Traveling Salesman Problem

The idea behind TSP was conceived by Austrian mathematician Karl Menger in mid 1930s who invited the research community to consider a problem from the everyday life from a mathematical point of view. A traveling salesman has to visit exactly once each one of a list of m cities and then return to the home city. He knows the cost of traveling from any city i to any other city j. Thus, which is the tour of least possible cost the salesman can take? In this book the problem of finding algorithmic technique leading to good/optimal solutions for TSP (or for some other strictly related problems) is considered. TSP is a very attractive problem for the research community because it arises as a natural subproblem in many applications concerning the every day life. Indeed, each application, in which an optimal ordering of a number of items has to be chosen in a way that the total cost of a solution is determined by adding up the costs arising from two successively items, can be modelled as a TSP instance. Thus, studying TSP can never be considered as an abstract research with no real importance

Hybrid ant colony system algorithm for static and dynamic job scheduling in grid computing

Grid computing is a distributed system with heterogeneous infrastructures. Resource management system (RMS) is one of the most important components which has great influence on the grid computing performance. The main part of RMS is the scheduler algorithm which has the responsibility to map submitted tasks to available resources. The complexity of scheduling problem is considered as a nondeterministic polynomial complete (NP-complete) problem and therefore, an intelligent algorithm is required to achieve better scheduling solution. One of the prominent intelligent algorithms is ant colony system (ACS) which is implemented widely to solve various types of scheduling problems. However, ACS suffers from stagnation problem in medium and large size grid computing system. ACS is based on exploitation and exploration mechanisms where the exploitation is sufficient but the exploration has a deficiency. The exploration in ACS is based on a random approach without any strategy. This study proposed four hybrid algorithms between ACS, Genetic Algorithm (GA), and Tabu Search (TS) algorithms to enhance the ACS performance. The algorithms are ACS(GA), ACS+GA, ACS(TS), and ACS+TS. These proposed hybrid algorithms will enhance ACS in terms of exploration mechanism and solution refinement by implementing low and high levels hybridization of ACS, GA, and TS algorithms. The proposed algorithms were evaluated against twelve metaheuristic algorithms in static (expected time to compute model) and dynamic (distribution pattern) grid computing environments. A simulator called ExSim was developed to mimic the static and dynamic nature of the grid computing. Experimental results show that the proposed algorithms outperform ACS in terms of best makespan values. Performance of ACS(GA), ACS+GA, ACS(TS), and ACS+TS are better than ACS by 0.35%, 2.03%, 4.65% and 6.99% respectively for static environment. For dynamic environment, performance of ACS(GA), ACS+GA, ACS+TS, and ACS(TS) are better than ACS by 0.01%, 0.56%, 1.16%, and 1.26% respectively. The proposed algorithms can be used to schedule tasks in grid computing with better performance in terms of makespan

Heterogeneous Ant Colony Optimisation Methods and their Application to the Travelling Salesman and PCB Drilling Problems

Ant Colony Optimization (ACO) is an optimization algorithm that is inspired by the foraging behaviour of real ants in locating and transporting food source to their nest. It is designed as a population-based metaheuristic and have been successfully implemented on various NP-hard problems such as the well-known Traveling Salesman Problem (TSP), Vehicle Routing Problem (VRP) and many more. However, majority of the studies in ACO focused on homogeneous artificial ants although animal behaviour researchers suggest that real ants exhibit heterogeneous behaviour thus improving the overall efficiency of the ant colonies. Equally important is that most, if not all, optimization algorithms require proper parameter tuning to achieve optimal performance. However, it is well-known that parameters are problem-dependant as different problems or even different instances have different optimal parameter settings. Parameter tuning through the testing of parameter combinations is a computationally expensive procedure that is infeasible on large-scale real-world problems. One method to mitigate this is to introduce heterogeneity by initializing the artificial agents with individual parameters rather than colony level parameters. This allows the algorithm to either actively or passively discover good parameter settings during the search. The approach undertaken in this study is to randomly initialize the ants from both uniform and Gaussian distribution respectively within a predefined range of values. The approach taken in this study is one of biological plausibility for ants with similar roles, but differing behavioural traits, which are being drawn from a mathematical distribution. This study also introduces an adaptive approach to the heterogeneous ant colony population that evolves the alpha and beta controlling parameters for ACO to locate near-optimal solutions. The adaptive approach is able to modify the exploitation and exploration characteristics of the algorithm during the search to reflect the dynamic nature of search. An empirical analysis of the proposed algorithm tested on a range of Travelling Salesman Problem (TSP) instances shows that the approach has better algorithmic performance when compared against state-of-the-art algorithms from the literature