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

Towards a multilevel ant colony optimization

Masteroppgave i Informasjons- og kommunikasjonsteknologi IKT590 Universitetet i Agder 2014Ant colony optimization is a metaheuristic approach for solving combinatorial optimization problems which belongs to swarm intelligence techniques. Ant colony optimization algorithms are one of the most successful strands of swarm intelligence which has already shown very good performance in many combinatorial problems and for some real applications. This thesis introduces a new multilevel approach for ant colony optimization to solve the NP-hard problems shortest path and traveling salesman. We have reviewed different elements of multilevel algorithm which helped us in construction of our proposed multilevel ant colony optimization solution. We for comparison purposes implemented our own multi-threaded variant Dijkstra for solving shortest path to compare it with single level and multilevel ant colony optimization and reviewed different techniques such as genetic algorithms and Dijkstra’s algorithm. Our proposed multilevel ant colony optimization was developed based on the single level ant colony optimization which we both implemented. We have applied the novel multilevel ant colony optimization to solve the shortest path and traveling salesman problem. We show that the multilevel variant of ant colony optimization outperforms single level. The experimental results conducted demonstrate the overall performance of multilevel in comparison to the single level ant colony optimization, displaying a vast improvement when employing a multilevel approach in contrast to the classical single level approach. These results gave us a better understanding of the problems and provide indications for further research

Evolutionary Computation and QSAR Research

[Abstract] The successful high throughput screening of molecule libraries for a specific biological property is one of the main improvements in drug discovery. The virtual molecular filtering and screening relies greatly on quantitative structure-activity relationship (QSAR) analysis, a mathematical model that correlates the activity of a molecule with molecular descriptors. QSAR models have the potential to reduce the costly failure of drug candidates in advanced (clinical) stages by filtering combinatorial libraries, eliminating candidates with a predicted toxic effect and poor pharmacokinetic profiles, and reducing the number of experiments. To obtain a predictive and reliable QSAR model, scientists use methods from various fields such as molecular modeling, pattern recognition, machine learning or artificial intelligence. QSAR modeling relies on three main steps: molecular structure codification into molecular descriptors, selection of relevant variables in the context of the analyzed activity, and search of the optimal mathematical model that correlates the molecular descriptors with a specific activity. Since a variety of techniques from statistics and artificial intelligence can aid variable selection and model building steps, this review focuses on the evolutionary computation methods supporting these tasks. Thus, this review explains the basic of the genetic algorithms and genetic programming as evolutionary computation approaches, the selection methods for high-dimensional data in QSAR, the methods to build QSAR models, the current evolutionary feature selection methods and applications in QSAR and the future trend on the joint or multi-task feature selection methods.Instituto de Salud Carlos III, PIO52048Instituto de Salud Carlos III, RD07/0067/0005Ministerio de Industria, Comercio y Turismo; TSI-020110-2009-53)Galicia. Consellería de Economía e Industria; 10SIN105004P

