Introduction Biological Inspiration The Algorithm Applications Conclusions

ANT COLONY OPTIMIZATION: THE ALGORITHM

AND ITS APPLICATIONS

Muhammad Adil Raja

Roaming Researchers, Inc.July 31, 2014

Introduction Biological Inspiration The Algorithm Applications Conclusions

OUTLINE

1 INTRODUCTION

2 BIOLOGICAL INSPIRATION

3 THE ALGORITHM

4 APPLICATIONS

5 CONCLUSIONS

Introduction Biological Inspiration The Algorithm Applications Conclusions

OUTLINE

1 INTRODUCTION

2 BIOLOGICAL INSPIRATION

3 THE ALGORITHM

4 APPLICATIONS

5 CONCLUSIONS

Introduction Biological Inspiration The Algorithm Applications Conclusions

OUTLINE

1 INTRODUCTION

2 BIOLOGICAL INSPIRATION

3 THE ALGORITHM

4 APPLICATIONS

5 CONCLUSIONS

Introduction Biological Inspiration The Algorithm Applications Conclusions

OUTLINE

1 INTRODUCTION

2 BIOLOGICAL INSPIRATION

3 THE ALGORITHM

4 APPLICATIONS

5 CONCLUSIONS

Introduction Biological Inspiration The Algorithm Applications Conclusions

OUTLINE

1 INTRODUCTION

2 BIOLOGICAL INSPIRATION

3 THE ALGORITHM

4 APPLICATIONS

5 CONCLUSIONS

Introduction Biological Inspiration The Algorithm Applications Conclusions

ANT COLONY OPTIMIZATION

A valuable technique for mathematical optimization.

Takes inspiration from foraging behavior of real antcolonies.

Useful for discrete and continuous optimization problems.

In telecommunications: Routing and load balancing.

Introduction Biological Inspiration The Algorithm Applications Conclusions

BIOLOGICAL INSPIRATION

Inception – early 90’s.

Observation of Ant colonies.

Ants are social insects.

Driven by the goal of community survival rather than beingfocused on survival of the individuals.

Ant’ foraging behavior: How ants can find shortest paths.

Shortest Paths: Between food sources and their nests.

Introduction Biological Inspiration The Algorithm Applications Conclusions

FORAGING BEHAVIOR OF ANTS

When searching for food ants:1 Initially explore the area surrounding their nest in a random

manner.2 Leave a chemical pheromone trail on the ground.3 Ants can smell pheromone.4 While choosing their way, they choose paths with strong

pheromone concentrations with strong probabilities.5 Evaluate the quality and quantity of a food source as soon

as it is found.6 Carry some of it back to the nest.7 The quantity of pheromone that is left on the ground may

depend on the quantity and quality of the food source.8 The pheromone trails guide other ants back to the food

source.

Introduction Biological Inspiration The Algorithm Applications Conclusions

BENEFITS

Indirect communication between ants enables them to findshortest paths between nests and food sources.

Communication happens through pheromone trails.

Stigmergy: The Phenomenon

Enables them to find shortest paths between their nestsand food sources.

Introduction Biological Inspiration The Algorithm Applications Conclusions

THE ALGORITHM

1 Initialize trail.2 Let each ant complete its tour.3 Local trail update (evaporate pheromone).4 Analyze tours.5 Perform a global trail update.6 Go back to step 2 and loop until your stopping criteria is

met.

Introduction Biological Inspiration The Algorithm Applications Conclusions

ROUTING PROBLEMS

One or more agents have to visit a predefined set oflocations.

Objective function depends on the ordering in which thelocations are visited.

Sequential ordering problem.

Vehicle routing problem.

Introduction Biological Inspiration The Algorithm Applications Conclusions

SEQUENTIAL ORDERING PROBLEM

To find a minimum weight Hamiltonian path on a directedgraph with weights on arcs and nodes subject toprecedence constraints.

Introduction Biological Inspiration The Algorithm Applications Conclusions

VEHICLE ROUTING PROBLEM

A central problem in distribution management.

N customers have to be served from one central dept.

