Tests for loop nuclei and a new criterion for a Latin square to be group-based

AbstractWe give a new and simple criterion for a Latin square to be group-based and we provide easy-to-implement tests for whether a given element of a loop lies in any one of its three nuclei

Row complete squares and a problem of A. Kotzig concerning P-quasigroups and eulerian circuits

AbstractAn n × n square L on n symbols is called row (column) complete if every ordered pair of the symbols of L occurs just once as an adjacent pair of elements in some row (column) of L. It is called row (column) latin if each symbol occurs exactly once in each row (column) of the square. A square which is both row latin and column latin is called a latin square. All known examples of row complete latin squares can be made column complete as well by suitable reordering of their rows and in the present paper we provide a sufficient condition that a given row complete latin square should have this property.Using row complete and column latin squares as a tool we follow this by showing how to construct code words on n symbols of the maximum possible length l = 12n(n − 1) + 1 with the two properties that (i) no unordered pair of consecutive symbols is repeated more than once and (ii) no unordered pair of nearly consecutive symbols is repeated more than once. (Two symbols are said to be nearly consecutive if they are separated by a single symbol.) We prove that such code words exist whenever n = 4r + 3 with r ≢ 1 mod 6 and r ≢ 2 mod 5. We show that the existence of such a code word for a given value of n guarantees the existence of an Eulerian circuit in the complete undirected n-graph which corresponds to a P-quasigroup, thus answering a question raised by A. Kotzig in the affirmative. (Kotzig has defined a P-groupoid as a groupoid (G, ·) having the following three properties: (i) a . a = a for all a ϵ G; (ii) a ≠ b implies a ≠ a . b and b ≠ a. b for all a, b ϵ G; and (iii) a . b = c implies c. b = a for all a, b, c ϵ G. Every decomposition of the complete undirected n-graph into disjoint closed circuits defines such a P-groupoid, as is easily seen by defining a . b = c if and only if a, b, c are consecutive edges of one such closed circuit. A P-groupoid whose multiplication table is a latin square is called a P-quasigroup.

Analysing heuristic subsequences for offline hyper-heuristic learning

This is the author accepted manuscript. The final version is available from ACM via the DOI in this recordThe paper explores the impact of sequences of search operationson the performance of an optimiser through the use of log returnsand a database of sequences. The study demonstrates that althoughthe performance of individual perturbation operators is important,understanding their performance in sequence provides greater op-portunity for performance improvements within and across opera-tions research domains

Semantic segmentation on small datasets of satellite images using convolutional neural networks

This is the final version. Available from SPIE via the DOI in this recordSemantic segmentation is one of the most popular and challenging applications of deep learning. It refers to the process of dividing a digital image into semantically homogeneous areas with similar properties. We employ the use of deep learning techniques to perform semantic segmentation on high-resolution satellite images representing urban scenes to identify roads, vegetation, and buildings. A SegNet-based neural network with an encoder–decoder architecture is employed. Despite the small size of the dataset, the results are promising. We show that the network is able to accurately distinguish between these groups for different test images, when using a network with four convolutional layers

H-ACO: A Heterogeneous Ant Colony Optimisation approach with Application to the Travelling Salesman Problem

This is the author accepted manuscript. The final version is available from the publisher via the link in this record.Ant Colony Optimization (ACO) is a field of study that mimics the behaviour of ants to solve computationally hard problems. The majority of research in ACO focuses on homogeneous artificial ants although animal behaviour research suggests that heterogeneity of behaviour improves the overall efficiency of ant colonies. Therefore, this paper introduces and analyses the effects of heterogeneity of behavioural traits in ACO to solve hard optimisation problems. The developed approach implements different behaviour by introducing unique biases towards the pheromone trail and local heuristic (the next hop distance) for each ant. The well-known Ant System (AS) and Max-Min Ant System (MMAS) are used as the base algorithms to implement heterogeneity and experiments show that this method improves the performance when tested using several Travelling Salesman Problem (TSP) instances particularly for larger instances. The diversity preservation introduced by this algorithm helps balance exploration-exploitation, increases robustness with respect to parameter settings and reduces the number of algorithm parameters that need to be set.We would like to thank the Faculty of Electronics and Computer Engineering (FKEKK), Technical University of Malaysia Malacca (UTeM) and the Ministry of Higher Education (MoHE) Malaysia for the financial support under the SLAB/SlAI program

