Opposition-based learning (OBL) was recently proposed to extend di erent machine learning algorithms. The main idea of OBL is to consider opposite estimates, actions or states as an attempt to increase the coverage of the solution space and to reduce exploration time. OBL has already been applied to reinforcement learning, neural networks and genetic algorithms. This thesis explores the application of OBL to ant algorithms. Ant algorithms are based on the trail laying and following behaviour of ants. They have been successfully applied to many complex optimization problems. However, like any other technique, they can benefit from performance improvements. Thus, this work was motivated by the idea of developing more complex pheromone and path selection behaviour for the algorithm using the concept of opposition. This work proposes opposition-based extensions to the construction and update phases of the ant algorithm. The modifications that focus on the solution construction include three direct and two indirect methods. The three direct methods work by pairing the ants and synchronizing their path selection. The two other approaches modify the decisions of the ants by using opposite-pheromone content. The extension of the update phase lead to an approach that performs additional pheromone updates using opposite decisions. Experimental validation was done using two versions of the ant algorithm: the Ant System and the Ant Colony System. The di erent OBL extensions were applied to the Travelling Salesman Problem (TSP) and to the Grid World Problem (GWP). Results demonstrate that the concept of opposition is not easily applied to the ant algorithm. One pheromone-based method showed performance improvements that were statistically significant for the TSP. The quality of the solutions increased and more optimal solutions were found. The extension to the update phase showed some improvements for the TSP and led to accuracy improvements and a significant speed-up for the GWP. The other extensions showed no clear improvement. The proposed methods for applying opposition to the ant algorithm have potential, but more investigations are required before ant colony optimization can fully benefit from opposition. Most importantly, fundamental theoretical work with graphs, specifically, clearly defining opposite paths or opposite path components, is needed. Overall, the results indicate that OBL ideas can be beneficial for ant algorithms.

Ant algorithms have been used for a variety of combinatorial optimization problems. One of these problems, where ant algorithms haven't been used, is the design of transition rules for cellular automata (CA). Which is a problem that this master's thesis is focused on. This work begins with an introduction into ant algorithms and a overview of its applications, followed by an introduction into CA. In the next part the author proposes a way how to encode rules of CA into a graph which is used in ant algorithms. The last part of this thesis contains an application of encoded graph on elitist ant system and MAX-MIN ant system. This is followed by experimental results of creating transition rules for CA problems by these algorithms.

The Vehicle Routing Problem has been around for more than 50 years and has been of major interest to the operations research community. The VRP pose a complex problem with major benefits for the industry. In every supply chain transportation occurs between customers and suppliers. In this thesis, we analyze the use of a multiple pheromone trial in using Ant Systems to solve the VRP. The goal is to find a reasonable solution for data environments of derivatives of the basic VRP. An adaptive object model approach is followed to allow for additional constraints and customizable cost functions. A parallel method is used to improve speed and traversing the solution space. The Ant System is applied to the local search operations as well as the data objects. The Tabu Search method is used in the local search part of the solution. The study succeeds in allowing for all of the key performance indicators, i.e. efficiency, effectiveness, alignment, agility and integration for an IT system, where the traditional research on a VRP algorithm only focuses on the first two. / Thesis (PhD)--University of Pretoria, 2010. / Industrial and Systems Engineering / unrestricted

Ant Colony Optimization (ACO) algorithms have been successful in solving a wide variety of NPhard optimization problems. The Traveling Salesman Problem (TSP) has served as a benchmarking problem for many novel ACO algorithms. The slightly harder Dynamic Traveling Salesman Problem (DTSP) is more realistic in the sense that real-time changes happen in the graph belonging to a TSP instance. This thesis studied the original ACO algorithm: the Ant System, and how the amount of pheromone deposited by the ants within the algorithm affected the performance when solving both TSP and DTSP problems. Additionally, 2-opt local search was added to the algorithm, to see how it impacted the performance. We found that when the ants deposited a greater amount of pheromone, the performance for TSP increased, while the performance for DTSP decreased. We concluded that the Ant System in its original form is unsuitable for solving the DTSP. 2-opt local search improved the performance in all instances. / Ant Colony Optimization-algoritmer (ACO) har visat sig vara bra på att lösa många olika NP-svåra optimeringsproblem. För att mäta prestandan för nya ACO-algoritmer har i många fall Handelsresandeproblemet (eng. TSP) använts. Den dynamiska varianten av TSP (eng. DTSP), är ett något svårare problem då förändringar i grafen kan ske i realtid. Denna uppsats utredde hur olika mängder feromon som avges av myrorna inuti algoritmen Ant System, påverkade prestandan för både TSPoch DTSP-instanser. Utöver detta studerades hur den lokala sökningsheuristiken 2-opt påverkade prestandan. Resultaten visade att om myrorna tilläts släppa mer feromoner, ökade prestantan för TSP, men minskade för DTSP. Därav drog vi slutsatsen att algoritmen Ant System i sin ursprungliga form ej är lämplig för att lösa DTSP. Den lokala söknigsheuristiken 2-opt förbättrade prestandan i alla tester.

