then cycle end;otherwise,set △τij(t)=0,the go to step 2

Modified algorithms

• Ant Cycle (O(NC.n3)



• Ant Density (Quantity Q)



• Ant Quantity (Quantity Q/dij)



Some inherent advantages:

• Positive Feedback accounts for rapid discovery of good solutions

• Distributed computation avoids premature convergence

• The greedy heuristic helps find acceptable solution in the early solution in the early stages of the search process.

• The collective interaction of a population of agents. Disadvantages in Ant Systems

• Slower convergence than other Heuristics

• Performed poorly for TSP problems larger than 75 cities.

• No centralized processor to guide the AS towards good solutions

ant colony system(ACS)

Strong elitist strategy



Pseudo-random proportional rule





4.MMAS



Code Link:https://github.com/hengfanz/franztao.Algorithm.io/tree/master/Advanced%20Algorithm/src/advancedalgorithm

Reference:

1.PPT of my teacher’s Jiangbin

2.the code is not coded by myself,which is from the website:/article/5856444.html

3.the book:多目标智能优化算法及其应用(雷德明）