An Efficient Local Search for Partial Latin Square Extension Problem

A partial Latin square (PLS) is a partial assignment of n symbols to an nxn grid such that, in each row and in each column, each symbol appears at most once. The partial Latin square extension problem is an NP-hard problem that asks for a largest extension of a given PLS. In this paper we propose an efficient local search for this problem. We focus on the local search such that the neighborhood is defined by (p,q)-swap, i.e., removing exactly p symbols and then assigning symbols to at most q empty cells. For p in {1,2,3}, our neighborhood search algorithm finds an improved solution or concludes that no such solution exists in O(n^{p+1}) time. We also propose a novel swap operation, Trellis-swap, which is a generalization of (1,q)-swap and (2,q)-swap. Our Trellis-neighborhood search algorithm takes O(n^{3.5}) time to do the same thing. Using these neighborhood search algorithms, we design a prototype iterated local search algorithm and show its effectiveness in comparison with state-of-the-art optimization solvers such as IBM ILOG CPLEX and LocalSolver.Comment: 17 pages, 2 figure

Sudoku solver based on human strategies an application in VBA

Mestrado Bolonha em Métodos Quantitativos para a Decisão Económica e EmpresariaO Sudoku é um puzzle popularmente conhecido, com aplicações em diversas áreas que se estendem desde a Criptografia à Medicina. Por ser um problema NP-completo, a maior parte dos esforços para o resolver focam-se em heurísticas e não em métodos exatos. Exemplo destes últimos são as estratégias humanas. A proposta deste Trabalho Final de Mestrado (TFM) consiste no desenvolvimento de um Sudoku Solver, em VBA. O solver desenvolvido é um algoritmo de duas fases que incorpora estratégias humanas (Fase 1) e backtracking (Fase 2). A Fase 2 só é executada se, terminada a Fase 1, não for encontrada uma solução admissível. Foi conduzida uma experiência computacional para testar a performance do solver para puzzles 9×9 de três níveis de dificuldade: fácil, moderado e difícil. Das 230 instâncias testadas, aproximadamente 55% foram resolvidas. O tempo máximo de resolução foi de 6,813 segundos, o tempo mínimo foi de 0,309 e a média do tempo total foi de 2,525 segundos.Sudoku is a popular puzzle, with applications in several areas ranging from Cryptography to Medicine. Because it is an NP-complete problem, most efforts to solve it focus on heuristics and not on exact methods. Examples of the latter are human strategies. The proposal of this Master’s Final Work (MFW) is the development of a Sudoku Solver, in VBA. The developed solver is a two-phase algorithm that incorporates human strategies (Phase 1) and a backtracking procedure (Phase 2). Phase 2 is only executed if a feasible solution has not been found after Phase 1 ends. It was conducted a computational experience to test the solver performance for 9×9 puzzles with three difficulty levels: easy, moderate, and hard. Among the 230 instances tested, approximately 55% were solved. The maximum running time was 6.813 seconds, the minimum time was 0.309, and the average total time was 2.525 seconds.info:eu-repo/semantics/publishedVersio

IST Austria Technical Report

Board games, like Tic-Tac-Toe and CONNECT-4, play an important role not only in development of mathematical and logical skills, but also in emotional and social development. In this paper, we address the problem of generating targeted starting positions for such games. This can facilitate new approaches for bringing novice players to mastery, and also leads to discovery of interesting game variants. Our approach generates starting states of varying hardness levels for player 1 in a two-player board game, given rules of the board game, the desired number of steps required for player 1 to win, and the expertise levels of the two players. Our approach leverages symbolic methods and iterative simulation to efficiently search the extremely large state space. We present experimental results that include discovery of states of varying hardness levels for several simple grid-based board games. Also, the presence of such states for standard game variants like Tic-Tac-Toe on board size 4x4 opens up new games to be played that have not been played for ages since the default start state is heavily biased

Underwater Robot Task Planning Using Multi-Objective Meta-Heuristics

Robotics deployed in the underwater medium are subject to stringent operational conditions that impose a high degree of criticality on the allocation of resources and the schedule of operations in mission planning. In this context the so-called cost of a mission must be considered as an additional criterion when designing optimal task schedules within the mission at hand. Such a cost can be conceived as the impact of the mission on the robotic resources themselves, which range from the consumption of battery to other negative effects such as mechanic erosion. This manuscript focuses on this issue by devising three heuristic solvers aimed at efficiently scheduling tasks in robotic swarms, which collaborate together to accomplish a mission, and by presenting experimental results obtained over realistic scenarios in the underwater environment. The heuristic techniques resort to a Random-Keys encoding strategy to represent the allocation of robots to tasks and the relative execution order of such tasks within the schedule of certain robots. The obtained results reveal interesting differences in terms of Pareto optimality and spread between the algorithms considered in the benchmark, which are insightful for the selection of a proper task scheduler in real underwater campaigns

Knowledge-based approaches to producing large-scale training data from scratch for Word Sense Disambiguation and Sense Distribution Learning

Communicating and understanding each other is one of the most important human abilities. As humans, in fact, we can easily assign the correct meaning to the ambiguous words in a text, while, at the same time, being able to abstract, summarise and enrich its content with new information that we learned somewhere else. On the contrary, machines rely on formal languages which do not leave space to ambiguity hence being easy to parse and understand. Therefore, to fill the gap between humans and machines and enabling the latter to better communicate with and comprehend its sentient counterpart, in the modern era of computer-science's much effort has been put into developing Natural Language Processing (NLP) approaches which aim at understanding and handling the ambiguity of the human language. At the core of NLP lies the task of correctly interpreting the meaning of each word in a given text, hence disambiguating its content exactly as a human would do. Researchers in the Word Sense Disambiguation (WSD) field address exactly this issue by leveraging either knowledge bases, i.e. graphs where nodes are concept and edges are semantic relations among them, or manually-annotated datasets for training machine learning algorithms. One common obstacle is the knowledge acquisition bottleneck problem, id est, retrieving or generating semantically-annotated data which are necessary to build both semantic graphs or training sets is a complex task. This phenomenon is even more serious when considering languages other than English where resources to generate human-annotated data are scarce and ready-made datasets are completely absent. With the advent of deep learning this issue became even more serious as more complex models need larger datasets in order to learn meaningful patterns to solve the task. Another critical issue in WSD, as well as in other machine-learning-related fields, is the domain adaptation problem, id est, performing the same task in different application domains. This is particularly hard when dealing with word senses, as, in fact, they are governed by a Zipfian distribution; hence, by slightly changing the application domain, a sense might become very frequent even though it is very rare in the general domain. For example the geometric sense of plane is very frequent in a corpus made of math books, while it is very rare in a general domain dataset. In this thesis we address both these problems. Inter alia, we focus on relieving the burden of human annotations in Word Sense Disambiguation thus enabling the automatic construction of high-quality sense-annotated dataset not only for English, but especially for other languages where sense-annotated data are not available at all. Furthermore, recognising in word-sense distribution one of the main pitfalls for WSD approaches, we also alleviate the dependency on most frequent sense information by automatically inducing the word-sense distribution in a given text of raw sentences. In the following we propose a language-independent and automatic approach to generating semantic annotations given a collection of sentences, and then introduce two methods for the automatic inference of word-sense distributions. Finally, we combine the two kind of approaches to build a semantically-annotated dataset that reflect the sense distribution which we automatically infer from the target text