In this work, we present a way to extend Ant Colony Optimization (ACO), so that it can be applied to both continuous and mixed-variable optimization problems. We demonstrate, first, how ACO may be extended to continuous domains. We describe the algorithm proposed, discuss the different design decisions made, and we position it among other metaheuristics.<p>Following this, we present the results of numerous simulations and testing. We compare the results obtained by the proposed algorithm on typical benchmark problems with those obtained by other methods used for tackling continuous optimization problems in the literature. Finally, we investigate how our algorithm performs on a real-world problem coming from the medical field—we use our algorithm for training neural network used for pattern classification in disease recognition.<p>Following an extensive analysis of the performance of ACO extended to continuous domains, we present how it may be further adapted to handle both continuous and discrete variables simultaneously. We thus introduce the first native mixed-variable version of an ACO algorithm. Then, we analyze and compare the performance of both continuous and mixed-variable<p>ACO algorithms on different benchmark problems from the literature. Through the research performed, we gain some insight into the relationship between the formulation of mixed-variable problems, and the best methods to tackle them. Furthermore, we demonstrate that the performance of ACO on various real-world mixed-variable optimization problems coming from the mechanical engineering field is comparable to the state of the art. / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished

The multiple constant multiplication (MCM) operation is a fundamental operation in digital signal processing (DSP) and digital image processing (DIP). Examples of the MCM are in finite impulse response (FIR) and infinite impulse response (IIR) filters, matrix multiplication, and transforms. The aim of this work is minimizing the complexity of the MCM operation using common subexpression elimination (CSE) technique and redundant number representations. The CSE technique searches and eliminates common digit patterns (subexpressions) among MCM coefficients. More common subexpressions can be found by representing the MCM coefficients using redundant number representations. A CSE algorithm is proposed that works on a type of redundant numbers called the zero-dominant set (ZDS). The ZDS is an extension over the representations of minimum number of non-zero digits called minimum Hamming weight (MHW). Using the ZDS improves CSE algorithms' performance as compared with using the MHW representations. The disadvantage of using the ZDS is it increases the possibility of overlapping patterns (digit collisions). In this case, one or more digits are shared between a number of patterns. Eliminating a pattern results in losing other patterns because of eliminating the common digits. A pattern preservation algorithm (PPA) is developed to resolve the overlapping patterns in the representations. A tree and graph encoders are proposed to generate a larger space of number representations. The algorithms generate redundant representations of a value for a given digit set, radix, and wordlength. The tree encoder is modified to search for common subexpressions simultaneously with generating of the representation tree. A complexity measure is proposed to compare between the subexpressions at each node. The algorithm terminates generating the rest of the representation tree when it finds subexpressions with maximum sharing. This reduces the search space while minimizes the hardware complexity. A combinatoric model of the MCM problem is proposed in this work. The model is obtained by enumerating all the possible solutions of the MCM that resemble a graph called the demand graph. Arc routing on this graph gives the solutions of the MCM problem. A similar arc routing is found in the capacitated arc routing such as the winter salting problem. Ant colony optimization (ACO) meta-heuristics is proposed to traverse the demand graph. The ACO is simulated on a PC using Python programming language. This is to verify the model correctness and the work of the ACO. A parallel simulation of the ACO is carried out on a multi-core super computer using C++ boost graph library.