A Sparse Multi-Scale Algorithm for Dense Optimal Transport

Discrete optimal transport solvers do not scale well on dense large problems since they do not explicitly exploit the geometric structure of the cost function. In analogy to continuous optimal transport we provide a framework to verify global optimality of a discrete transport plan locally. This allows construction of an algorithm to solve large dense problems by considering a sequence of sparse problems instead. The algorithm lends itself to being combined with a hierarchical multi-scale scheme. Any existing discrete solver can be used as internal black-box.Several cost functions, including the noisy squared Euclidean distance, are explicitly detailed. We observe a significant reduction of run-time and memory requirements.Comment: Published "online first" in Journal of Mathematical Imaging and Vision, see DO

Benchmarks for Parity Games (extended version)

We propose a benchmark suite for parity games that includes all benchmarks that have been used in the literature, and make it available online. We give an overview of the parity games, including a description of how they have been generated. We also describe structural properties of parity games, and using these properties we show that our benchmarks are representative. With this work we provide a starting point for further experimentation with parity games.Comment: The corresponding tool and benchmarks are available from https://github.com/jkeiren/paritygame-generator. This is an extended version of the paper that has been accepted for FSEN 201

A guided search non-dominated sorting genetic algorithm for the multi-objective university course timetabling problem

Copyright @ Springer-Verlag Berlin Heidelberg 2011.The university course timetabling problem is a typical combinatorial optimization problem. This paper tackles the multi-objective university course timetabling problem (MOUCTP) and proposes a guided search non-dominated sorting genetic algorithm to solve the MOUCTP. The proposed algorithm integrates a guided search technique, which uses a memory to store useful information extracted from previous good solutions to guide the generation of new solutions, and two local search schemes to enhance its performance for the MOUCTP. The experimental results based on a set of test problems show that the proposed algorithm is efficient for solving the MOUCTP

A self-organising mixture network for density modelling

A completely unsupervised mixture distribution network, namely the self-organising mixture network, is proposed for learning arbitrary density functions. The algorithm minimises the Kullback-Leibler information by means of stochastic approximation methods. The density functions are modelled as mixtures of parametric distributions such as Gaussian and Cauchy. The first layer of the network is similar to the Kohonen's self-organising map (SOM), but with the parameters of the class conditional densities as the learning weights. The winning mechanism is based on maximum posterior probability, and the updating of weights can be limited to a small neighbourhood around the winner. The second layer accumulates the responses of these local nodes, weighted by the learning mixing parameters. The network possesses simple structure and computation, yet yields fast and robust convergence. Experimental results are also presente

MaaSim: A Liveability Simulation for Improving the Quality of Life in Cities

Urbanism is no longer planned on paper thanks to powerful models and 3D simulation platforms. However, current work is not open to the public and lacks an optimisation agent that could help in decision making. This paper describes the creation of an open-source simulation based on an existing Dutch liveability score with a built-in AI module. Features are selected using feature engineering and Random Forests. Then, a modified scoring function is built based on the former liveability classes. The score is predicted using Random Forest for regression and achieved a recall of 0.83 with 10-fold cross-validation. Afterwards, Exploratory Factor Analysis is applied to select the actions present in the model. The resulting indicators are divided into 5 groups, and 12 actions are generated. The performance of four optimisation algorithms is compared, namely NSGA-II, PAES, SPEA2 and eps-MOEA, on three established criteria of quality: cardinality, the spread of the solutions, spacing, and the resulting score and number of turns. Although all four algorithms show different strengths, eps-MOEA is selected to be the most suitable for this problem. Ultimately, the simulation incorporates the model and the selected AI module in a GUI written in the Kivy framework for Python. Tests performed on users show positive responses and encourage further initiatives towards joining technology and public applications.Comment: 16 page

Framework for sustainable TVET-Teacher Education Program in Malaysia Public Universities

Studies had stated that less attention was given to the education aspect, such as teaching and learning in planning for improving the TVET system. Due to the 21st Century context, the current paradigm of teaching for the TVET educators also has been reported to be fatal and need to be shifted. All these disadvantages reported hindering the country from achieving the 5th strategy in the Strategic Plan for Vocational Education Transformation to transform TVET system as a whole. Therefore, this study aims to develop a framework for sustainable TVET Teacher Education program in Malaysia. This study had adopted an Exploratory Sequential Mix-Method design, which involves a semi-structured interview (phase one) and survey method (phase two). Nine experts had involved in phase one chosen by using Purposive Sampling Technique. As in phase two, 118 TVET-TE program lecturers were selected as the survey sample chosen through random sampling method. After data analysis in phase one (thematic analysis) and phase two (Principal Component Analysis), eight domains and 22 elements have been identified for the framework for sustainable TVET-TE program in Malaysia. This framework was identified to embed the elements of 21st Century Education, thus filling the gap in this research. The research findings also indicate that the developed framework was unidimensional and valid for the development and research regarding TVET-TE program in Malaysia. Lastly, it is in the hope that this research can be a guide for the nations in producing a quality TVET teacher in the future

Local search: A guide for the information retrieval practitioner

There are a number of combinatorial optimisation problems in information retrieval in which the use of local search methods are worthwhile. The purpose of this paper is to show how local search can be used to solve some well known tasks in information retrieval (IR), how previous research in the field is piecemeal, bereft of a structure and methodologically flawed, and to suggest more rigorous ways of applying local search methods to solve IR problems. We provide a query based taxonomy for analysing the use of local search in IR tasks and an overview of issues such as fitness functions, statistical significance and test collections when conducting experiments on combinatorial optimisation problems. The paper gives a guide on the pitfalls and problems for IR practitioners who wish to use local search to solve their research issues, and gives practical advice on the use of such methods. The query based taxonomy is a novel structure which can be used by the IR practitioner in order to examine the use of local search in IR

Decomposition, Reformulation, and Diving in University Course Timetabling

In many real-life optimisation problems, there are multiple interacting components in a solution. For example, different components might specify assignments to different kinds of resource. Often, each component is associated with different sets of soft constraints, and so with different measures of soft constraint violation. The goal is then to minimise a linear combination of such measures. This paper studies an approach to such problems, which can be thought of as multiphase exploitation of multiple objective-/value-restricted submodels. In this approach, only one computationally difficult component of a problem and the associated subset of objectives is considered at first. This produces partial solutions, which define interesting neighbourhoods in the search space of the complete problem. Often, it is possible to pick the initial component so that variable aggregation can be performed at the first stage, and the neighbourhoods to be explored next are guaranteed to contain feasible solutions. Using integer programming, it is then easy to implement heuristics producing solutions with bounds on their quality. Our study is performed on a university course timetabling problem used in the 2007 International Timetabling Competition, also known as the Udine Course Timetabling Problem. In the proposed heuristic, an objective-restricted neighbourhood generator produces assignments of periods to events, with decreasing numbers of violations of two period-related soft constraints. Those are relaxed into assignments of events to days, which define neighbourhoods that are easier to search with respect to all four soft constraints. Integer programming formulations for all subproblems are given and evaluated using ILOG CPLEX 11. The wider applicability of this approach is analysed and discussed.Comment: 45 pages, 7 figures. Improved typesetting of figures and table