Mining Aircraft Telemetry Data With Evolutionary Algorithms

The Ganged Phased Array Radar - Risk Mitigation System (GPAR-RMS) was a mobile ground-based sense-and-avoid system for Unmanned Aircraft System (UAS) operations developed by the University of North Dakota. GPAR-RMS detected proximate aircraft with various sensor systems, including a 2D radar and an Automatic Dependent Surveillance - Broadcast (ADS-B) receiver. Information about those aircraft was then displayed to UAS operators via visualization software developed by the University of North Dakota. The Risk Mitigation (RM) subsystem for GPAR-RMS was designed to estimate the current risk of midair collision, between the Unmanned Aircraft (UA) and a General Aviation (GA) aircraft flying under Visual Flight Rules (VFR) in the surrounding airspace, for UAS operations in Class E airspace (i.e. below 18,000 feet MSL). However, accurate probabilistic models for the behavior of pilots of GA aircraft flying under VFR in Class E airspace were needed before the RM subsystem could be implemented. In this dissertation the author presents the results of data mining an aircraft telemetry data set from a consecutive nine month period in 2011. This aircraft telemetry data set consisted of Flight Data Monitoring (FDM) data obtained from Garmin G1000 devices onboard every Cessna 172 in the University of North Dakota\u27s training fleet. Data from aircraft which were potentially within the controlled airspace surrounding controlled airports were excluded. Also, GA aircraft in the FDM data flying in Class E airspace were assumed to be flying under VFR, which is usually a valid assumption. Complex subpaths were discovered from the aircraft telemetry data set using a novel application of an ant colony algorithm. Then, probabilistic models were data mined from those subpaths using extensions of the Genetic K-Means (GKA) and Expectation- Maximization (EM) algorithms. The results obtained from the subpath discovery and data mining suggest a pilot flying a GA aircraft near to an uncontrolled airport will perform different maneuvers than a pilot flying a GA aircraft far from an uncontrolled airport, irrespective of the altitude of the GA aircraft. However, since only aircraft telemetry data from the University of North Dakota\u27s training fleet were data mined, these results are not likely to be applicable to GA aircraft operating in a non-training environment

Feature Selection for Classification with Artificial Bee Colony Programming

Feature selection and classification are the most applied machine learning processes. In the feature selection, it is aimed to find useful properties containing class information by eliminating noisy and unnecessary features in the data sets and facilitating the classifiers. Classification is used to distribute data among the various classes defined on the resulting feature set. In this chapter, artificial bee colony programming (ABCP) is proposed and applied to feature selection for classification problems on four different data sets. The best models are obtained by using the sensitivity fitness function defined according to the total number of classes in the data sets and are compared with the models obtained by genetic programming (GP). The results of the experiments show that the proposed technique is accurate and efficient when compared with GP in terms of critical features selection and classification accuracy on well-known benchmark problems

Preventing premature convergence and proving the optimality in evolutionary algorithms

http://ea2013.inria.fr//proceedings.pdfInternational audienceEvolutionary Algorithms (EA) usually carry out an efficient exploration of the search-space, but get often trapped in local minima and do not prove the optimality of the solution. Interval-based techniques, on the other hand, yield a numerical proof of optimality of the solution. However, they may fail to converge within a reasonable time due to their inability to quickly compute a good approximation of the global minimum and their exponential complexity. The contribution of this paper is a hybrid algorithm called Charibde in which a particular EA, Differential Evolution, cooperates with a Branch and Bound algorithm endowed with interval propagation techniques. It prevents premature convergence toward local optima and outperforms both deterministic and stochastic existing approaches. We demonstrate its efficiency on a benchmark of highly multimodal problems, for which we provide previously unknown global minima and certification of optimality

A Hybrid Lehmer Code Genetic Algorithm and Its Application on Traveling Salesman Problems

Traveling Salesman Problems (TSP) is a widely studied combinatorial optimization problem. The goal of the TSP is to find a tour which begins in a specific city, visits each of the remaining cities once and returns to the initial cities such that the objective functions are optimized, typically involving minimizing functions like total distance traveled, total time used or total cost. Genetic algorithms were first proposed by John Holland (1975). It uses an iterative procedure to find the optimal solutions to optimization problems. This research proposed a hybrid Lehmer code Genetic Algorithm. To compensate for the weaknesses of traditional genetic algorithms in exploitation while not hampering its ability in exploration, this new genetic algorithm will combine genetic algorithm with 2-opt and non-sequential 3-opt heuristics. By using Lehmer code representation, the solutions created by crossover parent solutions are always feasible. The new algorithm was used to solve single objective and multi-objectives Traveling Salesman Problems. A non Pareto-based technique will be used to solve multi-objective TSPs. Specifically we will use the Target Vector Approach. In this research, we used the weighted Tchebycheff function with the ideal points as the reference points as the objective function to evaluate solutions, while the local search heuristics, the 2-opt and non-sequential 3-opt heuristics, were guided by a weighted sum function