The customers are served by a fleet of vehicles of equalcapacity.The goal is to find a set of routes that minimizes the totaltravel time such that:

1 Each customer is served once by exactly one vehicle.2 The route of each vehicle starts and ends at the depot.3 The total demand covered by each vehicle does not exceed

its capacity.

VRP is is an NP-hard problem.

It contains TSP as a subproblem.

Introduction Biological Inspiration The Algorithm Applications Conclusions

ASSIGNMENT PROBLEMS

The task is to assign a set of items to a given number ofresources subject to some constraints.

Items: Objects, activities etc.

Resources: Locations, agents, etc.

Introduction Biological Inspiration The Algorithm Applications Conclusions

QUADRATIC ASSIGNMENT

Can be described as the problem of assigning a set offacilities to a set of locations with given distances betweenlocations and given flows between the facilities.

The goal is to place the facilities on locations in such a waythat the sum of the products between flows and distancesis minimized.

Backboard wiring, campus and hospital layout, typewriterkeyboard design can all be formulated as QAPs.

QAP is an NP-hard optimization problem.

Introduction Biological Inspiration The Algorithm Applications Conclusions

GENERALIZED ASSIGNMENT

A set of tasks has to be assigned to a set of agents in sucha way that a cost function is minimized.

Introduction Biological Inspiration The Algorithm Applications Conclusions

FREQUENCY ASSIGNMENT

We have a set of links, a set of frequencies, and channelseparation constraints.

For each pair of links, channel separation constraints givea minimum distance to be maintained between betweenthe frequencies assigned to the links.

Introduction Biological Inspiration The Algorithm Applications Conclusions

GRAPH COLORING PROBLEMS

Given an undirected graph the goal is to find the minimumnumber of colors to assign to nodes such that no pair ofadjacent nodes is assigned the same color.

Introduction Biological Inspiration The Algorithm Applications Conclusions

UNIVERSITY COURSE TIMETABLING PROBLEMS

Given are a set of time slots, a set of events, a set ofrooms, a set of features, a set of students, and two types ofconstraints; hard and soft constraints.

Hard constraints have to be satisfied by any feasiblesolution.

Soft constraints do not concern the feasibility of a solutionbut determine its quality.

The goal is to assign the events to the time slots and to therooms so that all hard constraints are satisfied

And an objective function, whose value depends on thenumber of violated soft constraints, is optimized.

Introduction Biological Inspiration The Algorithm Applications Conclusions

SCHEDULING PROBLEMS

Scheduling is concerned with the allocation of scarceresources to tasks over time.Scheduling problems are central to production andmanufacturing industries, but also arise in a variety of othersettings.Shop scheduling: where jobs have to processed on one orseveral machines such that some objective function isoptimized.In case jobs have to be processed on more than onemachine, the task to be performed on a machine forcompleting a job is called an operation.It is common for almost all the machine scheduling modelsthat:

1 The processing times of all jobs and operations are fixedand known beforehand.

2 The processing of jobs and operations cannot beinterrupted (scheduling without preemption)

Models:

Introduction Biological Inspiration The Algorithm Applications Conclusions

SUBSET PROBLEMS

A solution to the problem under consideration isrepresented as a subset of the set of available items(components) subject to problem-specific constraints.

Introduction Biological Inspiration The Algorithm Applications Conclusions

APPLICATION OF ACO TO OTHER NP-HARD PROBLEMS

Shortest Common Super-sequence problem.

Bin Packing

2D-HP protein folding.

COnstraint satisfaction.

Introduction Biological Inspiration The Algorithm Applications Conclusions

APPLICATIONS TO MACHINE LEARNING PROBLEMS

Learning of classification rules.

Learning the structure of Bayesian networks.

Introduction Biological Inspiration The Algorithm Applications Conclusions

CONCLUSIONS

A great algorithm.

Bio-inspiration is the key.

Emulation of real ant foraging behavior to artificial antcolonies.

Easy to comprehend.

Many variants.

Many applications.

Problem formulation is the real trick.

Inspiration (reference): Ant Colony Optimization, MarcoDorigo and Thomas Stutzle.