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

Different Applications of the Genetic Mutation Operator for Symetric Travelling Salesman Problem

This paper presents the results of an analysis of three algorithms for the Travelling Salesman Problem (TSP). The basic steps of genetic algorithms (GAs) and their benefits in solving combinatorial optimization problems are also presented. Moreover, several studies related to TPS and some approaches to its solution are discussed. An optimized version of the standard recursive algorithm for solving TSP using the backtracking method is presented. This algorithm is used to generate optimal solutions concerning the studied graphs. In addition, a standard genetic algorithm for solving TSP and its modification are also presented. The modified algorithm uses the genetic operator mutation in a different way. The results show that the recursive algorithm can be used successfully to solve the TSP for graphs with a small number of vertices, for instance, 25-30. The results of the two GAs were different. The modified GA found the optimal solutions for all tested graphs, while the standard GA found the optimal solutions in only 40% of the cases. These results were obtained for a reasonable time (in seconds), with appropriate values of the control parameters - population size and reproduction number. It appeared that the use of the genetic mutation operator yields better results when applied to identical solutions. If pairs of identical solutions are found in a population, then every second must mutate. The methodology and the conditions for conducting the experiments are described in details

The Pheromone-Based Harmony Search Algorithm for the Asymmetric Traveling Salesman Problem

This paper presents a modification of the Harmony Search algorithm (HS) adjusted to an effective solving of instances of the Asymmetric Traveling Salesman Problem. The improvement of the technique spans the application of a pheromone, which, by serving the role of long-term memory, enables the improvement of the quality of determined results, especially for tasks characterized by a significant number of vertices. The publication includes the results of tests that suggest the achievement of effectiveness improvement through the modification of the HS and recommendations concerning the proper configuration of the algorithm

Reactive approach for automating exploration and exploitation in ant colony optimization

Ant colony optimization (ACO) algorithms can be used to solve nondeterministic polynomial hard problems. Exploration and exploitation are the main mechanisms in controlling search within the ACO. Reactive search is an alternative technique to maintain the dynamism of the mechanics. However, ACO-based reactive search technique has three (3) problems. First, the memory model to record previous search regions did not completely transfer the neighborhood structures to the next iteration which leads to arbitrary restart and premature local search. Secondly, the exploration indicator is not robust due to the difference of magnitudes in distance matrices for the current population. Thirdly, the parameter control techniques that utilize exploration indicators in their feedback process do not consider the problem of indicator robustness. A reactive ant colony optimization (RACO) algorithm has been proposed to overcome the limitations of the reactive search. RACO consists of three main components. The first component is a reactive max-min ant system algorithm for recording the neighborhood structures. The second component is a statistical machine learning mechanism named ACOustic to produce a robust exploration indicator. The third component is the ACO-based adaptive parameter selection algorithm to solve the parameterization problem which relies on quality, exploration and unified criteria in assigning rewards to promising parameters. The performance of RACO is evaluated on traveling salesman and quadratic assignment problems and compared with eight metaheuristics techniques in terms of success rate, Wilcoxon signed-rank, Chi-square and relative percentage deviation. Experimental results showed that the performance of RACO is superior than the eight (8) metaheuristics techniques which confirmed that RACO can be used as a new direction for solving optimization problems. RACO can be used in providing a dynamic exploration and exploitation mechanism, setting a parameter value which allows an efficient search, describing the amount of exploration an ACO algorithm performs and detecting stagnation situations

Meta-heuristics development framework: Design and applications

Master'sMASTER OF SCIENC

The adaptation of the harmony search algorithm to the ATSP with the evaluation of the influence of the pitch adjustment place on the quality of results

The paper is an extended version of the conference article, which presents a modification of the Harmony Search algorithm, adapted to the effective resolution of the asymmetric case of the Traveling Salesman Problem. The efficacy of the proposed approach was measured with benchmarking tests and in a comparative study based on the results obtained with the Nearest Neighbor Algorithm, Greedy Local Search and Hill Climbing. The discussion also embraced the study of the convergence of the proposed algorithm and the analysis of the impact of the pitch adjustment place on the quality of the solutions

Hyper‐Heuristics and Metaheuristics for Selected Bio‐Inspired Combinatorial Optimization Problems

Many decision and optimization problems arising in bioinformatics field are time demanding, and several algorithms are designed to solve these problems or to improve their current best solution approach. Modeling and implementing a new heuristic algorithm may be time‐consuming but has strong motivations: on the one hand, even a small improvement of the new solution may be worth the long time spent on the construction of a new method; on the other hand, there are problems for which good‐enough solutions are acceptable which could be achieved at a much lower computational cost. In the first case, specially designed heuristics or metaheuristics are needed, while the latter hyper‐heuristics can be proposed. The paper will describe both approaches in different domain problems

Meta-RaPS Hybridization with Machine Learning Algorithms

This dissertation focuses on advancing the Metaheuristic for Randomized Priority Search algorithm, known as Meta-RaPS, by integrating it with machine learning algorithms. Introducing a new metaheuristic algorithm starts with demonstrating its performance. This is accomplished by using the new algorithm to solve various combinatorial optimization problems in their basic form. The next stage focuses on advancing the new algorithm by strengthening its relatively weaker characteristics. In the third traditional stage, the algorithms are exercised in solving more complex optimization problems. In the case of effective algorithms, the second and third stages can occur in parallel as researchers are eager to employ good algorithms to solve complex problems. The third stage can inadvertently strengthen the original algorithm. The simplicity and effectiveness Meta-RaPS enjoys places it in both second and third research stages concurrently. This dissertation explores strengthening Meta-RaPS by incorporating memory and learning features. The major conceptual frameworks that guided this work are the Adaptive Memory Programming framework (or AMP) and the metaheuristic hybridization taxonomy. The concepts from both frameworks are followed when identifying useful information that Meta-RaPS can collect during execution. Hybridizing Meta-RaPS with machine learning algorithms helped in transforming the collected information into knowledge. The learning concepts selected are supervised and unsupervised learning. The algorithms selected to achieve both types of learning are the Inductive Decision Tree (supervised learning) and Association Rules (unsupervised learning). The objective behind hybridizing Meta-RaPS with an Inductive Decision Tree algorithm is to perform online control for Meta-RaPS\u27 parameters. This Inductive Decision Tree algorithm is used to find favorable parameter values using knowledge gained from previous Meta-RaPS iterations. The values selected are used in future Meta-RaPS iterations. The objective behind hybridizing Meta-RaPS with an Association Rules algorithm is to identify patterns associated with good solutions. These patterns are considered knowledge and are inherited as starting points for in future Meta-RaPS iteration. The performance of the hybrid Meta-RaPS algorithms is demonstrated by solving the capacitated Vehicle Routing Problem with and without time windows