Multi-objective optimisation with a sequence-based selection hyper-heuristic

Hyper-heuristics have been used widely to solve optimisation problems, often single-objective and discrete in nature. Herein, we extend a recently-proposed selection hyper-heuristic to the multiobjective domain and with it optimise continuous problems. The MOSSHH algorithm operates as a hidden Markov model, using transition probabilities to determine which low-level heuristic or sequence of heuristics should be applied next. By incorporating dominance into the transition probability update rule, and an elite archive of solutions, MOSSHH generates solutions to multi-objective problems that are competitive with bespoke multi-objective algorithms. When applied to test problems, it is able to find good approximations to the true Pareto front, and yields information about the type of low-level heuristics that it uses to solve the problem

Alien Registration- Wyman, Gerald Keedwell S. (Canton, Oxford County)

https://digitalmaine.com/alien_docs/15687/thumbnail.jp

Offline Learning for Selection Hyper-heuristics with Elman Networks

This is the author accepted manuscript. The final version is available from the publisher via the link in this record.Offline selection hyper-heuristics are machine learning methods that are trained on heuristic selections to create an algorithm that is tuned for a particular problem domain. In this work, a simple selection hyper-heuristic is executed on a number of computationally hard benchmark optimisation problems, and the resulting sequences of low level heuristic selections and objective function values are used to construct an offline learning database. An Elman network is trained on sequences of heuristic selections chosen from the offline database and the network’s ability to learn and generalise from these sequences is evaluated. The networks are trained using a leave-one-out cross validation methodology and the sequences of heuristic selections they produce are tested on benchmark problems drawn from the HyFlex set. The results demonstrate that the Elman network is capable of intra-domain learning and generalisation with 99% confidence and produces better results than the training sequences in many cases. When the network was trained using an interdomain training set, the Elman network did not exhibit generalisation indicating that inter-domain generalisation is a harder problem and that strategies learned on one domain cannot necessarily be transferred to another

Markov Chain Selection Hyper-heuristic for the Optimisation of Constrained Magic Squares

UKCI 2015: UK Workshop on Computational Intelligence, University of Exeter, UK, 7-9 September 2015A square matrix of size n × n, containing each of the numbers (1, . . . , n2) in which every row, column and both diagonals has the same total is referred to as a magic square. The problem can be formulated as an optimisation problem where the task is to minimise the deviation from the magic square constraints and is tackled here by using hyper-heuristics. Hyper-heuristics have recently attracted the attention of the artificial intelligence, operations research, engineering and computer science communities where the aim is to design and develop high level strategies as general solvers which are applicable to a range of different problem domains. There are two main types of hyper-heuristics in the literature: methodologies to select and to generate heuristics and both types of approaches search the space of heuristics rather than solutions. In this study, we describe a Markov chain selection hyper-heuristic as an effective solution methodology for optimising constrained magic squares. The empirical results show that the proposed hyper-heuristic is able to outperform the current state-of-the-art method

An analysis of heuristic subsequences for offline hyper-heuristic learning

This is the final version. Available on open access from Springer Verlag via the DOI in this recordA selection hyper-heuristic is used to minimise the objective functions of a well-known set of benchmark problems. The resulting sequences of low level heuristic selections and objective function values are used to generate a database of heuristic selections. The sequences in the database are broken down into subsequences and the mathematical concept of a logarithmic return is used to discriminate between “effective” subsequences, which tend to decrease the objective value, and “disruptive” subsequences, which tend to increase the objective value. These subsequences are then employed in a sequenced based hyper-heuristic and evaluated on an unseen set of benchmark problems. Empirical results demonstrate that the “effective” subsequences perform significantly better than the “disruptive” subsequences across a number of problem domains with 99% confidence. The identification of subsequences of heuristic selections that can be shown to be effective across a number of problems or problem domains could have important implications for the design of future sequence based hyper-heuristics