Pheromone mark ant colony optimization with a hybrid node-based pheromone update strategy

Abstract

An improved ant colony optimization (ACO) algorithm called pheromone mark ACO abbreviated PM-ACO is proposed for the non-ergodic optimal problems. PM-ACO associates the pheromone to nodes, and has a pheromone trace of scatter points which are referred to as pheromone marks. PM-ACO has a node-based pheromone update strategy, which includes two other rules except a best-so-far tour rule. One is called r-best-node update rule which updates the pheromones of the best-ranked nodes, which are selected by counting the nodes’ passed ants in each iteration. The other one is called relevant-node depositing rule which updates the pheromones of the k-nearest-neighbor (KNN) nodes of a best-ranked node. Experimental results show that PM-ACO has a pheromone integration effect of some neighbor arcs on their central node, and it can result in instability. The improved PM-ACO has a good performance when applied in the shortest path problem.

Introduction

Ant Colony Optimization (ACO) [1] originating from the foraging behavior of the ant colony is a novel evolutionary algorithm. In reality, the ant individuals have simple behaviors when searching food, allocating tasks, cooperative transport, and so on. At the same time, the ant colonies show a emerged higher intelligence so that they can solve complex problems that in some cases far exceed the individual capabilities. ACO is firstly proposed by Dorigo et al. [2], and has some advantages such as highly parallelism, easy to be understood and implemented and so on. After that, some extensions as well as a number of changes were proposed by the scholars around the world. It has been successfully applied in many optimization problems. Hideki Katagiri introduced the incorporation of tabu search and ant colony optimization for solving k-minimum spanning tree problems (k-MST) [3]. To lower the power consumption in wireless sensor networks, Ho et al. [4] utilized the ladder diffusion phase to construct a route map, and then found a optimal path by ACO. Chen et al. [5] suggested a novel information exchange strategy ACO to get a optimal solution for each processor in a massively parallel processors condition. Sundareswaran and Srinivasarao Nayak [6] designed a feedback controller based on ant colony optimization to implement a closed induction motor starting system. Paplinski [7] proposed an Interpolated Ant Colony Optimization (IACO) for continuous domain optimization, and it was applied in linear dynamic systems identification.

Most of published papers concentrated on the hybridization of different algorithms, and there are seldom papers studying the generalized model of pheromone structure. Pheromone structure is a key module of the ACO, and the basic model of ACO solving problems is to build a path on a construction graph $G=(V,E)$ where the nodes set V corresponds to the elements of a solution for the considered problem and arcs set E corresponds to the connections of the elements [8]. It is droved by some artificial ants, which construct tours on the construction graph and deposit pheromones on the arcs, and eventually achieve the goal of getting an optimal path.