Combinatorial optimization and metaheuristics

Today, combinatorial optimization is one of the youngest and most active areas of discrete mathematics. It is a branch of optimization in applied mathematics and computer science, related to operational research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering. Its increasing interest arises for the fact that a large number of scientific and industrial problems can be formulated as abstract combinatorial optimization problems, through graphs and/or (integer) linear programs. Some of these problems have polynomial-time (“efficient”) algorithms, while most of them are NP-hard, i.e. it is not proved that they can be solved in polynomial-time. Mainly, it means that it is not possible to guarantee that an exact solution to the problem can be found and one has to settle for an approximate solution with known performance guarantees. Indeed, the goal of approximate methods is to find “quickly” (reasonable run-times), with “high” probability, provable “good” solutions (low error from the real optimal solution). In the last 20 years, a new kind of algorithm commonly called metaheuristics have emerged in this class, which basically try to combine heuristics in high level frameworks aimed at efficiently and effectively exploring the search space. This report briefly outlines the components, concepts, advantages and disadvantages of different metaheuristic approaches from a conceptual point of view, in order to analyze their similarities and differences. The two very significant forces of intensification and diversification, that mainly determine the behavior of a metaheuristic, will be pointed out. The report concludes by exploring the importance of hybridization and integration methods

Competitive Online Search Trees on Trees

We consider the design of adaptive data structures for searching elements of a tree-structured space. We use a natural generalization of the rotation-based online binary search tree model in which the underlying search space is the set of vertices of a tree. This model is based on a simple structure for decomposing graphs, previously known under several names including elimination trees, vertex rankings, and tubings. The model is equivalent to the classical binary search tree model exactly when the underlying tree is a path. We describe an online $O(\log \log n)$-competitive search tree data structure in this model, matching the best known competitive ratio of binary search trees. Our method is inspired by Tango trees, an online binary search tree algorithm, but critically needs several new notions including one which we call Steiner-closed search trees, which may be of independent interest. Moreover our technique is based on a novel use of two levels of decomposition, first from search space to a set of Steiner-closed trees, and secondly from these trees into paths

Searching for patterns in Conway's Game of Life

Conway’s Game of Life (Life) is a simple cellular automaton, discovered by John Conway in 1970, that exhibits complex emergent behavior. Life-enthusiasts have been looking for building blocks with specific properties (patterns) to answer unsolved problems in Life for the past five decades. Finding patterns in Life is difficult due to the large search space. Current search algorithms use an explorative approach based on the rules of the game, but this can only sample a small fraction of the search space. More recently, people have used Sat solvers to search for patterns. These solvers are not specifically tuned to this problem and thus waste a lot of time processing Life’s rules in an engine that does not understand them. We propose a novel Sat-based approach that replaces the binary tree used by traditional Sat solvers with a grid-based approach, complemented by an injection of Game of Life specific knowledge. This leads to a significant speedup in searching. As a fortunate side effect, our solver can be generalized to solve general Sat problems. Because it is grid-based, all manipulations are embarrassingly parallel, allowing implementation on massively parallel hardware

The development and application of metaheuristics for problems in graph theory: A computational study

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.It is known that graph theoretic models have extensive application to real-life discrete optimization problems. Many of these models are NP-hard and, as a result, exact methods may be impractical for large scale problem instances. Consequently, there is a great interest in developing e±cient approximate methods that yield near-optimal solutions in acceptable computational times. A class of such methods, known as metaheuristics, have been proposed with success. This thesis considers some recently proposed NP-hard combinatorial optimization problems formulated on graphs. In particular, the min- imum labelling spanning tree problem, the minimum labelling Steiner tree problem, and the minimum quartet tree cost problem, are inves- tigated. Several metaheuristics are proposed for each problem, from classical approximation algorithms to novel approaches. A compre- hensive computational investigation in which the proposed methods are compared with other algorithms recommended in the literature is reported. The results show that the proposed metaheuristics outper- form the algorithms recommended in the literature, obtaining optimal or near-optimal solutions in short computational running times. In addition, a thorough analysis of the implementation of these methods provide insights for the implementation of metaheuristic strategies for other graph theoretic problems

read:write. Digital possibilities for literature

This report was commissioned by the literature department of Arts Council England (ACE) to gather an overview of how companies, organisations and individuals in the commercial and funded sectors are using Web 2.0 to market fiction, poetry and live literature; spot writing talent; guide readers and potential readers; create, share and review writing. In particular the authors were asked to look at: what opportunities digitisation offers to writers, publishers and other literature organisations how funded organisations can achieve greater sustainability/self-sufficiency or lower costs by making use of technology how organisations can develop audiences and increase participation through use of digital media. The report was commissioned at a formative stage of ACE\u27s digital strategy development, so the research was conducted as an iterative process. The bulk of the research was conducted through interviews and desk research, informed by the experience and expertise of Institute personnel. Interviews informed the desk research and vice versa, and the direction and emphasis of the report evolved in a series of meetings with ACE personnel. The core of this report lies in the case studies. After an initial period of Web research and informal discussion with key individuals in the sector, the authors developed a baseline questionnaire covering key areas. These included technology, site maintenance, resourcing and future hopes and needs. Though each organisation interviewed had different needs and priorities, and the interview was adapted accordingly in each case, we used this baseline to identify themes that persisted across different areas. In addition to the interviews, the authors conducted extensive Web-based research covering both UK and international literature organisations. This formed the basis of subsector overviews that combine with the case studies