Scientific Programming

Volume 2016, Article ID 5136327, 12 pages

http://dx.doi.org/10.1155/2016/5136327

## AntStar: Enhancing Optimization Problems by Integrating an Ant System and Algorithm

College of Computer and Information Sciences (CCIS), King Saud University, P.O. Box 5117, Riyadh 11543, Saudi Arabia

Received 13 September 2015; Revised 17 December 2015; Accepted 24 December 2015

Academic Editor: Stéphane Caro

Copyright © 2016 Mohammed Faisal et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Recently, nature-inspired techniques have become valuable to many intelligent systems in different fields of technology and science. Among these techniques, Ant Systems (AS) have become a valuable technique for intelligent systems in different fields. AS is a computational system inspired by the foraging behavior of ants and intended to solve practical optimization problems. In this paper, we introduce the AntStar algorithm, which is swarm intelligence based. AntStar enhances the optimization and performance of an AS by integrating the AS and algorithm. Applying the AntStar algorithm to the single-source shortest-path problem has been done to ensure the efficiency of the proposed AntStar algorithm. The experimental result of the proposed algorithm illustrated the robustness and accuracy of the AntStar algorithm.

#### 1. Introduction

Natural swarms have inspired swarm intelligence. Many algorithms and techniques based on swarm intelligence have been developed to solve optimization problems, such as the Ant System (AS) [1, 2], particle swarm optimization (PSO) [3], artificial bee colony (ABC) [4, 5], Firefly Algorithm (FA) [6], and Intelligent Water Drops (IWD) [7, 8]. Dorigo et al. introduced the AS in the 1990s [1, 2]. AS is an optimization algorithm inspired by the foraging behavior of natural ant colonies. In nature, during foraging, ants manage to establish the shortest paths from their nests to food sources by depositing pheromones on the ground as they move. AS uses this same idea. Kennedy introduced PSO, which is inspired by the swarm of bird and fish schools [3] and which simulates the behaviors of bird flocking. ABC was introduced by Karaboga in 2005 [4, 5]. ABC tries to simulate the natural food foraging behavior of real honeybees, as broken into three groups: employed bees, scouts, and onlookers. In ABC, employed bees go to food sources to determine the amount of nectar present there. Next, ABC calculates the probability value of the food sources. The onlooker selects the preferred sources. The scouts are sent to search areas to discover new food sources. The Firefly Algorithm, introduced by Yang in 2009, was inspired by the flashing (flight) behavior of insects [6]. Shah-Hosseini proposed the IWD algorithm in 2007 [7, 8], trying to simulate natural river systems and the interaction between water drops and their environment. During movement, IWD velocity is increased nonlinearly, proportional to the inverse of the soil between the two locations. Soil in IWD is increased by removing some soil from the path between the two locations. This increase is inversely proportional to the time that IWD needs to pass from its current location to the next location. This time, in turn, is proportional to the velocity of the IWD and inversely proportional to the distance between the two locations. Many swarm intelligence systems have been used for path-planning problems. The advantages of such systems include the possibility to add expert knowledge to the search operation and the ability to work with several candidate solutions simultaneously rather than only exploring a single alternative. Głąbowski et al. used Ant Colony Optimization (ACO) to solve the shortest-path problem [9]. Hsiao et al. used ACO to search for the best path of a map [10]. Tan et al. used ACO for real-time planning of the globally optimal path for mobile robots [11]. Montiel et al. solved the path-planning problem of mobile robots using the Bacterial Potential Field (BPF) approach [12]. Contreras-Cruz et al. solved the mobile robot path-planning problem by combining an artificial bee colony algorithm as a local search procedure with an evolutionary programming algorithm that refines the feasible path found by the set of local procedures [13]. Mo and Xu combined biogeography-based optimization (BBO), PSO, and an Approximate Voronoi Boundary Network (AVBN) to plan the global path of mobile robots in a static environment [14]. Many swarm intelligence algorithms, such as AS, ACO, ABC, and FA, have been used to solve path-planning problems in the field of robotics [15]. In this paper, we propose AntStar, a technique based on swarm intelligence. AntStar enhances the performance of AS by inserting an evaluation function, the [16] algorithm, into the transition probability function of AS. This guides the random movements of ants in order that they perform an admissible search from the first iteration. Therefore, AntStar reaches a suboptimal solution early.

This paper is organized as follows. In Section 2, background is presented. The AntStar algorithm is explained in Section 3. Section 4 explains the application of the AntStar algorithm. The application of AntStar to a single-source, shortest-path problem is presented in Section 5; Section 6 explains the experiments with and performance of AntStar. Applying the AS to a single-source, shortest-path problem is presented in Section 7 in order to compare AntStar with AS in Section 8. Section 9 presents the discussion, and the conclusion is given in Section 10.

#### 2. Background

The proposed AntStar algorithm integrates AS and the algorithm. Therefore, this section discusses, as follows, the Natural Ant System, the Artificial Ant System, and the algorithm.

##### 2.1. Natural Ant System

In nature, ants work in colonies that differ in size. The main work of ants is to forage for food. Many researchers have studied ant behavior [1, 17–19]. Understanding the foraging behavior of natural ant colonies was one of the main problems studied by ethologists. Ants have trail-laying and trail-following behavior when foraging [20]. During foraging, ants manage to establish the shortest paths from their nests to food sources and then return. This is done by laying communications media (chemical substances called pheromones) in varying quantities on the ground, used for communication between individuals. Each ant lays information (pheromones) regarding their paths and decides where to go according to these pheromone trails. The foraging behavior of the natural ant can be described as follows:(1)At first, ants move randomly and lay down pheromone on the ground.(2)If a food source is discovered, the ants return to the nest and lay down a pheromone trail.(3)If a pheromone is discovered during movement, the probability of following the pheromone trail will increase.(4)If an ant reaches the nest, it goes again to search for a food source.

The collective behavior of ants is* autocatalytic*: the more the ants follow a trail, the more the trail becomes attractive to follow [21]. This operation can be characterized as positive feedback, where the probability of choosing a path increases with the number of ants that have before chosen the same path [21]. Consider Figure 1(a) [21]. The ants walk from nest A to food source E. The path the ants followed when free of obstacles is in Figure 1(a). Unexpectedly, an obstacle appears in the path, breaking it off, as in Figure 1(b). Thus, the ants at place B (ants walking from nest A to food source E) or at place D (ants walking from food source E to nest A in the opposite direction) must decide whether to go left or right. This decision is influenced by the degree of pheromones left by the preceding ants.