A Study of Parallel Approaches in MOACOs for Solving the

Bicriteria TSPA.M. Mora, J.J. Merelo, P.A. Castillo,

M.G. Arenas, P. García-Sánchez, J.L.J. LaredoDepartamento de Arquitectura y Tecnología de Computadores.

UNIVERSIDAD DE GRANADA

International Work-Conference on Artificial Neural Networks

INDEX

Ant Colony Optimization

Multi-Objective Problems

Bicriteria TSP

Parallelization

Experiments and Results

Conclusions and Future Work

Metaheuristic inspired in the behaviour of ants when search for food

They ‘build’ (after some time) the shortest paths between the nest and the food sources

They communicate using the environment Depositing and following pheromone

Ant Colony Optimization (I)BIO-INSPIRATION

Pheromone trail

?

Ant Colony Optimization (II)CHOOSING A PATH

Ant Colony Optimization (III)MAIN FEATURES

A set of independent artificial agents They move in graphs searching for solutions They use a pheromone matrix to decide

where to move In addition, they consider heuristic functions

to build the solutions

Multi-Objective ProblemsDEFINITION

There are some functions to optimise One solution must satisfy some criteria Dominance concept:

one solution dominates another one, if it has a better cost in one of the objectives and at least the same cost in the others

There is a set of solutions, the Pareto Set

Bicriteria TSPTHE PROBLEM

Search for the Hamiltonian circuit which minimizes the cost of the edges to go through (distance)

There is a MO-TSP, which has associated some costs to each edge

The Bicriteria TSP considered two costs

Parallelization (I)AIM

Two profits:• Yield better results• Improve the running time

Two Schemes (at colony level):• Space specialized

colonies• Objective specialized

colonies

Parallelization (II)APPROACHES

BIANT (by Iredi et al.)• It is an Ant System• Two pheromone matrices• Two heuristic functions• parameter to weight the objectives

MOACS (by Gambardella and Barán et al.)• It is an Ant Colony System• One pheromone matrix• Two heuristic and costs functions• parameter to weight the objectives

Bi-criteria KROA-100 Problem. 16 processors

Experiments and Results (I)BIANT

Bi-criteria KROA-100 Problem. 16 processors

Experiments and Results (II)MOACS

Bi-criteria KROA-100 Problem. 11 processors

Experiments and Results (III)MOACS (Pareto Set comparisons)

Solutions in each one of the processors

Global Pareto Set

Bi-criteria KROA-100 Problem. 16 processors

Experiments and Results (IV)Non-dominated solutions

Number of non-dominated solutions in the

global Pareto Set

Bi-criteria KROA-100 Problem. 16 processors

Experiments and Results (V)Running Time

Scalability graph

Two well-known MOACOs have been implemented in a parallel shape. Two different searching schemes have been applied (SSC and OSC). Improving in the sets of solutions. Improving in the running time.

Implement a heterogeneous scheme Test other instances and problems Implement an ant-level parallelization Use a higher number of processors

Conclusions and Future Work

Thank You!

The End