Coordination of Pheromone Deposition Might Solve Time-Constrained Travelling Salesman Problem

Ikuo Arizono,Tomoko Sakiyama

doi:10.1155/2018/6498218

Abstract

In this study, we develop two Ant Colony Optimization (ACO) models as new metaheuristic models for solving the time-constrained Travelling Salesman Problem (TSP). Here, the time-constrained TSP means a TSP in which several cities have constraints that the agents have to visit within prescribed time limits. In our ACO models, only agents that achieved tour under certain conditions defined in respective ACO models are allowed to modulate pheromone deposition. The agents in one model are allowed to deposit pheromone only if they achieve a tour satisfying strictly the above purpose. The agents in the other model is allowed to deposit pheromone not only if they achieve a tour satisfying strictly the above purpose, but also if they achieve a tour satisfying the above purpose in some degree. We compare performance of two developed ACO models by focusing on pheromone deposition. We confirm that the later model performs well to some TSP benchmark datasets from TSPLIB in comparison to the former and the traditional AS (Ant System) models. Furthermore, the agent exhibits critical properties; i.e., the system exhibits complex behaviors. These results suggest that the agents perform adaptive travels by coordinating some complex pheromone depositions.

Highlights

We found that the tolerant Ant Colony Optimization (ACO) model performed better than other two models
We developed the ACO models to deal with the time-constrained Travelling Salesman Problem (TSP)
The one was the strict ACO model in which the agents deposited pheromone if and only if agents found a tour that all the time-constrained cities were visited within limited time duration and that tour was better than any tours individuals achieved until

Summary

Introduction

The time-dependent/constrained TSP is widely studied as an important problem because, in natural conditions, the cost between any two cities can be varied based on the time evolutions [8, 9]. As a swarm intelligent system, artificial ants must make a decision individually using limited local information To this end, we propose ACO models for the timeconstrained TSP in which individual agents judge whether or not they deposit pheromones after each tour. Ants might coordinate the deposition of pheromones With reference to this feature, we construct the second ACO model in which agents deposit pheromones positively when they finish a tour by visiting not all cities with time constraints but some cities within a specified period of time. We found the “upregulated pheromone” in the second ACO model could serve as a key in order to find better solutions

Materials & Methods

Results

Discussion